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Published by Maney Publishing (c) IOM Communications Ltd Predicting onset of high speed gas metal arc weld bead defects using dimensional analysis techniques T. C. Nguyen 1,2 , D. C. Weckman* 1 and D. A. Johnson 1 The onset of geometric defects such as humping or discontinuous weld beads during gas metal arc welding (GMAW) frequently limits the use of higher welding speeds and increased productivity. In the present study, a dimensional analysis of the GMAW process was performed in order to identify a number of dimensionless groups formulated based on various GMAW process parameters and material properties that could be used to predict when humping or discontinuous weld beads would occur. Experimental data from bead on plate GMA welds in plain carbon steel plate made using argon and two different reactive shielding gases, welding powers between 5 and 12 kW and a range of welding speeds were then used to create dimensionless process maps. These maps showed the limiting welding speed above which the high speed weld defects occurred as a function of all influential process parameters. It was shown that all experimental data for limiting welding speeds could be collapsed onto two collinear dimensionless curves. Also, the transition from spray to rotational metal transfer was found to occur at a well defined value of one of these dimensionless parameters. The effects of workpiece preheat temperature on humping were correctly predicted and there was a good correlation between the dimensionless GMAW process map and experimental data from other independent studies. These results suggest that the occurrence of high speed weld bead defects such as humping and discontinuous weld beads as well as the transition from spray to rotational metal transfer can be predicted using these new dimensionless GMAW process maps. Keywords: Gas metal arc welding, Weld bead defects, High speed, Dimensional analysis Introduction Since its invention in the late 1940s, the gas metal arc welding (GMAW) process has become the most commonly used non-autogenous welding process in a wide range of manufacturing industries such as the construction, shipbuilding, automotive, aerospace and petrochemical industries. 1–4 The GMAW process is used for a wide range of manual and automatic welding applications. 4 It is used in joining most commercial metals and alloys of similar or dissimilar composition and is generally one of the most economical, efficient and versatile fusion welding processes for permanently joining engineering alloys. 1 As illustrated in Fig. 1, in the GMAW process, a welding power supply is used to create an electric arc between the workpiece and a consumable electrode wire which is fed through the contact tip in the welding torch and into the weld pool at a preset wire feedrate (WFR). As the torch is moved along the weld joint at a constant welding speed v ws , the arc melts both the electrode wire and part of the workpiece at the joint interface. Molten metal from the tip of the electrode wire is transferred across the arc to the weld pool, thereby providing filler metal to fill the joint gaps and create the desired weld bead profile. There are four basic filler metal transfer modes: short circuiting, globular, spray and rotational transfer. 3,4 The transfer mode is influenced by various GMAW process parameters including welding current I, welding voltage V, electrode diameter 1 e , electrode com- position, electrode extension, contact tip to workpiece distance (CTWD) and shielding gas composition. 1–3 Shielding of the molten metal from the atmosphere is provided by using an inert gas such as argon, a reactive gas such as CO 2 or various mixtures of Ar, CO 2 ,O 2 and He. The GMAW process is a multivariate process with many synergistic interactions between the numerous process parameters. This has made it difficult to develop comprehensive and reliable models of the process that might be used to predict the effects of various preset 1 Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada 2 Now at School of Engineering and Information Technology, Conestoga College, 299 Doon Valley Dr., Kitchener, Ontario N2G 4M4, Canada *Corresponding author, email [email protected] ß 2007 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 24 August 2006; accepted 17 August 2007 DOI 10.1179/174329307X236797 Science and Technology of Welding and Joining 2007 VOL 12 NO 7 634
15

Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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Page 1: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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Predicting onset of high speed gas metal arcweld bead defects using dimensional analysistechniques

T C Nguyen12 D C Weckman1 and D A Johnson1

The onset of geometric defects such as humping or discontinuous weld beads during gas metal

arc welding (GMAW) frequently limits the use of higher welding speeds and increased

productivity In the present study a dimensional analysis of the GMAW process was performed

in order to identify a number of dimensionless groups formulated based on various GMAW

process parameters and material properties that could be used to predict when humping or

discontinuous weld beads would occur Experimental data from bead on plate GMA welds in

plain carbon steel plate made using argon and two different reactive shielding gases welding

powers between 5 and 12 kW and a range of welding speeds were then used to create

dimensionless process maps These maps showed the limiting welding speed above which the

high speed weld defects occurred as a function of all influential process parameters It was shown

that all experimental data for limiting welding speeds could be collapsed onto two collinear

dimensionless curves Also the transition from spray to rotational metal transfer was found to

occur at a well defined value of one of these dimensionless parameters The effects of workpiece

preheat temperature on humping were correctly predicted and there was a good correlation

between the dimensionless GMAW process map and experimental data from other independent

studies These results suggest that the occurrence of high speed weld bead defects such as

humping and discontinuous weld beads as well as the transition from spray to rotational metal

transfer can be predicted using these new dimensionless GMAW process maps

Keywords Gas metal arc welding Weld bead defects High speed Dimensional analysis

IntroductionSince its invention in the late 1940s the gas metal arcwelding (GMAW) process has become the mostcommonly used non-autogenous welding process in awide range of manufacturing industries such as theconstruction shipbuilding automotive aerospace andpetrochemical industries1ndash4 The GMAW process is usedfor a wide range of manual and automatic weldingapplications4 It is used in joining most commercialmetals and alloys of similar or dissimilar compositionand is generally one of the most economical efficientand versatile fusion welding processes for permanentlyjoining engineering alloys1

As illustrated in Fig 1 in the GMAW process awelding power supply is used to create an electric arcbetween the workpiece and a consumable electrode wire

which is fed through the contact tip in the welding torchand into the weld pool at a preset wire feedrate (WFR)As the torch is moved along the weld joint at a constantwelding speed vws the arc melts both the electrode wireand part of the workpiece at the joint interface Moltenmetal from the tip of the electrode wire is transferredacross the arc to the weld pool thereby providing fillermetal to fill the joint gaps and create the desired weldbead profile There are four basic filler metal transfermodes short circuiting globular spray and rotationaltransfer34 The transfer mode is influenced by variousGMAW process parameters including welding current Iwelding voltage V electrode diameter 1e electrode com-position electrode extension contact tip to workpiecedistance (CTWD) and shielding gas composition1ndash3

Shielding of the molten metal from the atmosphere isprovided by using an inert gas such as argon a reactivegas such as CO2 or various mixtures of Ar CO2 O2 andHe The GMAW process is a multivariate process withmany synergistic interactions between the numerousprocess parameters This has made it difficult to developcomprehensive and reliable models of the process thatmight be used to predict the effects of various preset

1Department of Mechanical Engineering University of Waterloo WaterlooOntario N2L 3G1 Canada2Now at School of Engineering and Information Technology ConestogaCollege 299 Doon Valley Dr Kitchener Ontario N2G 4M4 Canada

Corresponding author email dweckmanmecheng1uwaterlooca

2007 Institute of Materials Minerals and MiningPublished by Maney on behalf of the InstituteReceived 24 August 2006 accepted 17 August 2007DOI 101179174329307X236797 Science and Technology of Welding and Joining 2007 VOL 12 NO 7 634

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weld process parameters on the resultant weldcharacteristics such as width depth weld bead shapeetc

To remain competitive in todayrsquos manufacturingenvironment companies must continuously improvetheir productivity without sacrificing the quality of theirproducts An increase in productivity often requires theuse of higher welding speeds however the heat inputmust also be increased to maintain the same energyinput per unit length of weld required for melting of thefiller and base metals and to keep the same welddimensions156 An unbounded increase in the weldingspeed and welding power is in practice not possiblebecause it is invariably limited by the deterioration ofthe quality of the weld bead profile and generation ofweld bead defects One of the most commonly occurringgeometric defects that have been observed at high weld-ing speeds is the humping phenomenon7ndash9 An exampleof a humped GMA weld bead is shown in Fig 2Humping can be described as a periodic undulation ofthe weld bead with humps and valleys Figure 2b and cshows the transverse sections at a valley and a humprespectively of the humped GMA weld bead in Fig 2aThe humping defect compromises the mechanicalintegrity of the weld joint thereby limiting the weldingspeed and thus overall production rates Humping hasbeen reported to occur in both non-autogenous weldingprocesses such as GMAW10ndash13 and autogenous pro-cesses such as gas tungsten arc welding (GTAW)1415

laser beam welding (LBW)1617 and electron beamwelding (EWB)18ndash20

Several phenomenological models of humping havebeen proposed in attempts to explain the physicalmechanisms responsible for humping in autogenousand non-autogenous welding processes101421ndash24

Nguyen et al13 have recently proposed the curved walljet model of humping in high speed GMAW which is

illustrated in Fig 3 They argued that the combinedactions of the arc force and the momentum of thedroplets from the electrode create a gouged region at thefront of the weld pool These actions push the liquidmetal to the back of the weld pool through a curved walljet where it accumulates and grows into a swelling orhumped bead as shown in Fig 2a and c Periodicallysolidification of the long narrow curved wall jet chokesoff flow of molten metal to the swelling and a newswelling begins to form further along the weld beadWhile models such as these are attempting to describethe physical phenomenon responsible for humpingand helping to identify the weld process parametersthat may cause humping they cannot be used toquantitatively predict under what conditions humpingwill occur

When GMA welds were made using the reactiveshielding gases and higher welding powers Nguyen

1 Schematic diagram of GMAW process in spray metal

transfer mode

a top view b transverse section of weld at valley ctransverse section at hump

2 Bead on plate GMA weld in AISI 1018 plain carbon

steel exhibiting humping weld defect

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 635

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et al2526 observed a transition from spray to rotationalmetal transfer and a new type of weld defect which theycalled the discontinuous weld bead defect Figure 4shows a discontinuous GMAW weld bead The regularperiodic behaviour of humping is no longer evidentrather there are segments of good weld beads that areinterrupted at random intervals along the length of theweld bead by depressions in the base metal where thebase metal has been melted and gouged but no weld orfiller metal is present

Nguyen et al2526 attributed the formation of theaperiodic discontinuous weld bead defect to the incon-sistent transfer of the molten filler metal from theelectrode wire to the weld pool when welding inrotational transfer mode with reactive shielding gasesFor example Fig 5a is a LaserStrobe video image27 ofthe rotational transfer mode with the filler metaldetaching as droplets or fragments from a character-istically long molten metal string on the end of theelectrode Occasionally a very long fragment or all ofthe molten metal string on the end of the electrode willdetach as shown in Fig 5b While the welding arc is stillpresent this temporary disruption of the transfer of themolten filler metal into the weld joint results in adepression or section where the weld bead has been arcgouged but no filler metal deposited

In their studies of high speed weld bead defects in theGMAW process Nishiguchi et al1112 and Nguyenet al132526 have developed parametric maps of weldingcurrent or power versus welding speed that show regionsof process parameters that produced good weld beadsand regions or conditions that resulted in humping andother weld defects For example Fig 6 is a process mapthat consolidates the limiting welding speed datadeveloped by Nguyen et al132526 during their studiesof humping and discontinuous weld bead defects inGMA welds in AISI 1018 plain carbon steel The plotshows regions of welding power and welding speed thatresulted in good and defective weld beads when usingargon Mig Mix Gold (MMG) (Praxair DistributionInc Kitchener ON Canada) (Arndash8CO2) and TIME(BOC Gases Canada Ltd Waterloo ON Canada) (Arndash8CO2ndash265Hendash05O2) shielding gases In this plot thelines represent the maximum or limiting welding speedsthat could be used to produce a GMA weld without adefective weld bead profile From this plot the limitingwelding speed was a function of the shielding gas thewelding speed and the welding power When usingthe MMG and TIME reactive shielding gases and thewelding power of 9 kW the usable welding speed waslimited by the occurrence of humping1326 The limitingwelding speed was significantly less when using argonshielding gas With the welding power of 9 kW welds

3 Curved wall jet model for humping during high speed

GMAW (after Nguyen et al81326)

4 Top view of bead on plate GMA weld showing discon-

tinuous weld bead defect

a detachment of long molten metal string fragment bcomplete detachment of molten metal filament andwelding without filler metal transfer during formation ofdepression

5 LaserStrobe video images of rotational metal transfer

during formation of discontinuous weld bead defect

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 636

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made using the argon shielding gas exhibited humpingwhereas the discontinuous weld bead defect wasobserved when using the reactive shielding gases andthere was a distinct point of inflection between thelimiting welding speed lines for humping versus thediscontinuous weld bead defect This point of inflectionand change in behaviour at welding powers 9 kW isindicative that a transition has taken place in thephysical phenomena taking placing during the GMAWincluding a change in the filler metal transfer mechanismfrom spray to rotational transfer

While weld process maps such as that shown in Fig 6are valuable in identifying relationships and trendsbetween the various controllable process parameters theyare of limited value in predicting when humping will occurin new applications because all preset welding processparameters such as the shielding gas composition thetorch angle CTWD 1e electrode composition etc arekept constant when generating these process maps Achange of any one of these preset parameters wouldinvalidate the process map and necessitate an expensiveand time consuming series of experiments to generate anew process map Since the GMAW process is a multi-variate process with many independent parameters thenumber of experiments required to fully explore theinteractions between these parameters and the formationof high speed weld defects quickly becomes too large andimpractical to perform2829 In such cases it is advanta-geous to employ a dimensional analysis technique toreduce the dimensionality of the problem and the numberof experiments required without obscuring possiblerelationships between the process parameters and theonset of the high speed weld defects30

In their study of humping in GTA welds in 304stainless steel Mendez et al22ndash24 have performed adimensional analysis on specific aspects of the humpingphenomena and an order of magnitude scaling study inorder to identify the most important parameters andphysical phenomenon responsible for humping and also

to try to predict under what conditions humping willoccur In the context of the present study of high speedweld bead defects in GMAW however the use ofdimensional analysis has other advantages For exam-ple it is difficult to properly illustrate visualise andinterpret the effects of all process parameters on theonset of high speed weld defects using multidimensionalplots If these process parameters can be combined intodimensionless groups then their combined effects cansometimes be shown simultaneously on two-dimensionalplots thereby reducing the dimensions of the problemThus the dimensional analysis may provide a bettermethod to characterise and understand the relationshipbetween the various GMAW process parameters and theonset of high speed weld defects

The objective of the present study26 was to gain aninsight into the physical parameters responsible for theformation of high speed GMA weld bead defects byperforming a dimensional analysis of the high speedweld defect phenomena One of the primary goals of thisanalysis was to identify combinations of dimensionlessparameters that would collapse all dimensional weldingresults shown in Fig 6 onto a single dimensionless lineor value representative of the dimensionless limitingwelding speed thereby facilitating the prediction of theoccurrence high speed GMA weld defects This workwas performed in conjunction with the experimentaldata from Nguyen et alrsquos132526 previously reportedstudies of high speed GMA weld defects

Experimental apparatus and proceduresThe experimental data used for the present dimensionalanalysis were obtained from bead on plate GMA weldsthat were made using a Fanuc ARC Mate 120i 6-axiswelding robot and a Lincoln PowerWave 455 powersupply operating in constant voltage mode Welds weremade using a wide range of preset welding speeds andwelding powers Using a preset constant voltagedifferent welding powers were obtained by varying theWFR until the desired welding current was realised Allwelds were made using either spray or rotation metaltransfer A PC microcomputer was used with Labviewsoftware and National Instruments based data acquisi-tion system to record the welding voltages V andcurrents I These were then used to calculate the timeaveraged welding power P using P5VI Finally aLaserStrobe video imaging system27 was used to recordimages of the periodic humping and aperiodic discon-tinuous weld bead phenomena during GMAW

All bead on plate GMA welds were made in the flatposition on 65 mm (J0) thick cold rolled SAE-AISI 1018plain carbon steel plates using 09 mm (00350) diameterER70S-6 electrode wire and a 22 mm CTWD In all casesthe working angle of the GMAW torch was 90u and thetravel angle was 0u Three different shielding gases wereused argon MMG and TIME The composition of eachshielding gas is listed in Table 1 More comprehensivedescriptions of the experimental apparatus and proce-dures used may be found in Nguyen et al132526

Procedure for formulating dimensionlessgroupsIn dimensional analysis all relevant process parametersare assembled into groups of variables which are

6 Dimensional plot of limiting welding speeds before

onset of humping or discontinuous weld bead defects

in GMA welds made in AISI 1018 plain carbon steel

versus welding power when using argon MMG and

TIME shielding gases (taken from Nguyen et al132526)

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 637

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dimensionless According to Buckinghamrsquos theorem30

the number of dimensionless groups necessary tocompletely describe any physical system is equal to thenumber of controlling parameters minus the number offundamental dimensions used in that system In thisstudy of the GMAW process the fundamental dimen-sions are mass (kg) length (m) time (s) temperature (K)and current (A) Based on these fundamental dimensionsand Buckinghamrsquos theorem30 the total number ofdimensionless variables that can completely describe anobserved physical phenomenon will always be equal tothe number of process controlling parameters minusfive Therefore dimensional analysis will always reducethe dimensionality of the problem as well as the numberof experiments required

In dimensional analysis the formalised procedureused for formulating the various dimensionless groupsfrom different process parameters has three majorsteps3031

(i) identify the dependent and the physically rele-vant independent process parameters

(ii) assemble the process parameters into variousdimensionless groups and finally

(iii) express the dimensionless groups in combina-tions of well recognised dimensionless numbers

Dependent and independent dimensionalvariablesIn the first step of any dimensional analysis it is essentialto clearly identify dependent and physically relevantindependent dimensional variables of the process To besuccessful however thorough knowledge of the processand of the observed physical phenomenon is needed tocorrectly identify suitable dependent dimensional vari-ables and to critically evaluate the physical relevancy ofdifferent independent dimensional variables An inde-pendent variable is physically relevant if it has asignificant influence on the final value of the selecteddependent variable30 If a physically relevant independentvariable is overlooked or omitted then the final resultswill be very confusing and difficult to interpret

In any dimensional analysis the dependent variablemust be a measurable quantity that represents a certainaspect of the observed phenomenon For example thereis a welding speed beyond which high speed weld beaddefects will occur As shown in Fig 6 this limitingwelding speed is strongly dependent on various processparameters such as the power input and the shielding gascomposition Since the objective of a GMAW proceduredevelopment exercise is normally to achieve the highestpossible welding speed the limiting welding speed vl (ms)would be a suitable dependent variable

Possible physically relevant and independent variablesin the dimensional analysis are the GMAW processparameters the initial condition of the workpiece andthe material properties of the workpiece The GMAWprocess parameters that are physically relevant or thatare known to have strong influences on the limiting

welding speed are the welding voltage V (Volts or infundamental dimensions m2 kg s23 A21) the wire feedspeed (WFS) (ms) the CTWD (m) the diameter of thefiller metal electrode 1e (m) the shielding gas composi-tion and the electrical resistivity of the filler metal r (V mor in fundamental dimensions m3 kg s23 A22) In thepresent study the electrical resistivity of the filler metalis similar to that of the workpiece

Nguyen et al132526 found that the shielding gascomposition affects the arc current and power arclength the surface tension of molten metal in the weldpool and the area over which the molten filler metaldroplets impinged the weld pool surface These were allshown to affect the limiting welding speed As such theshielding gas composition is deemed to be a physicallyrelevant independent variable Initially the surfacetension c (N m21 or kg s22) of the molten weld metalcan be used to quantitatively represent the overall effectsof the shielding gas in the dimensional analysisHowever the arc length larc (m) and the weld widthww (m) were also used especially when considering thespray transfer mode of GMAW For the purpose of thisdimensional analysis the surface tension of molten steelin GMAW when using ER70S-6 electrode material anddifferent shielding gas compositions have been takenfrom the work of Subramaniam and White32 Thesesurface tensions are summarised in Table 2

In the list of influential GMAW process parametersdiscussed above the welding current I (A) was purposelyleft out since the Lincoln PowerWave 455 power supplywas used in the constant voltage mode throughout thestudy132526 In the constant voltage mode the weldingcurrent is a dependent variable and a consequence of thecombination of shielding gas composition V WFRCTWD 1e and r1 If I (A) is included with the otherindependent process parameters there will be a redun-dancy created which may obscure the actual relation-ships between various GMAW process parameters andthe onset of the high speed weld defects Nevertheless I (A)can be used to represent the combined effects ofshielding gas composition WFR CTWD 1e and r onvl (ms) In other words by using I (A) the number ofindependent dimensional variables is reduced by three inthe dimensional analysis In addition multiplication ofV (V) and I (A) can be used to represent the power P (Wor kg m2 s23) generated during welding

The remaining independent dimensional variables arethe initial temperature of the workpiece To (K) and thematerial properties of the SAE-AISI 1018 plain carbonsteel workpiece The initial temperature of the workpieceis a physically relevant independent variable since it hasbeen experimentally demonstrated that the limitingwelding speed in GMAW of plain carbon steel increasesas the initial temperature of the workpiece is increased33

In this dimensional analysis the initial temperature of

Table 2 Surface tension of molten steel in GMAW withdifferent shielding gas compositions32

Shielding gas Surface tension N m21

Pure argon 156MMG 115TIME 115Pure CO2 120Argon and 5O2 115

Table 1 Compositions of GMAW shielding gases used

Shielding gas Composition

Argon 100Ar (Ultra high purity grade)MMG 92Ar 8CO2

TIME 65Ar 8CO2 265He 05O2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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lishe

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Page 2: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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weld process parameters on the resultant weldcharacteristics such as width depth weld bead shapeetc

To remain competitive in todayrsquos manufacturingenvironment companies must continuously improvetheir productivity without sacrificing the quality of theirproducts An increase in productivity often requires theuse of higher welding speeds however the heat inputmust also be increased to maintain the same energyinput per unit length of weld required for melting of thefiller and base metals and to keep the same welddimensions156 An unbounded increase in the weldingspeed and welding power is in practice not possiblebecause it is invariably limited by the deterioration ofthe quality of the weld bead profile and generation ofweld bead defects One of the most commonly occurringgeometric defects that have been observed at high weld-ing speeds is the humping phenomenon7ndash9 An exampleof a humped GMA weld bead is shown in Fig 2Humping can be described as a periodic undulation ofthe weld bead with humps and valleys Figure 2b and cshows the transverse sections at a valley and a humprespectively of the humped GMA weld bead in Fig 2aThe humping defect compromises the mechanicalintegrity of the weld joint thereby limiting the weldingspeed and thus overall production rates Humping hasbeen reported to occur in both non-autogenous weldingprocesses such as GMAW10ndash13 and autogenous pro-cesses such as gas tungsten arc welding (GTAW)1415

laser beam welding (LBW)1617 and electron beamwelding (EWB)18ndash20

Several phenomenological models of humping havebeen proposed in attempts to explain the physicalmechanisms responsible for humping in autogenousand non-autogenous welding processes101421ndash24

Nguyen et al13 have recently proposed the curved walljet model of humping in high speed GMAW which is

illustrated in Fig 3 They argued that the combinedactions of the arc force and the momentum of thedroplets from the electrode create a gouged region at thefront of the weld pool These actions push the liquidmetal to the back of the weld pool through a curved walljet where it accumulates and grows into a swelling orhumped bead as shown in Fig 2a and c Periodicallysolidification of the long narrow curved wall jet chokesoff flow of molten metal to the swelling and a newswelling begins to form further along the weld beadWhile models such as these are attempting to describethe physical phenomenon responsible for humpingand helping to identify the weld process parametersthat may cause humping they cannot be used toquantitatively predict under what conditions humpingwill occur

When GMA welds were made using the reactiveshielding gases and higher welding powers Nguyen

1 Schematic diagram of GMAW process in spray metal

transfer mode

a top view b transverse section of weld at valley ctransverse section at hump

2 Bead on plate GMA weld in AISI 1018 plain carbon

steel exhibiting humping weld defect

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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et al2526 observed a transition from spray to rotationalmetal transfer and a new type of weld defect which theycalled the discontinuous weld bead defect Figure 4shows a discontinuous GMAW weld bead The regularperiodic behaviour of humping is no longer evidentrather there are segments of good weld beads that areinterrupted at random intervals along the length of theweld bead by depressions in the base metal where thebase metal has been melted and gouged but no weld orfiller metal is present

Nguyen et al2526 attributed the formation of theaperiodic discontinuous weld bead defect to the incon-sistent transfer of the molten filler metal from theelectrode wire to the weld pool when welding inrotational transfer mode with reactive shielding gasesFor example Fig 5a is a LaserStrobe video image27 ofthe rotational transfer mode with the filler metaldetaching as droplets or fragments from a character-istically long molten metal string on the end of theelectrode Occasionally a very long fragment or all ofthe molten metal string on the end of the electrode willdetach as shown in Fig 5b While the welding arc is stillpresent this temporary disruption of the transfer of themolten filler metal into the weld joint results in adepression or section where the weld bead has been arcgouged but no filler metal deposited

In their studies of high speed weld bead defects in theGMAW process Nishiguchi et al1112 and Nguyenet al132526 have developed parametric maps of weldingcurrent or power versus welding speed that show regionsof process parameters that produced good weld beadsand regions or conditions that resulted in humping andother weld defects For example Fig 6 is a process mapthat consolidates the limiting welding speed datadeveloped by Nguyen et al132526 during their studiesof humping and discontinuous weld bead defects inGMA welds in AISI 1018 plain carbon steel The plotshows regions of welding power and welding speed thatresulted in good and defective weld beads when usingargon Mig Mix Gold (MMG) (Praxair DistributionInc Kitchener ON Canada) (Arndash8CO2) and TIME(BOC Gases Canada Ltd Waterloo ON Canada) (Arndash8CO2ndash265Hendash05O2) shielding gases In this plot thelines represent the maximum or limiting welding speedsthat could be used to produce a GMA weld without adefective weld bead profile From this plot the limitingwelding speed was a function of the shielding gas thewelding speed and the welding power When usingthe MMG and TIME reactive shielding gases and thewelding power of 9 kW the usable welding speed waslimited by the occurrence of humping1326 The limitingwelding speed was significantly less when using argonshielding gas With the welding power of 9 kW welds

3 Curved wall jet model for humping during high speed

GMAW (after Nguyen et al81326)

4 Top view of bead on plate GMA weld showing discon-

tinuous weld bead defect

a detachment of long molten metal string fragment bcomplete detachment of molten metal filament andwelding without filler metal transfer during formation ofdepression

5 LaserStrobe video images of rotational metal transfer

during formation of discontinuous weld bead defect

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 636

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made using the argon shielding gas exhibited humpingwhereas the discontinuous weld bead defect wasobserved when using the reactive shielding gases andthere was a distinct point of inflection between thelimiting welding speed lines for humping versus thediscontinuous weld bead defect This point of inflectionand change in behaviour at welding powers 9 kW isindicative that a transition has taken place in thephysical phenomena taking placing during the GMAWincluding a change in the filler metal transfer mechanismfrom spray to rotational transfer

While weld process maps such as that shown in Fig 6are valuable in identifying relationships and trendsbetween the various controllable process parameters theyare of limited value in predicting when humping will occurin new applications because all preset welding processparameters such as the shielding gas composition thetorch angle CTWD 1e electrode composition etc arekept constant when generating these process maps Achange of any one of these preset parameters wouldinvalidate the process map and necessitate an expensiveand time consuming series of experiments to generate anew process map Since the GMAW process is a multi-variate process with many independent parameters thenumber of experiments required to fully explore theinteractions between these parameters and the formationof high speed weld defects quickly becomes too large andimpractical to perform2829 In such cases it is advanta-geous to employ a dimensional analysis technique toreduce the dimensionality of the problem and the numberof experiments required without obscuring possiblerelationships between the process parameters and theonset of the high speed weld defects30

In their study of humping in GTA welds in 304stainless steel Mendez et al22ndash24 have performed adimensional analysis on specific aspects of the humpingphenomena and an order of magnitude scaling study inorder to identify the most important parameters andphysical phenomenon responsible for humping and also

to try to predict under what conditions humping willoccur In the context of the present study of high speedweld bead defects in GMAW however the use ofdimensional analysis has other advantages For exam-ple it is difficult to properly illustrate visualise andinterpret the effects of all process parameters on theonset of high speed weld defects using multidimensionalplots If these process parameters can be combined intodimensionless groups then their combined effects cansometimes be shown simultaneously on two-dimensionalplots thereby reducing the dimensions of the problemThus the dimensional analysis may provide a bettermethod to characterise and understand the relationshipbetween the various GMAW process parameters and theonset of high speed weld defects

The objective of the present study26 was to gain aninsight into the physical parameters responsible for theformation of high speed GMA weld bead defects byperforming a dimensional analysis of the high speedweld defect phenomena One of the primary goals of thisanalysis was to identify combinations of dimensionlessparameters that would collapse all dimensional weldingresults shown in Fig 6 onto a single dimensionless lineor value representative of the dimensionless limitingwelding speed thereby facilitating the prediction of theoccurrence high speed GMA weld defects This workwas performed in conjunction with the experimentaldata from Nguyen et alrsquos132526 previously reportedstudies of high speed GMA weld defects

Experimental apparatus and proceduresThe experimental data used for the present dimensionalanalysis were obtained from bead on plate GMA weldsthat were made using a Fanuc ARC Mate 120i 6-axiswelding robot and a Lincoln PowerWave 455 powersupply operating in constant voltage mode Welds weremade using a wide range of preset welding speeds andwelding powers Using a preset constant voltagedifferent welding powers were obtained by varying theWFR until the desired welding current was realised Allwelds were made using either spray or rotation metaltransfer A PC microcomputer was used with Labviewsoftware and National Instruments based data acquisi-tion system to record the welding voltages V andcurrents I These were then used to calculate the timeaveraged welding power P using P5VI Finally aLaserStrobe video imaging system27 was used to recordimages of the periodic humping and aperiodic discon-tinuous weld bead phenomena during GMAW

All bead on plate GMA welds were made in the flatposition on 65 mm (J0) thick cold rolled SAE-AISI 1018plain carbon steel plates using 09 mm (00350) diameterER70S-6 electrode wire and a 22 mm CTWD In all casesthe working angle of the GMAW torch was 90u and thetravel angle was 0u Three different shielding gases wereused argon MMG and TIME The composition of eachshielding gas is listed in Table 1 More comprehensivedescriptions of the experimental apparatus and proce-dures used may be found in Nguyen et al132526

Procedure for formulating dimensionlessgroupsIn dimensional analysis all relevant process parametersare assembled into groups of variables which are

6 Dimensional plot of limiting welding speeds before

onset of humping or discontinuous weld bead defects

in GMA welds made in AISI 1018 plain carbon steel

versus welding power when using argon MMG and

TIME shielding gases (taken from Nguyen et al132526)

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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dimensionless According to Buckinghamrsquos theorem30

the number of dimensionless groups necessary tocompletely describe any physical system is equal to thenumber of controlling parameters minus the number offundamental dimensions used in that system In thisstudy of the GMAW process the fundamental dimen-sions are mass (kg) length (m) time (s) temperature (K)and current (A) Based on these fundamental dimensionsand Buckinghamrsquos theorem30 the total number ofdimensionless variables that can completely describe anobserved physical phenomenon will always be equal tothe number of process controlling parameters minusfive Therefore dimensional analysis will always reducethe dimensionality of the problem as well as the numberof experiments required

In dimensional analysis the formalised procedureused for formulating the various dimensionless groupsfrom different process parameters has three majorsteps3031

(i) identify the dependent and the physically rele-vant independent process parameters

(ii) assemble the process parameters into variousdimensionless groups and finally

(iii) express the dimensionless groups in combina-tions of well recognised dimensionless numbers

Dependent and independent dimensionalvariablesIn the first step of any dimensional analysis it is essentialto clearly identify dependent and physically relevantindependent dimensional variables of the process To besuccessful however thorough knowledge of the processand of the observed physical phenomenon is needed tocorrectly identify suitable dependent dimensional vari-ables and to critically evaluate the physical relevancy ofdifferent independent dimensional variables An inde-pendent variable is physically relevant if it has asignificant influence on the final value of the selecteddependent variable30 If a physically relevant independentvariable is overlooked or omitted then the final resultswill be very confusing and difficult to interpret

In any dimensional analysis the dependent variablemust be a measurable quantity that represents a certainaspect of the observed phenomenon For example thereis a welding speed beyond which high speed weld beaddefects will occur As shown in Fig 6 this limitingwelding speed is strongly dependent on various processparameters such as the power input and the shielding gascomposition Since the objective of a GMAW proceduredevelopment exercise is normally to achieve the highestpossible welding speed the limiting welding speed vl (ms)would be a suitable dependent variable

Possible physically relevant and independent variablesin the dimensional analysis are the GMAW processparameters the initial condition of the workpiece andthe material properties of the workpiece The GMAWprocess parameters that are physically relevant or thatare known to have strong influences on the limiting

welding speed are the welding voltage V (Volts or infundamental dimensions m2 kg s23 A21) the wire feedspeed (WFS) (ms) the CTWD (m) the diameter of thefiller metal electrode 1e (m) the shielding gas composi-tion and the electrical resistivity of the filler metal r (V mor in fundamental dimensions m3 kg s23 A22) In thepresent study the electrical resistivity of the filler metalis similar to that of the workpiece

Nguyen et al132526 found that the shielding gascomposition affects the arc current and power arclength the surface tension of molten metal in the weldpool and the area over which the molten filler metaldroplets impinged the weld pool surface These were allshown to affect the limiting welding speed As such theshielding gas composition is deemed to be a physicallyrelevant independent variable Initially the surfacetension c (N m21 or kg s22) of the molten weld metalcan be used to quantitatively represent the overall effectsof the shielding gas in the dimensional analysisHowever the arc length larc (m) and the weld widthww (m) were also used especially when considering thespray transfer mode of GMAW For the purpose of thisdimensional analysis the surface tension of molten steelin GMAW when using ER70S-6 electrode material anddifferent shielding gas compositions have been takenfrom the work of Subramaniam and White32 Thesesurface tensions are summarised in Table 2

In the list of influential GMAW process parametersdiscussed above the welding current I (A) was purposelyleft out since the Lincoln PowerWave 455 power supplywas used in the constant voltage mode throughout thestudy132526 In the constant voltage mode the weldingcurrent is a dependent variable and a consequence of thecombination of shielding gas composition V WFRCTWD 1e and r1 If I (A) is included with the otherindependent process parameters there will be a redun-dancy created which may obscure the actual relation-ships between various GMAW process parameters andthe onset of the high speed weld defects Nevertheless I (A)can be used to represent the combined effects ofshielding gas composition WFR CTWD 1e and r onvl (ms) In other words by using I (A) the number ofindependent dimensional variables is reduced by three inthe dimensional analysis In addition multiplication ofV (V) and I (A) can be used to represent the power P (Wor kg m2 s23) generated during welding

The remaining independent dimensional variables arethe initial temperature of the workpiece To (K) and thematerial properties of the SAE-AISI 1018 plain carbonsteel workpiece The initial temperature of the workpieceis a physically relevant independent variable since it hasbeen experimentally demonstrated that the limitingwelding speed in GMAW of plain carbon steel increasesas the initial temperature of the workpiece is increased33

In this dimensional analysis the initial temperature of

Table 2 Surface tension of molten steel in GMAW withdifferent shielding gas compositions32

Shielding gas Surface tension N m21

Pure argon 156MMG 115TIME 115Pure CO2 120Argon and 5O2 115

Table 1 Compositions of GMAW shielding gases used

Shielding gas Composition

Argon 100Ar (Ultra high purity grade)MMG 92Ar 8CO2

TIME 65Ar 8CO2 265He 05O2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 3: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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et al2526 observed a transition from spray to rotationalmetal transfer and a new type of weld defect which theycalled the discontinuous weld bead defect Figure 4shows a discontinuous GMAW weld bead The regularperiodic behaviour of humping is no longer evidentrather there are segments of good weld beads that areinterrupted at random intervals along the length of theweld bead by depressions in the base metal where thebase metal has been melted and gouged but no weld orfiller metal is present

Nguyen et al2526 attributed the formation of theaperiodic discontinuous weld bead defect to the incon-sistent transfer of the molten filler metal from theelectrode wire to the weld pool when welding inrotational transfer mode with reactive shielding gasesFor example Fig 5a is a LaserStrobe video image27 ofthe rotational transfer mode with the filler metaldetaching as droplets or fragments from a character-istically long molten metal string on the end of theelectrode Occasionally a very long fragment or all ofthe molten metal string on the end of the electrode willdetach as shown in Fig 5b While the welding arc is stillpresent this temporary disruption of the transfer of themolten filler metal into the weld joint results in adepression or section where the weld bead has been arcgouged but no filler metal deposited

In their studies of high speed weld bead defects in theGMAW process Nishiguchi et al1112 and Nguyenet al132526 have developed parametric maps of weldingcurrent or power versus welding speed that show regionsof process parameters that produced good weld beadsand regions or conditions that resulted in humping andother weld defects For example Fig 6 is a process mapthat consolidates the limiting welding speed datadeveloped by Nguyen et al132526 during their studiesof humping and discontinuous weld bead defects inGMA welds in AISI 1018 plain carbon steel The plotshows regions of welding power and welding speed thatresulted in good and defective weld beads when usingargon Mig Mix Gold (MMG) (Praxair DistributionInc Kitchener ON Canada) (Arndash8CO2) and TIME(BOC Gases Canada Ltd Waterloo ON Canada) (Arndash8CO2ndash265Hendash05O2) shielding gases In this plot thelines represent the maximum or limiting welding speedsthat could be used to produce a GMA weld without adefective weld bead profile From this plot the limitingwelding speed was a function of the shielding gas thewelding speed and the welding power When usingthe MMG and TIME reactive shielding gases and thewelding power of 9 kW the usable welding speed waslimited by the occurrence of humping1326 The limitingwelding speed was significantly less when using argonshielding gas With the welding power of 9 kW welds

3 Curved wall jet model for humping during high speed

GMAW (after Nguyen et al81326)

4 Top view of bead on plate GMA weld showing discon-

tinuous weld bead defect

a detachment of long molten metal string fragment bcomplete detachment of molten metal filament andwelding without filler metal transfer during formation ofdepression

5 LaserStrobe video images of rotational metal transfer

during formation of discontinuous weld bead defect

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 636

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made using the argon shielding gas exhibited humpingwhereas the discontinuous weld bead defect wasobserved when using the reactive shielding gases andthere was a distinct point of inflection between thelimiting welding speed lines for humping versus thediscontinuous weld bead defect This point of inflectionand change in behaviour at welding powers 9 kW isindicative that a transition has taken place in thephysical phenomena taking placing during the GMAWincluding a change in the filler metal transfer mechanismfrom spray to rotational transfer

While weld process maps such as that shown in Fig 6are valuable in identifying relationships and trendsbetween the various controllable process parameters theyare of limited value in predicting when humping will occurin new applications because all preset welding processparameters such as the shielding gas composition thetorch angle CTWD 1e electrode composition etc arekept constant when generating these process maps Achange of any one of these preset parameters wouldinvalidate the process map and necessitate an expensiveand time consuming series of experiments to generate anew process map Since the GMAW process is a multi-variate process with many independent parameters thenumber of experiments required to fully explore theinteractions between these parameters and the formationof high speed weld defects quickly becomes too large andimpractical to perform2829 In such cases it is advanta-geous to employ a dimensional analysis technique toreduce the dimensionality of the problem and the numberof experiments required without obscuring possiblerelationships between the process parameters and theonset of the high speed weld defects30

In their study of humping in GTA welds in 304stainless steel Mendez et al22ndash24 have performed adimensional analysis on specific aspects of the humpingphenomena and an order of magnitude scaling study inorder to identify the most important parameters andphysical phenomenon responsible for humping and also

to try to predict under what conditions humping willoccur In the context of the present study of high speedweld bead defects in GMAW however the use ofdimensional analysis has other advantages For exam-ple it is difficult to properly illustrate visualise andinterpret the effects of all process parameters on theonset of high speed weld defects using multidimensionalplots If these process parameters can be combined intodimensionless groups then their combined effects cansometimes be shown simultaneously on two-dimensionalplots thereby reducing the dimensions of the problemThus the dimensional analysis may provide a bettermethod to characterise and understand the relationshipbetween the various GMAW process parameters and theonset of high speed weld defects

The objective of the present study26 was to gain aninsight into the physical parameters responsible for theformation of high speed GMA weld bead defects byperforming a dimensional analysis of the high speedweld defect phenomena One of the primary goals of thisanalysis was to identify combinations of dimensionlessparameters that would collapse all dimensional weldingresults shown in Fig 6 onto a single dimensionless lineor value representative of the dimensionless limitingwelding speed thereby facilitating the prediction of theoccurrence high speed GMA weld defects This workwas performed in conjunction with the experimentaldata from Nguyen et alrsquos132526 previously reportedstudies of high speed GMA weld defects

Experimental apparatus and proceduresThe experimental data used for the present dimensionalanalysis were obtained from bead on plate GMA weldsthat were made using a Fanuc ARC Mate 120i 6-axiswelding robot and a Lincoln PowerWave 455 powersupply operating in constant voltage mode Welds weremade using a wide range of preset welding speeds andwelding powers Using a preset constant voltagedifferent welding powers were obtained by varying theWFR until the desired welding current was realised Allwelds were made using either spray or rotation metaltransfer A PC microcomputer was used with Labviewsoftware and National Instruments based data acquisi-tion system to record the welding voltages V andcurrents I These were then used to calculate the timeaveraged welding power P using P5VI Finally aLaserStrobe video imaging system27 was used to recordimages of the periodic humping and aperiodic discon-tinuous weld bead phenomena during GMAW

All bead on plate GMA welds were made in the flatposition on 65 mm (J0) thick cold rolled SAE-AISI 1018plain carbon steel plates using 09 mm (00350) diameterER70S-6 electrode wire and a 22 mm CTWD In all casesthe working angle of the GMAW torch was 90u and thetravel angle was 0u Three different shielding gases wereused argon MMG and TIME The composition of eachshielding gas is listed in Table 1 More comprehensivedescriptions of the experimental apparatus and proce-dures used may be found in Nguyen et al132526

Procedure for formulating dimensionlessgroupsIn dimensional analysis all relevant process parametersare assembled into groups of variables which are

6 Dimensional plot of limiting welding speeds before

onset of humping or discontinuous weld bead defects

in GMA welds made in AISI 1018 plain carbon steel

versus welding power when using argon MMG and

TIME shielding gases (taken from Nguyen et al132526)

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 637

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dimensionless According to Buckinghamrsquos theorem30

the number of dimensionless groups necessary tocompletely describe any physical system is equal to thenumber of controlling parameters minus the number offundamental dimensions used in that system In thisstudy of the GMAW process the fundamental dimen-sions are mass (kg) length (m) time (s) temperature (K)and current (A) Based on these fundamental dimensionsand Buckinghamrsquos theorem30 the total number ofdimensionless variables that can completely describe anobserved physical phenomenon will always be equal tothe number of process controlling parameters minusfive Therefore dimensional analysis will always reducethe dimensionality of the problem as well as the numberof experiments required

In dimensional analysis the formalised procedureused for formulating the various dimensionless groupsfrom different process parameters has three majorsteps3031

(i) identify the dependent and the physically rele-vant independent process parameters

(ii) assemble the process parameters into variousdimensionless groups and finally

(iii) express the dimensionless groups in combina-tions of well recognised dimensionless numbers

Dependent and independent dimensionalvariablesIn the first step of any dimensional analysis it is essentialto clearly identify dependent and physically relevantindependent dimensional variables of the process To besuccessful however thorough knowledge of the processand of the observed physical phenomenon is needed tocorrectly identify suitable dependent dimensional vari-ables and to critically evaluate the physical relevancy ofdifferent independent dimensional variables An inde-pendent variable is physically relevant if it has asignificant influence on the final value of the selecteddependent variable30 If a physically relevant independentvariable is overlooked or omitted then the final resultswill be very confusing and difficult to interpret

In any dimensional analysis the dependent variablemust be a measurable quantity that represents a certainaspect of the observed phenomenon For example thereis a welding speed beyond which high speed weld beaddefects will occur As shown in Fig 6 this limitingwelding speed is strongly dependent on various processparameters such as the power input and the shielding gascomposition Since the objective of a GMAW proceduredevelopment exercise is normally to achieve the highestpossible welding speed the limiting welding speed vl (ms)would be a suitable dependent variable

Possible physically relevant and independent variablesin the dimensional analysis are the GMAW processparameters the initial condition of the workpiece andthe material properties of the workpiece The GMAWprocess parameters that are physically relevant or thatare known to have strong influences on the limiting

welding speed are the welding voltage V (Volts or infundamental dimensions m2 kg s23 A21) the wire feedspeed (WFS) (ms) the CTWD (m) the diameter of thefiller metal electrode 1e (m) the shielding gas composi-tion and the electrical resistivity of the filler metal r (V mor in fundamental dimensions m3 kg s23 A22) In thepresent study the electrical resistivity of the filler metalis similar to that of the workpiece

Nguyen et al132526 found that the shielding gascomposition affects the arc current and power arclength the surface tension of molten metal in the weldpool and the area over which the molten filler metaldroplets impinged the weld pool surface These were allshown to affect the limiting welding speed As such theshielding gas composition is deemed to be a physicallyrelevant independent variable Initially the surfacetension c (N m21 or kg s22) of the molten weld metalcan be used to quantitatively represent the overall effectsof the shielding gas in the dimensional analysisHowever the arc length larc (m) and the weld widthww (m) were also used especially when considering thespray transfer mode of GMAW For the purpose of thisdimensional analysis the surface tension of molten steelin GMAW when using ER70S-6 electrode material anddifferent shielding gas compositions have been takenfrom the work of Subramaniam and White32 Thesesurface tensions are summarised in Table 2

In the list of influential GMAW process parametersdiscussed above the welding current I (A) was purposelyleft out since the Lincoln PowerWave 455 power supplywas used in the constant voltage mode throughout thestudy132526 In the constant voltage mode the weldingcurrent is a dependent variable and a consequence of thecombination of shielding gas composition V WFRCTWD 1e and r1 If I (A) is included with the otherindependent process parameters there will be a redun-dancy created which may obscure the actual relation-ships between various GMAW process parameters andthe onset of the high speed weld defects Nevertheless I (A)can be used to represent the combined effects ofshielding gas composition WFR CTWD 1e and r onvl (ms) In other words by using I (A) the number ofindependent dimensional variables is reduced by three inthe dimensional analysis In addition multiplication ofV (V) and I (A) can be used to represent the power P (Wor kg m2 s23) generated during welding

The remaining independent dimensional variables arethe initial temperature of the workpiece To (K) and thematerial properties of the SAE-AISI 1018 plain carbonsteel workpiece The initial temperature of the workpieceis a physically relevant independent variable since it hasbeen experimentally demonstrated that the limitingwelding speed in GMAW of plain carbon steel increasesas the initial temperature of the workpiece is increased33

In this dimensional analysis the initial temperature of

Table 2 Surface tension of molten steel in GMAW withdifferent shielding gas compositions32

Shielding gas Surface tension N m21

Pure argon 156MMG 115TIME 115Pure CO2 120Argon and 5O2 115

Table 1 Compositions of GMAW shielding gases used

Shielding gas Composition

Argon 100Ar (Ultra high purity grade)MMG 92Ar 8CO2

TIME 65Ar 8CO2 265He 05O2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 638

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 639

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 640

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

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made using the argon shielding gas exhibited humpingwhereas the discontinuous weld bead defect wasobserved when using the reactive shielding gases andthere was a distinct point of inflection between thelimiting welding speed lines for humping versus thediscontinuous weld bead defect This point of inflectionand change in behaviour at welding powers 9 kW isindicative that a transition has taken place in thephysical phenomena taking placing during the GMAWincluding a change in the filler metal transfer mechanismfrom spray to rotational transfer

While weld process maps such as that shown in Fig 6are valuable in identifying relationships and trendsbetween the various controllable process parameters theyare of limited value in predicting when humping will occurin new applications because all preset welding processparameters such as the shielding gas composition thetorch angle CTWD 1e electrode composition etc arekept constant when generating these process maps Achange of any one of these preset parameters wouldinvalidate the process map and necessitate an expensiveand time consuming series of experiments to generate anew process map Since the GMAW process is a multi-variate process with many independent parameters thenumber of experiments required to fully explore theinteractions between these parameters and the formationof high speed weld defects quickly becomes too large andimpractical to perform2829 In such cases it is advanta-geous to employ a dimensional analysis technique toreduce the dimensionality of the problem and the numberof experiments required without obscuring possiblerelationships between the process parameters and theonset of the high speed weld defects30

In their study of humping in GTA welds in 304stainless steel Mendez et al22ndash24 have performed adimensional analysis on specific aspects of the humpingphenomena and an order of magnitude scaling study inorder to identify the most important parameters andphysical phenomenon responsible for humping and also

to try to predict under what conditions humping willoccur In the context of the present study of high speedweld bead defects in GMAW however the use ofdimensional analysis has other advantages For exam-ple it is difficult to properly illustrate visualise andinterpret the effects of all process parameters on theonset of high speed weld defects using multidimensionalplots If these process parameters can be combined intodimensionless groups then their combined effects cansometimes be shown simultaneously on two-dimensionalplots thereby reducing the dimensions of the problemThus the dimensional analysis may provide a bettermethod to characterise and understand the relationshipbetween the various GMAW process parameters and theonset of high speed weld defects

The objective of the present study26 was to gain aninsight into the physical parameters responsible for theformation of high speed GMA weld bead defects byperforming a dimensional analysis of the high speedweld defect phenomena One of the primary goals of thisanalysis was to identify combinations of dimensionlessparameters that would collapse all dimensional weldingresults shown in Fig 6 onto a single dimensionless lineor value representative of the dimensionless limitingwelding speed thereby facilitating the prediction of theoccurrence high speed GMA weld defects This workwas performed in conjunction with the experimentaldata from Nguyen et alrsquos132526 previously reportedstudies of high speed GMA weld defects

Experimental apparatus and proceduresThe experimental data used for the present dimensionalanalysis were obtained from bead on plate GMA weldsthat were made using a Fanuc ARC Mate 120i 6-axiswelding robot and a Lincoln PowerWave 455 powersupply operating in constant voltage mode Welds weremade using a wide range of preset welding speeds andwelding powers Using a preset constant voltagedifferent welding powers were obtained by varying theWFR until the desired welding current was realised Allwelds were made using either spray or rotation metaltransfer A PC microcomputer was used with Labviewsoftware and National Instruments based data acquisi-tion system to record the welding voltages V andcurrents I These were then used to calculate the timeaveraged welding power P using P5VI Finally aLaserStrobe video imaging system27 was used to recordimages of the periodic humping and aperiodic discon-tinuous weld bead phenomena during GMAW

All bead on plate GMA welds were made in the flatposition on 65 mm (J0) thick cold rolled SAE-AISI 1018plain carbon steel plates using 09 mm (00350) diameterER70S-6 electrode wire and a 22 mm CTWD In all casesthe working angle of the GMAW torch was 90u and thetravel angle was 0u Three different shielding gases wereused argon MMG and TIME The composition of eachshielding gas is listed in Table 1 More comprehensivedescriptions of the experimental apparatus and proce-dures used may be found in Nguyen et al132526

Procedure for formulating dimensionlessgroupsIn dimensional analysis all relevant process parametersare assembled into groups of variables which are

6 Dimensional plot of limiting welding speeds before

onset of humping or discontinuous weld bead defects

in GMA welds made in AISI 1018 plain carbon steel

versus welding power when using argon MMG and

TIME shielding gases (taken from Nguyen et al132526)

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 637

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dimensionless According to Buckinghamrsquos theorem30

the number of dimensionless groups necessary tocompletely describe any physical system is equal to thenumber of controlling parameters minus the number offundamental dimensions used in that system In thisstudy of the GMAW process the fundamental dimen-sions are mass (kg) length (m) time (s) temperature (K)and current (A) Based on these fundamental dimensionsand Buckinghamrsquos theorem30 the total number ofdimensionless variables that can completely describe anobserved physical phenomenon will always be equal tothe number of process controlling parameters minusfive Therefore dimensional analysis will always reducethe dimensionality of the problem as well as the numberof experiments required

In dimensional analysis the formalised procedureused for formulating the various dimensionless groupsfrom different process parameters has three majorsteps3031

(i) identify the dependent and the physically rele-vant independent process parameters

(ii) assemble the process parameters into variousdimensionless groups and finally

(iii) express the dimensionless groups in combina-tions of well recognised dimensionless numbers

Dependent and independent dimensionalvariablesIn the first step of any dimensional analysis it is essentialto clearly identify dependent and physically relevantindependent dimensional variables of the process To besuccessful however thorough knowledge of the processand of the observed physical phenomenon is needed tocorrectly identify suitable dependent dimensional vari-ables and to critically evaluate the physical relevancy ofdifferent independent dimensional variables An inde-pendent variable is physically relevant if it has asignificant influence on the final value of the selecteddependent variable30 If a physically relevant independentvariable is overlooked or omitted then the final resultswill be very confusing and difficult to interpret

In any dimensional analysis the dependent variablemust be a measurable quantity that represents a certainaspect of the observed phenomenon For example thereis a welding speed beyond which high speed weld beaddefects will occur As shown in Fig 6 this limitingwelding speed is strongly dependent on various processparameters such as the power input and the shielding gascomposition Since the objective of a GMAW proceduredevelopment exercise is normally to achieve the highestpossible welding speed the limiting welding speed vl (ms)would be a suitable dependent variable

Possible physically relevant and independent variablesin the dimensional analysis are the GMAW processparameters the initial condition of the workpiece andthe material properties of the workpiece The GMAWprocess parameters that are physically relevant or thatare known to have strong influences on the limiting

welding speed are the welding voltage V (Volts or infundamental dimensions m2 kg s23 A21) the wire feedspeed (WFS) (ms) the CTWD (m) the diameter of thefiller metal electrode 1e (m) the shielding gas composi-tion and the electrical resistivity of the filler metal r (V mor in fundamental dimensions m3 kg s23 A22) In thepresent study the electrical resistivity of the filler metalis similar to that of the workpiece

Nguyen et al132526 found that the shielding gascomposition affects the arc current and power arclength the surface tension of molten metal in the weldpool and the area over which the molten filler metaldroplets impinged the weld pool surface These were allshown to affect the limiting welding speed As such theshielding gas composition is deemed to be a physicallyrelevant independent variable Initially the surfacetension c (N m21 or kg s22) of the molten weld metalcan be used to quantitatively represent the overall effectsof the shielding gas in the dimensional analysisHowever the arc length larc (m) and the weld widthww (m) were also used especially when considering thespray transfer mode of GMAW For the purpose of thisdimensional analysis the surface tension of molten steelin GMAW when using ER70S-6 electrode material anddifferent shielding gas compositions have been takenfrom the work of Subramaniam and White32 Thesesurface tensions are summarised in Table 2

In the list of influential GMAW process parametersdiscussed above the welding current I (A) was purposelyleft out since the Lincoln PowerWave 455 power supplywas used in the constant voltage mode throughout thestudy132526 In the constant voltage mode the weldingcurrent is a dependent variable and a consequence of thecombination of shielding gas composition V WFRCTWD 1e and r1 If I (A) is included with the otherindependent process parameters there will be a redun-dancy created which may obscure the actual relation-ships between various GMAW process parameters andthe onset of the high speed weld defects Nevertheless I (A)can be used to represent the combined effects ofshielding gas composition WFR CTWD 1e and r onvl (ms) In other words by using I (A) the number ofindependent dimensional variables is reduced by three inthe dimensional analysis In addition multiplication ofV (V) and I (A) can be used to represent the power P (Wor kg m2 s23) generated during welding

The remaining independent dimensional variables arethe initial temperature of the workpiece To (K) and thematerial properties of the SAE-AISI 1018 plain carbonsteel workpiece The initial temperature of the workpieceis a physically relevant independent variable since it hasbeen experimentally demonstrated that the limitingwelding speed in GMAW of plain carbon steel increasesas the initial temperature of the workpiece is increased33

In this dimensional analysis the initial temperature of

Table 2 Surface tension of molten steel in GMAW withdifferent shielding gas compositions32

Shielding gas Surface tension N m21

Pure argon 156MMG 115TIME 115Pure CO2 120Argon and 5O2 115

Table 1 Compositions of GMAW shielding gases used

Shielding gas Composition

Argon 100Ar (Ultra high purity grade)MMG 92Ar 8CO2

TIME 65Ar 8CO2 265He 05O2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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dimensionless According to Buckinghamrsquos theorem30

the number of dimensionless groups necessary tocompletely describe any physical system is equal to thenumber of controlling parameters minus the number offundamental dimensions used in that system In thisstudy of the GMAW process the fundamental dimen-sions are mass (kg) length (m) time (s) temperature (K)and current (A) Based on these fundamental dimensionsand Buckinghamrsquos theorem30 the total number ofdimensionless variables that can completely describe anobserved physical phenomenon will always be equal tothe number of process controlling parameters minusfive Therefore dimensional analysis will always reducethe dimensionality of the problem as well as the numberof experiments required

In dimensional analysis the formalised procedureused for formulating the various dimensionless groupsfrom different process parameters has three majorsteps3031

(i) identify the dependent and the physically rele-vant independent process parameters

(ii) assemble the process parameters into variousdimensionless groups and finally

(iii) express the dimensionless groups in combina-tions of well recognised dimensionless numbers

Dependent and independent dimensionalvariablesIn the first step of any dimensional analysis it is essentialto clearly identify dependent and physically relevantindependent dimensional variables of the process To besuccessful however thorough knowledge of the processand of the observed physical phenomenon is needed tocorrectly identify suitable dependent dimensional vari-ables and to critically evaluate the physical relevancy ofdifferent independent dimensional variables An inde-pendent variable is physically relevant if it has asignificant influence on the final value of the selecteddependent variable30 If a physically relevant independentvariable is overlooked or omitted then the final resultswill be very confusing and difficult to interpret

In any dimensional analysis the dependent variablemust be a measurable quantity that represents a certainaspect of the observed phenomenon For example thereis a welding speed beyond which high speed weld beaddefects will occur As shown in Fig 6 this limitingwelding speed is strongly dependent on various processparameters such as the power input and the shielding gascomposition Since the objective of a GMAW proceduredevelopment exercise is normally to achieve the highestpossible welding speed the limiting welding speed vl (ms)would be a suitable dependent variable

Possible physically relevant and independent variablesin the dimensional analysis are the GMAW processparameters the initial condition of the workpiece andthe material properties of the workpiece The GMAWprocess parameters that are physically relevant or thatare known to have strong influences on the limiting

welding speed are the welding voltage V (Volts or infundamental dimensions m2 kg s23 A21) the wire feedspeed (WFS) (ms) the CTWD (m) the diameter of thefiller metal electrode 1e (m) the shielding gas composi-tion and the electrical resistivity of the filler metal r (V mor in fundamental dimensions m3 kg s23 A22) In thepresent study the electrical resistivity of the filler metalis similar to that of the workpiece

Nguyen et al132526 found that the shielding gascomposition affects the arc current and power arclength the surface tension of molten metal in the weldpool and the area over which the molten filler metaldroplets impinged the weld pool surface These were allshown to affect the limiting welding speed As such theshielding gas composition is deemed to be a physicallyrelevant independent variable Initially the surfacetension c (N m21 or kg s22) of the molten weld metalcan be used to quantitatively represent the overall effectsof the shielding gas in the dimensional analysisHowever the arc length larc (m) and the weld widthww (m) were also used especially when considering thespray transfer mode of GMAW For the purpose of thisdimensional analysis the surface tension of molten steelin GMAW when using ER70S-6 electrode material anddifferent shielding gas compositions have been takenfrom the work of Subramaniam and White32 Thesesurface tensions are summarised in Table 2

In the list of influential GMAW process parametersdiscussed above the welding current I (A) was purposelyleft out since the Lincoln PowerWave 455 power supplywas used in the constant voltage mode throughout thestudy132526 In the constant voltage mode the weldingcurrent is a dependent variable and a consequence of thecombination of shielding gas composition V WFRCTWD 1e and r1 If I (A) is included with the otherindependent process parameters there will be a redun-dancy created which may obscure the actual relation-ships between various GMAW process parameters andthe onset of the high speed weld defects Nevertheless I (A)can be used to represent the combined effects ofshielding gas composition WFR CTWD 1e and r onvl (ms) In other words by using I (A) the number ofindependent dimensional variables is reduced by three inthe dimensional analysis In addition multiplication ofV (V) and I (A) can be used to represent the power P (Wor kg m2 s23) generated during welding

The remaining independent dimensional variables arethe initial temperature of the workpiece To (K) and thematerial properties of the SAE-AISI 1018 plain carbonsteel workpiece The initial temperature of the workpieceis a physically relevant independent variable since it hasbeen experimentally demonstrated that the limitingwelding speed in GMAW of plain carbon steel increasesas the initial temperature of the workpiece is increased33

In this dimensional analysis the initial temperature of

Table 2 Surface tension of molten steel in GMAW withdifferent shielding gas compositions32

Shielding gas Surface tension N m21

Pure argon 156MMG 115TIME 115Pure CO2 120Argon and 5O2 115

Table 1 Compositions of GMAW shielding gases used

Shielding gas Composition

Argon 100Ar (Ultra high purity grade)MMG 92Ar 8CO2

TIME 65Ar 8CO2 265He 05O2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 6: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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the workpiece will be expressed as the temperaturedifference with respect to absolute 0 K ie DTo (K)5To

(K)ndash0 K5T (K)

The material properties of the steel workpiece includethermal conductivity k (W m21 K21 or kg m s23 K21)specific heat cp (J kg21 K21 or m2 s22 K21) density r(kg m23) and electrical resistivity r (V m or m3 kg s23 A22)During welding there is a large temperature gradientalong the GMA electrode wire as the wire leaves thecontact tip at room temperature and is heated to itsmelting point at the tip of the electrode Similarly aportion of the workpiece located directly underneath thewelding arc will exceed the melting temperature whilethe material at the edge of the workpiece may still be atroom temperature Since the material properties aretemperature dependent these large differences in tem-perature result in significant differences in the materialproperties throughout the workpiece and the electrodewire In a dimensional analysis a single value isnormally required for a material property Thereforethe material properties must be based on an appropriateaverage value of each specific material property over thetemperature range experienced by the material

Since the density of steel is a relatively weak functionof temperature a constant value of 7844 kg m23 wasused in the present study for all temperatures34 On theother hand k cp and r of the steel are strongly affectedby temperature34ndash36 An average value for k cp and rwas obtained by numerically integrating their valuesbetween room temperature (293 K) and the meltingpoint of steel (1800 K) and then divided by thetemperature range ie

yaverage~

ETH1800

293

y(T)|dT

1800293(1)

where yaverage is the average material property of interestand T is the temperature in degrees Kelvin Thus usingthe data published by Pehlke et al34 the integratedaverage thermal conductivity of the steel is356 W m21 K21 Using the correlations between cp

and T obtained from Watt et al35 the integratedaverage specific heat is 8343 J kg21 K21 Finally theintegrated average electrical resistivity of the steel is73961027 V m36

Table 3 contains a summary of the initial dependent andindependent variables used in the present dimensionalanalysis The dependent dimensional variable is vl (m s21)while there are ten independent dimensional variables V

WFS CTWD 1e c To and the material properties k cpr and r Previously published experimental data ofteninclude welding power as a dependent variable Howeverdirect comparisons with these data cannot be made usingthe independent variables listed in Table 3 because thewelding power cannot be explicitly represented in thedimensionless numbers generated by the dependent vari-able in this list If the welding current is included in Table 3as an independent variable then it can be multiplied by thevoltage to form the welding power However with theaddition of I the parameters WFS CTWD 1e and r mustbe left out to avoid any redundancy As shown in Table 3the final list of independent process variables has beensignificantly reduced from ten to six These are the power P(kg m2 s23) c (kg s22) DTo (K) cp (m2 s22 K21) k(kg m s23 K21) and r (kg m23) Note that by using thewelding power P as an independent process variable thefundamental dimension of current (A) is no longerrequired in the analysis

Assembling dimensionless variablesIn dimensional analysis the lsquoprsquo label with numericalsubscript is traditionally used to represent a dimension-less group of variables In this case according to theBuckinghamrsquos theorem30 with seven dimensional vari-ables and four fundamental dimensions there will bethree dimensionless groups p1 p2 and p3 To assembleor form a dimensionless group of welding parameters p0

for example vl will be grouped with DTo cp k and rsince these independent variables contain the funda-mental dimensions (ie kg m s and K) that are suitableto form the foundation for each dimensionless groupPhysically p0 can be interpreted as a dimensionlesslimiting welding speed Initially the exponent of eachdimensional variable in the group is unknown and canbe expressed mathematically as

p0~(vl)x1 (DTo)x2 (k)x3 (cp)x4 (r)x5 (2)

where x1ndashx5 are the unknown exponents and thedimensional variables vl DTo cp k and r are as pre-viously defined Since the unit of each dimensionalvariable can be expressed in terms of fundamentaldimensions of mass (kg) length (m) time (s) andtemperature (K) the overall dimension of equation (2) is

p0frac12 ~m

s

x1

Keth THORNx2kgm

s3K

x3 m2

s2K

x4 kg

m3

x5

~kg0m0s0K0 (3)

where [p0] refers to the dimension of p0

Table 3 Summary of dependent and independent variables used in dimensional analysis

Dependent variable Initial set of independent variables Final set of independent variables

Limiting welding speed vl Voltage setting VWFSCTWDDiameter of electrode wire Oslashe

Effects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weldwidth ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density rElectrical resistivity r

Welding power PEffects of shielding gas as representedby the surface tension of the moltenmetal c the arc length larc and the weld width ww

Initial temperature of the workpiece To

Thermal conductivity kSpecific heat cp

Density r

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 639

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 640

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 641

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 642

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 643

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 646

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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As indicated in equation (3) the sum of the exponentsof each fundamental dimension m kg s and K mustequal 0 since p0 is dimensionless This requirementresults in the creation of four simultaneous equationswith five unknown exponents To solve for theexponents x1 is often assumed equal to 1 and thesimultaneous equations can then be used to solve forthe remaining exponents Once the exponents areknown the dimensionless group p0 can be assembledaccording to equation (2)

The procedure required to form one dimensionlessgroup can be long mathematically cumbersome andprone to arithmetic errors To speed up the process andto minimise the chance of obtaining erroneous solutionsa more concise algebraic based procedure of simulta-neously forming several dimensionless groups has beendeveloped30 A brief description of this procedure asapplied to the current set of independent and dependentparameters is presented in the Appendix The followingdimensionless parameters were derived using thisprocedure and the seven dimensional process parameterslisted in Table 3

p1~vl

DTo|cp

1=2(4)

p2~Pc15

p r

DToeth THORN1=2k2

(5)

p3~c cp

1=2

DToeth THORN1=2k

(6)

Recognising that the material properties and initialtemperatures are preset constants p1 is representative ofa dimensionless limiting welding speed and p2 is adimensionless welding power Finally p3 may bethought of as a dimensionless number that representsthe effects of shielding gas composition on the surfacetension of the metal

Expressing dimensionless groups inrecognisable dimensionless numbersThe newly formed dimensionless groups in equa-tions (4)ndash(6) can often be expressed as a combinationof well recognised named dimensionless numbers In thepresent example p1 contains vl DTo and cp Thisdimensionless group contains the same variable typesand has a similar form to the Eckert number Ec30 TheEckert number is the square of velocity divided by theproduct of the specific heat capacity and the temperaturedifference Therefore p1 can be precisely expressed as

p1~vl

DTocp

1=2~ Eceth THORN1=2

(7)

The Eckert number can be physically interpreted as theratio of kinetic energy to the enthalpy of the materialUsing this approach the other dimensionless groups canalso be expressed in terms of other recognised dimen-sionless numbers

Results and discussion

Initial analysisTo determine if there are any correlations between thedimensionless groups p1 p2 and p3 the experimental

data from the previous studies by Nguyen et al132526

were used to calculate the corresponding dimensionlessnumbers and these were then plotted and examined Forexample Fig 7 contains the experimental data in a plotof p1 versus p3 where p1 consists of the parameters vl cp

and DTo while p3 is a function of c cp DTo and k (seeequations (4) and (6)) If there is no correlation betweenp1 and p3 the data in Fig 7 would be randomlydistributed However the dimensionless group p3 maybe seen to stratify the data into two distinct groupsWhen p3 is about 861022 the data points belong to theGMA welds produced using argon shielding gasMeanwhile the other data at about p35661022 containdata from welds produced using the reactive shieldinggases MMG or TIME These results show the influencesof the reactive shielding gases as reflected through thesurface tension of molten weld metal However for agiven value of p3 ie reactive versus inert shielding gasthere is a great deal of scatter in the p1 data and no clearcorrelation Thus the correlation between p3 and p1 isnot very meaningful

Figure 8 shows a plot between dimensionless variablesp1 and p2 The dimensionless variable p2 includes thepower P5VI and the material properties r DTo cp andk For each type of shielding gas the line represents theboundary separating the good and the defective weldbead regions ie the dimensionless limiting weldingspeed p1 Good weld beads were produced in the regionunderneath each line while defective weld beads wereproduced in the region above each line Note that Fig 8is identical in form to the dimensional plots of thedimensional experimental data in Fig 6 because allother parameters in p1 and p2 are constants Thus thedimensionless limiting welding speed p1 is a function ofthe dimensionless power p2 and the shielding gascomposition

The relationships displayed in Fig 8 were based ondata generated using various welding powers while DTo

was constant However Finlayson33 has shown thathumping can be avoided by preheating the workpieceie by increasing DTo For example Fig 9a is the top

7 Relationships between dimensionless variables p1 and

p3

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 642

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

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view of a GMA weld exhibiting humping that wasproduced using TIME shielding gas a welding speed of50 mm s21 a welding power of 82 kW and an initialtemperature of DTo15298 K (25uC) while Fig 9b showsa good weld bead that was produced using the samewelding parameters while preheating the workpiece toDTo25423 K (150uC) Using the welding process para-meters for the weld made using DTo15298 K the valuesof p1 and p2 are 10061025 and 8546107 respectivelyAs shown in Fig 10 this combination of p1 and p2 isclearly located in the defective weld bead region and is inagreement with the observed humped weld beadgeometry (see Fig 9a) Similarly by preheating theworkpiece to 423 K the values of p1 and p2 become84261025 and 7166107 respectively As shown inFig 10 these dimensionless numbers are correctlypredicted to be in the good weld bead region Thus intheir current form p1 and p2 have correctly captured theinfluence of the initial temperature of the workpiece onthe occurrence of the humping in GMA weld beads

Revisions to initial analysisAs shown in Fig 7 when the experimental data wereplotted as p1 versus p3 there was no apparentcorrelation between these two dimensionless parametersother than the segregation of the p3 data between the Arand the other two reactive shielding gases However

when plotted as p1 versus p2 (see Fig 8) there appear tobe correlations as the data fall along three distinct linesUnfortunately the dimensionless limiting welding speedlines shown in Fig 8 are still segregated according to thetype of shielding gas used This suggests that our initialselection of influential dimensional process parametersused to derive p1 and p2 was incomplete and that theeffects of all influential variables have not yet beenincluded Thus further judicious revisions to theseoriginal dimensionless groupings are required to facil-itate the collapse of these data onto a single dimension-less line

In Fig 8 when p2 is 956107 the mode of fillermetal transfer is rotational and p1 for all shielding gasesis independent of p2 The limiting welding speeds of thereactive shielding gases are the same at about p15461025 However p1 of the welds produced using argonshielding gas was consistently lower at about p15361025 While the effects of shielding gas composition onthe welding current and power have already beenincorporated in p2 through the inclusion of V and Ithe effects of shielding gas composition on the surfacetension of the molten metal has not yet been includedFrom Fig 7 the dimensionless surface tension of themolten weld metal p3 appears to strongly influence p1

by stratifying the experimental data into two groupsPerhaps the observed separation in the current dimen-sionless plots is caused in part by the effect of theshielding gas on the surface tension of molten weldmetal To investigate this hypothesis a new dimension-less variable is formed using the following equation

p4~p1|p3~vl

DTocp

1=2|

c cp

1=2

DToeth THORN1=2k

~vlc

DTok(8)

where p1 p3 and other dimensional variables are aspreviously defined

Figure 11 is a plot of the new dimensionless variablep4 versus the original dimensionless variable p2 Notethat p4 includes the variables vl c DTo and k Bycombining the surface tension of the molten weld metaland the limiting welding speed into one dimensionless

8 Correlation between dimensionless variables p1 and p2

9 Top view of GMA welds produced with initial work-

piece temperature of a 298 K (25uC) exhibiting hump-

ing and b 423 K (150uC) without humping

10 Effect of initial workpiece temperature on occurrence

of high speed weld defects when using TIME shield-

ing gas

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 643

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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variable the limiting welding speeds when using thedifferent shielding gases merge into a single line whenp2gt956107 and rotational filler metal transfer modeoccurred (see Fig 11) Thus high speed GMA weldbead defects are predicted to occur when p2gt956107

and p4gt2261026

The collapse of the experimental data into a singlecurve p2gt956107 strongly suggests that the previouslyobserved separation in data was caused by the effect ofshielding gas on the surface tension of the molten weldmetal during rotational metal transfer However asshown in Fig 11 including the effect of the shielding gason the surface tension of the molten weld metal does notbring together the boundaries in the spray filler metaltransfer region (when p2(956107) This suggests thatother influential effects have not yet been included in thedimensionless variable p4 in the spray transfer regime

When welding using the same power and spray metaltransfer Nguyen et al132526 found that in addition tothe surface tension the area over which the filler metaldroplets impinged on the top surface of the weld pooland the arc length were strongly influenced by theshielding gas composition Gas metal arc welds pro-duced using reactive shielding gases had a shorter arclength and a larger filler metal droplet impingement areathan welds produced with argon shielding gas A shortarc length reduces the distance over which the fillermetal droplets can be accelerated by the arc plasma Asa result the overall momentum of the filler metaldroplets will be lower when they enter the weld poolthereby lowering the propensity for humpingMeanwhile with the reactive shielding gases the areaover which the filler metal droplets enter the top surfaceof the weld pool is larger thereby spreading out thedistribution of the incoming filler metal droplets Basedon the curved wall jet model of humping in GMAW1326

illustrated in Fig 3 both of these effects will reduce thelikelihood of creating a gouged weld pool surface andreduce the momentum of the backward flow of themolten weld metal thereby suppressing the humpingdefect until higher welding speeds However these latter

influences of the shielding gas have not yet been includedin the dimensional analysis

To include the additional effects of the shielding gason the filler metal droplet impingement characteristicsand the humping phenomenon during spray metaltransfer measurable quantities that represent the addi-tional effects of the shielding gas must be included asphysically relevant variables in the dimensional analysisFrom the above observations the arc length and thefiller metal droplets impingement area are two variablesthat can quantify the additional influences of theshielding gas on the humping phenomenon The arclength during GMAW was measured directly usingthe LaserStrobe video imaging system27 In addition thearea over which the filler metal droplets impinged onthe top surface of the weld pools was measured Thefiller metal droplet impingement area was found tocorrelate well to the weld width132526 a quantity thatcan be more easily measured during or after weldingConsequently in the present study the weld width wasused instead of the diameter of the filler metal dropletimpingement area

To examine the influences of shielding gas on the arclength and the weld width different welding power levelsmust be used in the experiments Since the arc lengthremains unchanged with higher welding speeds it can bemeasured using the LaserStrobe video imaging system27

at any welding speed welding power and shielding gascombination On the other hand the weld widthdecreases with increasing welding speeds Thus properwelding speeds must be selected when making the weldwidth measurements

The measured arc lengths and the weld widths areplotted against welding power in Fig 12 The data aregrouped according to the power levels In addition theplots also show the welding speeds at which thesemeasurements were made For instance the weldingspeeds used to measure the arc length and weld widthare 9 10 11 and 12 mm s21 for 5 6 75 and 8 kWwelding powers respectively These welding speedsdefine the boundary between good and humped weldbead regions when using argon shielding gas Againwith the exception of the shielding gases used otherGMAW process parameters were kept constant FromFig 12 argon shielded welds had longer arc lengths andnarrower weld widths than those produced using thereactive shielding gases Also welds produced using thereactive shielding gas MMG had longer arc lengths andslightly narrower weld widths than those made using theTIME shielding gas

Beyond the limiting welding speeds shown in Fig 12all argon shielded welds exhibited humping At eachlimiting welding speed the observed increase in arclength and decrease in weld width of the argon shieldedwelds relative to the welds made using the reactiveshielding gases are representative of the effects of theshielding gases on the limiting welding speed Since shortarc length and wide weld width suppresses the onset ofhumping until higher welding speeds these new vari-ables are arranged as a ratio to modify the dimensionlessvariable p4 as follows

p5~p4|larc

ww~

vlc

DTok|

larc

ww(9)

where larc is the arc length (m) and ww is the weld width (m)

11 Plot of new dimensionless variables p4 versus p2

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 10: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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The arc length and the weld width were measured foreach shielding gas and welding power level using thecorresponding limiting welding speed of the argonshielded welds

Thus far all of the modifications of the dimensionlessparameters have concentrated on the dimensionlesslimiting welding speed p4 in order to account for theobserved influences of the shielding gases on thedimensionless limiting welding speed The dimensionlesswelding power variable p2 has been left unaltered Aspreviously discussed when p2 is increased beyond956107 the filler metal transfer mode switches fromspray to rotational transfer In other words the transi-tion from spray to rotational transfer mode apparentlydepends only on the welding power level This is not

correct The transition from spray to rotational transfermode is known to be dependent not only on weldingpower but also on the diameter of the filler metalelectrode and the electrode stickout5 A long electrodestickout and a small electrode diameter will promote thetransition from spray to rotational transfer modes at lowwelding currents or welding powers The diameter of thefiller metal wire is an independent process parameterselected before welding On the other hand the electrodestickout is the distance the electrode extends from thecontact tip during welding (see Fig 1) This is adependent parameter For each combination of shield-ing gas and welding power the electrode stickoutdepends on the CTWD an independent process para-meter that is usually set before welding Thus instead ofusing the electrode stickout the CTWD will be used indeveloping a new dimensionless number

As previously explained the welding current can beused to represent the combined effects of WFS CTWD1e and r However 1e and CTWD also play a criticalpart in the transition from spray to rotational transfermodes This is further evidence of the complex inter-actions and interdependence of the various GMAWprocess parameters Therefore in addition to thewelding power 1e and CTWD (ie the electrodestickout) must also be included to properly account forthe transition from spray to rotational filler metaltransfer modes With CTWD and 1e the dimensionlessvariable p2 can be modified to a new dimensionlessvariable p6 as follows

p6~p2|CTWD

1e

~VI c3

p

1=2

r

DToeth THORN1=2k2

|CTWD

1e

(10)

Figure 13 shows a plot of the weld data using the newdimensionless variables p5 and p6 In this plot thetransition from spray to rotational transfer occurs atp65236109 For values of p6 236109 where spraytransfer mode occurred the inclusion of the ratio oflarcww in the dimensionless variable p5 has removed thepreviously observed differences in the dimensionless

13 Plot of modified dimensionless variables p5 and p6

12 Plots of a arc length and b weld width versus weld-

ing power for different shielding gases and at differ-

ent welding speeds

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

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lishe

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Man

ey P

ublis

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(c)

IOM

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mun

icat

ions

Ltd

using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 646

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lishe

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Man

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ublis

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(c)

IOM

Com

mun

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Ltd

Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

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20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 11: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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limiting welding speeds when using the differentshielding gases and collapsed the data onto a singlecurve for limiting welding speed Once the rotationaltransfer mode is achieved however the dimensionlesslimiting welding speed remains constant at y2661026 and becomes independent of p6 For therotational transfer mode larcww is set equal to 1 sincethe inclusion of the dimensionless surface tensionterm in p5 has already been successful in merging thelimiting welding speed lines of the different shieldinggases (see Fig 11) In other words during the rotationaltransfer mode the most significant influence of theshielding gas composition on the welding processappears to be its effect on the surface tension of themolten weld metal

Forming dimensionless variables withrecognisable dimensionless numbersThe dimensionless variables p5 and p6 can now beexpressed in term of recognisable dimensionless num-bers Definitions and the physical interpretation of thesewell recognised dimensionless numbers may be found inSzires30 Using these the dimensionless variable p5 canbe shown to consist of the Peclet (Pe) the Eckert (Ec)and the Weber (We) numbers ie

p5~vlclarc

DTokww~

PeEc

We(11)

Similarly p6 can be expressed in terms of the Pe numberthe Ec number and j1 ie

p6~VI c3

p

1=2

rCTWD

DToeth THORN1=2k21e

~j1Pe

Eceth THORN1=2(12)

where j1 is a dimensionless power input that is definedby the following equation37

j1~VI

DTokL(13)

j1 was derived by Weckman et al37 by non-dimensio-nalising the Gaussian distributed surface heat fluxboundary condition that is frequently used in modellingGTAW and LBW processes In the present study thecharacteristic length scale L in p6 and j1 is set equal tothe diameter of the filler metal electrode 1e

The Peclet number Pe in equation (12) can bephysically interpreted as the ratio of heat transferredby bulk motion or advection of the base metal to theheat transferred in the base metal by conduction It isexpressed mathematically as30

Pe~vcprL

k(14)

where v is the welding speed (m s21) L is a characteristiclength (m) cp r and k are material properties TheEckert number Ec is defined as30

Ec~v2

DTocp

(15)

where DTo is the temperature difference betweenthe material and the surrounding (K) Finally theWeber number We represents the ratio of thesurface tension to the inertial force in a liquid and isdefined as30

We~vr2L

c(16)

Validating results of dimensional analysisIn Fig 13 the good and the defective weld bead regionsare separated by a boundary on a two-dimensional plotof two dimensionless parameters p5 and p6 Knowingthis boundary it is possible to predict whether a good ora defective weld bead would form based on the GMAWprocess parameters However to further ensure thereliability of the analysis experimental data from otherresearchers can be plotted and compared against theresults of the present study

The results from GMAW experiments by Bradstreet10

and Nishiguchi et al10 are plotted on the dimensionlessplot of p5 versus p6 in Fig 14 The solid circles representthree different humped welds produced by Bradstreet10

using CO2 (labelled C) argon (labelled B) and argonplus 5O2 (labelled A) shielding gases respectivelyMeanwhile the broken line is the limiting welding speedfrom Nishiguchi et alrsquos11 GMA welds with CO2 as theshielding gas Finally in Fig 14 best fit lines weredetermined using regression analysis and the limitingwelding speed data from the present study These are asfollows

p5~(32p26136p6z168)|106 for

p6v19|109

p5~26|106 for p6cent19|109 (17)

with a coefficient of determination of 086 Theboundary between these two lines and the humpingand discontinuous weld bead defects occurs at p65

236109 This can also be considered as a transitionpoint from spray to rotational filler metal transfermodes

When plotting the experimental data from the worksof Bradstreet10 and Nishiguchi et al11 in Fig 14 thevalue of p5 was calculated based on the assumption thatthe ratio of the arc length to the weld width was unity

14 Dimensionless boundary between good and defective

weld bead regions

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 644

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This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

Pub

lishe

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Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 646

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lishe

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Man

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(c)

IOM

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Ltd

Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 12: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

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lishe

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ey P

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Com

mun

icat

ions

Ltd

This was necessary because the arc length and weldwidths were not measured or reported With thisassumption the experimental data from bothBradstreet10 and Nishiguchi et al11 show good agree-ment with the data obtained from the present study Asmay be seen from Fig 14 the limiting welding speedfrom Nishiguchi et alrsquos work11 correlates well with thelimiting welding speed obtained in the present dimen-sional analysis Meanwhile the humped GMA weldsfrom Bradstreetrsquos work10 that were produced usingargon or Arndash5O2 shielding gas lie on or above thelimiting welding speed line obtained in the presentdimensional analysis and are correctly predicted toexhibit humping Meanwhile the weld produced usingCO2 shielding gas and globular transfer is well withinthe humped weld bead region Perhaps the weldingspeed of this humped weld was much greater than thelimiting welding speed for this particular set of processparameters The agreement between these three sets ofexperimental data suggests that the results of thedimensional analysis can be used with confidence todetermine whether a good or a defective weld bead willbe produced based on the values of the initial presetprocess parameters

Second variation of dimensional analysis ofhigh speed weld defectsDuring the formulation of the various dimensionlessparameters the dependent variable I (A) was used torepresent the combined effects of shielding gas composi-tion WFS CTWD 1e and r on the critical weldingspeed at which high speed weld bead defects would beproduced This substitution reduced the initial numberof independent variables from ten to seven andsuccessfully facilitated collapse of the data onto twocollinear dimensionless lines (see Fig 14 and equa-tion (17)) This suggests that all important physicalparameters responsible for the onset of high speed GMAweld bead defects have been included in these dimen-sionless parameters However the use of these dimen-sionless parameters as predictive tools is somewhatlimited because I is a dependant parameter that must bemeasured from actual welds The overall utility of thedimensional analysis as a predictive tool would beimproved if the preset independent weld process para-meters WFS CTWD 1e and r were used in place of Iwhen formulating the dimensionless parameters Thusthe dimensional analysis was performed again withoutsubstitution of the welding current and with insteadWFS CTWD 1e and r From this analysis a newdimensionless parameter p7 was formed as follows

p7~V2|WFS|CTWD|1e| cp|DTm

1=2

r|DTo|k|a2

~j2PeCTWDPe1e

Eceth THORN1=2(18)

As shown in equation (18) this new dimensionlessvariable p7 can also be expressed as a combination ofthe Peclet numbers Pe the Eckert number Ec and j2For the Pe number in the dimensionless parameter p7WFS is used for the velocity term The PeCTWD numberhas the CTWD as its characteristic length MeanwhilePe1e uses the diameter of the filler metal electrode as itscharacteristic length Ec consists of WFS DTm and cp

Lastly the term j2 is defined as

j2~V2

rDTok(19)

As before j2 can be interpreted as a dimensionless heatinput term modelled after the dimensionless heat inputterm used by Weckman et al37

A plot of the GMAW limiting welding speed data asfunctions of p5 versus the new dimensionless parameterp7 is shown in Fig 15 In this plot the dimensionlessvariable p5 is as previously defined When p75561013the filler metal transfer mode changed from spray torotational transfer The results in Fig 15 show thegeneral trends previously observed in the results ofearlier dimensional analysis The limiting welding speedinitially decreases with higher values of p7 When p7 is3861013 the dimensionless variable p5 becomesindependent of p7 and equal to 2661026 Theequations for the best fit limiting welding speed lines are

p5~(03p2723p7z77)|106 for p7v38|1013

p5~26|106 for p7cent38|1013 (20)

where p5 and p7 are as defined in the plot of Fig 15 andthe coefficient of determination is 07

Although the trends observed in Fig 15 are similar tothose observed in the previous analysis there is oneadvantage associated with this latter dimensionalanalysis The dimensionless variable p7 is now composedentirely of independent GMAW process parameterswhich are usually selected and preset before weldingFrom Fig 15 users of the GMAW process can predict ifdefective weld beads will be made based on the selectionof various preset welding parameters Thus from theuserrsquos point of view the results of the latter dimensionalanalysis are of considerably more practical value Theseresults and the derived dimensionless variables providevaluable insights into possible welding techniques thatcould be used to weld at higher welding speeds withoutthe occurrence of high speed weld bead defects

ConclusionsDetailed observations of the sequence of events takingplace during the formation of weld bead defects duringhigh speed bead on plate GMAW of plain carbon steel

15 Dimensionless plot of p5 versus p7

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 645

Pub

lishe

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Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 646

Pub

lishe

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Man

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ublis

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(c)

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Com

mun

icat

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Ltd

Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 13: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

using Ar and two reactive shielding gases MMG andTIME have been used in conjunction with phenomen-ological models of humping and the discontinuous weldbead defect to perform a dimensional analysis of theprocess Two dimensionless variables were developedusing dimensional analysis techniques which were basedupon preset process parameters These dimensionlessvariables were then used with the experimental data togenerate dimensionless weld process maps that docu-mented the effect of different influential GMAW processparameters on the limiting welding speed and the onsetof the two different high speed weld defects The firstdimensionless variable p5 combined the limiting weldingspeed and the influences of the shielding gas while thesecond dimensionless variable p7 represented the weld-ing power used during GMAW

It was shown that the different limiting welding speedlines observed when plotting the dimensional experi-mental data could be collapsed onto two collineardimensionless curves of p5 versus p7 one for the regionin which spray metal transfer and humping occurred andthe other for the region in which rotational transferoccurred and either humping or the discontinuous weldbead defect was observed Also the transition fromspray transfer to rotational metal transfer was found tooccur at a given value of p7 thus p7 can also be used topredict when this transition will occur Use of thedimensionless parameters reduced the dimensionality ofthe problem and allowed predictions of the occurrenceof the high speed weld defects to be simultaneouslyrelated to various influential GMAW process para-meters on one single two-dimensional plot

The dimensionless parameters and process map wereshown to correctly predict the observed effects of work-piece preheat temperature on the occurrence of humpingIn addition there was good correlation between thedimensionless GMAW process map and previouslypublished experimental data from a number of indepen-dent studies Thus the occurrence of high speed welddefects such as humping or the discontinuous weld beadand the transition from spray to rotational metal transfercan be predicted for the first time using the predeterminedvalue of various process parameters in conjunction withthe dimensionless GMAW process map of p5 versus p7

AppendixThe procedure required to form dimensionless groupscan be long mathematically cumbersome and prone toarithmetic errors To speed up the process and minimisethe chance of obtaining erroneous solutions a moreconcise algebraic based procedure of simultaneouslyforming several dimensionless groups has been devel-oped30 This procedure can be classified into fourdistinctive steps

(i) composing a dimensional matrix

(ii) partitioning the dimensional matrix

(iii) calculating additional matrices(iv) forming the dimensional set

Composing dimensional matrixAs the first step to assemble the dimensional variablesfrom the list of dependent and independent variablesinto dimensionless groups a dimensional matrix must beconstructed Table 4 shows the dimensional matrix forthe dependent variable vl and the independent variablesP c DTo cp k and r Each row corresponds to afundamental dimension while each matrix element orcell contains the exponent of the fundamental dimen-sions of the variable For example P has a unit of Wattor in the fundamental dimensions kg m2 s23 As aresult under the P column in the dimensional matrixthe elements are 2 for length (m) 1 for mass (kg) 23 fortime (s) and 0 for temperature (K) The elements in thedimensional matrix for the remaining variables can alsobe found in the same manner Since vl is the dependentvariable as a rule it must be in the first or the leftmostcolumn of the dimensional matrix30 The remainingcolumns represent the independent variables

Partitioning dimensional matrixThe dimensional matrix in Table 4 must now bepartitioned into matrix A and matrix B This partition-ing is necessary to allow the calculation of twoadditional matrices that will be required Table 5 showsthe partitioning of the dimensional matrix into matrix Aand matrix B Matrix A is a square matrix whose orderis equal to the number of fundamental dimensions in theproblem In our example there are four fundamentaldimensions (ie kg m s and K) As a result matrix Awill be a 464 matrix This square matrix is formed byselecting the four rightmost columns of the originaldimensional matrix Since the columns of matrix Arepresent four independent dimensional variables theseindependent variables will be utilised repeatedly toform the foundation for each dimensionless groupMeanwhile the remaining columns of the originaldimensional matrix are used to form the matrix B

In the current example the columns of matrix Aconsist of the independent variables DTo cp k and r (seeTable 4) This is one of the many possible forms ofmatrix A since any four of the independent variables Pc DTo cp k and r can be used to create matrix A Infact during a typical dimensional analysis differentcombinations of the independent variables are used inthe formulation of matrix A The final form of matrix Ashould allow an easy and meaningful physical inter-pretation of the resulting dimensionless groups Inaddition it is essential that matrix A has a non-zerodeterminant since the inverse of matrix A will be used ina subsequent calculation If the determinant of matrix Ais zero then the columns of the original dimensionalmatrix must be interchanged until a square matrix withnon-zero determinant is found

Table 4 Dimensional matrix of some of dependent andindependent GMAW variables

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

Table 5 Partitioning of original dimensional matrix inTable 4 into matrix A and matrix B

Matrix B Matrix A

1 2 0 0 2 1 230 1 1 0 0 1 121 23 22 0 22 23 00 0 0 1 21 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 646

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 14: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

Calculating additional working matricesOnce the original dimensional matrix has been parti-tioned two new matrices are calculated before theassembly of the dimensionless groups The first newmatrix or matrix C is calculated using both matrices Aand B and is based on the following equation

Cfrac12 ~ Afrac12 1| Bfrac12

T

(21)

where [A] [B] and [C] are matrix A B and Crespectively [A]21 is the inverse operation of matrix Awhile lsquoTrsquo represents the matrix transpose operationUsing equation (4) matrix C in the present example isequal to

Cfrac12 ~05 05 0 0

05 15 2 1

05 05 1 0

264

375 (22)

The second additional required matrix or matrix D is aunit or identity matrix as shown in equation (23) Thissecond matrix is a diagonal matrix with all non-zeroelements equal to 1 Matrix D has the same number ofrows as matrix C while its number of columns is thesame as that of matrix B Both new matrices are requiredto assemble the dimensionless groups

Dfrac12 ~1 0 0

0 1 0

0 0 1

264

375 (23)

Forming dimensional setIn the last step of the procedure a dimensional set mustbe created To create the dimensional set matrices Aand B are first recombined to form the originaldimensional matrix (ie to undo the partitioning of theoriginal dimensional matrix) Then the identity matrixD is placed directly below matrix B while matrix C ispositioned underneath matrix A Thus the dimensionalset is an amalgamation of the original dimensionalmatrix and two new matrices that are strategicallyplaced as illustrated in Table 6 The dimensional setconsists of matrix B in the upper left corner matrix A inthe upper right corner matrix D in the lower left cornerand matrix C in the lower right corner The combinationof matrices D and C forms three new bottom rows of thedimensional set

In this example according to the Buckinghamrsquostheorem30 with seven dimensional variables and fourfundamental dimensions there will be three dimension-less groups p1 p2 and p3 The last three rows of thedimensional set in Table 6 contain the information thatis used to assemble the dimensional variables together

into various dimensionless groups While the elementsof the original dimensional matrix are the exponentof the dimension of each variable the elements in thelast three rows of the dimensional set are the exponentof the variables in the dimensionless groups Forexample from Table 6 the non-zero elements on thep1 row correspond to vl DTo and cp The limitingwelding speed has the exponent of 1 while DTo and cp

have exponents of 205 As a result the first dimension-less group p1 consists of vl (ie exponent equals to 1)divided by the square root of the product of DTo and cp

(ie exponents equal to 205) ie p15vl(DTo6cp)12The other two dimensionless groups p2 and p3 aredetermined in similar manners The final overall resultsof this example of dimensional analysis are shown inequations (3)ndash(6)

Acknowledgements

The present work was supported by Natural Sciencesand Engineering Research Council of Canada(NSERC) Ontario Research and DevelopmentChallenge Fund (ORDCF) and its partners AlcanInternational Babcock amp Wilcox Canadian LiquidAir Ltd Centerline (Windsor) Ltd John DeereMagna International Inc Ventra Loan of roboticGMAW equipment by Lincoln Electric Company ofCanada Ltd and Fanuc Robotics Canada Ltd isgratefully acknowledged The TIME shielding gas usedin the present study was supplied by BOC Gas

References1 H B Cary lsquoModern welding technologyrsquo 5th edn 2002 Toronto

ON Prentice Hall Canada Inc

2 A F Manz Weld J 1990 69 (1) 67ndash68

3 lsquoWelding handbook ndash Part 1 Welding processesrsquo Vol 2 9th edn

147ndash203 2004 Miami FL American Welding Society

4 K A Lyttle Weld J 1983 62 (3) 5ndash23

5 Leonard P Connor in lsquoWelding handbookrsquo 8th edn Vol 1

lsquoWelding science and technologyrsquo 50 1991 Miami FL American

Welding Society

6 in lsquoASM handbookrsquo Vol 6 lsquoWelding brazing and solderingrsquo (ed

Davies et al) 1993 Materials Park OH ASM International 25

7 R L OrsquoBrien in lsquoWelding handbookrsquo 8th end Vol 2 lsquoWelding

processesrsquo 112ndash116 1991 Miami FL American Welding Society

8 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2006 11 (6) 618ndash633

9 E Soderstrom and P Mendez Sci Technol Weld Join 2006 11

(5) 572ndash579

10 B J Bradstreet Weld J 1968 47 (6) 314sndash322s

11 K Nishiguchi K Matsuyama K Terai and K Ikeda Proc 2nd

Int Symp on lsquoAdvanced welding technologyrsquo Osaka Japan

August 1975 Japan Welding Society Paper 2-2-(10)

12 K Nishiguchi and A Matsunawa Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975 Japan

Welding Society Paper 2-2-(5)

13 T C Nguyen D C Weckman D A Johnson and H W Kerr

Sci Technol Weld Join 2005 10 (4) 447ndash459

14 T Yamamoto and W Shimada Proc 2nd Int Symp on

lsquoAdvanced welding technologyrsquo Osaka Japan August 1975

Japan Welding Society Paper 2-2-(7)

15 W F Savage E F Nipples and K Agusa Weld J 1979 58 (7)

212sndash224s

16 S Hiramoto M Ohmine T Okuda and A Shinmi Proc Int

Conf on lsquoLaser advanced material processing ndash science and

applicationrsquo Osaka Japan May 1987 High Temperature Society

of Japan and Japan Laser Processing Society 157ndash162

17 C E Albright and S Chiang J Laser Appl 1988 1 (1) 18ndash24

18 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1983 25 (2) 62ndash67

19 S Tsukamoto H Irie M Inagaki and T Hashimoto Trans Natl

Res Inst Met 1984 26 (2) 133ndash140

Table 6 Combined set of dimensional set matrices [A][B] [C] and [D]

vl P c DTo cp k r

Length m 1 2 0 0 2 1 23Mass kg 0 1 1 0 0 1 1Time s 21 23 22 0 22 23 0Temperature K 0 0 0 1 21 21 0

p1 1 0 0 205 205 0 0p2 0 1 0 205 15 22 1p3 0 0 1 205 05 21 0

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 647

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648

Page 15: Predicting onset of high speed gas metal arc weld bead ... · weld bead defects using dimensional analysis techniques ... high speed weld defects ... resulted in good and defective

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

20 M Tomie N Abe and Y Arata Trans Japn Weld Res Inst

1989 18 (2) 175ndash180

21 U Gratzke P D Kapadia J Dowden J Kross and G Simon

J Phys D 1992 25D (11) 1640ndash1647

22 P F Mendez and T W Eagar Proc 5th Int Conf on lsquoTrends in

welding researchrsquo (ed J M Vitek et al) 13ndash18 1998 Materials

Park OH ASM International

23 P F Mendez and T W Eagar Proc Conf on lsquoMathematical

modelling of weld phenomena 5rsquo (ed H Cerjak and H K D H

Bhadeshia) 67ndash94 2001 London Institute of Materials

24 P F Mendez and T W Eagar Weld J 2003 82 (10) 296sndash306s

25 T C Nguyen D C Weckman and D A Johnson submitted to

Weld J 2007 86 (11)

26 T C Nguyen lsquoWeld defects in high-speed gas metal arc weldingrsquo

PhD thesis University of Waterloo Waterloo ON Canada 2005

27 lsquoLaserStrobe model 4Z ndash Operation manualrsquo 1999 Idaho Fall ID

Control Vision Inc

28 S B Jones J Doherty and G R Salter Weld J 1977 56 (7) 19ndash31

29 J Biglou D C Weckman G W Bennett and H W Kerr Sci

Technol Weld Join 2001 6 (1) 51ndash62

30 T Szires lsquoApplied dimensional analysis and modelingrsquo 1998

Toronto ON McGraw-Hill

31 H E Huntley lsquoDimensional analysisrsquo 1967 New York Rinehart

amp Company Inc

32 S Subramanian and D R White Metall Trans B 2001 32B

313ndash318

33 S M Finlayson lsquoParametric modelling of high-speed gas metal arc

weldingrsquo MASc thesis University of Waterloo Waterloo ON

Canada 2001

34 R D Pehlke A Jeyarajan and H Wada lsquoSummary of thermal

properties of casting alloys and mold materialsrsquo Report No NSF

MEA-82028 NSF Applied Research Division University of

Michigan Ann Arbor MI USA 1982

35 D F Watt L Coon M Bibby J Goldak and C Henwood Acta

Metall 1988 36 (11) 3029ndash3035

36 in lsquoThe metals black bookrsquo (ed J E Bringas) Vol 1 213ndash

214 1992 Edmonton Alberta Canada CASTI Publishing

Inc

37 D C Weckman H W Kerr and J T Liu Metall Trans B 1997

28B (4) 687ndash700

Nguyen et al Predicting onset of high speed gas metal arc weld bead defects

Science and Technology of Welding and Joining 2007 VOL 12 NO 7 648