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3 4 N O V E M B E R / D E C E M B E R 2 0 0 6 GEAR TECHNOLOGY www.gear technology.com www.powert ransmiss ion.com

Figure 1Local stock removal depending on the process strategy.

IntroductionDiscontinuous gear profile grinding is com-

monly used in the manufacture of large-modulegears. And because the batch sizes are typicallysmall to medium, the process must be highly flex-

ible. In order to achieve this flexibility, dress-ablerather than CBN-platedgrinding wheelscan be applied. But in using these tools, theprocess robustness can be compromised by localstructural damagesuch as grinding burntothe external zone.

In tooth-flank profile grinding, due to thevariation of contact conditions along the profilebetween grinding wheel and tooth flank, processoptimization is difficult. And in comparison withother grinding processes, these conditions clearlylead to varying grinding conditions along the

profile. Examination of the complex geometricaland contact conditions requires fundamental tech-nological investigations in an analogy process.In this way, the relationship between variousmaterial removal conditions can be investigatedas functions of the machining parameters andgrinding wheel specifications.

The purpose of this article is to develop abetter process understanding in order to usenew potentials for process optimization. Theknowledge gained in the analogy process is thebasis for a new mathematical model, allowing

that understanding to be transferred to the real

Optimization of the Gear Profile GrindingProcess Utilizing an Analogy Process

Christof Gorgels, Heiko Schlattmeier, and Fritz Klocke

Management SummaryThe requirements for transmission gears have con-

tinuously increased in past years, leading to the necessityfor improvements in manufacturing processes. On theone hand, the material strength is increasing, while on theother there is a demand for higher manufacturing quality.For those reasons, increasing numbers of gears have tobe hard-finished.

The appearance of grinding burn in gear profilegrinding, especially when using dressable grindingwheels, seemed to increase over the past years. As weknow, grinding burn reduces the load-carrying capacityof gears tremendously. Conversely, costs need to be cutin order to assure a companys competitive position in theglobal market. And yet, reducing the machining times ingear grinding still increases the risk of producing grind-ing burn (Ref. 1).

In order to grind gears burn-free and as produc-tively as possible, a better understanding of the processis required. This is especially important for gear profilegrinding, due to the complex contact conditions betweenworkpiece and grinding wheel (Refs. 23). In this article,an analogy process and a process model will be presentedin order to gain a closer look into the process. Finally,different process strategies will be analyzed using thepresented process model in order to give examples for theuse of the described calculations.

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www.powert ransmiss ion.com www.gear technology.com GEAR TECHNOLOGY N O V E M B E R / D E C E M B E R 2 0 0 6 3 5

Dipl.-Ing. Christof Gorgels is a research engineerat the WZL Laboratory for Machine Tools andProduction Engineering. His area of expertise isgear manufacturing, gear hard finishing and espe-cially gear grinding and grinding burn.

Dr.Ing. Heiko Schlattmeier is in charge of tooland fluid management for drivetrain manufactur-ing at BMW in Dingolfing, Germany. The research

reflected in this article was conducted during histime as the chief engineer of the WZL Gear ResearchDepartment of Aachen University of Technology,where his area of specialty was hard gear finishingand gear form grinding.

Prof. Dr.Ing. Fritz Klocke is head of the Chairof Manufacturing Technology and a member of thedirectory board of the Laboratory for Machine Toolsand Production Engineering (WZL), a department ofthe Aachen University of Technology in Germany.Also, he is head of the Fraunhofer Institute forProduction Technology in Aachen, Germany.

process. Finally, a process optimization for gearprofile grinding using this mathematical modelwill be presented.

Local Stock Removal and Grinding Burnin Gear Profile Grinding

Local grinding conditions along the profilein gear profile grinding . Basically, there are twoprocess strategies that are commonly used forgear profile grinding in industrial practice. Theleft side of Figure 1 shows a grinding processwith the removal of an equidistant stock alongthe profile. These are typical contact conditionsoccurring in single-flank grinding, with an in-feed realized by a rotation of the workpiece(Refs. 2, 4).

The right side of Figure 1 shows the removalof a constant stock in the radial direction, real-ized by a radial infeed of the grinding wheelin multiple steps. This is the process strategymost commonly used in industrial practice. Itis obvious that the initial stock removal is notconstant along the profile. In the first cut, stockis removed in the area of the root flank only.With further infeed, the area of stock removal isincreasing. The whole stock in the tooth root isremoved in the last cut only.

Appearance of grinding burn in gear pro-file grinding . Typically, grinding burn appearsonly locally along the tooth profile in gear profilegrinding. This is due to either the chosen processstrategy or heat distortions and centering defaults.In this article, two examples of local grindingburndependent upon the process strategywill be shown. For these trials, a typical truckgear from the case-hardened steel 20MnCr5E hasbeen ground using a dressable, white corundumgrinding wheel and using different process strate-gies. The tooth gaps have all been pre-ground inorder to remove the influence of heat distortionsand to ensure a constant stock removal in eitherinfeed or equidistant direction.

The results for a radial infeed of the grindingwheel without grinding the tooth root are shownin Figure 2. In the trials, a variation of the spe-cific stock removal rateQ'w has been realized bya variation of the axial feed speedf a. The picturein the lower left shows the tooth flanks after nitaletching. It is readily apparent that the grindingburn appears only in the area of the tip flank.

Additionally, technological trials have beenconducted with a constant stock removal alongthe gear tooth profile (see results in Figure 3).The specific stock removal rateQ'w varies inthis operation along the tooth profile. The valuesshown in the chart are calculated at the index-ing diameter in order to be comparable to theprevious results. The picture in the lower-left

Figure 2Typical grinding burn for radial infeed of the grinding wheel.

Figure 3Typical grinding burn for equidistant infeed of the grinding wheel.

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corner shows the gear after nital etching, andthe tempered zone has moved from tip flank toroot flank. Again, this is a typical phenomenonfor this process strategy of removing a constantstock along the profile.

These results show that process strategygreatly influences local grinding conditions and,in turn, the area where grinding burn can appear.But why this area in particular shows thermaldamage from grinding burn is not obvious. Asthe diagrams showing the specific spindle powerP'c clearly reveal, the grinding burn nearlyalways appears before the spindle power shows adisproportionate increase.

Analogy Process for GearProfile Grinding

The main difference between gear profilegrinding and standard grinding is the varying pro-file angle along the tooth flank. Investigationsof gear profile grinding can only show totaleffects over the whole profile height and varyinggrinding conditions. This is a major reason whyit is difficult to find out what leads to grindingburn occurring only locally on the tooth flank.

In order to investigate the technologicalconditions separately along the tooth flank, ananalogy process has been developed at the WZLlaboratory at RWTH Aachen University. Thebasic setup of this analogy process is shown inFigure 4. The left picture shows the varying con-tact conditions along the tooth flank for a radialinfeed of the grinding wheel into a pre-groundtooth gap. The radial infeedae is constant alongthe profile height, while the stock in normaldirections varies with the local profile angle .

On the right side of Figure 4, the analogyprocess is shown. The local contact conditions,infeed ae, stock s and profile angle of oneposition of the gear tooth profile are transferredto the grinding of a rectangular workpiece. In thisway, all possible grinding conditions occurringalong the profile can be examined separately.

The first trials using the analogy process havebeen carried out using a corundum-white grindingwheel, commonly used in industrial practice forgear profile grinding. The machining parametershave also been adjusted to those common in gearprofile grinding. The trials were conducted on aKapp VAS55P gear grinding machine in order tokeep the pre-conditions in the analogy process asclose to gear profile grinding as possible.

The workpieces are rectangular parts of thecase-hardened steel 16MnCr5E, with a hardeningdepth of 0.9 mm. In the trials, a maximum totalstock of s = 0.4 mm was removed in the grind-ing process. The hardness of 61 HRC was nearlyconstant from the surface to this depth. The

Figure 4Analogy process for gear profile grinding.

Figure 5Workpiece data.

Figure 6Grinding forces depending on the profile angle.

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tion of profile grinding processes, an empiricalprocess model was developed to allow applica-tion of the results from the analogy process toprofile grinding. In the analogy process, a largenumber of trials with profile angles varying from = 2 to = 90, and a stock varying froms = 0.05 mm to s = 0.4 mm, were conducted.A function shown in Figure 8 was chosen as anapproach in order to calculate the grinding forcesin profile grinding, based on the results of theanalogy process. The coefficients were deter-mined using the least-squares method. Grindingforces for conditions within the parameters testedin the analogy process are calculated using linearinterpolation.

The graphs in Figure 8 show the correlationbetween the measured value and the calculatedvalue for all three grinding forces in the differentcoordinate directions. A perfect result would begained if all points were on the 45 line, mean-ing that the measured values are exactly thesame as the calculated values. In this case, thegraph shows quite clearly that the points are very

workpieces were also ground before the trials inorder to assure a constant surface quality and toremove the distortions from heat treatment. Thematerial structure, the hardness and the residualstress profile are shown in Figure 5.

In Figure 6, the grinding forces in the nor-mal direction (Fn) and in the tangential direc-tion (Ft)depending on the stock removal fordifferent profile angles and a constant stock ofs = 0.2 mmare shown. It is obvious that, witha smaller profile angle, grinding forces increaseand the possible stock removal is significantlylower. Especially in the steep areas, with a pro-file angle of = 2, the initial grinding force isvery high, and it increases rapidly, indicating thatthere is high wear of the grinding wheel.

However, for a large profile angle of = 30, there is hardly any increase of the grind-ing forces with the stock removal. Thus, hardlyany wear of the grinding wheel occurs. It cantherefore be stated that the larger the local profileangle, the more material can be removed beforea dressing operation of the grinding wheel isneeded.

A reason for the tendency of the grindingwheel to wear earlier with a smaller profileangle can be attributed to the increasing contactlength caused by a decreasing profile angle.The dependency of the grinding forces on theremoved stock s is shown in Figure 7. Thegrinding forces in the tangential direction (Ft)and the direction normal to the surface (Fn)are displayed, depending on the stock removalfor different s and a profile angle of = 10.The grinding forces increase with the stock s,especially the maximum stock removal, until thesuper-proportional increase of grinding forcesbegins lowering significantly.

The results in the analogy process providea better understanding of the effects occurringin gear profile grinding. It has been shown thatgear geometries with a rather small profile anglelead to high grinding forces and to increasedwear of the grinding wheel. And yet, it is ratherdifficult to transfer the results to the gear profilegrinding process directly. At this point, one mustanalyze the local grinding conditions along theprofile and attempt to find similar conditionsin the analogy process. In order to more eas-ily compare the profile grinding process to theanalogy process, developing a process model isrequired. The model that has been developed isexplained below.

Transfer of the Analogy Results to theReal Process of Gear Profile Grinding

Development of an empirical process model .As a first approach to the technological descrip-

Figure 7Grinding forces depending on the stock s.

Figure 8Development of an empirical process model.

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close to this line, and that there is a very goodcorrelation between the measured and calcu-lated values. Additionally, the stability indexamounts to values between r = 0.93 for thetangential grinding force, andr = 0.98 for thegrinding force in the direction of the x-axisagood result in this case.

Calculation of local grinding forces ingear profile grinding . For the transfer ofthese results to the profile grinding process,a typical spur pinion with a gear geometryof the FZG-C gear was chosen. It hasz = 16teeth; a module of m n = 4.5 mm; a pressureangle of n = 20; and an outside diameter ofd a = 82.638 mm. The grinding wheel diameterused to calculate the geometrical contact lengthlg isd s = 200 mm.

As a good first example, a grinding processwith a constant stock s along the profile waschosen. This is a typical process occurring insingle-flank grinding with an in-feed realizedby the rotation of the workpiece. The stockamounts to s = 0.1 mm constantly along theprofile geometry. The radial infeedae differsalong the tooth flank due to the changingprofile angle . It amounts to a maximum ofae max = 1.239 mm in the area of the minimumprofile angle min 3 on the root flank. Thedistribution of the stock and the profile angleversus the local radius is shown in the upperdiagram of Figure 9.

The lower diagram shows the calculatedgeometrical contact length along the profile,which varies fromlg = 4 mm in the tooth root,lg max = 16 mm on the root flank, andlg = 5 mmin the tip flank area. The stock removal relatedto the length of the considered contour elementamounts to a constant value of Vw/ld = 2 mm/mm along the profile. So it can be concludedthat, using this process strategy, the extremevalues for the infeedae, as well as for the con-tact length lg, can be found in the area of theroot flank below the root form radius.

The grinding forces have been calculatedfor grinding 1, 16, 50 and 100 gaps. Eventhough the workpiece does not have more than16 gaps, these calculations make sense in orderto show the behavior of the grinding forcesafter a high stock removal, which can occurwhen grinding a similar gear with a muchlarger face width.

By knowing the local contact conditions,it is now possible to apply the results gainedfrom the analogy trials to the gear profilegrinding process. The first step is to transferthe analogy trials contact conditions to eachpoint of the gear profile. These calculated con-

Figure 9Local contact conditions in gear profile grinding with a constant stock s alongthe profile.

Figure 10Transference of the analogy results to gear profile grinding.

Figure 11Local grinding forces when removing a constant stock s along the profile.

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tact conditions are shown in Figure 10.The different curves showing the tangential

grinding forces versus the stock removal arerepresentative of contact conditions occurringin the gear profile grinding process. The x-axishas a second label indicating the number of gapsbeing ground after removing a certain amountof stock. This method is rather time consuming,and it is only possible to determine the grind-ing forces in areas of the profile, i.e., where thecontact conditions (stock s and profile angle )are known from the analogy process. Therefore,the calculations of the local contact conditionsare used in order to calculate local grindingforces, as opposed to using the process model.The results of the calculations of the tangentialgrinding forces related to the contour length ofld = 1 mm versus the workpiece radius are shownin Figure 11.

Those results show that the lowest grindingforces of Ft min/ld = 1.2 N/mm can be found inthe area of the largest profile angle, which isthe tooth root. Along the profile geometry, thegrinding forces are increasing up to a maximumof Ft max/ld = 2.3 N/mm in the area of the rootflank just below the root form radius, where theminimum profile anglemin is found. The grind-ing forces are then observed decreasing again, toFt/ld = 1.5 N/mm in the area of the tip flank witha rather high profile angle. Furthermore, thesecalculations show that the grinding forces areincreasing most when machining multiple gapsin the area with the maximum grinding forces.In this area, initial grinding burn can be expectedfor this process strategy. This has already beenshown by Schlattmeier (Ref. 2).

The most common process strategy in indus-trial practice is the radial infeed of the grindingwheel. In this case, the local stock s variesalong the profile geometry. For typical trials, aswell as for these calculations, a pre-ground gap isused in order to make sure that infeed ae is con-stant along the profile. The important geometricvalues for a radial in-feed ofae = 0.235 mmversus the workpiece radius are shown inFigure 12.

The local stock shows a maximum ofsmax = 0.235 mm =ae in the area of the toothroot, and lowers to a minimum short below theroot form diameter of smin = 0.02 mm. Towardsthe tip flank, it increases againto a localmaximum of s = 0.2 mm. The contact lengthlg is constant along the profile, but the orientedstock removal shows an absolute maximum inthe tooth root, a minimum short below the rootform radius, and a local maximum in the area ofthe tip flank.

Figure 12Local grinding conditions for a radial infeed of the grinding wheel.

With this data, it is now possible to calculatethe local grinding forces along the gear profilegeometry. The calculations of the tangentialgrinding forces Ft versus the workpiece radiusare shown in Figure 13.

The grinding force Ft shows a maximumin the tooth root and a minimum in the area ofthe root flank, just below the root form radius.Another local maximum can be observed in thearea of the tip flank. After grinding multiple gapsin the area of the minimum forces, there is hardlyany increase. But in the areas of the tooth rootand the tip flank, grinding forces are increasingwith the number of ground gaps. Increased grind-ing wheel wear can be expected, and grindingburn is most likely to occur in these areas.

With these calculations, it is known thatin the areas found to be critical, grinding burnoccurs when using a radial infeed strategy ingear profile grinding (Ref. 2). When grindingthe gear with a radial infeed including the toothroot, a grinding burn occurs mostly at the toothroot. When grinding the gear with a radial infeed

Figure 13Tangential grinding forces for a radial infeed of the grinding wheel.

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without the tooth root, the grinding burn is mostlikely to occur at the tip flank. These are the areaswhere, based on these calculations, the maximumgrinding forces can be found.

Evaluation of Process StrategiesUsing the Process Model

Following is an example for the evaluationof process strategies, using the empirical pro-

cess model to calculate local grinding forces.Grinding forces are calculated not only for onegrinding step, but also for an infeed strategyusing multiple steps, including deviations fromthe desired shape that can be due, for example,to centering deviations. It is only necessary tobe able to calculate the local stock removed inthe evaluated cut, as well as in the local profileangle. An example of this using the grinding ofa test gear will be simulated with three radialinfeed steps of 0.2 mm each. This means that thefirst cut takes place at a center distance between

grinding wheel and gear which is increased by

Figure 15Tangential grinding forces for a radial infeed of the grinding wheel.

0.4 mm, compared to the final center distancecreating the final contour.

In Figure 14, the local stock in the directionnormal to the tooth flank s and the stock ininfeed direction ae are shown. In the first grind-ing step, material is removed from the gear flankonly in the area of the root flank. In the infeeddirection, the infeed into the material is up toa

e = 1.0 mm, which means that a stock in normal

direction of s = 0.13 mm is removed. The resultis that, in the area of the root flank, nearly all thestock is removed by completion of the first step.In the last step, material is removed along thewhole profile, and the radial infeed amounts toae = 0.2 mm.

This is because the whole profile height hasbeen ground in the second step. In the area of theroot flank, only a very small amount of stock isremoved in the normal direction. While in thearea of the root and tip flanks, nearly all stock is

removed in the last cut.The resulting grinding forces for these con-tact conditions are shown in Figure 15. Theupper diagram shows the grinding forces in cut-ting and normal direction for the first cut. Thedrawn-through lines show the grinding forceswhen grinding the first gap with a newly-dressedgrinding wheel. The broken lines show thegrinding forces for grinding the sixteenth andlast gap in order to gain an impression of thedevelopment of the grinding forces with the set-in time of the grinding wheel.

In the area of the root flank, very high localgrinding forces can be seen, and those forces areincreasing quite a lot with an increasing stockremoval. This means that this area is susceptibleto grinding burn in the first grinding step. Toreduce that burn risk, the center distance betweenthe grinding wheel and the workpiece must beincreased. However, this will require more cutsand thus increase the manufacturing time on themachine tremendously.

In the last grinding step, the grinding forcesare smaller than in the first. There is also a small-

er increase of those forces, with an observedincrease of material removal. It is neverthelessapparent that the grinding forces are increasingtowards the tip flank and the tooth root. Thismeans that these areas are very sensitive togrinding burn when using an infeed strategy fora radial infeed of the grinding wheel. These areasare known to be most critical towards grindingburn, which can be seen in the grinding forces(Ref. 2).

It can thus be concluded that the areas mostcritical to grinding burn can be evaluated by a

calculation of the local grinding forces. While

Figure 14Local stock removal in infeed direction ae and normal to the profile s.

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the area of the root flank is most susceptibleto grinding burn occurring in the first grindingstep, the areas of the tooth root and the tip flankare most susceptible for burn in the last grind-ing step. Using this calculation of the grindingforces, it can be evaluated qualitatively how criti-cal a gear geometry is in relation to grinding burntowards another, and if the chosen infeed strategyis critical as well.

Summary and Outlook Gear profile grinding, especially using dress-

able grinding wheels, is a process rather sensi-tive to grinding burn. It therefore is importantto understand the process well in order to eitherprevent grinding burn or, at minimum, if a grind-ing burn appears, to be able to change the processin a way that prevents it. This is especially impor-tant since grinding burn reduces the hardness ofthe external layer, and leads to tensile stresseswhich reduce the load-carrying capacity of thegear, thereby making gear failures more likely.

The main consideration when trying to betterunderstand the process of gear profile grinding isthe constantly changing contact conditions alongthe profile. In real process trials, only effectsresulting from all those contact conditions alongthe profile can be observed. And since grind-ing burn, in most cases, occurs only locally, theeffect on values like grinding power or grindingforces often cannot be seen initially.

In order to attain better knowledge of theeffect of local grinding conditions on the processbehavior, an analogy process was established toanalyze them.

Rectangular workpieces were ground in aclamping fixture that can be turned in order toset the different profile angles occurring on atooth flank. Particularly in this analogy process,grinding forces have been measured. The resultsreveal that grinding steep profile angles leads toa high risk of grinding burn, which can be dueto the increasing contact length, and, in turn,can lead to a higher amount of energy conductedinto the workpiece. The main goal of these testsis to facilitate an understanding of the real-timeprocess.

Since the amount of heat conducted into thematerial is proportional to the cutting force, aprocess model has in fact been developed forcalculation of local grinding forces. This modelenables calculation of local grinding forces, pro-vided local contact conditions and the set-in timeof the grinding wheel are known.

With the aid of this process model andCASTOR software (with the ability to simulatedifferent gear finishing processes), various pro-cess strategies in gear profile grinding can be

considered and analyzed. Calculations show thatin a radial infeed strategy of the grinding wheelin the first cut, maximum forces are calculated inthe root flank area. In the last cut, the maximumis calculated in the tooth root and the tip flankareas known to be most exposed to grinding burn.With these calculations, the reasons for this expo-sure can be demonstrated. They also demonstratethat for the removal of an equidistant stock alongthe profile, the maximum forces can be observedin the area of the root flank. This is also the areaknown from the real process of gear profile grind-ing to be most sensitive to grinding burn.

In order to evaluate the risk of grindingburn, both qualitatively and quantitatively, futureresearch must focus on developing a specificvalue. Since the level of grinding forces observeddepends very much on the ground profile angle,the goal in developing a specific value is find-ing a limit where, if the value exceeds the limit,grinding burn can be observed independent of thecontact conditions.

References1. Posa, J. Barkhausen Noise Measurement inQuality Control and Grinding Process Optimiza-tion in Small-Batch, Carburized-Steel GearGrinding,Proceedings of the 3rd InternationalConference on Barkhausen Noise and Micro -magnetic Testing , July 23, 2001, Tampere,Finland.2. Schlattmeier, H. Diskontinuierliches Zahn-flankenprofilschleifen mit Korund, Dissertation,RWTH Aachen, 2003.3. Klocke, F. and C. Gorgels. Anstze zurEntwicklung eines Schleifbrandkennwertes frdas Zahnflankenprofilschleifen,Proceedings ofthe 46th Conference on Gear and TransmissionResearch . WZL, RWTH Aachen University,2005.4. Klocke, F. and H. Schlattmeier. SurfaceDamage Caused by Gear Profile Grinding andIts Effects on Flank Load-carrying Capacity,Gear Technology , September/October 2004,pp. 4453.

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