Gear Coupling Misalignment Induced Forces & Their Effects on Machinery Vibrations

8/15/2019 Gear Coupling Misalignment Induced Forces & Their Effects on Machinery Vibrations

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GEA C UPLING MISALIGNMEN INDUCED C SAND HEI E EC S N MA HINE Y VI A I N

byAlan Palazzolo

Associate Professor, Department of Mechanical EngineeringTexas A&M UniversityCollege Station, Texas

Stephen LockeTurbomachinery Consultant

E. I. duPont deNemours and Company, IncorporatedOl Hickory, Tennessee

Michael Calis raPresident, Michael Calistrat and Associates

Missouri City, Texas

Rober W Clark, Jr.(Former Graduate Student, Texas A& University)

Senior EngineercDon e l Do g as Space Sys ems Company

Houston, Texas

AkramAyoub

Dan Calis raand

Punan TangStudents, College of Engineeri g

Texas A&M University

Colle e Station, Texas

Alan B Palazzolo, Associate P Mechanical Engineering at Te & eceived his B S (1976) om the of Toledo, and his M S M E ( )

Ph D , M E (1981) degrees o iversi of irginia He worked

Nevada (1977 78), Universi i(198 81 ) , Allis Chalmers (1 Southwest Research Institute (1 efore joining Texas A M, in 1985 He hase or ed resea ch du ing the summers of

1986 19 at ewis, and NASA Marshall (1 91 )Dr Pa azzo o s xperti e is in machine and structural vi ra

tions, rotord namics and de ections, nd stress For simulations, heemp o s trans er atrices, and nite and ounda elements He has

also een extensivel involved wi h eld trou leshooting of mechanica ma unctions in rotating and reciprocating machine Dr

Palazzolo has presented papers at AS E andASME Gas Tur ine andi ation Con erences, and has pu lished man papers in variou

engineering journals His current research includes c ogenic viration dampers, active vi rations co trol , uid lm earings, sha

currents, gear coup ings, magnetic earings and annular seals

83

Stephen R ocke is a Tur omach neConsultant with E duPont deN emou s andCompan , ncorporated He is located at theCum erland Regional Consulting g oup inOld Hick , Tennessee, and has 2 ears oftur omachine and rotating equipmentexperience with Dupont He consults on up grading pe ormance, mechanical rel a ili , and pec cation o repairs and new

equipment P ior to this, M ocke was a signed to a

tur omachine consu ing group in ilmington During his rst 1 ears at Dupont, he was assigned to a petrochemicals plant where he p ovided technica assistance to operations and maintenance, participated in several plant startups and the commissioning of severallarge process compressors

Mr ocke graduated om urdue nive si ( 19 ) with a B S degr e in Mechanical Engineering He has written two other paperson tu omachine and is a mem er o ASME


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84 PROCEEDINGS OF THE TWENTY-FIRST TURBOMACHINERY SYMPOSIUM

Michael M. Calistrat has outstanding ex- perience in the eld of power transmissionequipment, which he has accumulated work-ing with oil drilling equipment, gearing andexible coupling . He also has a solid back- ground in industrial gas turbines.

He is active in engineering societies and manufacturing associations. He chaired many technical commi tees for ASME,ASTM, and ALE, and was Chairman of the Inter-national Co erence on Power Transmis-

s on and ea ng. o the last three years, he was associate edi orof the ASME Jou nal of Machine De ign.

He has been a coauthor on three engineering manuals and has written many technical papers and articles in the United States,Japan, France, Canada, Holland, Italy, and Taiwan.

M . Calistrat was Manager of Research and Development for the Power Transmission Division of Koppers Company, where he wasinstrumental in the development of many products. Presently, heheads a consul ing company which specializes in rotating machine .

Mr. Calistrat received his M.S. degree inMechanicalEngineeringom the Unive si of Bucharest and holds 17 patents.

ABSTRACT

Ge r coupling c n produce l rge st tic forces nd mome ts th tcan ct the ibr tions of turbomachinery, e en with ne rlyper ct alignment Rese rch testing nd c se histories h e eri-ed this theory nd are reported Methods are suggested to controlthe direction of t ese forces for reduced ibration nd enh ncedturbom chinery reli bilit .

INTRODUCTION

Ge r coupl ngs re ery reliable, lightweight nd used exten-si ely in turbom chinery. An import nt, but little recognizedfactor in using these couplings, is the presence of st tic forces nd

moment hich can be quite l rge Underst nding these e fects c nhelp impro e nd/or explain the ibr tion beh ior of turbom -chinery. These forces h e the potential to signific ntly lterbe ring lo ds, stiffness nd d mping and result in high ibr tion.Obser ations of related beha ior in pl nt machinery led ocke toinitiate t is study.

The role of t e ideal ge r coupling is to tr nsmit torque from thedri en m c ine, whi e commod ting some degree of p r llel ndngul r mis lignment between the two sha ts. In re lity, the torqueabout the xis of the sh ft may produce bending moments bout heperpendiculars to this axis, by the following three mech nisms:

Pr ection of the sh ft torque ector onto the pe endicular oft e mis ligned sh ft,

Friction forces ue to torque nd sliding of the mis lignedteeth during rot tion nd,

Offset between cont ct points of the teeth on opposite sides ofthe coupling. These bending moments re re cted by the uid lmbe rings supporting the sha s The addition l prelo ds on the uidlm bearings a e a signific nt in uence on their stif ess nd mping. Critic l speeds, unb l nced respo se, nd st bility re itu directly in uenced by these bearing properties

One ery sur ising ch racteristic o gear couplings is that theamplitude of the friction l moments a d forces do not decreasewit impro ed lignment. Nearly perfect lignment c n make thedirection of t e forces uncertain wit no mal mac i e thermalch nges. Methods re suggested to control the directio of these

forces for reduced ibration and enh ced turbom chi eryreli bility.

MISALIGNMEN IND CE MOMENTSIN GEAR COUP INGS-THEORY

The liter ture contains se eral references on the subject of gecoupling moments. Not ble among these are those by M cu[1], Gibbons [2], d Crease [3]. M ncuso deri es equ tio s focouplings with crowned teeth nd ssumes that the torque tr nsmitted solely by two pairs of cont cting teeth, sep r ted b180 degrees. Cl rk [4] gener lized these results by deri ing equ -tions in which the number of teeth in co tact could be ried frotwo to "all. His work was guided by the earlier tests and analyof Calistr t

Working from t e diagrams in Figure 1, Cl rk deri ed thfollowing equations:

Out of Plane Moment (About or

M = 1=

D( sin F sin sin JF cos ) R sin sin F cos ))

In Plane Moment About or Y

where;

nd

R sin sin F sin cos F sin )D

cos F sin sin JF cos ))

I J, 0 < < = , = , or 2< < 22 T

F = _D cos +sin cos + Jsin sini=l

(1

2)

(3

(4

If it is ssumed that J and re ery sm ll, i e , the qu ntitiessin2 nd J sin are approximately zero and cos is pproximate1, that sin


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GEAR COUPL NG M SAL GNMENT NDUCED FORCES AND THE R EFFECTS ON MACH NERY V BRAT ON 85

spacerZr

=A gular lo at o om ax s f tooth

= M sal g me t gle

c s h s c

T h c t t =

Figure 1. Kinematic/Kinetic Diagrams for Moment EquationDerivation

assumed that only two teeth are in contact, Equations (5) and (6)reduce to

Out of Plane (Friction) Moment

(7)

In Plane (Kinematic) Moment

M = TRsinD 2 (8)

Equations(7) and (8) are the form for the moment equationswhich common y appear in the l terature The moment Mislabeled as the friction moment, because it is due solely to thecoefficient of ictionfwhereas the kinematic moment Missolely due to the crown radius (R), whi h displaces the contactpoint when considered at opposing sides of the gear So e com-mo ra ges of fquoted in the literature are Mancuso (0.004 t0.045), Gi ons (0.05 to 0.35) and Crease (0.005 to 0.30) [1, 2, 3].A comparison is shown in Figure 2 between predictions byClark's equations and Mancuso's (1971 test data, using thefo lowing test parameters;

D = pitch diameter= 4 2 inR = tooth curvature radius = 3 2 iP = diametral pitch =10Torque = T = 4500. i lbs

Load = in-lbBOO Mancuso /

Clark cf= /70

•60 ••

: ••4 - • /3 . /////

TMISA IGN ENT ( egrees )

Figure 2. Comparison Between Mancuso's Measured Moments and Clar 's Equation

The agreement betwee the measured d predicted moments isseen to be very good

M SAL GNMENT NDUCED MOMENTS NGEAR COUPL NGS-MEASUREMENT

A four square test rig was designed by Calistrat and fabricatedand assemble at Texas A&M University, to experimenta ly mea-

su e gear coupling bending moments an ictio coefficients InFigure 3, photographs are presented of the test rig sho ing thereverse indicator alignment bars, the center stand, which is inten-tionally misaligned and suppo ts the test coupling, the load cellswhich measure the bearing reaction forces, and the torquemeterThe rig is driven by a 10 hp electric motor through a 2 1 speedreducing belt system to the test (low speed) shaft The 1 2 speedincreasing gear box also drives the high speed sha t which includesthe torquemeter, measuring torque Note that

=2 (9)

in Equations (1 8). Properties of the industrial gear couplingsemployed in the testing are summarized in Ta le 1 T e low speed(test) shaft spins at 1800 m, and the axial oat (at zero tor ue)of each coupling was set to be at least 60 mils to allow themfreedom to ex The coupli gs were lubricated with turbine gradeoil or coupling grease and the torque was varied by pretwisti g ahigh speed sha t line coupling with a slotted bolt circle

he p rpose of the testing is to investigate the in ue ce ocoupling misalignment o s a t forces a d mome ts Therefore, insetting the test rig, sha ts are i tentionally misaligned at variouspre etermi ed values These misalignment values must be ti htlycontrolled in order to obtain useful information Misalig ment ofthe gear coupling test rig is attained utilizing the reverse indicatormethod of alignment T is method involves measuring t e exten-sio of one sha relative to the other sing dial indicators The dial


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GEAR COUPLING MISALIGNMENT INDUCED FORCES AND THEIR EFFECTS ON MACHINERY VIBRATION 87

During alignment procedures of the test rig, deviations invertical alignment were noted while jack bolts were being tightened To alleviate this:

spherical cap nuts were placed on the end of all jack bolts,and

reinforcement "trusses were designed and welded to thebottom of the test stand

·at reinforcement bars contained in the bearing houses werereplaced with angle ironThe "table top plate deformed and caused skewed alignmentreadings This plate wasrigidly welded to the test stand resultingin a significant reduction in its deformation

The outboard side gearbox was disassembled for routineins ction This inspection revealed a spinning outer race and apartially damaged bearing A new bearing and race were installedwith thread adhesive

Play in the gearbox shafts was reduced by giving ahigh rpreload to their bearings by removing approximately 24 mils ofaxial s im

Moments were measured following these mechanical integrityconfirmingproc dur s

The riction moment is determinedby imposing a symmetricalvertical misalignm nt and then byr cording the center standbearing's horizontal reaction forces( xl' x)as shown in Figure5 Equations relating the reaction forces and fr ction moment areobtained by considering symmetry, static equilibrium and thefriction moment directions, yielding:

(10

(1

r l- L•

Figure 5 Force and Moment Dir ctions sed in Deriving Equa-tions (10) and (1 I .

An estimate of the iction coefficient is then obtained bysolving either Equation (5 or Equation (7 for·The kinematic moment is dete nined by simultaneously imposing both symmetric horizontal and symmetric vertical misalignments, and then measuring the center stand bearing's horizontalreaction forces( \ , \ , as shown in Figure 6 Equationsrelating the reaction forces and kinematic moment are obtained byconsidering symmetry, static equilibrium and the kinematic moment directions, yielding:

(12

Sha tASh f

SA Shaft

S Shaft

(13

Shaft

Sh f

Figure 6 Force and Moment Directions sed in Deriving Equa-tions (12 and (13)

It is assumed that themagnitud of M only vari s slightlybetween the pure vertical misal gnment and simultaneous horizontal andv rtical misalignment cases Therefore the term MinEquation (3 is known from the purev rtical misalignment case

Testing was performed with bothtur in oil and coupling grease

as lubricants Figures 7, 8, 9 10, and1

correspond to theturbin

oil tests A typical plot of t e horizontal reaction forcesvs lowspeedtorqu for a pure vertical misalignmentis shown in Figure7 The outboard and motor end reaction forces are seen to be nearlye ual, as predicted by Equation (10 , over the torque range employed The friction moments, as determined from E uation (11and the measu ed reaction forces, are shown in Figure 8 for three

% 0.0 2 2 4 4 .8 6 7

Horizt g e de ee 8''' z'" g e de e18' d s de Motors de : 3 !'0 ' '

- 2

58

:2 60

Figure 7. Reaction Forces for a 40 Mil Pure Vertical Misalign- ment. (T urbin e Oil L ubric ated).


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%OF R TED TORQUE0.0 2 2 4 3 6 4 8 6 0 7 2

-IC ION MOM N Ve ica m isa ignm ent 0.159 degre . 30 n l

i - + · V i s a i m enl 0 202 de ee- 40 m l z6

;<6 20

2 4 0 12 0

LOW SPEE RQUE (in-lb)

Figure 8 Friction Moment Torque r Several Pure Vertical Misalignments. (Turbine Oil Lubricated).

z

<:

0 0

6

0

2

% F D TO Q

0 1 2 8 2 4 3 6 4 2 4 8 5 4 6 6 6

/

I

---- ---F CT CO FF T T de - lV m a! deg . llte lh con ct+wt co ct

0 .0 0 - 2 9 1 0 1 00

W SP E T RQUE ( n-lb

Figure 9 Friction Co cient s Torque Assuming Two Teeth andAll Teeth in Contact. (Turbine Oil Lubricated).

I TION OEF I IENT MI LIGN E GLE0 2

0 10

0 08f0 06

0 04

0 02

0.00

con ct

: _JTorqu l+ - - -- T_•_'"_ _ _ rl 0.0 0 0 0 .3 MISA IGNM NT degree)

Figure 10. Friction Coe icient Vs Misalignment Angle for Vari-ous Torques. (Turbine Oil Lubricated).

0

0£40z

" 30" 0"t:0

0

%O F D T O RQ 7 9 1 K w

- · ___ ___.-L

00 400 600 1000 00 400 1 00 00

E RQUE in lb

1

000

Figure I 1. Kinematic Moment Theor and Experiment Torque.(Turbine Oil Lubricated).

levels of purev rtical misalignment The riction moment is seento increase ith torquebut does not have a monotonicr lationshipith misal gnm nt

Thefriction coe cient is estimated bysolving Equation (5) or(7 for Plots of vs torque obtained by assuming either "t oteeth o "al teeth in contact are sho n in Figure 9 It isnote orthy to compare the values sho n in Figure 9 to thosee ployed by Mancuso (0 004 to 0 045),Gibbons (0 05 to 0 35),and Crease (0 005 to 0 30)[1, 2, 3] The iction coefficients inFigure 9 are seen to stayr lativ ly constant above torques of 400in/lb Thefriction factors sho n in FigureI0 are relatively insen-sitive tomisa ignm nt angle ove the measu edang (0 05 de-g ees to 0 4 degrees Typical predicted and measured kinematmom nts are sho n in Figure I The predicted values are calcu-lated with quations (6) and (8) usingvalu s of R, D, and n,obtained from the coupling manufacturer Them asur dd va uesa e obtained fro quation (13) by assuming that the frictionoment (M does not significant y vary from itsvalu at zerohorizonta l misalignment. T he agreement b tw n the pre dictedand m asu r d kinema tic moment s is s gnific an tly imp roved byassuming tha t only two tee th are in conta ct, as shown i n Figure 11.The di sagreement b etween theo ry and measu red results in this casemay be due to unce t ainty in the face adiu s, and small viola tions in the symme try assump tions made in der iving Equa tions ( 10, 11,12, 13)

The effects o f lubrican t type, turb ine oil v s coupling g rease, onthe coef ficien t of iction are co mpared in Figur e 12. Both lubri-cants have t he sa me mi salig nment angle and " all te eth in conta ctis ass umed in c alculating l · The e f fects of lubricant type on th e ki n mat ic mome nt for the sa me mi salign ment angle are co mpar edin Figure 13EFFECTS OF GEAR CO PLING MISALIGNMENTIND CED MOMENTS ON ROTOR RESPONSESIM LATION

A diagram of an air compressor rotor supported by three lo jou al bearings, and coup ed to the remainder of the train ithgear couplings is sho n in Figure 14 Parameters used in throtordynamic simulation of this rotor are presented in TableCoupling moments, bearing rotordynamic coefficients, beareccentricity, stability, odeshapes, and unbalance response e ecalculated for this rotor with software developed at Texas A Mfor the Turbomachinery Research Consortium The effects


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GEAR COUPLING MISALIGN ENT INDUCED FORCES AND THEIR EFFECTS ON MACHINERY VIBRATION 89

%O A O QUE0 0 2 2 4 3 4 8 0 .2

0 2

0 0z +>0 08

*">

0 06

z V0 H miY q mi0 02 ! i0 00

0

O B QUE (in-lb)

Figure 12. Friction Coe icient Vs Torque for Turbine Oil andGrease Lubricants

M U K MM M Ui n al angl ilal angl g il e 3::(

W Q( )Figure 13. Kinematic Moment Vs Torque for Turbine Oil andGrease Lubricants

varying the angle of misalignment, plane of misalignment (Figure15), and torque were examined in this study.

The predicted jou al equilibrium position is shown in Figure 16in the right bearingvs torque, as it is increased by 20 percentincrements of the values given in Table 2 The correspondingbearing loads, stiffnesses dampings, and equilibrium positions areshown in Table 3 Increasing torque has a significant effect onstabilizing this machine as is shown by the p ot of the real part ofthe eigenvalue in Figure 17 The change in the journal equilibriumposition is shown in Fig re 18 for vario s misalignment planes.The corresponding bearing loads and equilibrium position coordi-nates are shown in Table 4 The effects of misalignment plane on

n onnea ri n g J \ C upling B ournob b r nruunn r

Figure 14. First Stage Air Com ressor (Figure 2 Rotor Used forSimulation Study

Table 2. Sha and Coupling Data for the Rotordynamic Simulation

OTO LENGTH 59 in.BEA ING SPAN 36 in.

OTO WEIGHT 1033 lb.

PI CH DIAMETETO TH C OWN ADIUSLENGTHAPPLIED TO QUENUMBER OF TEETH

Coupling A7 5 in.100 0 in.15 0 in.147,000 in.lb.50

Coupling B7 5 in.100 0 in.6 4 in.123,000 in.lb.50

unbalance response is illustrated by the resul s in Figure 19 Theangle of misalignment (0 08 degrees) was held constant a ong iththe friction coefficient (0 04) for this case. To obtain this plot, themisalignment plane was rotated to 0 degree, 80 degrees, and 200degrees from the vertical direction. The bearing reactions weredetermined by static force and moment balances of the couplingbending moments and shaft weight. These reaction forces wereinserted in a bearing simulation code to determine the stiffnessesand dampings at various rotor speeds. The sha vibrations shownin Figure 19 are ver sensitive to the plane of misalignment of thegear couplings. The first critical speed, apparent at the 0 degreeorientation, is seen to be nearly eliminated with misalignmentplanes at 80 degrees and 200 degrees. In addition, the secondcritical's ampli cation factor is signi cantly reduced when themisalignment plane is rotated from 0 degrees to 200 degrees.

X

Figure 15. Angle and Plane of Misalignment at Gear Coupling

EFFECTS OF GEAR CO P NGS ON ROTORRESPONSE -CASE H STOR ES

he preceding sections have been based entirely on either theoryor lab testing. The initial impetuses for this work were the obser-vations and hypotheses made by Locke based on field test dataThis emphasizes the importance of studying case histories fcoupling connected mach nery w th vibrat ro e . h l owing case histories provide guidance and illumination into thisphenomena.


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90 PROCEEDI GS OF THE TWE TY-FIRST TURBOMAC ERY SYMPOSIUM

- AOT n N

0 .2

1

igure 16 Right Journal's Equilibrium Position VsTorque Atten-uation actor.

Table 3. Bearing Load, St ess, Damping and Equilibrium PositionVs Torque Attenuation actor (A ) (Torque/ ble 2 Torque)

LOAD ON BEARING lbs) DIS ANCE in 1Q 2A.F. FX FY X0. 00 -546. 7. -0.057 -0.060.400 -733. 9 . -0. 0 -0.0550.600 -9 0. 558. -0. 46 -0.040.800 - 07. 8 . -0. 7 .0 6.000 - 94. 086. -0. 87 -0.0

DAMPING lb.sec./in. S I NESS lb./in 1QA.F. Cxx Cxy Cyx Cyy Kxx Kxy Kyx K y0. 00 69. 788. 788. 9 . 59. 3. -305. 5 .

0.400 4006. 86 . 607. 75 . 759. 7 9. 335. 496.

0.600 59 . 579. . 64 . 6 9. 67. 97. 374.

0.800 8 9 . 34. -80 . 693. 8 4. 8 8. -847. 6 .

.000 0795. 46 . - 804. 867. 4377. 3347. 387. 59.

Table 4 Bearing Loads and Equilibrium Posi tion Vs Misalignment Plane

Load on Bearing (lbs) Position 100

RO lbs) FY lbs) X in) Y in). . 4. - .119 . 1

. 0 - . 1. - .1 1 .. 0 . . - . .0

1 .0 96. 9. - . 1 0. 191 .00 1 . . .0 0.

.00 5. 9 . 0.0 0.1

.000 . 1 4. . 4 0.

.000 . 11 . . 9 . 9

5!

55

5 _1 1 5 • · J15 J 5 1Q igure 17 Real Part of Eigenvalue VsTorque Atte uation actor.

XOT An N

y

igure 18 Lef Journal's Equilibrium Position Vs Plane of Misalignment.

a

.0 7

0

g 1

GRR R

o. . .

. ( 1 # '( < ,# , . \ ,. c ( )igure 19. Simulated Unbalance Response VsSpeed and Plane of

Misalignment.


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GEAR COUPLING MISALIGNMENT INDUCED ORCES AND THEIR E ECTS ON MACHINERY VIBRATION 9

Case

A large utility company experi nced an odd situation, in whichvibrations increased after it was decided to replace all gear couplings driving boiler feed pumps, with nonlubricated couplings

In order to help the engineering group select the best type ofcoupling to use, it was decided to try a few types Based onsuppliers' selections, a number of pumps were retrofitted, with avariety of coupling types To eliminate the possibility of bad

performance due to misalignment, laser equipment was used toperform as perfect an alignment as possibleIn all cases, the vibration levels of the pumps increased signif

icantly a ter the gear type couplings were replaced! Lacking asolution to solve the problem, the old gear type couplings werereinstalled, and the pumps again worked with acceptable levels ofvibrations!

What happened? The cause of the increased vibrations withperfectly aligned nonlubricated couplings was theunloading ofthe pump bearings Nonlubricated couplings operating at smallmisalignments create very small reaction forces, which allowedthe shafts to orbit unrestrained inside the bearings Gear couplings,on the other hand, created sufficient loads on the journal to allowsmooth operation

The conclusion in this case history was not meant to imply that

gear couplings must be used in boiler feed pumps The problemsin this case are not the couplings, rather, the plain cylindricalbearings EPRI papers have shown the need of pressure dam ortilted pad bearings for boi er feed pumps

Case 2

A paper plant experienced a situation in which vibration worsened a ter a turbine repair

The rotor of a large gas turbine driving a generator through age r reducer had to be replaced because of damage caused by aningested inlet guide vane Before restarting the unit, maintenancepeople decided to check the misalignment, which was found to beslightly larger than the one considered acceptable by the OEM'sinstruction manual

The machines were care ully aligned Upon startup, the pinion

bearing had very high vibration levels The third author analyzedthe problem and concluded that, originally, the OEM had intentionally misaligned the machines to avoid vibrations

Fortunately, the holes for the original dowel pins were stillavailable, and the turbine was moved in the original position Theunit started and operated with no problems!

The explanation was in the pinion bearing, which was notsufficiently loaded by the forces in the gear mesh, or by its weightMisaligning the machines created a stabilizing force in the bearings, which allowed a smooth operation

The type of coupling in this particular case was arigid coupling(no exible elements) As it is generally known, rigid couplingsoppose misalignment with very large reactions forces, and becauseof this relatively small change in alignment, help in stabilizing thevibrations

Case 3

Dupont had high vibration on a large process airompress r(Figure 20). The air compressor rotor was the one s mulatedFigures 14, 15, 16, 17, 18, and 19 Although the vibration was notextremely high, the investigators had mild wiping on the f rst casepinion side beari g on two occasions and could not identifyhecause Nearly all of the vibra i n was at running speed Even h ghspeed balancing of the rotor did not change the vibration, while theopposite end of the first case rotor and the pinion ran smoothlyThen they discovered that the vibration, probe gap, and alignmentchanged with ambient temperature This compressor was optically

aligned and the hot alignment was known very pre isely Theinvestigators traced the changing horizontal alignme t to a looseanchor bolt on the steel skid, and corrected the problem byinstalling a centerline guide between the skid and the concrete pierThe vertical changes in alignment of the rst case had to beaddressed differently Using the equations described herein, theyfound the hi hest forces at the shortest coupling, between the firstand second caseAlthough the misalignment forces were overthree times the ournal gravi y loads they had no problems withthese bearings! But, the net misalignment force on the problembearing turned out to be nearly equal to the gravity load

EEDI REASER

H T

P

C ZND S

O

P

Figure 20 Industrial Air Compression Train With Gear TypeCouplings

The alignment on the coupling mesh next to the problem bearingwas very nearly per ct when ambient temperature was hot, asshown in Figure 21. With this alignment, the normal changes in thefirst case elevation rom changing inlet temperature allowed thedirection of the forces to completely reverse When the ambienttemperature was high, as shown in Figures 22 and 23, the sha t ranin the bottom of the bearing and vibration was lower Whenambient temperature was low, the shaft ran in top of the bearing,but it was l ghtly loaded and h d higher vibration

The solution was to control the DIRECTION of the forces withdirection of the misalignment The magnitude of the ictionmoment depends only on friction and torque, not the amount ofmisalignment They shi ted the first case to the le of the pinion by

P AN VIE\ I S- :

_ - a ··t :

PINIONFIRST CASESECOND CE EV VIE\

OOSTf :·_ . : -

Figure 2 Diagrams for Initial Alignment of Air CompressionTrain


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2 PROC DINGS OF T TW TY-FIRST TURBOMACHIN RY SYMPOSIUM

8.07] 9.07.6 8.07.4


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GEAR COUPLING ISALIGNM NT INDUCED ORCES AND THEIR E ECTS ON MACHI ERY VIBRATION 93

20000000· 00200f

j 00200

TURBINE DR EN SINGLE STAGE E UNG BL WERBearing loads vs turbine locati n

=4- J.e outboard bearing load'

, +"

'''' dj , \ ,_-·- - - -· - - - et inboard bearing loa\ /xj,

\ ,\. ++. - - - - - - - Set Turbine here

cation of turbine to bloweras seen from turbine end

Figure 27 Total Downward Loads on the Overhung BlowerBearings Due to Gravi nd Gear Coupling Mo ents

P AN VI

1 0 1.0 MI S/IN1 _

- l -

TU N

V I

-Figure 28 Selective Directional Misalign ent Applied to theOverhung Blower Train

VIBRATION RELAT D ALIGNMENT GUIDELINES

The theory, test data, and case histories presented thus far wereutilized to establish guidelines for recognizing and diagnosingcoupling related vibrations These guidelines are summarizedbelow

Couplings have a strong inuence on machinery vibrations, andthis has been known for so e time; however, before actual studiesand tests were performed, there was a lot of misunderstandingabout how, and by what echanism couplings can ncrease ordecrease the amplitude of vibrations Perhaps the best known "oldwives tale about machinery vibrations was that resonance at t icesynchronous speed is caused by misalignment

L A A W - E ++++ +U B B

0L 0 0 - )(fH t L Figure 29 Diagra to Illustrate How Horizontal Misalign ent Produces Vertical Loading

BLD EREL V VIE

R2

Figure 30. Vertical Reaction Forces on the Blower Rotor Due tothe Selective Directional Misalign ent

..

.c .] .....

E CE VIB O on I LE AGE E HU G BLOWERby con ro i g r c iis 6g e t

H z MO HFigure 3 . Vibration Reduction Achieved by Applying SelectiveDirectional Misalign ent to the Single Stage Overhung Blower


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Couplings oppose misalignment. Th s has been shown bothqu l tat vely and quant tatively by the tests and studies descr bedhe e n. The react ve forces and moments are only to a very smallextent a funct on of the mount of m sal gnment (F gure 1)

Couplings do not c eate vibrations. It s through the forcesmposed on bear ngs that m sal gnment can e ther stab l ze ordestab l ze the orb t of a journal n ts bear ng. In fact, forcesgenerated by m sal gne coupl ngs can mod the shape of anorb t such as e ther the mpl tude of vibrat on decreases, or theequency of v brat on acqu res a two t mes synchronous compo-nent. Two such cond t ons a e exempl f ed n F gures 32 and 33 Inh ghly loaded bear ngs, the orb t of the shaft's centerl ne s anelongated ell pse, as shown n F gure 32

B

Figure 32 Misal gn ent Force Direction to Reduce Vibration inEl tical Orbit

B

Figure 33 Vibrations in a Lightly Loaded Bearing.

Coupling forces may alter vibrations. Assum ng that theforces generated by coupl ng m sal gnment are in the d rect on ofthe long ax s (F gure 32), the ampl tude of v brat ons decreases(dotte curve). Therefore, n such a case t s helpful to m sal gn the

mach nes; however, only a study of the o b t w ll nd cate correct d rect on of m sal gnment Assuming that the forces gerated by m sal gnment re n the d rect on of the short ax s (F g34), the ell pse becomes banana shaped (dotted cu ve), whshape has two peaks per revolut on. Therefore, the v bration htw ce synchronous component It should be noted that n this the forces generated by m sal gnment d d not affect the ampl tof v brat on, t only altered th shape of the shaft's orb t.

B

Figure 34 Misalign ent Force Distorting an Ell tical Orbit into a Banana Shape.

In a l ghtly loaded bearing (such as a p n on or bo le fepump), the orb t of the shaft' s c nte l ne s shown n F gure 33 Thorb t's shape s close to a c rcle because the unbalance forcesonl sl ghtly restra ned by the fo ces acting on the sha t. M saliment forces, n ependent of the r d rect on, decrease the ampl tof v bration (dotted curve). Therefore, n such a case, t s helto misal gn the mach nes. Obv ously, the most bene t s realf the forces created by m sal gnment are n the d rect on oflong ax s. As these examples have shown, t s necessary to sthe sha 's orb t to use misalignment as a v bration reduct on toTherefore, t is necessary to equ p mach nes w th X Y prox mprobes, at least at the bea ng next to the coupl ng.

M sal gnment and heat. The heat generated by m sal gnmof gear coupl ngs mposes a restr ct on on the pract ce of ntental m sal gnment for v brat on control. The ct on moment dpends only on fr ct on and torque, not al gnment. But m sal gnmn h gh speed turbomachinery must be kept small to avo d exs ve fr ct on heating, shown in Equat on (14), der ved by LocThe othe two moment terms o depend on al gnment and proach zero w th ve y good alignment. Because of the need to heat ng, the fr ct on moment w generally be the dom nmoment for tu bomachinery.

hpf = 4*J*sin( ) *HP (14)Coupling spool length. Shear forces are requ red for equ l b

r um as shown n the free body d agram n Figure 35 These sforces are a d rect funct on of the spool length per Equat on (and can mpose much larger react on forces on the rotors thanict on moments

sf=2 *M L (15)


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EAR COUPLIN MIS I NMENT INDUCED FORCES AND THEIR EFFECTS ON MACHINERY IBRATION 95

C o u p l i n gFre Bo yS o o ldl grs

M

Fig re 35 Shear Force Req ired to Balance Misalign ent In d ced Mo ents.

Although pure angular m sal gnment would in theory cancel theshear forces, pure angular al gnment would be very d fficult tosusta n on a machine bu lt or coll near al gnment So, whateverm sal gnment ex sts w ll most likely be parallel m sa gnment

As an example, est mate the forces on the rst case rotor fromthe pin on s de coupl ng from case history Assume the transm tted torque s 14 ,000 n lbf and the coe icient of fr ct on 0 05 hespool is 15 in between mesh centerl nes, rotor span s 6 in nd theshaft overhang 14 in he ict on moment nd resultant forces onthe rotor bear ngs are then:

Mf = 2/3 * * = 4900in lb (16)Rf = 4900in lb/ 6= 136 lbf (1 )

For a pure parallel offset al gnment, the ict on moments at theends of the coupl ng spool w ll be equal and addit ve hese mustbe counterbalanced by the shear forces and bear ng react onforces:

Sf= 2*Mf/L= 2*4900 n lbf/15 = 653lbf

Rlf = 906lbf, p nion end

R2f = 25 lbf, oppos te end

(18)

he oppos te end of the f rst case rotor has a much sho ter 5 5 nspool t at produces fr c onal shear forces about three t mes larger!he net bear ng loads on the first case depends on the al gnmentdirect on at both ends of the rotor Us ng an API standard 18 ncoupling spool would not reduce the bearing reaction forces belowthe normal jou al grav ty loads Even much longer couplingspools would still produce very large forces and may have ex bles aft critical speeds

C hecking for isalign ent forces Large m sal gnment forcesw ll produce attened or banana shape orb ts he locat on of theorb t n the bear ng nd cates the d rect on of t e actual otm salignment forces

Calc late j st the shear force co ponent he coeff c ent offr ct on for grease is typ cally 0 05, and 0 10 for o l Forces morethan half of the journal grav ty load, may interfe e w th reliableoperat on he actual net forces mposed on each bear ng n amult case mach ne has forces produced by each of the couplingsnvolv ng all three moment terms and correspond ng shear forces

Controlling force direction. he best approach to control theDIREC ION of the forces seems to be to use a SMALL amount of

parallel offset m salignment n a known direct on so that the mostcrit cal bear ngs are accommodated Where poss ble, make theforces add t ve to the normal grav ty loads or other mach ne loads,such as gear forces

A o nt of isalign ent he amount of m sal gnment shouldbe kept reasonable to l m t heat generat on n the teeth On themach ne n case history , there s normal wear on the coupl ngsw th 1 mil/ nch of m sal gnment, wh ch s a sl d ng veloc ty ofabout 5 n/sec at 8600 rpm his has been suff c ent m salignment to override chang ng al gnment from normal thermalvariat ons

Type of isalign ent Frict on forces act out of plane w th them sal gnment hus, parallel m salignment in the plan v ew loadsone bear ng vert cally up, and the other vert cally down h sworks well for an overhung mach ne w th one bearing grav tyloaded up, or where a gear runs n the top half of ts bearing It w llalso work in for between bearing mach nes where the forces are notthe s m lar in magn tude to the jou al grav ty loads he di ect onof rotat on dete m nes wh ch way the driver should be o fset to thedriven, as d scussed n case h story 4 Elevation view m sal gnment w ll load the bearing on oppos te s des, and may be benef c alfor mult case mach nes, where the forces are s m lar in magn tudeto the grav ty loads

CONCLUSIONS AND FUTUR WORK

he results n this study nclude:Presentat on of new eq ations for m salignment gear cou

pling bending moments w th an arbitrary number of tee h incontact

Results showing that the predicted bend ng moments dependon the assumed number of teeth n contact

Analys s and test con guration des g for exper mentallymeasur ng gear coupling be d ng moments and fr ct on factor

est results for fr ct on and bend ng moments, and for fr ct onfactor

Computer s mulat on results show ng the effect of t e bend-ng moments on the v bration of an ndustr al rotor supported onthree lobe u d lm bearings

ase h stor es llustrating how gear coupl ngs can affect, andcan be employed to control vibrations

Gu del nes for plant ma ntenance personnel and machinerydes gners to employ for v brat on d agnosis and control

Gear couplings are very reliable, l ghtw ght, and use extens vely n turbomachinery Nearly perfect alignment does not reduce the frict on force, degrades tooth lubr cation and makes themisal gnment d rect on uncerta n r ct onal shear forces willusually dominate and depe ds on the coe fic ent of ction, spoollength and direct on of m salig ment Good alig ment s necessary for long l fe an low tooth eat generationThe a thors do not advocate GE isalign ents to control the direction of the forces For many mac nes, 0 5 to 1 0 mil/ n o res dual m salignment in a KNOWN DIREC ION w ll prov de reasonable cont olof mis l gnment forces an e ance turbomachinery reliab l ty


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96 PROCEEDINGS OF THE TWENTY-FIRST TURBOMACHI ERY SYMPOSIUM

Finally, when the misalignment forces are large compared togra it loads, one should defin t ly consider the following:

Bearing CapacityBearing Stiffness and Damping, RotordynamicsDesired Bearing Load Angles and Required (Mis)alignment

NOMEN A RE

DpFHPhpfLMMM , M

RR ' R

T

JJ

Pitch d ameter of gearNormal force on gear toothHorsepowerHorsepower loss due to frictionSpool piece lengthFrictioninduc d momentKinematically induced momentMoments about x and y axes, respecti elyDiametral pitchFace (crown)radiusReaction forces on load cells in the test standShear forceTorque on couplingsee equation 3Torque measured in the high speed shaft of the test rigAngle of ith toothFriction coefficientMisalig ment angle

Angle of the misalignment plane relati e to the x(horizontal axis) in Figure 6

REFEREN ES

Mancuso, . R., "Moments and Forces Imposed on PowTransmission Systems Due to Misalignment of a CrowTo th Coupling, Zu Industries Engineering, ittsburgh,Report 71 E17, pp. 1 6 1971).

2. Gibbons, C. B., "Coupling Misalignment Forces, Proceed-ings othe Fifth Turbo achine Sy posiu TurbomachineryLaboratory, Department o echanical Engineering, Texas&M Uni ersity, College Station, Texas, pp. 1 1 116 ( 976

3. Crease, A. B., "Forces Generated by Gear Couplings, Pceedings of the International Conference of Flexible Couplfor High Powers and Speeds, Brighton, England, pp. B3. (1977).

4. Clark, R. W., r., "Gear Coupling Effects on Rotordy amicMaster's Thesis, Texas A&M Uni ersity, Mechanical Enneering (August1988).

A KNOW EDGEMEN S

The authors gratefullyacknowl dg the unding pro ided forthis pr ect b the 17 member companyTurbomachin ry ResearchConsortium at Texas A&MUni rsity. Appreciation is also ex-tended to Mr. Robert Munyon of Kop Flex for pro iding the couplings at a discounted rate. Special thanks is o red to MWendy Harding for her assistance in preparing the manuscrip

Gear Coupling Misalignment Induced Forces & Their Effects on Machinery Vibrations

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