AGMA-91FTM16-1991.pdf
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1、91 FTM 16 A V Contact Analysisof Gears Using a Combined FiniteElementand Surface IntegralMethod by: S. M. Vijayakar, Advanced Numerical Solutions and D. R. Houser, Ohio State University ,L AmericanGearManufacturersAssociation III TECHNICALPAPER Copyright American Gear Manufacturers Association Provi
2、ded by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:58:04 MDTNo reproduction or networking permitted without license from IHS -,-,- Contact Analysisof Gears Using a Combined Finite Element and Surface IntegralMethod S. M. Vijayakar, A
3、dvanced Numerical Solutions and D. R. Houser, Ohio State University The Statementsandopinionscontainedhereinarethoseof theauthorandshouldnotbeconstrued asanofficial actionor opinion of theAmerican Gear Manufacturers Association. ABSTRACT: Anewmethodis describedfor thesolutionofthecontactproblemingea
4、rs. Themethodusesacombinationofthefinite element method anda surfaceintegralformof theBousinesqand Cermtisolutions. Numericalexamplesarepresented of contacting hypoid gears, helical gears andcrossed axis helicalgears. Copyright 1991 American Gear Manufacturers Association 1500 King Street, Suite 201
5、 Alexandria, Virginia, 22314 October,1991 ISBN: 1-55589-614-6 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:58:04 MDTNo reproduction or networking permitted without license
6、from IHS -,-,- Contact Analysisof Gears using a CombinedFinite Elementand Surface Integral Method SandeepM. Vijayakar AdvancedNumericalSolutions 2085 Pine Grove Lane, Columbus OH 43232, and DonaldR. Houser Professor, Dept.of Mech. Eng. The Ohio State University ColumbusOH 43210 INTRODUCTION Research
7、in the mid and late eightiesshowedthat The completeandaccuratesolutionof thecontactthe gear contactproblemwas not unsurmountable,but problemof three-dimensionalgears has been,fortherequiredan approachthat combinedthe strengthsof pastseveraldecades,oneof themore soughtafter,thefiniteelementmethodwith
8、thoseofother albeitelusivesolutionsin the engineeringcommunity,techniquessuchasboundaryelementandsurface Eventhe arrivalof finiteelementtechniqueson theintegralmethods.Conceptsfrommathematical sceneinthemidseventiesfailedtoproducetheprogrammingcouldbe usedto advantagein solving solutiontoanybutthemo
9、stsimplegearcontactthe contact equations.An innovativeapproachtowards problems,theformulationofthefiniteelementsthemselves couldgoalongwaytowardssolvingthemesh The reasonsfor this are manyfold.When gearsaregenerationand geometricaccuracy problems.With the broughtin contact,the widthof the contactzon
10、eisideaof incorporatingthebestoftheseandother typicallyan order of magnitudesmallerthan the othertechnologiesinmind,developmentof whatis now dimensionsof the gears.This gives rise to the need forCAPP(ContactAnalysisProgramPackage)was begun a veryhighlyrefinedfiniteelementmeshnearthefour years ago. I
11、t has evolvedinto a powerfulcollection contactzone.But giventhe fact that the contactzoneof computerprogramsthat providethe geardesigner movesoverthe surfaceof the gear, one wouldneedawith an insightinto the state of stressin gearsthat has veryhighlyrefinedmeshalloverthecontactingthus far neverbeenp
12、ossible.Some of the featuresthat surface.Finiteelementmodelsrefinedto this extentCAPPsupportsare:friction,sub-surfacestress cannot be accommodatedon eventhe largest of todayscalculation,stresscontours,transmissionerror,contact computers.Compoundingthis difficultyis the fact thatpressuredistributions
13、and load distributioncalculation. thecontactconditionsareverysensitivetothe geometryof the contactingsurfaces.General purposeFigures1 to 5 showexamplesof gear sets for which finiteelementmodelscannotprovidethe requiredthis process has been successfullyused. levelof geometricaccuracy.Finally,the diff
14、icultiesof generatinganoptimalthree-dimensionalmeshthatCONTACT ANALYSIS can accuratelymodelthe stressgradientsin the critical regionswhileminimizingthe numberof degreesofIn earlierstudiesVijayakar1988,1989;Bathe 1985, freedomof themodelhavekeptthe finiteelementChowdhury1986of contactmodeling,a puref
15、inite methodfrom beingwidelyusedto solve the completeelementapproachwas used to obtain complianceterms gear contact problem,relatingtraction at one locationof a body to the normal displacementat anotherlocationonthecontacting 1 Copyright American Gear Manufacturers Association Provided by IHS under
16、license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:58:04 MDTNo reproduction or networking permitted without license from IHS -,-,- A v Figure 4- Contactanalysisof a 90 crossedaxis external helicalgear set. Figure1- Contactanalysisof helical gears. Fi
17、gure 5- Contact an_YSciSl ga9_tcrossedaxis external gearbody.Itbecameapparentthatinordertoobtain sufficientresolutionin the contactarea,the size of the Figure2-Contactanalysis of hypoidgears,finiteelementmodelwouldhaveto be inordinately large.Afiniteelementmeshthatis locallyrefined aroundthecontactr
18、egioncannotbe usedwhenthe contactzonetravelsover the surfacesof the two bodies. Otherresearchersworkingin the tribologyareade Mul1985,Seabra1987, Lubrecht1987 haveobtained compliancerelationshipsin surfaceintegralformby integratingthe Greensfunctionfor a pointloadon the surfaceof a half space(the Bo
19、usinesqsolution)overthe areasofindividualcellsdemarcatedon thecontact zone. Thismethodworkswell as longas the extentof thecontactingbodiesismuchlargerthanthe dimensionsof the contactzone,and the contactzoneis far enoughfromthe othersurfaceboundariesso that the twocontactingbodiesmaybe treatedas elas
20、tic halfspaces.Theseconditionsare, however,not satisfied by gears The approachthatis describedhere is basedon the assumptionthatbeyonda certaindistancefromthe contactzone,thefiniteelementmodelpredicts deformationswell.Theelastichalfspacemodelis Figure3- Contactanalysis of worm gears,accuratein predi
21、ctingrelativedisplacementsof points Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:58:04 MDTNo reproduction or networking permitted without license from IHS -,-,- J=-6 nearth
22、e contactzone.Undertheseassumptions,it is Apossibleto makepredictionsof surfacedisplacements_0 thatmakeuseof the advantagesof both,the finite velementmethod,aswellasthesurfaceintegral approach. Thismethodisrelatedto asymptoticmatching methodsthatarecommonlyusedto solvesingular perturbationproblems.S
23、chwartz and HarperSchwartz 1971 haveusedsuch an asymptoticmatchingmethod cylinderspressedagainstan elasticcylinderin plane strain. In orderto combinethesurfaceintegralsolution withthefiniteelementsolution,areferenceor matchinginterfaceembeddedin the contactingbody isFigure6- Computationalgrid in the
24、 contact zone of the used.Thismatchingsurfaceis farenoughremovedgears. fromthe principalpointof contact so thatthe finite elementpredictionof displacementsalongthis surface is accurateenough.At the same time, it is close enoughforce appliedat the locationp which is on the surface of to the principal
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