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中国矿业大学08届本科毕业设计第1页翻译部分英文原文FiniteElementAnalysisofinternalGearinHighSpeedPlanetaryGearUnitsAbstractThestressandtheelasticdeflectionofinternalringgearinhighspeedspurplanetarygearunitsareinvestigated.Arimthicknessparameterisdefinedastheflexibilityofinternalringgearandthegearcase.ThefiniteelementmodelofthewholeinternalringgearisestablishedbymeansofPro/EandANSYS.Theloadsonmeshingteethofinternalringgearareappliedaccordingtothecontactratioandtheloadsharingcoefficient.WiththefiniteelementanalysisFEA,theinfluencesofflexibilityandfittingstatusonthestressandelasticdeflectionofinternalringgeararepredicted.Thesimulationrevealsthattheprincipalstressanddeflectionincreasewiththedecreaseofrimthicknessofinternalringgear.Moreover,largerspringstiffnesshelpstoreducethestressanddeflectionofinternalringgear.Therefore,theflexibilityofinternalringgearmustbeconsideredduringthedesignofhighspeedplanetarygeartransmissions.KeywordsplanetarygeartransmissionsinternalringgearfiniteelementmethodHighspeedplanetarygeartransmissionsarewidelyusedinaerospaceandautomotiveengineeringduetotheadvantagesoflargereductionratio,highloadcapacity,compactnessandstability.Greatattentionhasbeenpaidtothedynamicpredictionofgearunitsforthepurposeofvibrationreductionandnoisecontrolinthepastdecades18.asoneofthekeyparts,internalgearmustbedesignedcarefullysinceitsflexibilityhasastronginfluenceonthegeartrainsperformance.studieshaveshownthattheflexibilityofinternalgearsignificantlyaffectsthedynamicbehaviorsofplanetarygeartrains9.inordertogetstressesanddeflectionsofringgear,severalfiniteelementanalysismodelswereproposed1014.however,mostofthemodelsdealtwithonlyasegmentoftheinternalringgearwithathinrim.thegearsegmentwasconstrainedwithcorrespondingboundaryconditionsandappointloadwasexertedonasingletoothalongthelineofactionwithoutconsideringthechangeoverbetweenthesingleanddoublecontactzoneinacompletemeshcycleofagiventooth.Afiniteelement/semianalyticalnonlinearcontractmodelwaspresentedtoinvestigatetheeffectofinternalgearflexibilityonthequasistaticbehaviorofa中国矿业大学08届本科毕业设计第2页planetarygearset15.Byconsideringthedeflectionsofallgearsandsupportconditionsofsplines,thestressesanddeflectionswerequantifiedasafunctionofrimthickness.Comparedwiththepreviouswork,thismodelconsideredthewholetransmissionsystem.However,themethoddescribedinRef.15requiresahighlevelofexpertisebeforeitcanevenbesuccessful.Thepurposeofthispaperistoinvestigatetheeffectsofrimthicknessandsupportconditionsonthestressandthedeflectionofinternalgearinahighspeedspurplanetarygeartransmission.Firstly,afiniteelementmodelforacompleteinternalgearfixedtogearcasewithstraightsplinesiscreatedbymeansofPro/EandANSYS.Then,properboundaryconditionsareappliedtosimulatingtheactualsupportconditions.Meanwhilethecontactratioandloadsharingareconsideredtoapplysuitableloadsonmeshingteeth.Finally,withthecommercialfiniteelementcodeofAPDLinANSYS,theinfluencesofrimthicknessandsupportconditiononinternalringgearstressanddeflectionareanalyzed.1finiteelementmodel1.1examplesystemAthreeplanetplanetarygearsetquenchedandtemperedsteel5140definedinTab.1istakenasanexampletostudytheinfluenceofrimthicknessandsupportconditions.AsshowninFig.1,threeplanetsareequallyspacedaroundthesungearwith120apartfromeachother.Here,allthegearsinthegearunitarestandardinvolutespurgears.Thesungearischosenastheinputmemberwhilethecarrier,whichisnotindicatedinFig.1forthesakeofclarity,ischosenastheoutputmember.Theinternalringgearissetstationarybyusing6splinesevenlyspacedroundtheoutercircletoconstraintherigidbodymotionofringgear.中国矿业大学08届本科毕业设计第3页Adimensionlessinternalgearrimthicknessparameterisdefinedastheratioofrimthicknesstothetoothheightasfollows1Wherer0,rf,raaretheouter,dedendumandaddendumradiusofinternalgear,respectively.Asmallerindicatesamoreflexibleringgearandviceversa.internalgearswithdifferentvaluesof1.0,1.5,2.0,2.5areinvestigatedinthispaper.Inallthesecases,thewidthsofringgearare44mm,andtheconnectingsplinesare34mminlengthand14mminwidth,whiletheheightsofsplinesineachcaseare5mm,6mm,7mmand8mm,respectively.Afiniteelementmodelfortheinternalgearwith1.5isshowninFig.2,whichcontains69813elementsand112527nodes.Fig.2Finiteelementmodelofinternalringgear1.2loadsandboundaryconditionsTheinternalgearisfixedtogearcasethroughsplinesandmesheswithplanetgears.Assumingthattheloadisevenlydistributedtoeachplanetandallfrictionsarenegligible,the中国矿业大学08届本科毕业设计第4页meshingforcebetweeneachplanetandtheringisasfollowsWhereTcistheoveralloutputtorqueiscistheoverallreductionratiorsistheradiusofsungearnpdenotesthenumberofplanetsisthepressureangle.Inaddition,byconsideringthecontactratioandloadsharingfactors,wecanfinallydeterminethemeshpositionsandtheproportionsoftheloadcarriedbyeachtoothofthering.TheloadstateoftheringisshowninFig.3.Here,thephaseanglebetweeneachplanetis120。andFi1,.,6isthenormalmeshingforceactingontheteethofinternalgear.Forclaritypurpose,onlytheteethinmeshareplottedinFig.3.afterobtainingthemeshingforcesactingoninternalgear,wecanapplythemtothefiniteelementmodel.Tobespecific,themeshingforcesareevenlydistributedtothecorrespondingnodesalongthelineofengagement.Assupportconditionscanbeverycomplicatedifconsideringthecontactproblems,specialsubstitutemustbemadetomodeltheactualcontactsatthesplines.Inthispaper,thesplinesarecoupledwiththeringbytheoverlappednodesandsixspringsequallyspacedbetweentheoutersurfaceoftheringandthehousingsurfaceareappliedtosimulatingthesupportconditions.Thesupportconditionbetweentheringandthehousingisindicatedthroughthestiffnessofthesesprings.Theprocesscanbedetailedasfollows.Asinglenodeneedstobedefinedforeachsplinetohousingconnection.ThisisachievedsuingCOMBINE14elementsateachsplineposition,whichconnectthesplinestothepointsatthehousingsurfacewithaninfinitestiffness.AlldegreeoffreedomsDOFsofthesepredefinednodes
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