中國礦業(yè)大學08屆本科畢業(yè)設計第1頁翻譯部分英文原文FiniteElementAnalysisofinternalGearinHigh-SpeedPlanetaryGearUnitsAbstract:Thestressandtheelasticdeflectionofinternalringgearinhigh-speedspurplanetarygearunitsareinvestigated.Arimthicknessparameterisdefinedastheflexibilityofinternalringgearandthegearcase.ThefiniteelementmodelofthewholeinternalringgearisestablishedbymeansofPro/EandANSYS.Theloadsonmeshingteethofinternalringgearareappliedaccordingtothecontactratioandtheload-sharingcoefficient.Withthefiniteelementanalysis(FEA),theinfluencesofflexibilityandfittingstatusonthestressandelasticdeflectionofinternalringgeararepredicted.Thesimulationrevealsthattheprincipalstressanddeflectionincreasewiththedecreaseofrimthicknessofinternalringgear.Moreover,largerspringstiffnesshelpstoreducethestressanddeflectionofinternalringgear.Therefore,theflexibilityofinternalringgearmustbeconsideredduringthedesignofhigh-speedplanetarygeartransmissions.Keywords:planetarygeartransmissions；internalringgear；finiteelementmethodHigh-speedplanetarygeartransmissionsarewidelyusedinaerospaceandautomotiveengineeringduetotheadvantagesoflargereductionratio,highloadcapacity,compactnessandstability.Greatattentionhasbeenpaidtothedynamicpredictionofgearunitsforthepurposeofvibrationreductionandnoisecontrolinthepastdecades(1-8).asoneofthekeyparts,internalgearmustbedesignedcarefullysinceitsflexibilityhasastronginfluenceonthegeartrainsperformance.studieshaveshownthattheflexibilityofinternalgearsignificantlyaffectsthedynamicbehaviorsofplanetarygeartrains(9).inordertogetstressesanddeflectionsofringgear,severalfiniteelementanalysismodelswereproposed(10-14).however,mostofthemodelsdealtwithonlyasegmentoftheinternalringgearwithathinrim.thegearsegmentwasconstrainedwithcorrespondingboundaryconditionsandappointloadwasexertedonasingletoothalongthelineofactionwithoutconsideringthechangeoverbetweenthesingleanddoublecontactzoneinacompletemeshcycleofagiventooth.Afiniteelement/semi-analyticalnonlinearcontractmodelwaspresentedtoinvestigatetheeffectofinternalgearflexibilityonthequasi-staticbehaviorofa中國礦業(yè)大學08屆本科畢業(yè)設計第2頁planetarygearset(15).Byconsideringthedeflectionsofallgearsandsupportconditionsofsplines,thestressesanddeflectionswerequantifiedasafunctionofrimthickness.Comparedwiththepreviouswork,thismodelconsideredthewholetransmissionsystem.However,themethoddescribedinRef.(15)requiresahighlevelofexpertisebeforeitcanevenbesuccessful.Thepurposeofthispaperistoinvestigatetheeffectsofrimthicknessandsupportconditionsonthestressandthedeflectionofinternalgearinahigh-speedspurplanetarygeartransmission.Firstly,afiniteelementmodelforacompleteinternalgearfixedtogearcasewithstraightsplinesiscreatedbymeansofPro/EandANSYS.Then,properboundaryconditionsareappliedtosimulatingtheactualsupportconditions.Meanwhilethecontactratioandloadsharingareconsideredtoapplysuitableloadsonmeshingteeth.Finally,withthecommercialfiniteelementcodeofAPDLinANSYS,theinfluencesofrimthicknessandsupportconditiononinternalringgearstressanddeflectionareanalyzed.1finiteelementmodel1.1examplesystemAthree-planetplanetarygearset(quenchedandtemperedsteel5140)definedinTab.1istakenasanexampletostudytheinfluenceofrimthicknessandsupportconditions.AsshowninFig.1,threeplanetsareequallyspacedaroundthesungearwith120apartfromeachother.Here,allthegearsinthegearunitarestandardinvolutespurgears.Thesungearischosenastheinputmemberwhilethecarrier,whichisnotindicatedinFig.1forthesakeofclarity,ischosenastheoutputmember.Theinternalringgearissetstationarybyusing6splinesevenlyspacedroundtheoutercircletoconstraintherigidbodymotionofringgear.中國礦業(yè)大學08屆本科畢業(yè)設計第3頁Adimensionlessinternalgearrimthicknessparameterisdefinedastheratioofrimthicknesstothetoothheightasfollows:(1)Wherer0,rf,raaretheouter,dedendumandaddendumradiusofinternalgear,respectively.Aernalgearswithdifferentvaluesof=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中國礦業(yè)大學08屆本科畢業(yè)設計第4頁meshingforcebetweeneachplanetandtheringisasfollows:WhereTcistheoveralloutputtorque；iscistheoverallreductionratio；rsistheradiusofsungear；npdenotesthenumberofplanets；isthepressureangle.Inaddition,byconsideringthecontactratioandloadsharingfactors,wecanfinallydeterminethemeshpositionsandtheproportionsoftheloadcarriedbyeachtoothofthering.TheloadstateoftheringisshowninFig.3.Here,thephaseanglebetweeneachplanetis120。andFi(1,.,6)isthenormalmeshingforceactingontheteethofinternalgear.Forclaritypurpose,onlytheteethinmeshareplottedinFig.3.afterobtainingthemeshingforcesactingoninternalgear,wecanapplythemtothefiniteelementmodel.Tobespecific,themeshingforcesareevenlydistributedtothecorrespondingnodesalongthelineofengagement.Assupportconditionscanbeverycomplicatedifconsideringthecontactproblems,specialsubstitutemustbemadetomodeltheactualcontactsatthesplines.Inthispaper,thesplinesarecoupledwiththeringbytheoverlappednodesandsixspringsequallyspacedbetweentheoutersurfaceoftheringandthehousingsurfaceareappliedtosimulatingthesupportconditions.Thesupportconditionbetweentheringandthehousingisindicatedthroughthestiffnesso