ROMAC齿轮与齿轮传动系统分析PPT文档格式.pptx

ROMAC齿轮与齿轮传动系统分析PPT文档格式.pptx

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,Talk25AnalysisofGearsandGearedSystems,JasonKaplanPaulAllaireTimDimondBradNicholsAmirYounan,TableofContents,IntroductionObjectivesMotivationModelingofgearmeshstiffnessExternalParallelShaft-StagesSpurgearsHelicalgearsPlanetaryStagesApplicationsSteam-Turbine/GeneratorGearboxNRELWindTurbineGearboxConclusions/Futurework,07/26/2011,2,ROMACObjectives,GearedsystemsarequiteimportanttomanyrotatingmachinesNomajorROMACgearedsystemscodecurrentlyNewmajoradvanceinROMACcodesBlakeStringerdeveloped12x12generalizedgearstiffnessmatrixin2006NeedstobemergedwithMatlabRotorcodecombinedlateral,torsional,axialmotionsNowexpandedintoplanetarygearsandothernewmodelingofgearedsystemcomponentsManynewapplications,07/26/2011,3,FromthegearboxesinthecarstotheJetengines.Alsointhehelicopterspeciallyintherotorshatanditstransmissionsystem.ThefocusofourtalktodayintheModelsofthesegearsstiffness,PW-1000GGearedTurbofan,JetEngineinAircraft,Introduction（GearApplication）,4,AH-64DApacheLon0g7b/2o6w/2011,Automotivegearbox,OH-58DKiowaWarrior,Motivation,GearingexistsinalargevarietyofdifferentrotatingmachineswherespeedandtorqueconversionisnecessaryGearmeshstiffnesshassignificanteffectsonthemodeshapesandcriticalspeedsforthecoupledlowandhighspeedshaftsStatictransmissionerrorandothergeometricimperfectionsmayproducesignificantexcitationforcesFailuretoproperlymodelgearmeshstiffnessandexcitationsourceswouldhindertheabilitytopredictmachinevibrationlevels,07/26/2011,5,Thefirstistherotordynamicwherethegearislookatasaconnectionbetweentwopoint.Inthesemodels,theforcesofthegearismodeledinastiffnessmatrixtoconnectbetweentwonodes.Onasmallerlevel,thecontactbetweenthesurfaceofthegearinmeshareaffectedwiththeEHLwhichtakesplace.EHLcontributetothestiffnessbetweentheteethduetotheelasticdeformationoftheteethaswellasthecompressibilityoftheoil.Thethirdpartisthetoothcomplianceasseenasacontiliver.Thosethreestiffnessarethethreemajorcontributortobuildafullgearstiffness.WewillbefocusingontheRotordynamicandEHLstiffness,Introduction（MainIdea）,EHLStiffnessModels,ToothComplianceModels,RotorDynamicsModels,FullGearStiffnessmodel,07/26/2011,6,Thestiffnessmatrixisfunctionofthedimensionofthegearaswellastheorientationanglesoftheforce.Alsothismatrixisfunctionofthestiffnesscoefficientwhichismultipliedbythematrix.Inthesametime,theEHLanalysisfocusonthepressuredistributionofthelubricantandtheelasticdeformationwhichtakesplacebetweentheteeth.Asseenintherightdiagram.Theelasticityofthesurfaceaswellasthecompressibilityofthelubricantaffectsthestiffnessofgear.Here,itcametheideaofmergingtheworkdoneonthegeardynamicwiththeEHLlubricationtocomeupwithageneralmodelforthestiffness,Introduction（OurFocus）,07/26/2011,7,x,y,K,r2,r1,2,O2,O1,1,1RotordynamicAnalysis,（Stringer,2008）,SpurGearsvs.HelicalGears,Forcesandmomentsactinxy-planeonly（2-Dspace）Functionofpressureangle（an）only3-DOFmodel（x,y,qz）,Forcesandmomentsin3-DspaceFunctionofpressureangle（an）andhelicalangle（b）6-DOFmodel（x,y,z,qx,qyqz）,07/26/2011,8,General12-DOFMeshStiffnessMatrix,Constructedbyusingdirectmethodalongline-of-action.,Matrixisafunctionofaxisorientation（j）,pressureangle（an）,helicalangle（b）,gearandpinionpitchradii（riandrj）,andaveragegearmeshstiffness（Kg）.,x,y,K,rj,ri,j,Oj,Oi,i,i,07/26/2011,9,j,Why12Degrees-of-Freedom?

@#@,12-DOFmodelssparseinliteratureApplicabletospurgears（3DOFs）andhelicalgears（6DOFs）Ifmodelingaspurgearmesh,helicalanglewillbesettozero,andtheextraDOFsreducetozeroNumberofDOFsaregenerallyreducedbyconvenientchoiceofaxes.Convenientchoicesarenotalwaysavailable（i.e.,rotorcrafttransmission）,12DOFmodelnecessary,x,y,K,rj,ri,j,Oj,Oi,i,07/26/2011,10,Averagegearmeshstiffness,（Spotts,1985）Formulaappliesforsingle-tooth-to-toothcontactwhere,b=facewidthE1=ElasticmodulusofpinionE2=Elasticmodulusofgear,ImageFromWikipedia,07/26/2011,11,Averagegearmeshstiffness,Factorof1.3addedtoaccountfortheaveragenumberofteethincontact（Stringer,2008）NowautomaticallyincludedincodeActualstiffnessistime-varyingasnumberofcontactpairschanges,TradeI,07/26/2011,12,Force/MomentDisplacementRelationship,x,NodesiandjcontaintheDOFsolutionsforthecoupledshaftsatthelocationsofthegearandpinion.AllelementsofKmesharethenaddedintotheglobalstiffnessmatrixsuchthattheDOFsatnodesiandjmatchtheDOFsatthenodallocationsofthegearsontheshaft.y,K,rj,ri,j,Oj,Oi,i,i,07/26/2011,13,j,General12-DOFMeshStiffnessMatrix,07/26/2011,14,PlanetaryStageModeling,SunnPlanetsCarrierAnnulus,Kahraman,1994,rji