外文翻译--一种滚子链传动的动力学建模 中文版.pdf

CHINESEJ0URNALOFMECHANICALENGINEERINGVo123，No3，2010367DOI：103901CJME201003367，availableonlineatwwwcjmenettom；wwwcjmenettomcnDynamicModelingofaRollerChainDriveSystemofInputShaftConsideringtheFlexibilityxuLixin，YANGYuhu一，CHANGZongyu，andLIUJianping1SchoolofMechanicalEngineering,TianjinUniversity,23anjin300072，China2CollegeofEngineering,OceanUniversityofChina,Qingdao266100,ChinaReceivedJune16，2009；revisedFebruary5，2010；acceptedFebruary10，2010；publishedelectronicallyFebruary25，2010Abstract：Rollerchaindrivesarewidelyusedinvarioushigh-speed，high-loadandpowertransmissionapplications，buttheircomplexdynamicbehaviorisnotwellresearchedMoststudieswereonlyfocusedOlltheanalysisofthevibrationofchaintightspan，andinthesemodels，manyfactorsareneglectedInthispaper，amathematicalmodelisdevelopedtocalculatethedynamicresponseofarollerchaindriveworkingatconstantorvariablespeedconditionInthemodel，thecompletechaintransmissionwithtwosprocketsandthenecessarytightandslackspansisusedTheeffectoftheflexibilityofinputshaftondynamicresponseofthechainsystemistakenintoaccount，aswellastheelasticdeformationinthechain，theinertialforces，thegravityandthetorqueondrivenshaftThenonlinearequationsofmovementarederivedfromusingLagrangeequationsandsolvednumericallyGiventhecenterdistanceandthetwoinitialpositionanglesofteethondrivinganddrivensprocketscorrespondingtothefirstseatingrolleroneachsideofthetightspan，dynamicsofanyrollerchaindrivewithtwosprocketsandtwospanscallbeanalyzedbytheprocedureFinally，anumericalexampleisvenandthevalidityoftheproceduredevelopedisdemonstratedbyanalyzingthedynamicbehaviorofatypicalrollerchaindriveThemodelcanwellsimulatethetransverseandlongitudinalvibrationofthechainspansandthetorsionalvibrationofthesprocketsThisstudycanprovideaneffectivemethodfortheanalysisofthedynamiccharacteristicsofallthechaindrivesystemsKeywords：rollerchain，dynamicmodeling，Lagrangeequations1IntroduetioRAsaneffectivewayoftransmittingpower,chaindrivesimpact，polygonalactionandexternalperiodicloadwereconsideredThen，arefineddynamicmodelofrollerchaindrivewasdevelopedbyKIM，etal，thecollisionsandreboundsoftheengagingrollerwerestudiedTheauthorscanbefoundextensivelyinnearlyallmechanicalaboveallusedthesimplifiedmodelandhavestudiedaengineeringareasThemajoradvantagesofchaindrivesaretheflexibilityinselectingshaftcenter,theabilitytodrivemorethanoneshaftthehighreliabilityanddurabilityHowever,theapplicationofchaindrivesintroducesproblemssuchasnoiseandvibration，whichmotivatedresearcherstoinvestigatetl1edynamicbehaviorofthemforvariousengineeringpurposesForacomprehensivereviewonthissubject，thereaderisreferredtoWANGetaltForrecentwork，VEIKOS，etal【。devisedarealisticanalyticalprocedureforthedynamicanalysisofrollerchaindrivesManytestcaseshadbeenperformedusingthisprocedurewithvarioustypesofchains，operatingatdirentspeeds，sprocketratiosandloadsCHOI，etal4developedamodelbasedonaxiallymovingmaterialtostudytransversevibrationofrollerchaindrivesThechainspanwasapproximatedasrigidbaratlowspeedsandelasticbaratmoderateorhighspeedsInthismodel，theCorrespondingauthorE-mail：ThisprojectissupportedbyNationalNaturalScienceFoundationofChina(GrantNo50605060)，andTiinMunicipalScienceFoundationofChina(GrantNo06YFJMJC03300)sprocketandthetightsideofthechaindriveWhelltheemphasisisonthesystemsgloba1vibrationanddynamicbehavior,acompletechain仃ansmissionwhichregardsthechainspansastwoaxiallymovingstringswimtheirendsfixedtotworigidsprocketswasdevelopedbyWANG【oJInthesubsequentworkLIU。etal【integratedthelocalmeshingphenomenawiththeglobalchainsprocketsystemdynamicbehaviorInordertoanalyzethediscretenatureofthechainspansinglobalchainsprocketsystem，thechainstrandwasmodeledasaseriesofindividuallumpedmassconnectedtogetherbymasslessspringsdamperlThefirsttousethecompletegeometrywithadynamicmodelfordeterminingtheloaddistributionsalongthesprocketsandtheforcesalongthechainwasTROEDSSON，etaltjInthemode1thechaintransmissionwasdividedintofourseparateparts：thetightspan，slackspan，drivingsprocketanddrivensprocket，andeachpartwasmodeledandanalyzedseparatelyBecausethecompatibilitybetweenthepartsmustbeconsideredinacompletemodel，theboundaryconditioncheckingandsolvingprocedurearecomplicatedAmodelofaroller：!：竺里坐!兰!里!erChainDriveSystemConsideringtheFlexibilityofInputShaftchaindriveincludingtheimpactbetweenthechainandguidebarswasdevelopedbyPEDERSENetalJJJInthemodel，arealtoothprofileisreplacedbyacirculartoothprofileandthecontactsbetweenrollersandsprocketteetharedetectedbykinematicconstraintsofusingunilateralconstraintmethodologyFiniteelementtechniquesandnumericalsimulationsoftwarewereusedbvZHENGetal，forpredictingthemeshingnoiseduetotheimpactofchainrollersagainstthesprocketofchaindrivesInthemodel，thecompletestandardgeometryofsprocketsandal1componentsofchainlinkswereusedwithminorgeometrysimplificationTheobjectiveinthisstudyistodescribeanautomatedgenerallyapplicablecomputerproceduretowardspredictivedesignandanalysisofthecompleterollerchaindrivesunderdynamicconditionsAmathematicalmodelisdevelopedandthenonlinearequationsofmovementarederivedfro而usingLagrangeequationsTheeffectoftheflexibilityofinputshaftondynamicresponseofthechainsystemistakenintoaccountaswellastheelasticdeformationinthechaintheinertialforcesthegravityandthetorqueondrivenshaftArollersprockettoothmotionneglected(7)Allpartsofthemodel，bothchainandsprocketsareregardedastwodimensionalbodiesandallvariationsinthedirectionalongtherotationaxisofthesprocketsareneglectedFig1showsamodelofatypicaldrivingsprocketwithchainlinksarounditAcoordinatesystemisdefinedinthecentreofthedrivingsprocketThisistheglobalcoordinatesystem，usedtodescribethegeometry,whencalculatingthepositionoftherollersandthesprocketsThepositionofanylumpedmasspointfcanbeexpressedinxandYidirectionsThestretchingforcesinthetwoconnectinglinksarecalled一1andThecontactforcebetweenthesprocketandtherolleriscalledandthegravitationforceismgInertialforcesinthechainoneintheradialdirection：mR1andoneinthetangentialdirectiont=mR。l1，areconsideredsincetherotationofsprocketsisnotatanearlyconstantangularvelocityIntheseforcesthestretchingforcesandthecontactforcecanbeexpressedasthespring-dampingforcesAdditionally,itissupposedthatalltheforcesactatmasscenterInthemodel，theinputshaftissimplifiedasatorsionspringwithconstantandcontactdetectionanalysisisdescribedindetailinthistorsionalstiffnessanddampingTheconstantorvariablestudyComparedwiththeworkmadebyTR0EDSS0Netal【JwhatisthesimplestnodivisionisneededinthecompletechainmodelandtheboundaryconditioncheckingiseasDynamicsofanyrollerchaindrivewithtwosprocketsandtwospanscanbeanalyzedbytheprocedure，ifthreenecessaryparameters，thecenterdistance5andthetwoinitialpositionanglesofteethand07ondrivinganddrivensprocketscorrespondingtothefirstseatingrolleroneachsideofthetightspan，aregivenFinally,anumericalexampleisgivenandtheproceduredevelopedhereisdemonstratedbyanalyzingthedynamicbehaviorofatypicalchaindrive。2DynamicModel-Forpurposesofanalysis，thechainstrandwillbeapproximatedasaseriesofpointmasseslumpedattherollercenterswhichareconnectedtogetherbymasslessspringsdamperasusedintheoreticalworks”Forsimplifyingcomplexityofthemodel，thefollowingassumptionsaremadeinthederivationofthechainequationsofmotion(1、A11thelinkshaveequalmass，stiffnessandundeformedpitchOnehalfofthetotal1inkmassislumpedateachroller(2、Therotationalinertiaoftherollersabouttheircenterofgravityisneglected(3)Thechainpitchisequaltothesprocketpitch(4、Allmechanicalclearancesareneglected(5)ArealtoothprofileisreplacedbyacirculartoothprofiletllJ(6、ThefrictionbetweentherollerandthetoothflankinthepartofthechainincontactwiththesprocketisspeedsboundaryconditioncanbeimposedontherotationanglefofinputshaftWhentherollerengagesintothedrivensprocket，itsforceconditionisalmostthesameasitondrivingsprocketAtorqueMisimposedonthedrivensprocketshaftinordertosimulatetheworkingloadmR。1，clg，一一，)Fig1ModelofsprocketwiththecontactingchainpartFig1showsastandardgeometryofsprockettoothwiththreearcsandonestraightlineModelingthefu11sprocketgeometryanddetectingthecontactbetweenitandrollerinmovementisquitedifficultSointhisstudyarealtoothprofileisreplacedbyacirculartoothprofileasusedintheworkt“JasshowninFig2TheadvantageofthissimplificationisthatthecontactsbetweenrollersandteethcanbedeterminedeasilyTheradiusofthecirculartoothprofileisR+andtherollerradiusisR，yieldingaclearanceofAR=RtRIntheengagingprocess，onlyCHrNESEJOURNALoFMECHANICALENGINEEIUNG369onesinglepointatthetoothsurfacecansimultaneouslybeincontactwiththesameroller(a)Realtoothprofile(b)CirculartoothprofileFig2SimplificationofthetoothprofileThechainspanisfinallymodeledasaseriesofmasspointsconnectedwithmasslessspringelementsasshowninFig3Bothofthevibrationsinandydirectionscanbereflectedbythemode1Thelinksinboththetightandtheslackspanssufferthee佰：ctofgravityInthemovementtheengagementanddisengagementphenomenonbetweenrollersandsprocketteethwilloccurperiodicallyThecontactdetectionbetweenthemwillbespecifiedinnextpart：motionandcontactdetectionanalysisFig3Modelofthechainspan3MotionandContactDetectionAnalysisAnexampleofageneralchaintransmissionisshowninFig4ItrepresentsthesimplestkindoftransmissionsinceitonlyincludestwosprocketsandonechainOnesprocketisdriving，theotheroneisdrivenandthechaintransmitsthepowerbetweenthemThetwosprocketcentersareassumedtobelocatedatthesameheightwiththegravitationalforceactinginthenegativevdirection辨N-1)rNrlr2r3llgntslae-xi鼍。iideA一：sprocke一f：，slacks囝一Fig4CompletechaintransmissioninglobalcoordinatesystemTodescribethemodelafewparametershavetobedefinedAsshowninFig4，thereareNlinksinthechainThefirstlinkseatedonthedrivingsprockettoothwillbeindexed订，alongthearrowpointingdirectionthenumberincreaseItisassumedthatthefirstlinkseatedonthedrivensprockettoothwillbeindexedrp，andthelastoneintheehainisindexedrN(1p)Theinitialpositionanglesofteethmeshedwithrollerr1andrpondrivinganddrivensprocketsaredefinedandrespectivelyIntheanticlockwiserotationofdrivingsprocketthepositionanglesofsprocketteethcorrespondingtorollerrlandrpcanbeexpressedasfollows：=+，0pl=02+2，(1)(2)where1and2aretherotationalangleofdrivinganddrivensprockets，respectivelyThen，thepositionanglesofthecorrectseatingteethcorrespondingtoroller订ondrivinganddrivensprocketscanbederivedfrom=+一=O2+2+01)x360。(pf)360。Z2(3)(4)wherezlandz2arenumbersofteethofdrivinganddrivensprockets，respectivelyInthemovement，thedeviationofrollerrifromtheircorrectseatingpositionsondrivinganddrivensprocketsdenotedbysfandpfareexpressedasfollows：。f=R。f一，pf=Rpf一，whichcanbewrittenassf=pfR1cos一Rs1sinfYf(5)(6)(7)(8)whereR。1，Rs2arethepitchradiusforthedrivinganddrivensprockets；isthecenterdistancebetweenthetwosprocketsWhenthecontacthappens，twokinematicconstraintsarerequiredtomeetForthecontactbetweenrollerriandthecorrectseatingtoothondrivingsprocket，theconstraintis(9)Forthecontactbetweenrollerrianditscorrectseatingtoothondrivensprocket，theconstraintis量=R，【：!：坚!璺里竺!苎!垦!里!SystemConsideringtheFlexibility。fInputShRRtR，(10)fk(yHR。2Generally,thenumberoflinksinthechainisnotanintegralmultipleofthenumberofsprocketteethTherefore，whenthechainlinkrlengagesintothedrivingsprocketagain，theseatingtoothiSnotthepreviousoneAtthispoint，inord