外文翻译--一种滚子链传动的动力学建模 中文版.pdf

CHINESEJ0URNALOFMECHANICALENGINEERINGVo123，No3，2010·367·DOI：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：yangyuhutju。edu。cnThisprojectissupportedbyNationalNaturalScienceFoundationofChina(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，onlyCHrNESEJOURNALoFMECHANICALENGINEEIUNG·369·onesinglepointatthetoothsurfacecansimultaneouslybeincontactwiththesameroller(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(1<p<)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，inordertokeepthecorrectmeshingeffects，thekinematicconstraintsbetweenrollersandsprocketteethneedtoberedefinedWiththesamecasewhenthechainlinkrpengagesintothedrivensprocketagain，thekinematicconstraintsbetweenrollersandsprocketteethalsoneedtoberedefined4DerivationofEquationsofMotionk(yf卜hik(。1sin0sfYf)×RtR(Rlcos0sfXi)+(。1sin0sfYi)qik。(。2sin0pfYi)×RtR+Theequ砒i。fm。i。n酊ederVedmusingc(j2i_1-f)+c(一川)一c。fblR。1sin(+90Lagran。)一geequationsasz，、lI十lICSl一S。，dI_+：Qi)a口fJagfga口Thederivationofthekineticenergy,deformationenergy,dissipationfunctionandgeneralizedforceofthesystemareshowninAppendixThentheapplicationofLagrangeequationsleadsto2Jv+2equationsofmotionTheequationsoflinksinXandydirectionsarelistedasfollows：m2fk(xf一1一Xi)L1k(xfXi+1)11(一lXi)+(一Yi)hikc(1cos0s一Xf)×RtR(1cOS0sfXi)+(1sin0sfqik。(+R2cos0pff)×RtR+f一qic。×。2sin(Opf+90。)一f+g=Qs+Qp(13)Theequationsofmotionofdrivinganddrivensprocketsareasfollows：Xf)sinf十Rs1(Rs1sin0sfYf)cos0sfIxRtR(lcos0s一Xi)+(R1sin0sfYi)+v一RRcos(0s+90。)一毫×i=lsin(0sf+90。)+lR。1ARlsin(0sf+90。)一×cos(0+90。)一-rp1)一c一)=0，(14)22+gfko一R。2(fi+R。2cOS0pff)sin0pf+i=1R2(2sinOpYi)cosOpfIxRt(b2R22R2cos(0f+90。)一毫Ix+c(Xi_l-Xi)+c(Xi-2i+1卜cc1Rslcosf+90。)一sif+90o)：n(”9oof×毫卜gfcc【s2×c。(+90。)一戈f=“+Qpr】2、c。s(pi+90o)：(15)r121。，JJSOCR一+=：厂Cg