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外文翻译--一种滚子链传动的动力学建模 中文版.pdf

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外文翻译--一种滚子链传动的动力学建模 中文版.pdf

CHINESEJ0URNALOFMECHANICALENGINEERINGVo1.23,No.3,2010367DOI10.3901/CJME.2010.03.367,availableonlineatwww.cjmenet.tomwww.cjmenet.tom.cnDynamicModelingofaRollerChainDriveSystemofInputShaftConsideringtheFlexibilityxuLixin,YANGYuhu一,CHANGZongyu,andLIUJianping1SchoolofMechanicalEngineering,TianjinUniversity,23anjin300072,China2CollegeofEngineering,OceanUniversityofChina,Qingdao266100,ChinaReceivedJune16,2009revisedFebruary5,2010acceptedFebruary10,2010publishedelectronicallyFebruary25,2010AbstractRollerchaindrivesarewidelyusedinvarioushighspeed,highloadandpowertransmissionapplications,buttheircomplexdynamicbehaviorisnotwellresearched.MoststudieswereonlyfocusedOlltheanalysisofthevibrationofchaintightspan,andinthesemodels,manyfactorsareneglected.Inthispaper,amathematicalmodelisdevelopedtocalculatethedynamicresponseofarollerchaindriveworkingatconstantorvariablespeedcondition.Inthemodel,thecompletechaintransmissionwithtwosprocketsandthenecessarytightandslackspansisused.Theeffectoftheflexibilityofinputshaftondynamicresponseofthechainsystemistakenintoaccount,aswellastheelasticdeformationinthechain,theinertialforces,thegravityandthetorqueondrivenshaft.ThenonlinearequationsofmovementarederivedfromusingLagrangeequationsandsolvednumerically.Giventhecenterdistanceandthetwoinitialpositionanglesofteethondrivinganddrivensprocketscorrespondingtothefirstseatingrolleroneachsideofthetightspan,dynamicsofanyrollerchaindrivewithtwosprocketsandtwospanscallbeanalyzedbytheprocedure.Finally,anumericalexampleisvenandthevalidityoftheproceduredevelopedisdemonstratedbyanalyzingthedynamicbehaviorofatypicalrollerchaindrive.Themodelcanwellsimulatethetransverseandlongitudinalvibrationofthechainspansandthetorsionalvibrationofthesprockets.Thisstudycanprovideaneffectivemethodfortheanalysisofthedynamiccharacteristicsofallthechaindrivesystems.Keywordsrollerchain,dynamicmodeling,Lagrangeequations1IntroduetioRAsaneffectivewayoftransmittingpower,chaindrivesimpact,polygonalactionandexternalperiodicloadwereconsidered.Then,arefineddynamicmodelofrollerchaindrivewasdevelopedbyKIM,etal,thecollisionsandreboundsoftheengagingrollerwerestudied.Theauthorscanbefoundextensivelyinnearlyallmechanicalaboveallusedthesimplifiedmodelandhavestudiedaengineeringareas.Themajoradvantagesofchaindrivesaretheflexibilityinselectingshaftcenter,theabilitytodrivemorethanoneshaft.thehighreliabilityanddurabilityHowever,theapplicationofchaindrivesintroducesproblemssuchasnoiseandvibration,whichmotivatedresearcherstoinvestigatetl1edynamicbehaviorofthemforvariousengineeringpurposes.Foracomprehensivereviewonthissubject,thereaderisreferredtoWANG.etalt.Forrecentwork,VEIKOS,etal【。devisedarealisticanalyticalprocedureforthedynamicanalysisofrollerchaindrives.Manytestcaseshadbeenperformedusingthisprocedurewithvarioustypesofchains,operatingatdirentspeeds,sprocketratiosandloads.CHOI,etal4.developedamodelbasedonaxiallymovingmaterialtostudytransversevibrationofrollerchaindrives.Thechainspanwasapproximatedasrigidbaratlowspeedsandelasticbaratmoderateorhighspeeds.Inthismodel,theCorrespondingauthor.Emailyangyuhutju。edu。cnThisprojectissupportedbyNationalNaturalScienceFoundationofChinaGrantNo.50605060,andTiinMunicipalScienceFoundationofChinaGrantNo.06YFJMJC03300sprocketandthetightsideofthechaindrive.Whelltheemphasisisonthesystemsgloba1vibrationanddynamicbehavior,acompletechain仃ansmissionwhichregardsthechainspansastwoaxiallymovingstringswimtheirendsfixedtotworigidsprocketswasdevelopedbyWANG【oJ.Inthesubsequentwork.LIU。etal【.integratedthelocalmeshingphenomenawiththeglobalchain/sprocketsystemdynamicbehavior.Inordertoanalyzethediscretenatureofthechainspansinglobalchain/sprocketsystem,thechainstrandwasmodeledasaseriesofindividuallumpedmassconnectedtogetherbymasslesssprings.damperl.ThefirsttousethecompletegeometrywithadynamicmodelfordeterminingtheloaddistributionsalongthesprocketsandtheforcesalongthechainwasTROEDSSON,etaltⅧj.Inthemode1.thechaintransmissionwasdividedintofourseparatepartsthetightspan,slackspan,drivingsprocketanddrivensprocket,andeachpartwasmodeledandanalyzedseparately.Becausethecompatibilitybetweenthepartsmustbeconsideredinacompletemodel,theboundaryconditioncheckingandsolvingprocedurearecomplicated.Amodelofaroller竺里坐兰里erChainDriveSystemConsideringtheFlexibilityofInputShaftchaindriveincludingtheimpactbetweenthechainandguidebarswasdevelopedbyPEDERSEN.etalJJJ.Inthemodel,arealtoothprofileisreplacedbyacirculartoothprofileandthecontactsbetweenrollersandsprocketteetharedetectedbykinematicconstraintsofusingunilateralconstraintmethodology.FiniteelementtechniquesandnumericalsimulationsoftwarewereusedbvZHENG.etal,forpredictingthemeshingnoiseduetotheimpactofchainrollersagainstthesprocketofchaindrives.Inthemodel,thecompletestandardgeometryofsprocketsandal1componentsofchainlinkswereusedwithminorgeometrysimplification.Theobjectiveinthisstudyistodescribeanautomated.generallyapplicablecomputerproceduretowardspredictivedesignandanalysisofthecompleterollerchaindrivesunderdynamicconditions.Amathematicalmodelisdevelopedandthenonlinearequationsofmovementarederivedfro而usingLagrangeequations.Theeffectoftheflexibilityofinputshaftondynamicresponseofthechainsystemistakenintoaccount.aswellastheelasticdeformationinthechain.theinertialforces.thegravityandthetorqueondrivenshaft.Aroller/sprockettoothmotionneglected.7Allpartsofthemodel,bothchainandsprocketsareregardedastwodimensionalbodiesandallvariationsinthedirectionalongtherotationaxisofthesprocketsareneglected.Fig.1showsamodelofatypicaldrivingsprocketwithchainlinksaroundit.Acoordinatesystemisdefinedinthecentreofthedrivingsprocket.Thisistheglobalcoordinatesystem,usedtodescribethegeometry,whencalculatingthepositionoftherollersandthesprockets.ThepositionofanylumpedmasspointfcanbeexpressedinxandYidirections.Thestretchingforcesinthetwoconnectinglinksarecalled一1and.Thecontactforcebetweenthesprocketandtherolleriscalledandthegravitationforceismg.Inertialforcesinthechain.oneintheradialdirectionmR1andoneinthetangentialdirectiontmR。l1,areconsideredsincetherotationofsprocketsisnotatanearlyconstantangularvelocity.Intheseforces.thestretchingforcesandthecontactforcecanbeexpressedasthespringdampingforces.Additionally,itissupposedthatalltheforcesactatmasscenter.Inthemodel,theinputshaftissimplifiedasatorsionspringwithconstantandcontactdetectionanalysisisdescribedindetailinthistorsionalstiffnessanddamping.Theconstantorvariablestudy.ComparedwiththeworkmadebyTR0EDSS0N.etal【J.whatisthesimplest.nodivisionisneededinthecompletechainmodelandtheboundaryconditioncheckingiseasDynamicsofanyrollerchaindrivewithtwosprocketsandtwospanscanbeanalyzedbytheprocedure,ifthreenecessaryparameters,thecenterdistance5andthetwoinitialpositionanglesofteethand07ondrivinganddrivensprocketscorrespondingtothefirstseatingrolleroneachsideofthetightspan,aregiven.Finally,anumericalexampleisgivenandtheproceduredevelopedhereisdemonstratedbyanalyzingthedynamicbehaviorofatypicalchaindrive。2DynamicModelForpurposesofanalysis,thechainstrandwillbeapproximatedasaseriesofpointmasseslumpedattherollercenterswhichareconnectedtogetherbymasslesssprings.damperasusedintheoreticalworks.Forsimplifyingcomplexityofthemodel,thefollowingassumptionsaremadeinthederivationofthechainequationsofmotion.1、A11thelinkshaveequalmass,stiffnessandundeformedpitch.Onehalfofthetotal1inkmassislumpedateachroller.2、Therotationalinertiaoftherollersabouttheircenterofgravityisneglected.3Thechainpitchisequaltothesprocketpitch.4、Allmechanicalclearancesareneglected.5ArealtoothprofileisreplacedbyacirculartoothprofiletllJ.6、Thefrictionbetweentherollerandthetoothflankinthepartofthechainincontactwiththesprocketisspeedsboundaryconditioncanbeimposedontherotationanglefofinputshaft.Whentherollerengagesintothedrivensprocket,itsforceconditionisalmostthesameasitondrivingsprocket.AtorqueMisimposedonthedrivensprocketshaftinordertosimulatetheworkingload.mR。1~\,c④lg\/,一///一\,Fig.1.ModelofsprocketwiththecontactingchainpartFig.1showsastandardgeometryofsprockettoothwiththreearcsandonestraightline.Modelingthefu11sprocketgeometryanddetectingthecontactbetweenitandrollerinmovementisquitedifficult.So.inthisstudyarealtoothprofileisreplacedbyacirculartoothprofileasusedintheworktJ.asshowninFig.2.Theadvantageofthissimplificationisthatthecontactsbetweenrollersandteethcanbedeterminedeasily.TheradiusofthecirculartoothprofileisRandtherollerradiusisR,yieldingaclearanceofARRtR.Intheengagingprocess,onlyCHrNESEJOURNALoFMECHANICALENGINEEIUNG369onesinglepointatthetoothsurfacecansimultaneouslybeincontactwiththesameroller.aRealtoothprofilebCirculartoothprofileFig.2.SimplificationofthetoothprofileThechainspanisfinallymodeledasaseriesofmasspointsconnectedwithmasslessspringelementsasshowninFig.3.Bothofthevibrationsinandydirectionscanbereflectedbythemode1.Thelinksinboththetightandtheslackspanssufferthee佰ctofgravity.Inthemovement.theengagementanddisengagementphenomenonbetweenrollersandsprocketteethwilloccurperiodically.Thecontactdetectionbetweenthemwillbespecifiedinnextpartmotionandcontactdetectionanalysis.Fig.3.Modelofthechainspan3MotionandContactDetectionAnalysisAnexampleofageneralchaintransmissionisshowninFig.4.Itrepresentsthesimplestkindoftransmissionsinceitonlyincludestwosprocketsandonechain.Onesprocketisdriving,theotheroneisdrivenandthechaintransmitsthepowerbetweenthem.Thetwosprocketcentersareassumedtobelocatedatthesameheightwiththegravitationalforceactinginthenegativevdirection.辨N1rNrlr2r3llgntslae.xi鼍。iideA一.sprocke一f,slacks囝一Fig.4.CompletechaintransmissioninglobalcoordinatesystemTodescribethemodelafewparametershavetobedefined.AsshowninFig.4,thereareNlinksinthechain.Thefirstlinkseatedonthedrivingsprockettoothwillbeindexed订,alongthearrowpointingdirection.thenumberincrease.Itisassumedthatthefirstlinkseatedonthedrivensprockettoothwillbeindexedrp,andthelastoneintheehainisindexedrN1pⅣ.Theinitialpositionanglesofteethmeshedwithrollerr1andrpondrivinganddrivensprocketsaredefinedandrespectively.Intheanticlockwiserotationofdrivingsprocket.thepositionanglesofsprocketteethcorrespondingtorollerrlandrpcanbeexpressedasfollows,0pl022,12where1and2aretherotationalangleofdrivinganddrivensprockets,respectively.Then,thepositionanglesofthecorrectseatingteethcorrespondingtoroller订ondrivinganddrivensprocketscanbederivedfrom一O2201x360。pf360。Z234wherezlandz2arenumbersofteethofdrivinganddrivensprockets,respectively.Inthemovement,thedeviationofrollerrifromtheircorrectseatingpositionsondrivinganddrivensprocketsdenotedbysfandpfareexpressedasfollows。fR。f一,pfRpf一,whichcanbewrittenassfpfR1cos一Rs1sinfYf5678whereR。1,Rs2arethepitchradiusforthedrivinganddrivensprocketsisthecenterdistancebetweenthetwosprockets.Whenthecontacthappens,twokinematicconstraintsarerequiredtomeet.Forthecontactbetweenrollerriandthecorrectseatingtoothondrivingsprocket,theconstraintis9Forthecontactbetweenrollerrianditscorrectseatingtoothondrivensprocket,theconstraintis∞.量R≥≤,..............【坚璺里竺苎垦里SystemConsideringtheFlexibility。fInputShR≥RtR,10fkyH≤R。2.Generally,thenumberoflinksinthechainisnotanintegralmultipleofthenumberofsprocketteeth.Therefore,whenthechainlinkrlengagesintothedrivingsprocketagain,theseatingtoothiSnotthepreviousone.Atthispoint,inordertokeepthecorrectmeshingeffects,thekinematicconstraintsbetweenrollersandsprocketteethneedtoberedefined.Withthesamecase.whenthechainlinkrpengagesintothedrivensprocketagain,thekinematicconstraintsbetweenrollersandsprocketteethalsoneedtoberedefined.4DerivationofEquationsofMotionkyf卜hik。1sin0sfYfRt~RRlcos0sfXi。1sin0sfYiqik。。2sin0pfYiRt~RTheequ砒i。。fm。i。n酊ederVedmusingcj2i_1fc一川一c。fblR。1sin90Lagran。一geequationsasz,、lI十l/ICSl一\S。,dI_Qi.a口fJagfga口Thederivationofthekineticenergy,deformationenergy,dissipationfunctionandgeneralizedforceofthesystemareshowninAppendix.ThentheapplicationofLagrangeequationsleadsto2Jv2equationsofmotion.TheequationsoflinksinXandydirectionsarelistedasfollowsm2fkxf一1一XiL1kxfXi111√一lXi一Yihikc1cos0s一XfRtR1cOS0sfXi1sin0sfqik。R2cos0pffRtRf一qic。。2sinOpf90。一fgQsQp13TheequationsofmotionofdrivinganddrivensprocketsareasfollowsXfsinf十Rs1Rs1sin0sf~Yfcos0sfIxRtRlcos0s一XiR1sin0sfYi.v∑{一RRcos0s90。一毫ilsin0sf90。lR。1ARlsin0sf90。一cos090。}}一rp1一c一0,14Ⅳ22∑gfko一R。2fiR。2cOS0pffsin0pfi1R22sinOp~YicosOpfIxRt~b2R22R2cos0f90。一毫IxcXi_lXicXi2i1卜cc1Rslcosf90。一sif90on9oof毫卜gfcc【s2c。90。一戈fQpr】2、c。spi90o}}.15r121。,JJ~SOCR一∑厂£Cg∑

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