外文翻译--一种滚子链传动的动力学建模 中文版.pdf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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CHINESEJ0URNALOFMECHANICALENGINEERINGVO1.23,NO.3,2010367DOI10.3901/CJME.2010.03.367,AVAILABLEONLINEATWWW.CJMENET.TOM;WWW.CJMENET.TOM.CNDYNAMICMODELINGOFAROLLERCHAINDRIVESYSTEMOFINPUTSHAFTCONSIDERINGTHEFLEXIBILITYXULIXIN,YANGYUHU一,CHANGZONGYU,ANDLIUJIANPING1SCHOOLOFMECHANICALENGINEERING,TIANJINUNIVERSITY,23ANJIN300072,CHINA2COLLEGEOFENGINEERING,OCEANUNIVERSITYOFCHINA,QINGDAO266100,CHINARECEIVEDJUNE16,2009;REVISEDFEBRUARY5,2010;ACCEPTEDFEBRUARY10,2010;PUBLISHEDELECTRONICALLYFEBRUARY25,2010ABSTRACTROLLERCHAINDRIVESAREWIDELYUSEDINVARIOUSHIGHSPEED,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.WHELLTHEEMPHASISISONTHESYSTEM’SGLOBA1VIBRATIONANDDYNAMICBEHAVIOR,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.INTHISSTUDYAREALTOOTHPROFILEISREPLACEDBYACIRCULARTOOTHPROFILEASUSEDINTHEWORKT“J.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.THEPOSITIONANGLESOFSPROCKETTEETHCORRESPONDINGTOROLLERRLANDRPCANBEEXPRESSEDASFOLL
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