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外文翻译--凸轮速度对凸轮系统影响的实验研究 英文版.pdf

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外文翻译--凸轮速度对凸轮系统影响的实验研究 英文版.pdf

PergamonMech.Mach.TheoryVol.31,No.4,pp.397412,1996Copyright©1996ElsevierScienceLtd0094114X95000879PrintedinGreatBritain.Allfightsreserved0094114X/9615.000.00ANEXPERIMENTALSTUDYOFTHEEFFECTSOFCAMSPEEDSONCAMFOLLOWERSYSTEMSH.S.YANandM.C.TSAIDepartmentofMechanicalEngineering,NationalChengKungUniversity,Tainan70101,Taiwan,RepublicofChinaM.H.HSUDepartmentofMechanicalEngineering,KungShahInstituteofTechnologyandCommerce,Yungkang,Tainan71016,Taiwan,RepublicofChinaReceived9September1994receivedforpublication26October1995AltraetTraditionally,inacamfollowersystem,thecamisoftenoperatedataconstantspeedandthemotioncharacteristicsofthefolloweraredeterminedoncethecamdisplacementcurveisdesigned.Fromthekinematicpointofview,theapproachbyvaryingcaminputdrivingspeedisanalternativewayforimprovingthefollowermotioncharacteristics.Hereweshowhowtofindapolynomialspeedtrajectoryforreducingthepeakvaluesofthemotioncharacteristics.Furthermore,constraintsandsystematicdesignproceduresforgeneratinganappropriatetrajectoryofthecamangularvelocitiesaredeveloped.Designexamplesaregiventoillustratetheprocedureforgettinganappropriatespeedtrajectoryasvariablespeedcamfollowersystems.Furthermore,anexperimentalsetupwithaservocontrollerisdevelopedtostudythefeasibilityofthisapproach.Experimentaldatashowthattheresultsareveryclosetothoseoftheory.NOMENCLATUREaaccelerationofthefollowerA,Atnormalizedaccelerationofthefollowerc,d,e,n,Ta,Tb,x,yconstantparametershmaximumdisplacementofthefollowerjjerkofthefollowerJ,JcnormalizedjerkofthefollowersdisplacementofthefollowerSnormalizeddisplacementofthefollowerttimeforthecamtorotatethroughangle0T,Tp,Tpj,TpvnormalizedtimevvelocityofthefollowerV,Vcnormalizedvelocityofthefollowertcamanglerotationfortotalrisehtim,t2,f13,t4camrotationanglenormalizedcamangleofrotationOcamangleofrotationtimeofcamrotationfortotalrisehT,,,r4timeofcamrotationcacamangluarvelocityCOaveaveragecamangularvelocityofacompletecycletOsm,cos2,co,,co4averagecamangularvelocityinafollowermotionperiodohthe1stderivativeofco6bthe2ndderivativeoftotnormalizedcamangularvelocitytFthe1stderivativeoffthe2ndderivativeoffINTRODUCTIONInacamfollowersystem,theloadproducedbyinertiaforcesispronetodeflectionandcreatesvibrationsandtheloadintroducedbyjerksmaycausevibrationsaswell,Thesewillaffecttheoperatinglifeofthecam.Therefore,thedesignofmotioncurvestominimizedynamicloadingisofimportanceforhighspeedcammechanisms.Itiswellknownthatthevelocityandaccelerationcurvesarerequiredtobecontinuousandtohavesmallerpeakvalues.Inaddition,thejerkcurveshouldbefinite.397398H.S.Yanetal.Acamisoftenassumedtobeoperatedataconstantspeedindesigningacamfollowersystem.However,themotioncharacteristicsofthefollowerarechangedasthecamspeedvaries,Traditionally,toachievethedesiredmotionisanapplicationofsynthesisforobtainingnewdisplacementcurveswhichhavebetterdynamiccharacteristics.Inthispaper,weproposeanalternativemethodbyvaryingthecamspeeds.Theconceptofusingvariablespeedsinacamfollowersystemdesignwasseldomstudiedintheliterature.Rothbart\1\designedavariablespeedcammechanisminwhichtheinputtothecamistheoutputofaWithworthquickreturnmechanism.TesarandMatthew\2\derivedthemotionequationsofthefollowerbyconsideringthecaseofvariablespeedcams.ThecriteriaforselectingproperangularvelocitieswhichwilleliminatethediscontinuityinmotioncharacteristicsofthefollowerareinvestigatedbyYanetal.\3\.Fromthekinematicpointofview,theobjectiveofthisworkistofindcamspeedtrajectoryforreducingthepeakvaluesofthefolloweroutputmotion.Furthermore,constraintsandsystemdesignproceduresforgeneratingapropertrajectoryofthecamangularvelocitiesaredeveoped.Designexamplesaregiventoillustratetheprocedureforgettingaproperangularspeedforagivenfollowersystem.Anexperimentalcamfollowersystemissetupinwhichaservomotoriscontrolledtogeneratethedesiredspeedtrajectoryforperformanceevaluations.MOTIONEQUATIONSForacamfollowersystem,thefollowerdisplacement,st,isafunctionofcamrotationangleOt.Mathematically,itcanbeexpressedasstfOt1whereOtisthecamrotationangleattimet.Thefollowervelocity,vt,ofthefolloweristhengivenbyvtfOot2wherefOdfO/dO,andcotdOt/dtisthecamangularvelocity.Furthermore,thecorrespondingfolloweracceleration,at,andjerk,jt,areatfOco2tfOdgt3jtfOco3t3fOcotcbtfO6Jt4wherefOdf2O/dO2,fOdf3O/dO3,tdcot/dt,andc3tdcoZt/dt2.Equations14presenttherelationshipbetweencaminputangularvelocitycotandfolloweroutputmotionsst,vt,at,andjt.Obviouslyifcotisaconstant,theycanbegreatlysimplified.Lethbethetotaldisplacementofthefollowerasthecamrotatesanangleintimeperiod3.Furthermore,denoteTt/r,0/8,andSs/h.NowwehaveT\0,1\,Vt\0,r\,\0,1\,V0\0,//\andSe\0,1\,Vs\0,h\.Then,equations14canberewrittenintermsoftheirnormalizedformsasfollowsstSTg,h5VTgyt2T6ATgyfl2TIgyilT7JTgy3T3g7t2TtITgyT8wheret2TdyT/dTisthenormalizedcamangularvelocityandVT,AT,andJTarethenormalizedvelocity,acceleration,andjerkofthefollower,respectively.Therelationshipbetweenequations1to8canbefoundasshs9hvv10TEffectsofcamspeedsoncamfollowersystems399haAll_hjj.12Whenthecamoperatesataconstantspeed,i.e.fT1,thenormalizedvelocity,VcT,acceleration,AtT,andjerk,J¢T,ofthefollowercanbeexpressedasVTg713AcTg714JTg15where7TT.CRITERIAFORDESIGNTForagivencamfollowersystem,thepeakvaluesofthenormalizedvelocity,acceleration,andjerkresultingfromaconstantdrivingspeedmaypossiblybereducedifweproperlycontrolitsinputspeedtrajectoryfT.Forexample,toreducethepeakvaluesofnormalizedvelocity,fTcanbechosensothatIVTpvl0,i.e.thedirectionofcamspeedisnotchanged.Asaresult,designcriteriaforselectingfZTtoreducethepeakvaluesoffolloweroutputsareaIforthecaseofreducingthepeakvalueofthenormalizedvelocityl0.Letequations58representthenormalizedmotioncharacteristicsofthefollowerintherisingperiod.Then,themotioncharacteristicsinthefallingperiodareST1g22VTg,fZT23ATgfZ2TgT24JTg,n3T3grnTtTgrtT.25Itiseasytofindthattheabsolutevaluesofthenormalizedvelocity,acceleration,andjerkinthefallingperiodareequaltothoseintherisingperiod,respectively.Hence,wehavethefollowingfactIfthesamedisplacementcurveisusedintherisingandfallingperiodsofafollower,thefunctionsofflTinthesetwoperiodsareidentical.ANGULARVELOCITYfTConsideracamfollowersystemwhichhasacamprovidingacycloidalmotioncurvewherecaminputfZtisapolynomial.Intherisingorfallingperiodandapplyingcriteriaaandgtoreducethepeakvaluesofmotioncurves,wechoosethefollowingpolynomialfZT,Fig.1.....t___.3.....dtitiT0TaTb1Fig.1.Polynomialangularvelocityinrisingorfallingperiod.

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