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外文翻译--用矢量方程计算共轭凸轮轮廓 英文版.pdf

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外文翻译--用矢量方程计算共轭凸轮轮廓 英文版.pdf

http//pic.sagepub.com/EngineeringScienceEngineers,PartCJournalofMechanicalProceedingsoftheInstitutionofMechanicalhttp//pic.sagepub.com/content/217/10/1117TheonlineversionofthisarticlecanbefoundatDOI10.1243/09544060332251713511172003217ProceedingsoftheInstitutionofMechanicalEngineers,PartCJournalofMechanicalEngineeringScienceLIWuCalculatingconjugatecamprofilesbyvectorequationsPublishedbyhttp//www.sagepublications.comOnbehalfofInstitutionofMechanicalEngineerscanbefoundatEngineeringScienceProceedingsoftheInstitutionofMechanicalEngineers,PartCJournalofMechanicalAdditionalservicesandinformationforhttp//pic.sagepub.com/cgi/alertsEmailAlertshttp//pic.sagepub.com/subscriptionsSubscriptionshttp//www.sagepub.com/journalsReprints.navReprintshttp//www.sagepub.com/journalsPermissions.navPermissionshttp//pic.sagepub.com/content/217/10/1117.refs.htmlCitationsWhatisThisOct1,2003VersionofRecordatShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromCalculatingconjugatecamprobullet5lesbyvectorequationsLIWuDepartmentofPowerMechanicalEngineering,NationalTsingHuaUniversity,Hsinchu30013,TaiwanAbstractThispaperpresentsananalyticalapproachfordeterminingtheprobullet5lesofconjugatedisccams.Foraconjugatecammechanism,itstwonormallinesthroughthepointsofcontactandthelineofcentresmustalwaysintersectatacommonpoint,whichisaninstantcentre.Onthisbasis,thecontactpointsbetweentheconjugatecamandthefollowercanbedeterminedaccordingtothelocationsofinstantcentresandfollowerposition.Thecamprobullet5les,thepathsofthecutterandthepressureanglescanthenbeexpressedintheformofparametricvectorequations.Forvarioustypesofconjugatecams,theequationsforsuchexpressionsareformulated,andexamplesareprovidedtoillustratetheapproach.Theprocedureisespeciallysimpletoprogram.Keywordsconjugatecamprobullet5le,instantcentre,vectorNOTATIONAcontactpointBcontactpointCrollercentreddistancebetweentherollercentres,breadthofthebullet6atfacedfollowerDrollercentreefolloweroffsetEpointfdistancefromthecamcentretothefollowerpivotpointGcuttercentreHcuttercentreI12,I13,I23instantcentresiunitvectorjunitvectorlarmlengthofthefollowerLdistanceofthefollowercentrefromthecamcentremeasuredparalleltotherollertranslationˆLy†O2bullet5xedpivotofthecamO3bullet5xedpivotoftheoscillatingfollowerqdistancefromthecamcentretotheinstantcentreI23QlocationoftheinstantcentreI23rbbasecircleradiusrccutterradiusrfradiusoftherollerfollowerSfollowermotionprogramˆSy†ttimeVQspeedofpointQX,YCartesiancoordinatesystembullet5xedonthecamaA,aBanglesZsubtendingangleofthefollowerarmsycamrotationanglexAangulardisplacementfunctionofthefollowerˆxAy†fA,fBpressureangleso2angularvelocityofthecam1INTRODUCTIONInacammechanism,thefollowermustalwaysbeheldincontactwiththecamthroughoutthemotioncycle,andthisisusuallyaccomplishedbyapositivedriveorareturnspring.Anormalconjugatecammechanismcaneliminatethereturnspringforceandthusresultinlowercontactstresses,whencomparedwiththespringloadedtype.Thisimportantadvantagemakesitespeciallysuitableforhighspeedapplications.Toperformsafelyandreliablyitsintendedfunction,however,theconjugatecamsmustbeproperlydesignedandaccuratelymanufactured.Therefore,thecamprobullet5lesandthepathsofthecuttercentreshouldbedeterminedanalytically.HansonandChurchill1,employingthetheoryofenvelopes,presentedananalyticalmethodforcomputingdisc–camprobullet5lecoordinates.Althoughthetheoryofenvelopesisnotalwaystaughtinthecollegecourseofcalculus,thismethodhasbeenwidelyadopted.Ontheotherhand,Davidson2suggestedanothermethodTheMSwasreceivedon9September2002andwasacceptedafterrevisionforpublicationon4August2003.1117C11702IMechE2003Proc.InstnMech.EngrsVol.217PartCJ.MechanicalEngineeringScienceatShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromusinginstantcentres,buthiscontributionseemstohaveattractedlittleattentionfromkinematicians.Asamatteroffact,theanalyticalmethodusingtheinstantcentreapproachcanprovideaconvenientmeansfordeterminingthedisc–camprobullet5leandcuttercoordinates.Inaddition,itisapplicabletonotonlythecommonspringloadedtypebutalsotheconjugatecammechanism.2CONJUGATECAMSWITHANOFFSETTRANSLATINGROLLERFOLLOWERFigure1showsaconjugatecammechanismwithanoffsettranslatingrollerfollower.TherearetwocamsAandB,bullet5xedonacommonshaft.TwofollowerrollersCandD,mountedtoacommonfollower,areeachpushedinoppositedirectionsbytheconjugatecams.SettingupaCartesiancoordinatesystemX,Ybullet5xedonthecamandwithitsoriginatthebullet5xedpivotO2,thecamprobullet5lecoordinatesmaybeexpressedintermsofthecamrotationangley,whichismeasuredagainstthedirectionofcamrotationfromthereferenceradialtocamcentrelineparalleltorollertranslation.Aconjugatecammechanismmaybeconsideredasapermanentcriticalformandmustalwayshavethreevelocityinstantcentres3.AsshowninFig.1,thismeansthatthetwonormallinesthroughthepointsofcontactandthelineofcentresmustalwaysintersectatacommonpoint,theinstantcentreI23,whereIdenotestheinstantcentreandsubscriptsindicatetherelatedlinks.Forsimplicity,inthefollowing,thegroundlinkwillbeconsistentlynumberedas1,thecamas2andthefolloweras3.Forthesakeofclarity,twootherinstantcentresI12andI13arealsolocatedandlabelledinthebullet5gure.BylabellinginstantcentreI23asQandO2Qˆq,thespeedofpointQonthecamcanbeexpressedasVQˆqo21†whereo2istheangularvelocityofthecam.Inordertoletyhaveacounterclockwiseangle,inthispaper,thecamistorotateclockwise.Ontheotherhand,foratranslatingfollower,allpointsonthefollowerhavethesamevelocity.Therefore,thespeedofpointQonthefollowercanbeexpressedasVQˆdLy†dtˆdLy†dydydtˆdLy†dyo22†whereLy†isthedisplacementfunctionofthefollowerLy†ˆbullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3rb‡rf†2¡e2q‡Sy†3†whererbisthebasecircleradiusofcamA,rfistheradiusoftherollerfollower,eistheoffsetandSy†isthefollowermotionprogram.Sincethecamistorotateclockwise,thequantityeisnegativeiftheoffsetistotherightinthepositionshownitispositive.Bydebullet5nitionoftheinstantcentre,instantcentreI23pointQisapointcommontolinks2conjugatecamand3followerhavingthesamevelocity.Therefore,fromequations1and2,qˆdLy†dyˆdSy†dy4†Asaresult,afterrb,rf,eandSy†havebeenselected,foreachspecibullet5edvalueofy,therollercentreCmaybelocatedbyapplicationofequation3andpointQbyapplicationofequation4.Thepressureangleistheanglebetweenthecommonnormalatthecontactpointandthedirectionofmotionofthefollower4.ForcamA,itistheanglebetweenlinesCQandCE.From4CQE,thepressureanglefAofcamAcanbeexpressedasfAˆtan¡1q¡eLy†ˆtan¡11Ly†dSy†dy¡eµ¶c187¼5†Therefore,theparametricequationsfortheprobullet5leFig.1ConjugatedisccamswithanoffsettranslatingrollerfollowerLIWU1118Proc.InstnMech.EngrsVol.217PartCJ.MechanicalEngineeringScienceC11702IMechE2003atShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromcoordinatesofcamAareO2AˆO2E‡EC‡CA6†whereO2Eˆecosy‡90¯†i‡esiny‡90¯†j7†ECˆLy†cosyi‡Ly†sinyj8†CAˆrfcosy‡180¯¡fA†i‡rfsiny‡180¯¡fA†j9†Inthesamemanner,afterthedistancebetweenrollercentresdhasbeenselected,theotherrollercentreDmaybelocated.From4DQE,thepressureanglefBofcamBcanbeexpressedasfBˆtan¡1q¡ed¡Ly†ˆtan¡11d¡Ly†dSy†dy¡eµ¶c187¼10†Similarly,theparametricequationsfortheprobullet5lecoordinatesofcamBareO2BˆO2E‡ED‡DB11†whereEDˆd¡Ly†‰Šcosy‡180¯†i‡d¡Ly†‰Šsiny‡180¯†j12†DBˆrfcosy‡fB†i‡rfsiny‡fB†j13†Inpractice,thecutterorgrindingwheelisfrequentlychosenlargerthanthefollowerrollerforreasonablegrindingwearlife5.ThelocationsofthecuttercentresforcuttingcamsAandBarealsoshowninFig.1.Becausethecutterandrollercentresmustlieonacommonnormaltothecamprobullet5le5,normallyoutwardextendingthecamprobullet5lebyalengthofcutterradiusrcobtainsthelocationofthecuttercentre.Inotherwords,forcamA,thecuttercentreGandpointsQ,AandCmustalwayslieonaline.Therefore,theparametricequationsforthecoordinatesofthecuttercentreGareO2GˆO2E‡EC‡CG14†whereCGˆrc¡rf†cosy¡fA†i‡rc¡rf†siny¡fA†j15†ThelocationofthecuttercentreHforcuttingcamBcanalsobelocatedinthesamewayO2HˆO2E‡ED‡DH16†whereDHˆrc¡rf†cosy‡180¯‡fB†i‡rc¡rf†siny‡180¯‡fB†j17†Infact,theconjugatecamprobullet5lesofFig.1havebeendrawn,byapplyingtheseequations,tomeetthefollowingrequirements.Thefolloweristorise20mmwithcycloidalmotionwhilethecamrotatesclockwisefrom08to1008,dwellforthenext508,returnwithcycloidalmotionfor1008camrotationanddwellfortheremaining1108.Bothfollowerrollershavethesameradiusof10mm.Theoffseteis12mmandthedistancebetweentherollercentres,d,is113mm.ThebasecircleradiusofcamAis40mm.3CONJUGATECAMSWITHATRANSLATINGFLATFACEDFOLLOWERFigure2showsaconjugatecammechanismwithatranslatingbullet6atfacedfollower.SettingupaCartesiancoordinatesystemX,Ybullet5xedonthecamandwithitsFig.2Conjugatedisccamswithatranslatingbullet6atfacedfollowerCALCULATINGCONJUGATECAMPROFILESBYVECTOREQUATIONS1119C11702IMechE2003Proc.InstnMech.EngrsVol.217PartCJ.MechanicalEngineeringScienceatShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfrom

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