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外文翻译--凸轮形状设计的混合方法和一般的盘形凸轮轮廓加工的机制 英文版.pdf

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外文翻译--凸轮形状设计的混合方法和一般的盘形凸轮轮廓加工的机制 英文版.pdf

INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3,pp.419427JUNE2010/419DOI10.1007/s12541010004861.IntroductionPlatecammechanismisawidelyusedmachinecomponentwiththecontinuouscontactmotionofcamandfollower,andcaneasilyproduceanyfunctionalmotionoffollowerduetotherotationofcam.Cammechanismhasthediversetypesbythecombinationofdifferentshapeofcamandmotionoffollowerplateorcylindricalcam,rollerorflatfacedfollower,andreciprocatingoroscillatingmotion.Inspiteoftheadvantagesofafewnumberoflinks,simplestructure,positivemotion,andcompactsize,cammechanismsrequiretheaccurateshapedesignandprecisemachiningproceduresforsatisfyingthemechanicalrequirements.Underthelowleveleddesignandmanufacturing,cammechanismsgivetheheavyeffectsonvibration,noise,separation,andoverloadingtoanoverallsystem.Toavoidtheseeffects,cammechanismmustbewelldesignedaccuratelyandmachinedprecisely.Actually,ahybridCAD/CAMapproachmaybethebestsolutionthattheshapedatafromthedesignprocessaredirectlycombinedtothemachiningdataforthemanufacturingprocess.Lineinterpolationandcircularinterpolationarecommonlyusedinconstructionofthemachiningdatafromtheprofiledataofcam.LineinterpolationhasthelowaccuracyandcircularinterpolationcannotkeeptheaccuracybecauseofthedisconnectiveradiiofcurvaturesorthediscontinuousslopesattheconnectedpointbytwocirculararcsaspresentedinShinetal..13Recently,parametericinterpolationusingBsplineandNURBScurvearesuggestedinJungetal.5andYangetal..6Alsobiarcinterpolationiswidelyusedanddeeplydependentonthedirectionangletowardcentersofbiarccurves.Bolton7describedabiarccurvebasedonthetangentialanglesattwopoints,ParkinsonandMoreton8madeabiarccurvebasedonaquadraticequationatthreepoints,MeekandWalton9usedsplinetypesforconstuctionofbiarccurve.Schonherr10introducedanapproachtominimizetheradiiofbiarccurves.Commonlytheseinterpolationmethodsmakethemachiningpointsincreasingandthentheexcessivedataformachiningacurvedshapemakethemachiningerrorsincreased.Thus,theprecisemachiningprocessrequiresminimizationofthemachiningpointstokeeptheaccuracyunderagivenmachiningtolerance.Thispaperintroduces3stepsofahybridCAD/CAMAHybridApproachforCamShapeDesignandProfileMachiningofGeneralPlateCamMechanismsJoongHoShin1,SoonManKwon1andHyoungchulNam1,1DepartmentofMechanicalDesignManufacturing,ChangwonNationalUniversity,9,Sarimdong,Changwon,Kyungnam,SouthKorea,641773CorrespondingAuthor/Emailnhchulchangwon.ac.kr,TEL82552671106,FAX82552671106KEYWORDSPlatecammechanism,Cam,Follower,Shapedesign,Profilemachining,Contactpoint,NCdata,Instantvelocitycenter,BiarccurvefittingPlatecammechanismcaneasilyproducethepositiveandfunctionalmotionsincontactofcamandfollower.Generallycammechanismisusedinmanyfieldsofmechanicalcontrol,automation,andindustrialmachinery.Toobtaintheaccuratemotionoffollower,theprofileofcammustbedesignedandmachinedprecisely.Thispaperproposesaninstantvelocitycentermethodfortheprofiledesignandabiarcfittingmethodfortheprofilemachiningto4differenttypesofplatecammechanismswithreciprocatingoroscillatingmotionandrollerorflatfacedfollowers.Thekeyofthispaperistheintroductionofahybridsystemcombinedthedesignproceduresandthemanufacturingprocedures.Themainideaisthattheminimummachiningdataarebuiltbytheaccuratebiarccurvesfitteddirectlyfromthedesignparameters.Theradialdirectionanglestowardbiarccentersfortheaccuratebiarccurvefittingcanbedefineddirectlybythecontactangleofcamandfollowergiveninthedesignprocedures.AnapplicationoftheproposedapproachisverifiedtheaccurateprofilesofadesignedcamandamachiningcamusingtheminimumNCdatawithinagivenmachiningtolerance.ManuscriptreceivedJuly16,2009/AcceptedFebruary18,2010©KSPEandSpringer2010420/JUNE2010INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3approach11for4differenttypesofplatecammechanisms.Firstly,theshapeofcamisdeterminedbythekinematicconstraintsatinstantvelocitycentersandthecontactangleatthecontactpointbetweencamandfollower.Thesecondstepistotransformthecontactanglesintothecenterdirectionanglesandthentocalculatetheradiiofbiarccurve.Finally,themachiningdataareminimizedthroughexpandingorcontractingthebiarcsectionwhetherthecamprofilepointsarelocatedinsideoroutsidetherangeofagivenmachiningtolerance.2.ClarificationofAccuracyonBiarcFitting13Onlytheprofiledataofcamshapearedefinedincommondesignprocessofaplatecam.Then,themachiningdatamustbedevelopedbyanycurvefittingforNCNumericalcontrolprocess.Thecircularfitting,whichismostwidelyusedinmachining,hasunreliabilityasshowninFig.1.Acircledevelopedbythreepoints1,P2,P3Phasaradius1Randtheotherbypoints2,P3,P4Phas2.RIntheviewsofcircularfittingtwocirclespasstheprofilepoints1,P2,P3,P4,Pbutthediscontinuousslopesaremadeatthesepointsandalsothedisconnectiveradiiatpointsinmidspan.Thesedefectsmakethefittedcurveinlowaccuracyandthenhighervibrationinhighspeedoperationofcammechanism.P4P3P2P1O2O1R1R2S1S2∆SSlope1Slope2Fig.1Defectsoncircularfittingθ32θ31R4R2P4P3O4O3S3S2R3S1P2O2O1P1R1θ21θ11θ22θ12Fig.2ContinuousfittingbybiarcFig.2showsacontinuouscurvefittedbybiarcs,whichpassestheprofilepoints1,P2,P3,P4.PThebiarccurvehas4radiiinthiscase.Radius1Rpasses1Pto1,S2Rfor1Sto2.S3Rfor2Sto3,Sand4Rfor3Sto4.PTheslopesofthebiarccurvearecontinuousanduniqueateverypoint.Alsomidpoints1,S2,S3Sarecontinuouswithoutjumpinradii.Thus,thebiarccurvecankeepthehigherlevelofaccuracy.AsshowninFig.2,biarcfittingishighlydependentonradialdirectionangles.θThecommondesignprocessofcammechanismdefinesonlytheprofiledataandthenmachiningprocessmustusetheanglesfromthecircularfitting.Thisprocessgivestheloweraccuracybecauseoftheincorrectangles.Buttheproposedapproachinthispapercandefinethecorrectangles,whicharegivendirectlybydesignprocessofcamprofile,andthenkeepthehigheraccuracyforthemachiningdata.3.ShapeDesignofPlateCam3.1DisplacementcharacteristicsofcammechanismForaplatecammechanismwithreciprocatingrollerfollowershowninFig.3,thekinematicpropertiesoffollowermotioncanbedefinedaslineardisplacement,Yfirstderivative,Y′andsecondderivativeY′′totherotationalanglecθofcam.Andthepropertiesaregivenasangulardisplacementincaseofoscillatingfollower.Theinstantvelocitycentermethodgiveninthispaperusesthedisplacementsandthe1stderivativesfordeterminingthecamshape.CamFollowerContactpointcoordinateCamshapecoordinateθcCRSyxFig.3Platecammechanismwithreciprocatingrollerfollower3.2Shapedesignbasedoninstantvelocitycenters4AsshowninFig.4,PointQisdefinedbyalinethroughcontactpointCfromrollercenterandahorizontallineandthenitbecomesinstantvelocitycenter.ThevelocityatpointQisproportionaltoarotatingspeedofcamasinEq.1andthevelocityofrolleratpointRisdefinedinEq.2asthelinearvelocityoffollower.cQQdVLdtθ1cRcdYdYdVdtddtθθ2INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3JUNE2010/421Bythekinematiccharacteristicsofcammechanism,thevelocityattheinstantvelocitycenter,QVissameasthevelocityoffollower.RVThus,thevelocityconditiongivesthelocationoftheinstantvelocitycenterinEq.3.QcdYLYdθ′3ψQRRx,RyLQVQVRθcRrYxyCCx,CyFig.4ContactpositionofcamandfollowerThecontactangleshowninFig.4isdefinedinEq.4byaanglebetweenaslidingvelocitylineandanormallineatacontactpointoffollowerroller.ThecoordinatesofthecontactpointaregiveninEq.5wherethecoordinatesofarollercenter,xRyRcanbecalculatedfromthedisplacementYandthegeometricconditionsprimecircleandeccentricityofagivencammechanism,andwhererRistheradiusofroller.Finally,thecontactpointxCandyCisgiveninEq.51tanQxyLRRψ−−4sinsinxxryyrCRRCRRψψ−5QLQVQVfθcYxCCx,CyFFx,FyFig.5PlatecamwithreciprocatingflatfacedfollowerFig.5showsacammechanismwithreciprocatingflatfacedfollower.InstantvelocitycenterQislocatedonthehorizontallineanddefinedinEq.6basedonthevelocityconditionsatinstantvelocitycenters.Then,thecontactpointisdefinedinEq.7QcdYLdθ6xQyyCLCF7ForamechanismwithoscillatingrollerfollowerasinFig.6,thedistanceofinstantvelocitycenterfromcamcenterbecomesinEq.8.ThecontactanglebetweencamandrollerisexpressedinEq.9andthenthecontactpointisdefinedinEq.10.Here,Zxyisthedistancetoapivotfromcamcenter.1fxycQfcdZdLddθθθθ81tanQxyLRRψ−−9sinsinxxryyrCRRCRRψψ−10ψθfQLQVQVRRZLZxyθcRRx,RyxyCCx,CyRrFig.6PlatecamwithoscillatingrollerfollowerInacaseofcammechanismwithoscillatingflatfacedfollowerasshowninFig.7,thelocationofinstantvelocitycenterisformulatedasinEq.11andthecontactpointisgiveninEq.121fxycQfcdZdLddθθθθ112coscossinxxyxyQfyxyQffCZZLCZLθθθ−−−12422/JUNE2010INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3θfQLQVQVfVfZLZxyθcxyCCx,CyFFx,FyFig.7PlatecamwithoscillatingflatfacedfollowerFinally,theprofileofcamshapecanbedeterminedbytransformingthecontactpointwiththereverseangleofcamrotationasinEq.13,wherexSandySarethecoordinatesofcamprofile.cossinsincosxxcycyxcycSCCSCCθθθθ−133.3InternalnormalangleatcontactpointThenormallineateachcontactpointisshowninFigs.47for4differentcasesoftheplatecammechanisms.InthispaperaninternalnormalangleδisdefinedasananglebetweenlinesconnectedtocamcenterandtoinstantvelocitycenterfromcontactpointasshowninFig.8.Becausetoolcentersformachiningandbiarccentersforcurvefittingarelocatedonthenormaldirectionlinethroughcontactpoint,theinternalnormalanglemustbetransferredtothemachiningdataprocessinordertoguaranteethepreciseshapeofcam.ThepositionanglecδofcontactpointshowninFig.8iseasilydefinedasinEq.14.AlsothenormallineanglefδatcontactpointforcammechanismwithrollerfollowerinFig.8aandFig.8cissameasinEq.15.ThenormallineanglesaredefinedinEq.16forreciprocatingflatfacedfollowerFig.8bandinEq.17foroscillatingflatfacedfollowerFig.8d,respectively.1tanycxCCδ−141tanyyfxxRCRCδ−−−1590ffaceslopeangleδ±°161tan90yyfxxCZCZδ−−±°−17Finally,theinternalnormalangleatcontactpointoncamprofilecanbeexpressedinEq.18forplatecammechanismsasshowninFig.8.fcδδδ−18CamFollowerδfδcδRollercoordinateContactpointcoordinateCRyxairplaneaReciprocatingrollerfollowerCamFollowerδcδδffaceslopeangleContactpointcoordinateCyxQbReciprocatingflatfacedfollowerCamFollowerδfδcδRollercoordinateContactpointcoordinateCRyxQcOscillatingrollerfollowerCamFollowerδfδcδContactpointcoordinatePivotcoordinateCZx,ZyyxQdOscillatingflatfacedfollowerFig.8Internalnormalanglesofplatecammechanism

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