ScienceinChinaSeriesE:TechnologicalSciences2007ScienceinChinaPressSpringer-VerlagStudyofutilizingdifferentialgeartraintoachievehybridmechanismofmechanicalpressHEYuPeng1,ZHAOShengDun2,ZOUJun2&ZHANGZhiYuan21SchoolofMechanicalEngineering,NanjingUniversityofScience&Technology,Nanjing210094,China；2SchoolofMechanicalEngineering,XianJiaotongUniversity,Xian710049,ChinaTheproblemsofhybridinputofmechanicalpressarestudiedinthispaper,withdifferentialgeartrainastransmissionmechanism.Itisproposedthat“adjustable-speedamplitude”or“differential-speedratio”istheimportantparametersforthehybridinputmechanism.Itnotonlydefinestheamplitudeoftheadjustablespeed,butalsodeterminestheratioofthepoweroftheservomotortothepoweroftheconventionalmotor.Thecalculatingequationsoftheratiooftransmissioninallaxes,thepoweroftwomotors,andtheworkingloaddistributionarededuced.Thetwokindsofdrivingschemesareputforwardthattheservomotorandtheconventionalmotorsimultaneouslydriveandtheservomotorandtheconventionalmotorseparatelydrive.Thecalculatingresultsdemonstratethatthelatterschemecanusemuchlowerpoweroftheservomotor,sothisschememakesmanufactureandusecostmuchlower.Thelatterschemeproposesafeasiblewaytoapplythehybridmechanismofmechanicalpressinpracticeengineering.mechanicalpress,hybridmechanism,differentialgeartrain,adjustable-speed1IntroductionAtpresenttherearemanyresearchpapersaboutthehybridmechanismofmechanicalpress,andithasbecomeahotresearchtopic.Thehybridmechanismisamechanismwith2-degree-offreedom(alsocalleddifferentialspeedmechanism),andwhentwoindependentmotionsareinputatthesametime,theoutputthatcansatisfysomemotionrequirementsisobtainedthroughthemotioncompositionofthemechanism.Thehybridmechanismisalsocalledcontrollablemechanism,orhybridmachine.Thepurposeofresearchonhybridmechanismofmechanicalpressisusingconventionalmotorwithbigpowercarryingflywheeltofinishstampingworkpieces；andusesservomotorwithlowpowertoadjustthesliderspeed.Theadvantagesofthehybridmechanismappliedinthemechanicalpressarethatitnotonlycanreducemuchlowermanufacturingcostthanservopress,butalsohasaflexibleworkingvelocityofslider1.Sothemechanicalpressofhybridmechanismarousesmanyresearchersinterestinworkingonit；andthesestudiesaremainlyfocusedonthemulti-barhybridmechanism.DuandGuo1,2havecomprehensivelydiscussedtheseven-barhybridmechanismofmechanicalpress,includingthefeasibleconditionsofcompositionofthelinkagemechanism,theslidermotionanalysis,andthetorqueandpowerdistributionbetweenthetwomotorsaswellastheoptimaldesign.Thetrajectoryplanningbasedonpolynomialinterpolationisalsoinvestigated,andthecomputersimulationshowsthattheresultisindeedattractive.Inaddition,Meng3hasalsoinvestigatedthekinematicalanalysisoftheseven-barmechanism,andtheoptimaldesignhasbeencompletedbasedontheminimumpoweroftheservomotormotor,andMenghasproposedthatthehybridmechanismisaresearchdirectionofthemechanicalpress.Tokuz4firstputforwardofthehybridmechanismandanalyzedthevelocitysynthesisbyusingthedifferentialgeartrain.Hisexperimentconfirmedthefeasibilityofhisconception.Theconceptsoftheadjustable-speedamplitudeanddifferential-speedratioarenotmentionedintheirworks,andtherelationshipbetweenthevelocityvariationandthepowerofthetwomotorswerenotclearlygiven58.Buttheseconceptsareveryimportantandabsolutelynecessaryforthehybridmechanismtoselectthetwomotorspoweranddeterminetheworkingloaddistributionbetweenconventionalmotorandtheservomotor.Inrefs.13theyusedlinkagemechanismtoimplementthehybridinputofmechanicalpress.Themethodisverycomplexbecausethechangeofthelengthandpositionoftheeachbarinlinkagemechanismwillhaveaneffectonthemotionoftheslideofthemechanicalpress.Sosomeprincipalproblemsareusuallyignoredinresearchhybridmechanismcourse,andtheresearchresultsdonnotalwayscoincidewiththepracticeengineeringconditions911.Thegeardifferentialtrainhastwofreedoms,andtheratiosoftransmissionbetweenarbitrarytwoaxesareaconstant.Inordertosimplifythemechanicalmodelandmaketheproblemsmuchprojected,thedifferentialgeartrainisusedastransmissionmechanismtostudythehybridproblemsofthemechanicalpressinthispaper.Thispaperaddressestherelationshipbetweentheadjustable-speedamplitudeandthepowerofthetwomotors,theworkingloaddistributionbetweenthetwomotors,andputsforwardtwodriveschemesoftheconventionalmotorandtheservomotorsimultaneouslyworking,andtwomotorsseparatelyworking.Withthe200-tonmechanicalpressastheengineeringbackground,adrivesystemofthehybridmechanismofthemechanicalpressisdesigned,andthefeasibilityofthetwodriveschemesinmechanicalpressisanalyzed.2TheprincipleofthehybridmechanismTheworkingprincipleofthehybridmechanismofthemechanicalpresswithdifferentialgeartrainisillustratedinFigure1.Thesystemconsistsofconventionalmotor(alsocalledACmachinewithconstantspeed),servomotor,reducingunitI,reducingunitII,differentialgeartrain,andcrankslidemechanism.Theoutputaxisofthedifferentialgeartrainisconnectedwiththecrankshaftofthecrankslidemechanism.Oneofthetwoinputaxeslinkstheconventionalmotorthroughthereducingunit；theotherinputaxislinkstheservomotorthroughthereducingunitII.Thereforethemotionofthecrankshaftiscompletelycontrolledbythemotionsoftheconventionalmotorandtheservomotor.ThereducingunitandthereducingunitIIarerespectivelyinstalledbetweenthetwomotorsandthedifferentialgearunitinthewayofserialinordertobearapartofreducingvelocitytaskofthealltransmissionsystem,becausetoobigdriveratioofthedifferentialgeartrainwillmakeitsdrivingefficiencydecreased.Theangularvelocityoftheconventionalmotorisconstant,soitspriceischeaper.Theangularvelocityoftheservomotorisadjustable,soitspriceisexpensive.Inthesystemofthehybridmechanismtheconstantspeedoftheoutputaxisisprovidedbyhighpowerconventionalmotor；andtheservomotorprovidesitsadjustablespeed.Therefore,inthisway,itnotonlymakestheoutputmotionofthecrankshaftofthemechanicalpressflexible,butalsoavoidsusinghighpowerservomotor.Henceitcouldsaveboththemachinemanufacturingcostsandthemachineoperatingcosts.Figure1Workingprincipleofhybridmechanismofdifferentialgeartrain.3ThevelocitycharacteristicsofthemechanicalpressslideTheworkofthemechanicalpresspresentstheregularityoftheperiodicchange12.ThedisplacementandvelocitychangesofthemechanicalpressslideinanidealworkcirculationareillustratedintheFigure2.Theslidestartstomovefromtopdeadcentertotheworkingstartpointathighvelocity(calledquickfeedingstage).Whentheslideofmechanicalpressapproachestheworkingpoint,itshighvelocityisshiftedtoslowvelocityandthenitbeginstostampworkpieceatlowvelocity(calledlowworkingstage).Thelowvelocityoftheslideistoavoidgreatimpactonthedie,andbenefittheplasticshapingoftheworkpiece.Aftertheslidefinishesthestampingworkandreachesthebottomdeadcenter,theslidecomesbackathighvelocityandstopsatthetopdeadcenter(calledquickbackstage).Hence,themotionvelocityofthemechanicalpressslidecanbedividedthreekinds:highdownvelocityV1,slowworkingvelocityV2,andhighbackvelocityV3.ThevelocityV1andvelocityV3shouldbeaspossibleashighandthevelocityV2shouldbeslowandflexibleinordertoensurehighworkingtimesofthemechanicalpressperminuteandsatisfytherequirementsofdifferenttechnologies.Actuallythemechanicalpressonlyworksinaveryshortcoursebeforethebottomdeadcenter,andintheothercoursesitdoesnotdoworktotheworkpiece.4Thenomenclaturesandequationsofthehybridmechanism4.1TherelationshipoftheangularvelocityinallaxesTherearethreeexternalaxesinthedifferentialgeartrainasillustratedinFigure1.Inordertoconvenientlyexpresstherelationshipofthethreeaxes,theaxisconnectedwiththeconventionalmotoriscalledaxis1,theaxisconnectedwithservomotoriscalledaxis2,andtheaxisconnectedwithcrankshaftiscalledaxis0.Theangularvelocitiesofthethreeaxesarerespectivelyexpressedasn1,n2andn0.ThetorquesofthethreeaxesarerespectivelyexpressedasM1,M2andM0.Becausetherearetwofreedomsinthedifferentialgeartrain,onlythethirdaxisisfixed,suchthatthedriveratiooftheothertwoaxescanbedetermined.Sotherelationshipsofdriveratioandangularvelocityofthethreeaxesneedtobeexpressedasthecharacterwithsuperscriptandsubscript.Figure2Idealdisplacementcureoftheslide.4.1.1Theconventionalmotorsinfluenceontheoutputmotion.Whentheservomotorstops,n2=0,onlytheangularvelocityoftheconventionalmotoraffectstheoutputangularvelocitynTheservomotorsinfluenceontheoutputmotion.Whentheconventionalmotorstops,n1=0,onlytheangularvelocityoftheservomotoraffectstheoutputangularvelocityn0,where1n0representsaxis0angularvelocity,and1i20representstotaldriveratiofromaxis2toaxis0includingdifferentialgeartrainandreducingunitIIwhenaxis1(servomotoraxis)isfixed.4.1.3Theconventionalmotorsandservomotorsinfluenceontheoutputmotion.Whentheconventionalmotorandtheservomotorrunatthesametimethroughthecompositionofthedifferentialgeartrain,theoutputvelocitycanbeexpressedas.Becausetheservomotorcanrunatarbitraryangularvelocitybetweenthezeroandspecificvelocityinbothpositiveandnegativedirections,n2canbeexpressedas.whereKistheratiooftheactualangularvelocitytothespecificangula