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www.88doc88.comwww.88doc88.comScienceinChinaSeriesETechnologicalSciences©2007ScienceinChinaPressSpringerVerlagStudyofutilizingdifferentialgeartraintoachievehybridmechanismofmechanicalpressHEYuPeng1†,ZHAOShengDun2,ZOUJun2ZHANGZhiYuan21SchoolofMechanicalEngineering,NanjingUniversityofScienceTechnology,Nanjing210094,China2SchoolofMechanicalEngineering,XianJiaotongUniversity,Xian710049,ChinaTheproblemsofhybridinputofmechanicalpressarestudiedinthispaper,withdifferentialgeartrainastransmissionmechanism.Itisproposedthatadjustablespeedamplitudeordifferentialspeedratioistheimportantparametersforthehybridinputmechanism.Itnotonlydefinestheamplitudeoftheadjustablespeed,butalsodeterminestheratioofthepoweroftheservomotortothepoweroftheconventionalmotor.Thecalculatingequationsoftheratiooftransmissioninallaxes,thepoweroftwomotors,andtheworkingloaddistributionarededuced.Thetwokindsofdrivingschemesareputforwardthattheservomotorandtheconventionalmotorsimultaneouslydriveandtheservomotorandtheconventionalmotorseparatelydrive.Thecalculatingresultsdemonstratethatthelatterschemecanusemuchlowerpoweroftheservomotor,sothisschememakesmanufactureandusecostmuchlower.Thelatterschemeproposesafeasiblewaytoapplythehybridmechanismofmechanicalpressinpracticeengineering.mechanicalpress,hybridmechanism,differentialgeartrain,adjustablespeed1IntroductionAtpresenttherearemanyresearchpapersaboutthehybridmechanismofmechanicalpress,andithasbecomeahotresearchtopic.Thehybridmechanismisamechanismwith2degreeoffreedomalsocalleddifferentialspeedmechanism,andwhentwoindependentmotionsareinputatthesametime,theoutputthatcansatisfysomemotionrequirementsisobtainedthroughthemotioncompositionofthemechanism.Thehybridmechanismisalsocalledcontrollablemechanism,orhybridmachine.Thepurposeofresearchonhybridmechanismofmechanicalpressisusingconventionalmotorwithbigpowercarryingflywheeltofinishstampingworkpiecesandusesservomotorwithlowpowertoadjustthesliderspeed.Theadvantagesofthehybridmechanismappliedinthemechanicalpressarethatitnotonlycanreducemuchlowermanufacturingcostthanservopress,butalsohasaflexibleworkingvelocityofslider1.Sothemechanicalpressofhybridmechanismarousesmanyresearchersinterestinworkingonitandthesestudiesaremainlyfocusedonthemultibarhybridmechanism.DuandGuo1,2havecomprehensivelydiscussedthesevenbarhybridmechanismofmechanicalpress,includingthefeasibleconditionsofcompositionofthelinkagemechanism,theslidermotionanalysis,andthetorqueandpowerdistributionbetweenthetwomotorsaswellastheoptimaldesign.Thetrajectoryplanningbasedwww.88doc88.comwww.88doc88.comonpolynomialinterpolationisalsoinvestigated,andthecomputersimulationshowsthattheresultisindeedattractive.Inaddition,Meng3hasalsoinvestigatedthekinematicalanalysisofthesevenbarmechanism,andtheoptimaldesignhasbeencompletedbasedontheminimumpoweroftheservomotormotor,andMenghasproposedthatthehybridmechanismisaresearchdirectionofthemechanicalpress.Tokuz4firstputforwardofthehybridmechanismandanalyzedthevelocitysynthesisbyusingthedifferentialgeartrain.Hisexperimentconfirmedthefeasibilityofhisconception.Theconceptsoftheadjustablespeedamplitudeanddifferentialspeedratioarenotmentionedintheirworks,andtherelationshipbetweenthevelocityvariationandthepowerofthetwomotorswerenotclearlygiven58.Buttheseconceptsareveryimportantandabsolutelynecessaryforthehybridmechanismtoselectthetwomotorspoweranddeterminetheworkingloaddistributionbetweenconventionalmotorandtheservomotor.Inrefs.13theyusedlinkagemechanismtoimplementthehybridinputofmechanicalpress.Themethodisverycomplexbecausethechangeofthelengthandpositionoftheeachbarinlinkagemechanismwillhaveaneffectonthemotionoftheslideofthemechanicalpress.Sosomeprincipalproblemsareusuallyignoredinresearchhybridmechanismcourse,andtheresearchresultsdonnotalwayscoincidewiththepracticeengineeringconditions911.Thegeardifferentialtrainhastwofreedoms,andtheratiosoftransmissionbetweenarbitrarytwoaxesareaconstant.Inordertosimplifythemechanicalmodelandmaketheproblemsmuchprojected,thedifferentialgeartrainisusedastransmissionmechanismtostudythehybridproblemsofthemechanicalpressinthispaper.Thispaperaddressestherelationshipbetweentheadjustablespeedamplitudeandthepowerofthetwomotors,theworkingloaddistributionbetweenthetwomotors,andputsforwardtwodriveschemesoftheconventionalmotorandtheservomotorsimultaneouslyworking,andtwomotorsseparatelyworking.Withthe200tonmechanicalpressastheengineeringbackground,adrivesystemofthehybridmechanismofthemechanicalpressisdesigned,andthefeasibilityofthetwodriveschemesinmechanicalpressisanalyzed.2TheprincipleofthehybridmechanismTheworkingprincipleofthehybridmechanismofthemechanicalpresswithdifferentialgeartrainisillustratedinFigure1.ThesystemconsistsofconventionalmotoralsocalledACmachinewithconstantspeed,servomotor,reducingunitI,reducingunitII,differentialgeartrain,andcrankslidemechanism.Theoutputaxisofthedifferentialgeartrainisconnectedwiththecrankshaftofthecrankslidemechanism.OneofthetwoinputaxeslinkstheconventionalmotorthroughthereducingunitІtheotherinputaxislinkstheservomotorthroughthereducingunitII.Thereforethemotionofthecrankshaftiscompletelycontrolledbythemotionsoftheconventionalmotorandtheservomotor.ThereducingunitІandthereducingunitIIarerespectivelyinstalledbetweenthetwomotorsandthedifferentialgearunitinthewayofserialinordertobearapartofreducingvelocitytaskofthealltransmissionsystem,becausetoobigdriveratioofthedifferentialgeartrainwillmakeitsdrivingefficiencydecreased.Theangularvelocityoftheconventionalmotorisconstant,soitspriceischeaper.Theangularvelocityoftheservomotorisadjustable,soitspriceisexpensive.Inthesystemofthehybridmechanismtheconstantspeedoftheoutputaxisisprovidedbyhighpowerconventionalmotorandtheservomotorprovidesitsadjustablespeed.Therefore,inthisway,itnotonlymakestheoutputmotionofthecrankshaftofthemechanicalpressflexible,butalsoavoidsusinghighpowerservomotor.Henceitcouldsaveboththemachinemanufacturingcostsandthemachineoperatingcosts.www.88doc88.comwww.88doc88.comFigure1Workingprincipleofhybridmechanismofdifferentialgeartrain.3ThevelocitycharacteristicsofthemechanicalpressslideTheworkofthemechanicalpresspresentstheregularityoftheperiodicchange12.ThedisplacementandvelocitychangesofthemechanicalpressslideinanidealworkcirculationareillustratedintheFigure2.Theslidestartstomovefromtopdeadcentertotheworkingstartpointathighvelocitycalledquickfeedingstage.Whentheslideofmechanicalpressapproachestheworkingpoint,itshighvelocityisshiftedtoslowvelocityandthenitbeginstostampworkpieceatlowvelocitycalledlowworkingstage.Thelowvelocityoftheslideistoavoidgreatimpactonthedie,andbenefittheplasticshapingoftheworkpiece.Aftertheslidefinishesthestampingworkandreachesthebottomdeadcenter,theslidecomesbackathighvelocityandstopsatthetopdeadcentercalledquickbackstage.Hence,themotionvelocityofthemechanicalpressslidecanbedividedthreekindshighdownvelocityV1,slowworkingvelocityV2,andhighbackvelocityV3.ThevelocityV1andvelocityV3shouldbeaspossibleashighandthevelocityV2shouldbeslowandflexibleinordertoensurehighworkingtimesofthemechanicalpressperminuteandsatisfytherequirementsofdifferenttechnologies.Actuallythemechanicalpressonlyworksinaveryshortcoursebeforethebottomdeadcenter,andintheothercoursesitdoesnotdoworktotheworkpiece.4Thenomenclaturesandequationsofthehybridmechanism4.1TherelationshipoftheangularvelocityinallaxesTherearethreeexternalaxesinthedifferentialgeartrainasillustratedinFigure1.Inordertoconvenientlyexpresstherelationshipofthethreeaxes,theaxisconnectedwiththeconventionalmotoriscalledaxis1,theaxisconnectedwithservomotoriscalledaxis2,andtheaxisconnectedwithcrankshaftiscalledaxis0.Theangularvelocitiesofthethreeaxesarerespectivelyexpressedasn1,n2andn0.ThetorquesofthethreeaxesarerespectivelyexpressedasM1,M2andM0.Becausetherearetwofreedomsinthedifferentialgeartrain,onlythethirdaxisisfixed,suchthatthedriveratiooftheothertwoaxescanbedetermined.Sotherelationshipsofdriveratioandangularvelocityofthethreeaxesneedtobeexpressedasthecharacterwithsuperscriptandsubscript.www.88doc88.comwww.88doc88.comFigure2Idealdisplacementcureoftheslide.4.1.1Theconventionalmotorsinfluenceontheoutputmotion.Whentheservomotorstops,n20,onlytheangularvelocityoftheconventionalmotoraffectstheoutputangularvelocityn0.4.1.2Theservomotorsinfluenceontheoutputmotion.Whentheconventionalmotorstops,n10,onlytheangularvelocityoftheservomotoraffectstheoutputangularvelocityn0,where1n0representsaxis0angularvelocity,and1i20representstotaldriveratiofromaxis2toaxis0includingdifferentialgeartrainandreducingunitIIwhenaxis1servomotoraxisisfixed.4.1.3Theconventionalmotorsandservomotorsinfluenceontheoutputmotion.Whentheconventionalmotorandtheservomotorrunatthesametimethroughthecompositionofthedifferentialgeartrain,theoutputvelocitycanbeexpressedas.Becausetheservomotorcanrunatarbitraryangularvelocitybetweenthezeroandspecificvelocityinbothpositiveandnegativedirections,n2canbeexpressedas.whereKistheratiooftheactualangularvelocitytothespecificangularvelocityoftheservomotorthevalueisarbitrarybetween−1and1,includingzero.n2eisthespecificangularvelocityoftheservomotor.4.2Adjustablespeedamplitudeanddifferentialspeedratio4.2.1Adjustablespeedamplitude.Inordertocorrectlydenotethevariablevelocityofthedifferentialgeartrainofthehybridmechanism,theconceptofadjustablespeedamplitudeisintroduced.AsshowninFigure1,adjustablespeedamplitudeistheratioorpercentageofabsolutevalueofupanddownadjustableamounttothebasespeed.Inthedifferentialgeartrainofthehybridmechanism,theadjustablespeedamplitudeequalstheratiovalueofaxis0outputspeedofoperatingasingleservomotoratthespecificspeedtoaxis0outputspeedofoperatingasingleconventionalmotor13.Inthedifferentialgeartrainofthehybridmechanism,theadjustablespeedamplitudeisthemostbasicandthemostimportanttechnologyparameter.Itnotonlydeterminesthematchingrelationshipofthespeedofthetwoinputaxes,butalsodecidesthematchingrelationshipoftheinstalledcapacityoftheservomotorandtheconventionalmotorwww.88doc88.comwww.88doc88.com4.2.2Differentialspeedratio.Thedifferentialspeedratioisusuallyusedtoexpressadjustablespeedtechnologyperformanceinthedifferentialgeartrain.Itisanimportanttechnologyparameterofthedifferentialeffectinthedifferentialsystem.Thedifferentialspeedratioequalsthereciprocalvalueoftheadjustablespeedamplitude.ItcanbeexpressedasAccordingtothefactthattheangularvelocityisininverseproportiontoitstorqueandthatthesameloadisdrivenbyconventionalmotorandservomotor,anequationexpressedwiththepowersofthetwomotorscanbededuced,whereP1isthepoweroftheconventionalmotor,P1M1n1.P2isthepoweroftheservomotor,P2M2n2e.4.3TheworkingloadpowerdistributionSupposingthattheworkingloadpowerofthemechanicalpressisP0,thepowerrelationshipbetweentheconventionalmotor,theservomotorandworkingloadcanbeexpressedasbelowFigure3Physicalsenseoftheadjustablespeedamplitude.Fromeqs.911,theoutputpowersoftheconventionalmotorandtheservomotoraredeterminedbythevalueoffactorK,whichisactuallyequaltothechangeratioofangularvelocityoftheservomotor.Hencewhentheoutputangularvelocityrunsindifferentworkingregion,theratioofbearingloadofthetwomotorsisdifferent,too.4.3.1Theoutputaxisrunningatthebasicspeed.Whentheoutputangularvelocityoftheservomotorequalszero,thatis,K0,P20,fromeq.9,wehave.Heretheconventionalmotorbearsalltheloadingpower.4.3.2Theoutputaxisrunningintheincreasingspeedregion.Theservomotorrunsinthepositivedirection,0≤K≤1,andbothP1andP2arepositivevalues,soboththeconventionalmotorandtheservomotorbearapartoftheworkingload.Thustheconventionalmotorbears90.9100workingloadandtheservomotorbearsonly09.1workingload.Thevalueoftheadjustablespeedandthedifferentialspeedratiodeterminetheloaddistributionbetweenthetwomotors.4.3.3Theoutputaxisrunninginthedecreasingspeedregion.Inthedecreasingspeedregion,theservomotorrunsinnegativedirection,andtherangevalueofKis−1≤K≤0.Byeqs.9and10,theP1ispositive,andtheP2isnegative.Thenegativevalueoftheservomotorpowershowsthattheservomotorpowerisalreadytheworkingresistance.Hencewww.88doc88.comwww.88doc88.comtheconventionalmotorisnotonlydoingworktotheworkingload,butalsodoingworktotheservomotorpower,Whentheangularspeedisintheregion0n2e,theloadoftheconventionalmotorisThuswhentheoutputangularspeedisinthedecreasingregion,theconventionalmotorconsumesmoreenergythanintheotherregions.Thedecreaseoftheoutputspeedisatthepriceofconsumingtheservomotorinputpower.Inordertosaveenergy,theoutputangularspeedshouldavoidorreducerunninginthedecreasingregion.4.4ThetwodriveschemesofthehybridmechanismofthemechanicalpressAccordingtoeq.3,theoutputangularvelocityofthehybridmechanismisequaltothereducedvalueoftheirsumoftheangularvelocitiesofboththeconventionalmotorandtheservomotor.AsshowninFigure1,theoutputangularvelocityofthedifferentialgeartrainisconnectedwiththecrankaxisofthemechanicalpress,sothetwoaxeshavethesameangularvelocity.Wheneitheroftheconventionalmotorortheservomotorisdriven,orwhenbothofthemaredriven,thedifferentangularvelocityofthecrankshaftofthemechanicalpresscanbeobtained.Therefore,twokindsoftheschemesofthehybridmechanismofthemechanicalpressareproposeditheconventionalmotorandtheservomotoraresimultaneouslydrivenandiitheconventionalmotorandtheservomotorareseparatelydriven.4.4.1Theconventionalmotorandtheservomotorbeingsimultaneouslydriven.ThisschemeshowsthattheangularvelocityofthecrankshaftofthemechanicalpressiscomposedoftheangularvelocityoftheconventionalmotorasthebasicspeedandtheangularvelocityoftheservomotorastheadjustablespeedFigure3.Theangularvelocityandthepowerscanbecalculatedbyusingeqs.118.4.4.2Theconventionalmotorandtheservomotorbeingseparatelydriven.Thisschemeshowsthatonlyonemotorisdriveninthehybridinputcourseandatthesametimeanothermotorisbraked,i.e.whenthecrankshaftisindifferentialrunningstage,theconventionalmotorandtheservomotorareseparatelyoperatedthusthedifferentangularvelocityofthecrankshaftcanbeobtained.Theflexiblelowspeedoperation.Whentheconventionalmotorisbrakedandtheservomotorisoperated,n10,thebelowequationcanbeobtainedfromeq.5Because−1≤K≤1,theoutputangularvelocityofthecrankshaftisadjustableandthecrankshafthastworotatingdirectionsthereforeitisflexible.Abigvalueofthedriveratio1i20canbedesigned,soaverysmalloutputangularvelocity1n0canbeachieved.Henceinthiscoursetheoutputangularvelocityisflexibleandlow.Whentheservomotorisbrakedandtheconventionalmotorisoperated,n20,fromeq.5,wehave.Crankshafthastworotatingdirectionsthereforeitisflexible.www.88doc88.comwww.88doc88.comFigure4Physicalsenseofthecomparisonofthetwooutputangularspeed.Becausedriveratios2i10and1i20areindependentofeachother,andtheoperationandtheservomotoroperationoftheconventionalmotorsareindependentofeachothertoo,thevaluesofthetwodriveratioscanbeassignedaverydifferentvalueoneisverysmall,andtheotherisverybig,sothetwooutputangularvelocitiesmaydiffergreatly.Sodoingcansatisfythemotionrequirementsofthemechanicalpressslideindifferentstages.ThephysicalsenseofcomparisonofthetwooutputangularspeedisillustratedasinFigure4.5ConclusionAccordingtothevelocitycharacteristicsofthemechanicalpress,thedifferentialgeartrainisappliedinthehybridmechanismofthemechanicalpress.Throughtheaboveanalysisandcalculation,thefollowingconclusionscanbereached1Theadjustablespeedamplitudeanddifferentialspeedratioareimportantparametersofthehybridmechanism.Theyarenotonlytheratiooftheadjustablespeedtothebasicspeed,butalsotheratioofthepoweroftheservomotortothepoweroftheconventionalmotor.2Withtheschemeoftheconventionalmotorandtheservomotorbeingsimultaneouslydriven,thepowerofthetwomotorshastobeassignedhighvalueinordertosatisfythevelocityrequirementsofthemechanicalpress.Sodoingincreasesthemanufacturingcostandtheoperationcostofthemechanicalpress,andthereforeisvaluelessinpracticalapplication.3Withtheschemeoftheconventionalmotorandtheservomotorbeingseparatelydriven,thepoweroftheservomotorcanbeassignedlowvalueinordertosatisfythevelocityrequirementsofthemechanicalpress.Sodoingdecreasesthemanufacturingcostandtheoperationcostofthemechanicalpress.Therefore,thisschemeproposesafeasiblewayinpracticalindustrialengineering.
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