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附录ControlofaNonOrthogonalReconfigurableMachineToolReuvenKatzJohnYookYoramKorenReceivedJanuary3,2003revisedSeptember16,2003AbstractComputerizedcontrolsystemsformachinetoolsmustgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceaccuratelyapredeterminedpathofthecuttingtoolrelativetotheworkpiece.However,sincethedynamicpropertiesoftheindividualmachineaxesarenotexactlyequal,undesiredcontourerrorsaregenerated.Thecontourerrorisdefinedasthedistancebetweenthepredeterminedandactualpathofthecuttingtool.ThecrosscouplingcontrollerCCCstrategywasintroducedtoeffectivelydecreasethecontourerrorsinconventional,orthogonalmachinetools.Thispaper,however,dealswithanewclassofmachinesthathavenonorthogonalaxesofmotionandcalledreconfigurablemachinetoolsRMTs.ThesemachinesmaybeincludedinlargescalereconfigurablemachiningsystemsRMSs.Whentheaxesofthemachinearenonorthogonal,themovementbetweentheaxesistightlycoupledandtheimportanceofcoordinatedmovementamongtheaxesbecomesevengreater.InthecaseofanonorthogonalRMT,inadditiontothecontourerror,anothermachiningerrorcalledindeptherrorisalsogeneratedduetothenonorthogonalnatureofthemachine.Thefocusofthisstudyisontheconceptualdesignofanewtypeofcrosscouplingcontrollerforanonorthogonalmachinetoolthatdecreasesboththecontourandtheindepthmachiningerrors.Varioustypesofcrosscouplingcontrollers,symmetricandnonsymmetric,withandwithoutfeedforward,aresuggestedandstudied.Thestabilityofthecontrolsystemisinvestigated,andsimulationisusedtocomparethedifferenttypesofcontrollers.Weshowthatbyusingcrosscouplingcontrollersthereductionofmachiningerrorsaresignificantlyreducedincomparisonwiththeconventionaldecoupledcontroller.Furthermore,itisshownthatthenonsymmetriccrosscouplingfeedforwardNSCCFFcontrollerdemonstratesthebestresultsandistheleadingconceptfornonorthogonalmachinetools.©2004ASMEContributedbytheDynamicSystems,Measurement,andControlDivisionofTHEAMERICANSOCIETYOFMECHANICALENGINEERSforpublicationintheASMEJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROL.ManuscriptreceivedbytheASMEDynamicSystemsandControlDivisionJanuary3,2003finalrevisionSeptember16,2003.AssociateEditorJ.Tu.Keywordsmachinetool,crosscouplingcontroller,nonorthogonal,RMT1IntroductionCurrentlymanufacturingindustrieshavetwoprimarymethodsforproducingmediumandhighvolumemachinedpartsdedicatedmachiningsystemsDMSsandflexiblemanufacturingsystemsFMSsthatincludeCNCmachines.TheDMSisanidealsolutionwhenthepartdesignisfixedandmassproductionisrequiredtoreducecost.Ontheotherhand,theFMSisidealwhentherequiredquantitiesarenotsohighandmanymodificationsinthepartdesignareforeseen.Incontrasttothesetwoextremes,KorendescribesaninnovativeapproachofcustomizedmanufacturingcalledreconfigurablemanufacturingsystemsRMS.ThemainadvantageofthisnewapproachisthecustomizedflexibilityinthesystemtoproduceapartfamilywithlowerinvestmentcostthanFMS.AtypicalRMSincludesbothconventionalCNCmachinesandanewtypeofmachinecalledtheReconfigurableMachineTool.TheEngineeringResearchCenterERCforReconfigurableMachiningSystemsRMSattheUniversityofMichiganwithitsindustrialpartnershasdesignedanexperimentalReconfigurableMachineToolRMT。ThismachineallowsERCresearcherstovalidatemanyofthenewconceptsandmachinetooldesignmethodologiesthathavebeenalreadydevelopedinthecenter.TherearemanytypesofRMTs.ThispaperdescribesanarchtypenonorthogonalmultiaxisRMTmachine。TheeconomicjustificationofRMTsisgiveninsection2ofthispaper.Acontouringmotionrequiresthatthecuttingtoolmovesalongadesiredtrajectory.Typically,computerizedcontrolsystemsformachinetoolsgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceapredeterminedpathofthecuttingtoolrelativetotheworkpiece.Toreducethecontouringerror,whichisdefinedasthedistancebetweenthepredeterminedandtheactualpath,therehavebeentwomaincontrolstrategies.Thefirstapproachistousefeedforwardcontrolinordertoreduceaxialtrackingerrors.however,theyarelimitedwhennonlinearcutsarerequired.Theotherapproachistousecrosscouplingcontrolinwhichaxialfeedbackinformationissharedbetweenthemovingaxes.Thecrosscouplingcontrollerisusedinadditiontotheconventionalaxialservocontroller.Ateachsamplingtime,thecrosscouplingcontrollercalculatesthecurrentcontourerrorandgeneratesacommandthatmovesthetooltowardtheclosestpointonthedesiredtoolpath.ThiscontrolstrategyofthecrosscouplingcontrollerCCCeffectivelydecreasesthecontourerror.AdvancedcontrolmethodshavebeenappliedtofurtherimprovethecontrolpropertiesoftheoriginalcrosscouplingcontrollerCCC.AnoptimalCCCissuggestedin,toimprovethecontrollerperformancewhenhighcontouringspeedswererequired.Anothermethodtoovercomethesameproblemforhighercontourfeedratesisaddressedin,whichusesadaptivefeederatecontrolstrategytoimprovethecontrollerperformance.Thelatesttrendofcrosscouplingcontrollerimprovementistheapplicationoffuzzylogic.Allthesemethods,however,donotworkformachineswithnonorthogonalaxes.Surfacecute.g.,acircularcutintheXYplaneona3axisorthogonalmillingmachinerequiresamotionoftwoaxese.g.,XandY.However,surfacecutsinthenonorthogonalRMTrequiresimultaneousmotionofallthreeaxes.Therefore,inadditiontothecontourerror,thismotioncreatesanothererror,calledtheindeptherror,whichisintheZdirection.Thiserroraffectsthesurfacefinishqualityoftheworkpiece.Whilecontouring,thetooltipoftheRMThasnotonlytofollowthepredeterminedpath,butalsotocontrolcontinuouslythedepthofcut.Thesimultaneouscontrolofbotherrors,theconventionalcontourerrorandtheindeptherror,requiresanewcontrolstrategysincethestandardCCCalgorithmscannotbedirectlyapplied.Inotherwords,theRMTcontroldesignproblemrequiresanewcontrolapproachthatisabletocorrectsimultaneouslytwotypesofcuttingerrors.Thisproblemhasnotbeenaddressedintheliterature.Inthispaper,wedescribethreetypesofcontrollersaimedatreducingthecontourandindeptherrorsimultaneously.FirstweinvestigateasymmetricalcrosscouplingSCCcontroller,whichunfortunatelydoesnotshowgoodperformanceinreducingbotherrors.ThepoorperformanceisduetotheconflictingdemandsinreducingthetwoerrorsandthelackofinformationsharingbetweenthetwopairsofaxesXYandYZ,whichareresponsibleforerrorcompensation.Toovercomethisproblem,therequiredmotioninformationofonepairofaxesisfedforwardtotheother.Thisidearesultsintwonewcontrollertypes,symmetricalcrosscouplingfeedforwardSCCFFcontrollerandnonsymmetricalcrosscouplingfeedforwardNSCCFFcontroller.Finally,theinfluenceofthereconfigurableangularpositionofthecuttingtoolonsystemstabilityisinvestigated.2MachineCharacteristicsandtheControlProblemInthissectionweexplaintheeconomicadvantageoftheRMT,anddevelopthemathematicalrepresentationofthecontourerrorandtheindeptherror.aMachineCharacteristicsTypicalCNCmachinetoolsarebuiltasgeneralpurposemachines.Theparttobemachinedhastobeadaptedtoagivenmachinebyutilizingprocessplanningmethodologies.ThisdesignprocessmaycreateacapitalwasteSincetheCNCmachineisdesignedattheoutsettomachineanypartwithinagivenenvelope,itmustbebuiltwithgeneralflexibility,butnotallthisflexibilityisutilizedformachiningaspecificpart.TheconceptofRMTsreversesthisdesignorderThemachineisdesignedaroundaknownpartfamily.Thisdesignprocesscreatesalesscomplex,althoughlessflexiblemachine,butamachinethatcontainsallthefunctionalityandflexibilityneededtoproduceacertainpartfamily.TheRMTmaycontain,forexample,asmallernumberofaxes,whichreducescostandenhancesthemachinereliability.Therefore,inprinciple,aRMTwithcustomizedflexibilitywouldbelessexpensivethanacomparableCNCthathasgeneralflexibility.AconceptualexampleofaRMTdesignedtomachineapartwithinclinedsurfacesof45degisshowninFig.1.IfaconventionalCNCisusedtomachinethisinclinedsurface,a4or5axismachineisneeded.Inthisexample,however,onlythreeaxesareneededonanewtypeof3axisnonorthogonalmachinetool.Nevertheless,onemayarguethatitsnoteconomicaltobuildasproductnonorthogonalmachinetoolsfor45deg.Therefore,wedevelopeda3axisnonorthogonalmachineinwhichtheangleoftheZaxisisadjustableduringreconfigurationperiods,asshowninFig.2.Thesimpleadjustingmechanismisnotservocontrolledanddoesnothavetherequirementsofaregularmovingaxisofmotion.ThedesignedRMTmaybereconfiguredintosixangularpositionsofthespindleaxis,between–15and60degwithstepsof15deg.ThemainaxesofthemachineareXaxistabledrivehorizontalmotion,Yaxiscolumndriveverticalmotionand
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