附錄外文文獻(xiàn)AMODULARMODELINGAPPROACHFORTHEDESIGNOFRECONFIGURABLEMACHINETOOLSTulgaErsalGraduateStudentResearchAssistantDepartmentofMechanicalEngineeringUniversityofMichigan,AnnAJeffreyL.SteinProfessorDepartmentofMechanicalEngineeringUniversityofMichigan,AnnALoucasS.LoucaLecturerDepartmentofMechanicalandManufacturingEngineeringUniversityofCypruslsloucaucy.ac.cyABSTRACTAnewgenerationofmachinetoolscalledReconfigurableMachineTools(RMTs)isemergingasameansforindustrytobemorecompetitiveinamarketthatexperiencesfrequentchangesindemand.Newmethodologiesandtoolsarenecessaryfortheefficientdesignofthesemachinetools.ItisthepurposeofthispapertopresentamodularapproachforRMTservoaxismodeling,whichispartofalargerefforttodevelopanintegratedRMTdesignandcontrolenvironment.Thecomponentsofthemachinetoolaremodeledinamodularway,suchthatthemodelofanygivenconfigurationcanbeobtainedbyassemblingthecorrespondingcomponentmodelstogetherbasedonthetopologyofthemachine.Thecomponentmodelsarebuiltusingthebondgraphlanguagethatenablesthestraightforwarddevelopmentoftherequiredmodularlibrary.Thesemachinetoolmodelscanbeusedfortheevaluation,designandcontroloftheRMTservoaxes.Theapproachisdemonstratedthroughexamples,andthebenefitsanddrawbacksofthisapproacharediscussed.TheresultsshowthattheproposedapproachisapromisingsteptowardsanautomatedandintegratedRMTdesignenvironment,andthechallengesinordertocompletethisgoalarediscussed.INTRODUCTIONTheever-growingcompetitionforcesmanufacturerstorespondmorequicklytochangesindemand.Asaresult,manufacturershavetodealwithshortproductlifecycles,shortramp-uptimesandfrequentchangesinproductmixandvolumes,withoutcompromisingproductqualityandcost.Beingtheheartofamanufacturingsystem,improvedmachinetoolsholdthekeyinmeetingtheabovementionedrequirements.Theshortcomingsofconventionalmachinetools,whichcanbeclassifiedasdedicatedandflexible,arebeingfeltmoretodaythaninthepast:Withtheirdesignfocusbeingasinglepart,dedicatedmachineslacktheflexibilityandscalabilitythattheflexiblemachinesoffer.Ontheotherhand,flexiblemachinescannotachievetherobustness,thecost-effectivenessandthethroughputlevelsofdedicatedmachines1.AnewgenerationofmachinetoolsisbeingdevelopedintheEngineeringResearchCenterforReconfigurableManufacturingSystemsattheUniversityofMichigan,AnnArbor,aspartofanefforttoovercometheinsufficienciesofcurrentmanufacturingsystems.ThesemachinetoolsarecalledReconfigurableMachineTools(RMTs)2,andtheycombinetheadvantagesoftheirdedicatedandflexiblecounterparts.Theyaredesignedaroundapartfamilyandtheirstructure,intermsofbothhardwareandsoftware,canbechangedquicklyandcost-effectivelytoachievetheexactfunctionalityandcapacitydesired3.Containingseveralconfigurationstoprovidetheneededflexibilityandscalability,RMTsintrinsicallyleadtomorecomplexmachinetooldesignproblems.MethodologiesandtoolsthatwouldhelpfacilitatethedesignofRMTscouldhighlybenefitandencouragetheemploymentofreconfigurablemanufacturingsystems4-6.OneimportantaspectoftheRMTdesignproblemisdevelopingdynamicmodelsforthedesign,evaluationandcontrolofservoaxes.WhatmakestheproblemofmodelingRMTsuniqueisthateventhoughthereisasinglemachinetool,thereexistseveralconfigurations,whichseparatemodelshavetobedevelopedfor.Developingdynamicmodelsforallpossibleconfigurationscouldbeacumbersomeandtime-consumingtaskifadhocmethodsareutilized.Moreover,withoutasystematicmethodologymodelingwouldrequirealotofexpertiseandwouldbepronetoerrors,whichwoulddegradetheefficiencyofusingmodelsinthedesign.InthispaperwepresentamethodologythatcouldhelpmaketheRMTmodelingtasklesstimedemanding,lesserror-proneandlesschallenging.ThekeyideaofthismethodologyistotakeadvantageofthemodularstructureoftheRMTsandadoptmodularmodelingconceptsintotheRMTmodelingmethodology.First,thephysicalcomponentsofanRMTaremodeledinamodularwayusingthebondgraphmodelingtool7.Thebondgraphmodelisencapsulatedinaschematicrepresentationwithdefinedconnectionports.Then,theschematiccomponentmodelsareassembledbyfollowingthetopologyofagivenconfigurationtoobtainthemodeloftheconfiguration.Theconfigurationmodelcanbeeasilyintegratedwiththemodulesofnon-energeticcomponentssuchasinterpolatorsandcontrollers,whichcanbeconvenientlyrepresentedwithblockdiagrams；howeverthisisbeyondthescopeofthispaper.BACKGROUNDTheRMTconceptwasintroducedbyKorenandKota2,andsincetheirintroduction,thedesignofRMTshasbeenanactiveresearcharea.MethodologiesandtoolsfordesigningRMTs4aswellasevaluatingstructuralstiffnesses5andtooltiperrors6ofdesignalternativeshavebeendeveloped.However,theproblemofdevelopingasystemlevelmodelingmethodologyforRTMshasnotbeenaddressedyet.Traditionally,machinetoolmodelsdepictthemachinetoolasagroupofservomotorandfeeddriveassembliesthataremodeledasfirstorsecondordersystems8,9.ChenandTlusty,however,showedthatthestructuraldynamicsofthefeeddrivecouldaffectthesystemperformanceoncehigh-speedmachinetoolsareconsidered10.Manyresearchersidentifiedthenecessitytousehigherordermodelsforhigh-speedmachinetoolstocopewithstructuraldynamicsinordertobeabletodesignthecontrolsystemsuccessfully11-13.Thesepublicationsclearlyindicatethatmodelingamachinetoolisnotatrivialtaskandcaremustbetakenwhendecidingonthecomplexityofthemodel,buttheydonotprovideasystematicwayofmodelingand,therefore,remainapplicationspecificapproaches.Therehavebeenresearcheffortstohelpthedesignandcontrolofmachinetoolfeeddrivesbyautomaticallyprovidingsimulationmodels.WilsonandSteindevelopedasoftwareprogramcalledModel-BuildingAssistanttoautomaticallysynthesizeaminimumordermodelofthemachinetooldrivesystemforagivenfrequencyrangeofinterest(FROI)14.Thecomplexityofthemodel,whichincludesaflywheel,atorsionalshaft,aballscrew,aballnut,aDCmotor,atorsionalcoupling,abelt-driveandagear-pairascomponents,isautomaticallyincreaseduntiltheeigenvaluesofthesystemfallbeyondthespecifiedFROI.Thisworkwasaproofofconceptforamodeldeductionalgorithmandcannotbeappliedtoanyrealmachinetoolsystem.However,suchalgorithmcanbeusedtodeterminetheappropriatemodelcomplexityafterthedevelopmentofthesystemmodel.Gautieretal.havedevelopedasoftwarepackagecalledSICOMAT(SimulationandControlanalysisofMachineTools)whichhelpswiththemodeling,simulation,modalanalysisandcontrollertuningofoneortwodecoupledortwocoupledmachinetoolaxes15.Theirmodelsdescribethedynamicsofthemechanicalsystembyanumberofmassesandsprings.Thisworkmakesthemodelingofamachinetoolprocessmoresystematic,andisthereforeavaluabletooltothemodelingengineer；however,itlacksthegenerality,modularityandflexibilitythattheRMTdesignmethodologydemands.TheRMTmodelingmethodologyFigure1showstheenvisionedRMTmodelingenvironment.ItisdesiredtoautomatethetaskofRMTmodeling,wherethemodelofagivenRMTconfigurationisautomaticallyassembledfromalibraryofmodularcomponentmodels.Thisway,allthecandidatedesigns,whicharegeneratedeithermanuallyorautomatically4,canbemodeledquicklyandthemodelscanbeusedtoevaluatethecandidatesintermsoftheirservoaxisdynamicperformanceandhelpwiththeirdesign.AsFigure1alsoimplies,themodularcomponentmodellibraryisakeypartfortheautomatedRMTmodelingenvironment.Therefore,thefirststepoftheproposedmethodologyistodevelopmodularmodelsforthecomponentsthatareusedtogeneratetheRMTconfigurations.Thispaperputstheemphasisonmechanicalpartsanddiscussestheirmodelinginamodularway,becausetheenergyinteractionbetweenthemechanicalcomponentsmakestheirmodularmodelingmoreintriguing.Modularmodelingofcomponentsthatonlyexchangesignals,erpolatorsandcontrollers,presentsarelativelysimplerproblemandarenotdiscussedhere.Topromotemodularityandtobeabletodealwiththeenergyinteractionsbetweenthecomponentsandtheirenvironmentrathereasily,bondgraphsareutilizedasthemodelinglanguage.Bondgraphsprovideapower-basedgraphicalrepresentationofaphysicalsystem.Moreover,bondgraphsdescribedifferentenergydomainsinaunifiedway,whichisarelevantadvantageforRMTmodeling,sincetheirservoaxesmayincludecomponentsfromdifferentenergydomains,suchasmechanical,electricalorhydraulic.Bondgraphsareonlyonelevelinthehierarchyofmodelrepresentationsusedinthiswork.Underneaththebondgraphlevelthemathematicalequationsrepresentthephysicalphenomenacapturedbythebondgraphandthismathematicalrepresentationisthelowestlevelinthehierarchy.Inthehighestlevelbondgraphsareencapsulatedinaschematicrepresentation,whichnotonlyallowsforacompactrepresentation,butalsoshowstheconnectionportswherethemodelcaninteractwithitsenvironment.Figure2illustratesthishierarchyofmodelrepresentations.Inthispaperallthemodelsareshownintheschematiclevel,becausethegoalofthispaperisnottodiscusstheirderivation,butrathertoshowwhatcanbedoneoncethosemodelsareobtained.Adetaileddescriptionofthemodelsusedinthispapercanbefoundin16.Inordertobeabletocopewithanyspatialmotionthatthemechanicalcomponentsmaygothroughindifferentconfigurations,modelsthatcapturethethree-dimensionaldynamicsareused.Moreover,theinitialassumptionismadethatinthemechanicaldomainallcomponentscanbeadequatelyrepresentedasrigidbodies.Figure3showstheschematicrepresentationofagenericrigidbodywithNconnectionports,whichisoneofthemainmodelmodulesinthelibrary.Theportscorrespondtopointsofinterestontherigidbody,wherethephysicalinteractionswiththeenvironmentoccur.Bonds(lineswithhalfarrows)areusedtoindicatethataportisapowerport,i.e.thebodycanexchangeenergywithitsenvironmentthroughthoseports,whereasactivebonds(lineswithfullarrows)indicatesignalports,i.e.onlyinformationistransferredthroughtheseports.Themodellibraryalsocontainsthree-dimensionaljointmodelsthatcanbeusedtodescribetherelativemotionsbetweenthecomponentmodels.Thesejointmodelsarealsodevelopedinamodularwaywithport