神经网络和有限元对冷轧的三维模拟

IntJAdvManufTechnol(2002)20:799–806OwnershipandCopyright2002Springer-VerlagLondonLimitedPredictionofRollingForceandDeformationinThree-DimensionalColdRollingbyUsingtheFinite-ElementMethodandaNeuralNetworkJ.C.LinDepartmentofMechanicalDesignEngineering,NationalHuweiInstituteofTechnology,Yulin,TaiwanInthisstudyofa3Drollingprocess,anincrementalupdatedLagrangianelasto-plasticfinite-elementmethodandaneuralnetworkhavebeenintegratedtopredicttherollingforceandthemaximumsurfaceerrorduringtherollingprocess.Aseriesof27setsoftoolsofdifferentgeometrywereusedforsimul-ationoftherollingprocess,withdifferentvariationsofdieradius,rollingratio,andmatchingforthedifferentthicknessesoftheproducts.Theresultsoftherollingforceandofthedeformationofthesurfacearetheninputtoaneuralnetworktoestablishamodelfortherollingvariables.Theresultsofrollingpro-cessingbythisdevelopedabductivenetworkcanbeaccuratelypredicted,oncetherollingcontrolparametersaregiven.Thisworkachievedasatisfactoryresultbasedonademonstrationofthesimulation,provingthatthisisanewandfeasibleapproachwhichcanbeusedforcontroloftherollingprocessformaterials.Keywords:Abductivenetwork;Finiteelement;Roll1.IntroductionTomaintaininternationalcompetitivenessarollmustbeabletoproduceproductscosteffectively.Customersinthesheetmetalindustryrequiregoodprecisionofthestripdimensionsandgooduniformityofthemechanicalproperties,andmostmajorsteel-makingcompanieshavedevelopedcommercialsoftware,oruse3Dfinite-elementsoftware,forstudyingandoptimisingtherollingprocessparameters.Themostdifficultpartinmodellingforceandwarpageinrollingistoestablishawell-definedmathematicalmodeloftherollingprocessthatincorporatesallthecomplexrelationshipsbetweendifferentfactorsandtheoperatingconditionsofthemachine.AnumberofmodelshavebeendevelopedduringCorrespondenceandoffprintrequeststo:ProfessorJ.C.Lin,Depart-mentofMechanicalDesignEngineering,NationalHuweiInstituteofTechnology,Yunlin632,Taiwan.E-mail:[e-mail]1943,Orowan[1]discardedtheassumptionofconstantyieldstressduringtherollingpassandpermittedthedirectuseofanexperimentallydeterminedstress–straincurve.Heusedadifficultgraphic-solution–numericalmethodofcompu-tationinordertodeterminetherollpressuredistribution.Intermsofelastic–plasticstudies,McmeekingandRice[2]developedfinite-elementanalysisofelastic–plasticmaterialsin1975,basedonlargedeformation–largestraintheory.VenterandAbd-Rabbo[3]developedacomprehensive,self-containedcomputerisedsolutionforbothhotandcoldrollingproblemswithinhomogeneityofdeformationembeddedinthemodel.Freshwater[4]simplifiedtheequationforrollforce,rolltorque,androllpressure,withoutsacrificingaccuracy,byeliminatingthederivativeoftheyieldstresscurve.In1984,ChandraandMukerjee[5]notonlyconsideredthematerialsandnonlineargeometry,butalsoconsideredviscoplasticmetaldeformationwithstrainrateintheirfinite-elementmodel.Mostmajorsteel-makingcompanieshavedeveloped3Dfinite-elementsoftware,orusecommercialsoftware,forstudy-ingandoptimisinghot-rollingorcold-rollingoperations.Threedimensionsarenecessaryinrollingsimulation,sincemostindustrialproblemsinvolve3Daspects.MoriandOsakada[6]usedtherigid–plasticfinite–elementmethodtosimulatenon-steadystaterollingwitha3D-concaverollerundertheassump-tionofrigidrollers.Rolldeformation,arisingfromcontactstressandrolltemperaturedistribution,isamajoriteminstriprolling.Itisclearthatthestressesneartheedgesareinfluencedstronglybymaterialspreadsothatrollformationmodelsshouldtakeintoaccountthe3Dflowinthisarea[7].Anothersteady-statemetalrollinganalyticalapproachisthecombinationelementmethoddevelopedbyXiong[8].Thismethodcombinestheslabmethodandrigid–plasticfinite–elementmethodtostudy3Dshaperolling,tuberolling,draw-ing,andsqueezing.Intheirstudy,therollerwasassumedtobearigidbody.LinandLee[9],usedthelargedeformation–largestraintheory,theupdatedLagrangainformulation(ULF)andtheincrementalprincipletodevelopa3Delastic–plasticanalyticalmodelofaluminiumstriprolling.Theyproposedan800J.C.Liniterationproceduretocalculatethecontactforcebetweenthestripandworkroll,andthecontactdeformationoftheworkroll.Optimalschedulesshouldresultinmaximisedthroughputandminimisedoperatingcosts.WangandTieu[10]usedageneticalgorithm-basedoptimisationprocedurefortheschedul-ingoftandemcoldrolling.Larkioaetal.[11]usedphysicalmodelsandaneuralnetworktheorywhichwereintegratedinaprogrampackageinordertopredicttherollingforceincoldrolling.ThisstudyusesFEMsoftwareandaneuralnetworktoselecttheoptimalparametersforrolling,inordertominimisethestressandforcesintherollingprocess,andusesthefiniteelementstosimulatedifferentrollingprocessesundervariousparameters(differentrolldiameter,differentrollingrate,anddifferentmaterialthickness).Itusesanabductivenetworktoestablishtherelationshipofasmoothstraightrollingforceandarollparametersmodel.Basedontheabductivemodellingtechnique,itisabletorepresentthecomplicatedanduncertainrelationshipsbetweentheinputandoutputvariables.Oncetheabductivenetworkhasconstructedtherelationshipsofinputandoutputroll