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Simulation

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Simulation

    Simulation

476J.Mater.Sci.Techno1.,Vo1.17No.4,2001

    ;SimulationofMultipleColdRollsProgressiveForming

    ;forNon-symmetricalChannelSection

    ;ZhiwuHAN,

    ;ResearchInstitute

    ;CaiLIU

    ;ResearchInstitute

    ;WeipingLU

    ;forAgriculturalMachineryEngineering,JilinUniversity,Changchun130025,China

    ;ofRoilingMill,YanshanUniversity,Qinhuangdao066004,China ;ChangchunColdRolledFormingSectionSteelGeneralWorks,Changchun130042,China

    ;LuquanREN

    ;InstituteofAgriculturalMachineryEngineering,JilinUniversity,Changchun130025,China

    ;ManuscriptreceivedFebruary24,2000,inrevisedformApril13,20001 ;1.Introduction

    ;lncoldr0lJf0rmjngprocess,thesheetisprogressivelyformedintoaverycomp

lexthreedimen-

    ;sionaIsurface.ThedesignprocedurefortherolIformedproducts,f0rmingrolls,androlIpass

    ;sequenceswasconsideredmoreanartthanascience.GoodrolIpassdesignwasthekeyto

    ;SuccessfuIrolIforming.Inordertoreduceformingdefectsandtrialproductioncost,computer

    ;simulationofcoldroIlfl0rmingwasemployed.BasedontheUpdatedLagra

    ngemethodinthe

    ;def0rmationmechanics.atheoreticaImodeIofelastic-plasticlargedef0rmationsplinefinitestrip

    ;methodisproposedinthispaper.Themethodisemployedtoanalyzetheprogressiveform?

    ;ingprocessofnonsymmetricaIsection.andthedisplacement,thestressandthestrainalong

    ;rollingdirectionduringthemultiplecoldrollsformingprocessaregot.Thisprogramwrittenin

    ;CLanguagecanbeusedtoanalyzeothersimplecrosssectionaIprofilesalso. ;Coldrollformingisusedmoreandmoreuniver

    ;sally.Awiderangeofproductsfrommedicalequil>-

    ;menttoofficefurnitureismanufacturedthroughcold

    ;rollforming.Sincethedeformationprocessiscom-

;plex,coldrollforming,toalargeextent,hasbeende

    ;velopedonanempiricalbasisandfromexperimental ;knowledge[11.Inordertoleadtobetterrolldesignand ;eliminatesomeofthecommondefectslikeedgewave, ;twist,longitudinalcurvature.itisnecessarytostudy ;thegeometricalandthemechanicalcharacteristicsof ;thestripdeformationbetweentherollscarefully. ;ThereareseveralCADprogram8availableonthe ;marketforthedesignofrollformedproducts,form- ;ingrollsandrollpasssequences.However,thesepro- ;graresarebasedonrathersimplmedformulasoram- ;piricalrules[2j.Kiuchiandhiscoworkersemployed ;asinusoidal”shapefunction’’todescribethemiddle

    ;sheetsurfacebetweentherollstands[3j.

    ;Brunetused

    ;aPlanestrainfiniteelementanalysisforsheetbend

    ;inginrolls,andconsideredKiuchitheorytoanalyze ;longitudinalstrainst4j.

    ;McClureusedABAQUSpro-

    ;gramtoanalyzerollformingofaUchannelsteel[5I.

    ;PantonandDuncanstudiedthedeformationprocess ;andformingpathincoldrollforming[6j.

    ;Thispaperhasextendedfil1itestripmethodin ;structuralanalysis,andintroducedtheUpdated- ;tTowhomcorrespondenceshouldbeaddressed ;E-mail:hanzhiwu~public.cc.j1.cn

    ;LagrangemethodfU.L.method1offinitedeformation ;theoryofmechanicsofsohdstoit.Anelastic-plastic ;largedeformationsplinefinitestripanalysismodelof ;coldrollformingprocessisestablishedtoanalyzethe ;displacement,thestrainandthestressinformationof ;nonsymmetricalsectionformingprocessff1. ;2.TheoreticalBasisandAnalyticalModel

    ;2.IBsplinefinitestripdiscretizationandana/ytica/ ;modelestablishment

    ;Inthispaper,theseriesofrollsinprogressively ;formingprocessaredividedintoseveralstages.The ;deformedsheetmetalbetweentwostandsisconsid- ;eredasonestage.Theresearchobiectisthesheet ;metalinonestage.Theprogramwillsimulatethe ;formingprocessonestagebyonestage.Figure1is ;Bspline6l1itestripdiscretizationmode1. ;Inthistheoreticalmodel,whenthestripmovesout ;ofrollingmill,thefrictionisneglected.Considering

    ;thefixedfunctionofNo.+1upperrollandlowerrol1. ;thisendofstripisconsideredasaclampedend,and ;theotherendisconsideredasafreeend.Duringthe ;rollformingprocess,thestripdeformationbetween ;upperandlowerrollsisconsideredastheresultof ;theupperrollpressingthestriptothelowerroll[S1. ;Ineverystage,thestripdeformationisdividedinto ;Mdisplacementincrements.Thedeformationinroll ;formingdoasnottakeplaceoverthewholepassage, ;soineverydisplacementincrementofthedeformed ;strip,acontactiterationmethodisadoptedtodeter- ;minethecontactarea.

    ;

    ;J.Mater.Sci.Techno1.,Vo1.17No.4,2001

    ;Z

    ;mo

    ;Fig.1B-splinefinitestripdiscretization ;X

    ;Insimulationoftherollforming.whenthede. ;formedstripmovesoutofNo.i.1rollingmill,thestrip ;afterspringbackisconsideredastheinitialanalyti

    ;calconfiguration.Thestressstateofthestripatthis

    ;timeisconsideredastheinitialstressstateforstrip ;deformationanalysisofnextstand.Theinformation ;ofthestripmovingoutofNo.i1rollrnmisconsidered

    ;astheinitialinformationforNo.irollingmil1.Thus, ;thewholeformingprocessisanalyzedcontinuously, ;andthedataofeverystandissaved.

    ;2.2Equilibriumequationandsolving

    ;IntheU.L.metho~,theconfigurationatthetime ;tisconsideredasreferenceconfiguration.Thevirtual ;workequationatthetimet+Atisshownas:

    ;=面两+A(1)

    ;whereVandAtarethezoneofobjectconfiguration ;andtheboundaryofouterforceatthetimet,respec

    ;tively.andaretheloadvectorofbodyloadand ;thesurfaceloadreferencetotimet,respectively.Eis ;Greenstrainatthetimet+At,SisKirchhoffstress ;atthetimet+At,isvirtualdisplacement.

    ;entheconstitutiverelationissubstitutedinto ;equilibriumequation,thestripelementstiffnessma- ;tr.?isgiveby:

    ;gl.=g01.+【】.+g,l.(2)

    ;wherej1.iselasticplasticstiffnessmatrixofsmall

    ;displacement,[Ky1.isinitialstressstiffnessmatrix, ;and[.iselasticplasticstiffnessmatrixoflargedis

    ;placement.

    ;Equation(2)isanonlinearequationforrollform- ;ingprocess,includinggeometricalandmaterialnon

    ;linearity.Duringthesolvingofequilibriumequation, ;thelineartreatmentoftheequilibriumequationmust ;becarriedon,e.g.ignoringthelargedisplacement ;stiffnessmatrix1..Atthesametime,theload

    ;non-equilibriumtermiterationiscarriedon,andin ;everyiteration,[j.,[.and{R)aremodifiedac

    ;cordingtotheiterationresultoftheprevioustime. ;f}istheinitialstressnodalloadcolumnmatrix. ;Figure2showsthesimulationflowchart.

    ;477

    ;lGeometryandmaterialparaetersinputf

    ;l

    ;?

    ;Stripdiscretization.andnodallinecoordinatesformingI ;

    ;IIncremental1oadadding.

    ;?

;fStriploadcohmnmatrixformingi

    ;l

    ;Stripdisplacementfunction.stiffnessmatrixforming1

    ;Coordinatestransfor~ation.totalstiffness ;matrixandtotalloadco1omnmatrixforming ;Equi1bri?equation1ineartreatment

    ;Il

    ;?

    ;u…D…:.….:i

    ;Loadcolumnandstiffness~atrix

    ;modification

    ;Nonequi1ibri?term

    ;calculation

    ;l

    ;

    ;Coordir~tesmodification

    ;Fig.2Simulationflowchart

    ;3.CalculationExampleandResultsAnalysis ;Fornon-symmetricalsection,thetheoretical ;modelaboveisemployedtosimulateitsformingpro- ;cess.ThecalculationconditionsareshowninTa

    ;ble1.Figure3showsthecrosssectionofthenon-

    ;symmetricalproduct.Figures4and5showthe ;three-dimensionaldistributionoflongitudinalmem- ;branestrainafterthefirstpassageandthedistribu- ;tionsoflongitudinalmembranestrainalongthetotal ;deformationzone.respectively.isthedistancealong ;platewidthdirection.Figure6showsthetotalspace ;surfaceofnon-symmetricalsectionforming. ;Forthedistributionoflongitudinalmembrane ;strain,thepeaklongitudinalstretchmembranestrain ;isontheedgepartintheflangeofthedeformedstrip. ;Thereislittlestrainonthewebofthedeformedstrip. ;Thepeaklongitudihalstretchmembranestrainonthe ;longerflangepartislargerthanthatontheshorter ;flangepart.Thatisduetothenon-symmetricalchar

    ;acterofthedeformedstrip,whichisidenticaltothe ;phenomenaobservedinthepractice.

    ;一一

    ;

    ;478J.Mater.Sci.Techno1.,Vo1.17No.4,2001 ;Table1Calculationconditions

    ;N’———’o—....

    ;.....

    ;as/MPaH/GPaE/GPa ;210.00.3

    ;b/mm

    ;150.0

    ;t/mm

    ;2.5

    ;Standdistance

    ;L/mm

    ;5300.00300.0

    ;L/

    ;Fig.3Crosssectionofnon-symmetricalproduct(unit

    ;

    ;m

    ;m)

    ;Three.dimensional ;distributiononthe ;O.2O

    ;longitudinalmembranestrain

    ;firstpass

    ;Dish?}ccalongroUtr~~on,g/mm

    ;Fig.5Longitudinalmembranestraindistributionalong

    ;totaldeformationzone

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