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IntJAdvManufTechnol200219253–2592002SpringerVerlagLondonLimitedAnAnalysisofDrawWallWrinklinginaStampingDieDesignF.K.ChenandY.C.LiaoDepartmentofMechanicalEngineering,NationalTaiwanUniversity,Taipei,TaiwanWrinklingthatoccursinthestampingoftaperedsquarecupsandsteppedrectangularcupsisinvestigated.Acommoncharacteristicofthesetwotypesofwrinklingisthatthewrinklesarefoundatthedrawwallthatisrelativelyunsupported.Inthestampingofataperedsquarecup,theeffectofprocessparameters,suchasthediegapandblankholderforce,ontheoccurrenceofwrinklingisexaminedusingfiniteelementsimulations.Thesimulationresultsshowthatthelargerthediegap,themoresevereisthewrinkling,andsuchwrinklingcannotbesuppressedbyincreasingtheblankholderforce.Intheanalysisofwrinklingthatoccurredinthestampingofasteppedrectangularcup,anactualproductionpartthathasasimilartypeofgeometrywasexamined.Thewrinklesfoundatthedrawwallareattributedtotheunbalancedstretchingofthesheetmetalbetweenthepunchheadandthestepedge.Anoptimumdiedesignforthepurposeofeliminatingthewrinklesisdeterminedusingfiniteelementanalysis.Thegoodagreementbetweenthesimulationresultsandthoseobservedinthewrinklefreeproductionpartvalidatestheaccuracyofthefiniteelementanalysis,anddemonstratestheadvantageofusingfiniteelementanalysisforstampingdiedesign.KeywordsDrawwallwrinkleStampingdieSteppedrectangularcupTaperedsquarecups1.IntroductionWrinklingisoneofthemajordefectsthatoccurinthesheetmetalformingprocess.Forbothfunctionalandvisualreasons,wrinklesareusuallynotacceptableinafinishedpart.Therearethreetypesofwrinklewhichfrequentlyoccurinthesheetmetalformingprocessflangewrinkling,wallwrinkling,andelasticbucklingoftheundeformedareaowingtoresidualelasticcompressivestresses.Intheformingoperationofstampingacomplexshape,drawwallwrinklingmeanstheoccurrenceCorrespondenceandoffprintrequeststoProfessorF.K.Chen,DepartmentofMechanicalEngineering,NationalTaiwanUniversity,No.1RooseveltRoad,Sec.4,Taipei,Taiwan10617.EmailfkchenL50560w3.me.ntu.edu.twofwrinklesinthediecavity.Sincethesheetmetalinthewallareaisrelativelyunsupportedbythetool,theeliminationofwallwrinklesismoredifficultthanthesuppressionofflangewrinkles.Itiswellknownthatadditionalstretchingofthematerialintheunsupportedwallareamaypreventwrinkling,andthiscanbeachievedinpracticebyincreasingtheblankholderforcebuttheapplicationofexcessivetensilestressesleadstofailurebytearing.Hence,theblankholderforcemustliewithinanarrowrange,abovethatnecessarytosuppresswrinklesontheonehand,andbelowthatwhichproducesfractureontheother.Thisnarrowrangeofblankholderforceisdifficulttodetermine.Forwrinklesoccurringinthecentralareaofastampedpartwithacomplexshape,aworkablerangeofblankholderforcedoesnotevenexist.Inordertoexaminethemechanicsoftheformationofwrinkles,Yoshidaetal.1developedatestinwhichathinplatewasnonuniformlystretchedalongoneofitsdiagonals.Theyalsoproposedanapproximatetheoreticalmodelinwhichtheonsetofwrinklingisduetoelasticbucklingresultingfromthecompressivelateralstressesdevelopedinthenonuniformstressfield.Yuetal.2,3investigatedthewrinklingproblembothexperimentallyandanalytically.Theyfoundthatwrinklingcouldoccurhavingtwocircumferentialwavesaccordingtotheirtheoreticalanalysis,whereastheexperimentalresultsindicatedfourtosixwrinkles.NarayanasamyandSowerby4examinedthewrinklingofsheetmetalwhendrawingitthroughaconicaldieusingflatbottomedandhemisphericalendedpunches.Theyalsoattemptedtorankthepropertiesthatappearedtosuppresswrinkling.Theseeffortsarefocusedonthewrinklingproblemsassociatedwiththeformingoperationsofsimpleshapesonly,suchasacircularcup.Intheearly1990s,thesuccessfulapplicationofthe3Ddynamic/explicitfiniteelementmethodtothesheetmetalformingprocessmadeitpossibletoanalysethewrinklingprobleminvolvedinstampingcomplexshapes.Inthepresentstudy,the3Dfiniteelementmethodwasemployedtoanalysetheeffectsoftheprocessparametersonthemetalflowcausingwrinklesatthedrawwallinthestampingofataperedsquarecup,andofasteppedrectangularpart.Ataperedsquarecup,asshowninFig.1a,hasaninclineddrawwalloneachsideofthecup,similartothatexistinginaconicalcup.Duringthestampingprocess,thesheetmetalonthedrawwallisrelativelyunsupported,andistherefore254F.K.ChenandY.C.LiaoFig.1.Sketchesofaataperedsquarecupandbasteppedrectangularcup.pronetowrinkling.Inthepresentstudy,theeffectofvariousprocessparametersonthewrinklingwasinvestigated.Inthecaseofasteppedrectangularpart,asshowninFig.1b,anothertypeofwrinklingisobserved.Inordertoestimatetheeffectivenessoftheanalysis,anactualproductionpartwithsteppedgeometrywasexaminedinthepresentstudy.Thecauseofthewrinklingwasdeterminedusingfiniteelementanalysis,andanoptimumdiedesignwasproposedtoeliminatethewrinkles.Thediedesignobtainedfromfiniteelementanalysiswasvalidatedbyobservationsonanactualproductionpart.2.FiniteElementModelThetoolinggeometry,includingthepunch,dieandblankholder,weredesignedusingtheCADprogramPRO/ENGINEER.Boththe3nodeand4nodeshellelementswereadoptedtogeneratethemeshsystemsfortheabovetoolingusingthesameCADprogram.Forthefiniteelementsimulation,thetoolingisconsideredtoberigid,andthecorrespondingmeshesareusedonlytodefinethetoolinggeometryandFig.2.Finiteelementmesh.arenotforstressanalysis.ThesameCADprogramusing4nodeshellelementswasemployedtoconstructthemeshsystemforthesheetblank.Figure2showsthemeshsystemforthecompletesetoftoolingandthesheetblankusedinthestampingofataperedsquarecup.Owingtothesymmetricconditions,onlyaquarterofthesquarecupisanalysed.Inthesimulation,thesheetblankisputontheblankholderandthedieismoveddowntoclampthesheetblankagainsttheblankholder.Thepunchisthenmoveduptodrawthesheetmetalintothediecavity.Inordertoperformanaccuratefiniteelementanalysis,theactualstress–strainrelationshipofthesheetmetalisrequiredaspartoftheinputdata.Inthepresentstudy,sheetmetalwithdeepdrawingqualityisusedinthesimulations.Atensiletesthasbeenconductedforthespecimenscutalongplanescoincidingwiththerollingdirection0°andatanglesof45°and90°totherollingdirection.TheaverageflowstressH9268,calculatedfromtheequationH9268H11005H92680H110012H926845H11001H926890/4,foreachmeasuredtruestrain,asshowninFig.3,isusedforthesimulationsforthestampingsofthetaperedsquarecupandalsoforthesteppedrectangularcup.AllthesimulationsperformedinthepresentstudywererunonanSGIIndigo2workstationusingthefiniteelementprogramPAMFSTAMP.TocompletethesetofinputdatarequiredFig.3.Thestress–strainrelationshipforthesheetmetal.DrawWallWrinklinginaStampingDieDesign255forthesimulations,thepunchspeedissetto10msH110021andacoefficientofCoulombfrictionequalto0.1isassumed.3.WrinklinginaTaperedSquareCupAsketchindicatingsomerelevantdimensionsofthetaperedsquarecupisshowninFig.1a.AsseeninFig.1a,thelengthofeachsideofthesquarepunchhead2Wp,thediecavityopening2Wd,andthedrawingheightHareconsideredasthecrucialdimensionsthataffectthewrinkling.HalfofthedifferencebetweenthedimensionsofthediecavityopeningandthepunchheadistermedthediegapGinthepresentstudy,i.e.GH11005WdH11002Wp.Theextentoftherelativelyunsupportedsheetmetalatthedrawwallispresumablyduetothediegap,andthewrinklesaresupposedtobesuppressedbyincreasingtheblankholderforce.Theeffectsofboththediegapandtheblankholderforceinrelationtotheoccurrenceofwrinklinginthestampingofataperedsquarecupareinvestigatedinthefollowingsections.3.1EffectofDieGapInordertoexaminetheeffectofdiegaponthewrinkling,thestampingofataperedsquarecupwiththreedifferentdiegapsof20mm,30mm,and50mmwassimulated.Ineachsimulation,thediecavityopeningisfixedat200mm,andthecupisdrawntothesameheightof100mm.Thesheetmetalusedinallthreesimulationsisa380mmH11003380mmsquaresheetwiththicknessof0.7mm,thestress–straincurveforthematerialisshowninFig.3.Thesimulationresultsshowthatwrinklingoccurredinallthreetaperedsquarecups,andthesimulatedshapeofthedrawncupforadiegapof50mmisshowninFig.4.ItisseeninFig.4thatthewrinklingisdistributedonthedrawwallandisparticularlyobviousatthecornerbetweenadjacentwalls.Itissuggestedthatthewrinklingisduetothelargeunsupportedareaatthedrawwallduringthestampingprocess,also,thesidelengthofthepunchheadandthediecavityFig.4.WrinklinginataperedsquarecupGH1100550mm.openingaredifferentowingtothediegap.Thesheetmetalstretchedbetweenthepunchheadandthediecavityshoulderbecomesunstableowingtothepresenceofcompressivetransversestresses.Theunconstrainedstretchingofthesheetmetalundercompressionseemstobethemaincauseforthewrinklingatthedrawwall.Inordertocomparetheresultsforthethreedifferentdiegaps,theratioH9252ofthetwoprincipalstrainsisintroduced,H9252beingH9280min/H9280max,whereH9280maxandH9280minarethemajorandtheminorprincipalstrains,respectively.HosfordandCaddell5haveshownthatiftheabsolutevalueofH9252isgreaterthanacriticalvalue,wrinklingissupposedtooccur,andthelargertheabsolutevalueofH9252,thegreateristhepossibilityofwrinkling.TheH9252valuesalongthecrosssectionM–Natthesamedrawingheightforthethreesimulatedshapeswithdifferentdiegaps,asmarkedinFig.4,areplottedinFig.5.ItisnotedfromFig.5thatseverewrinklesarelocatedclosetothecornerandfewerwrinklesoccurinthemiddleofthedrawwallforallthreedifferentdiegaps.Itisalsonotedthatthebiggerthediegap,thelargeristheabsolutevalueofH9252.Consequently,increasingthediegapwillincreasethepossibilityofwrinklingoccurringatthedrawwallofthetaperedsquarecup.3.2EffectoftheBlankHolderForceItiswellknownthatincreasingtheblankholderforcecanhelptoeliminatewrinklinginthestampingprocess.Inordertostudytheeffectivenessofincreasedblankholderforce,thestampingofataperedsquarecupwithdiegapof50mm,whichisassociatedwithseverewrinklingasstatedabove,wassimulatedwithdifferentvaluesofblankholderforce.Theblankholderforcewasincreasedfrom100kNto600kN,whichyieldedablankholderpressureof0.33MPaand1.98MPa,respectively.Theremainingsimulationconditionsaremaintainedthesameasthosespecifiedintheprevioussection.Anintermediateblankholderforceof300kNwasalsousedinthesimulation.Thesimulationresultsshowthatanincreaseintheblankholderforcedoesnothelptoeliminatethewrinklingthatoccursatthedrawwall.TheH9252valuesalongthecrosssectionFig.5.H9252valuealongthecrosssectionM–Nfordifferentdiegaps.256F.K.ChenandY.C.LiaoM–N,asmarkedinFig.4,arecomparedwithoneanotherforthestampingprocesseswithblankholderforceof100kNand600kN.ThesimulationresultsindicatethattheH9252valuesalongthecrosssectionM–Narealmostidenticalinbothcases.Inordertoexaminethedifferenceofthewrinkleshapeforthetwodifferentblankholderforces,fivecrosssectionsofthedrawwallatdifferentheightsfromthebottomtothelineM–N,asmarkedinFig.4,areplottedinFig.6forbothcases.ItisnotedfromFig.6thatthewavinessofthecrosssectionsforbothcasesissimilar.Thisindicatesthattheblankholderforcedoesnotaffecttheoccurrenceofwrinklinginthestampingofataperedsquarecup,becausetheformationofwrinklesismainlyduetothelargeunsupportedareaatthedrawwallwherelargecompressivetransversestressesexist.Theblankholderforcehasnoinfluenceontheinstabilitymodeofthematerialbetweenthepunchheadandthediecavityshoulder.4.SteppedRectangularCupInthestampingofasteppedrectangularcup,wrinklingoccursatthedrawwalleventhoughthediegapsarenotsosignificant.Figure1bshowsasketchofapunchshapeusedforstampingasteppedrectangularcupinwhichthedrawwallCisfollowedbyastepD–E.Anactualproductionpartthathasthistypeofgeometrywasexaminedinthepresentstudy.Thematerialusedforthisproductionpartwas0.7mmthick,andthestress–strainrelationobtainedfromtensiletestsisshowninFig.3.Theprocedureinthepressshopfortheproductionofthisstampingpartconsistsofdeepdrawingfollowedbytrimming.Inthedeepdrawingprocess,nodrawbeadisemployedonthediesurfacetofacilitatethemetalflow.However,owingtothesmallpunchcornerradiusandcomplexgeometry,asplitoccurredatthetopedgeofthepunchandwrinkleswerefoundtooccuratthedrawwalloftheactualproductionpart,asshowninFig.7.ItisseenfromFig.7thatwrinklesaredistributedonthedrawwall,butaremoresevereatthecorneredgesofthestep,asmarkedbyA–DandB–EinFig.1b.Themetalistornapartalongthewholetopedgeofthepunch,asshowninFig.7,toformasplit.Inordertoprovideafurtherunderstandingofthedeformationofthesheetblankduringthestampingprocess,afiniteelementanalysiswasconducted.Thefiniteelementsimulationwasfirstperformedfortheoriginaldesign.ThesimulatedshapeofthepartisshownfromFig.8.ItisnotedfromFig.8thatthemeshatthetopedgeofthepartisstretchedFig.6.Crosssectionlinesatdifferentheightsofthedrawwallfordifferentblankholderforces.a100kN.b600kN.Fig.7.Splitandwrinklesintheproductionpart.Fig.8.Simulatedshapefortheproductionpartwithsplitandwrinkles.significantly,andthatwrinklesaredistributedatthedrawwall,similartothoseobservedintheactualpart.Thesmallpunchradius,suchastheradiusalongtheedgeA–B,andtheradiusofthepunchcornerA,asmarkedinFig.1b,areconsideredtobethemajorreasonsforthewallbreakage.However,accordingtotheresultsofthefiniteelementanalysis,splittingcanbeavoidedbyincreasingtheabovementionedradii.Thisconceptwasvalidatedbytheactualproductionpartmanufacturedwithlargercornerradii.Severalattemptswerealsomadetoeliminatethewrinkling.First,theblankholderforcewasincreasedtotwicetheoriginalvalue.However,justasfortheresultsobtainedintheprevioussectionforthedrawingoftaperedsquarecup,theeffectofblankholderforceontheeliminationofwrinklingwasnotfoundtobesignificant.Thesameresultsarealsoobtainedbyincreasingthefrictionorincreasingtheblanksize.Weconcludethatthiskindofwrinklingcannotbesuppressedbyincreasingthestretchingforce.Sincewrinklesareformedbecauseofexcessivemetalflowincertainregions,wherethesheetissubjectedtolargecompressivestresses,astraightforwardmethodofeliminatingthewrinklesistoadddrawbarsinthewrinkledareatoabsorbtheredundantmaterial.Thedrawbarsshouldbeaddedparalleltothedirectionofthewrinklessothattheredundantmetalcanbeabsorbedeffectively.Basedonthisconcept,twodrawbarsareaddedtotheadjacentwalls,asshowninFig.9,toabsorbtheexcessivematerial.Thesimulationresultsshowthatthe
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