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TSINGHUASCIENCEANDTECHNOLOGYISSN1007021410/24pp290293Volume9,Number3,June2004StressAnalysisandOptimumDesignofHotExtrusionDiesSHUAICijun帅词俊,XIAOGang肖刚,NIZhengshun倪正顺CollegeofMechanicalandElectronicEngineering,CentralSouthUniversity,Changsha410083,ChinaAbstractAthreedimensionalmodelofahotextrusiondiewasdevelopedbyusingANSYSsoftwareanditsseconddevelopmentlanguageANSYSparametricdesignlanguage.Afiniteelementanalysisandoptimumdesignwerecarriedout.Thethreedimensionalstressdiagramshowsthatthestressconcentrationisrathersevereinthebridgeofthehotextrusiondie,andthatthestressdistributionisveryuneven.Theoptimumdimensionsareobtained.Theresultsshowthattheoptimumheightoftheextrusiondieis89.596mm.Theoptimumradiiofdiffluenceholesare65.048mmand80.065mm.Thestressconcentrationisreducedby27.KeywordsthreedimensionalmethodmodelinghotextrusiondieoptimumdesignIntroductionWiththestandardoflivingcontinuouslyimproving,aluminiumpartsarewidelyusedineverywalkoflife.Productsarebecomingmoreandmorediverseandcomplicatedandprecisionsarehigherandhigher1,2.Theextrusiondieisthebasisoftheextrusionprocess.Itnotonlydeterminesproductshape,size,precision,andsurfacestate,butalsoaffectsproductperformance.Sotheextrusiondieisthekeytoextrusiontechnology.Studiestoimproveextrusiondiequalityandprolongitslifespanusuallyattempttosimplify3Dfiniteelementmodelto2D,butitisonlyrightforsimplestructuralshapes.Withouta3Dfiniteelementanalysis,theresultscannotgivepracticalmanufacturinghelpandofferusefulinformation35.Inthispaper,aluminiumprofileextrusiondiewasmodeledtogetinoptimumdesign68.1SolidModelingFigure1showsthemaledieofahotextrusionplanarcombineddie.Itsexternaldiameteris227.000mm,itsheightis80.000mm.OtherparametersareshowninFig.1.Themodelingmethodisasfollows.1.1CoordinatesofP1andP5ThecoordinatesofthepointofintersectionbetweenthebeelineLykxbandthecirculararcx2y2R2are22221,5211kbkbkbRxk−−−11,51,5ykxb21.2CoordinatesofP2andP6ThecoordinatesoftheintersectionpointP2betweenbeelineL1ykxbandbeelineL2yS1are﹡Received20031210selectedfromProceedingsoftheSymposiumonFrontiersandChallengesofMechanicalScienceandTechnologySupportedbytheFundfortheDoctoralProgramofHigherEducationofChinaNo.20010533010﹡﹡Towhomcorrespondenceshouldbeaddressed.Emailshuaicijun163.comTel86731883685812Sbxk−3y2S14ThecoordinatesoftheintersectionpointP6betweenSHUAICijun帅词俊etalStressAnalysisandOptimumDesignofHotExtrusionDies291Fig.1SketchmapofthehotextrusiondiebeelineL3ykxbandbeelineL4yS1arex6S25y6kx2b61.3CoordinatesofP3,P4,P7,andP8P3andP1aresymmetricabouttheyaxis.P4andP2arealsosymmetricabouttheyaxis.P7andP5aresymmetricaboutthexaxis.P8andP6arealsosymmetricaboutthexaxis.1.4VariablesintheequationsInEqs.16,forpointsP1andP2,b2121kTk−andRR1.ForpointsP5andP6,b2221kTk−andRR2.R1,R2,T1,T2,S1,andS2arethechangerulealongtheheightHofthedieexpressedasthefunctionsR1f1z,R2f2z,T1f3z,T2f4z,S1f5z,andS2f6z,z∈0,H.1.5SectionshapeatsomeheightWithlineslinkingP1P4,P5P8,withcirculararcfilletingatthepointofintersectionP1P8,thesectionshapeatsomeheightisobtained.1.6SectionshapeateveryheightHisdividedtointerfacialnumberINUMequalpartsINUMisdecidedbytheprecision,iftheINUMishigher,theprecisionisbetter.ThesectionshapeisdrawnateveryheightasshowninFig.2.Fig.2Dielinediagram1.7SmoothcurvedsurfaceUsingSKINcommandinANSYS,smoothcurvedsurfaceswerebuiltalongthelines.Theyarethesurfacesoftheinfluencehole.UsingtheVAitgeneratesavolumeboundedbyexistingareacommand,asolidwascreatedfromthosesurfaces.1.8SymmetryofthedieThemainbodyandkernelofthedieweredrawnusingtheBooleanoperationsofadd,subtract,etc.Fig.3.Thesymmetryofthediewasusedtoacceleratethecomputationsusinga1/4solidmodelforthefiniteelementanalysisFig.4.2ComputingModelAplanardiethatextrudesthealuminiumalloy6063AlMgSiwasusedasanexample.TheliquidoidofAlis657℃9,andthemelttemperatureofAlMg2Siis558℃.Takingtheextrusionpressureandtheproductsqualityintoaccount,theworkingtemperaturewas292TsinghuaScienceandTechnology,June2004,93290–293determinedtobe450℃.Thediematerialis4Cr5MoSiV1H13.Belowthe450℃,itsYoungmodulusandPossionratioare210GPaand0.25,respectively.Itsyieldstrengthis1200MPa.Thefrictioncoefficientis0.3.TheSolid923Dsolidelementwasusedtocarrythroughthefreemesh.Inordertoloadthefrictionalforcewhileextruding,thesurfaceeffectelementSurf154wasusedtoproducetheregularquadranglesFig.5.Forthe1600textruder,theextrusionintensitywascomputedusingEq.710.ThevaluesareshowninTable1.12zztdzzdPPPRTTTRTT′′′7Fig.5FrictionalforceloadedTable1IntensityofeachpartinthedieFig.3DiesolidmodelFig.4OnequarterofthesolidmodelMPaRzTzTtTdzR′zT′dT′P83.4227.41222.7219.53191.8053.2314.38612.54Thebridgecollapseoftentakesplaceinthedie.Anditsstrengthisdeterminedbytheheightandthedistributionofthediffluenceholes.Inthispaper,theheightHandtheradiiR1andR2ofthediffluenceholeswereusedasdesignvariablesandthemaximumequivalentpressureσmaxwasusedasthegoalfunction.ThedesignvariablerangesarelistedinTable2.Table2DesignvariablerangeR1/mmR2/mmH/mmθ1/˚θ2/˚65.00085.00080.00098.00060.00090.00020.00040.00020.00040.0003ComputedResultsFigure6istheequivalentstressdiagram.FromFig.6wecanseethatthestressislargestatthebridge,asexpected24maximumequivalentstressvaluesarelistedinTable3fromlargetosmall.Thedatashowsthatthenodalmaximumequivalentstressis1066.5MPa,whichis14.5higherthanthesecondone912.0MPa,andthatthestressconvergenceisverysevereinthebridge,thispartisapttoproducecrack.Fig.6MaximumequivalentstressTable3NodesstressvaluesNodecode97152871969839507141156702727710723700σr/MPa1066.5912.0832.7811.6804.4795.3789.9778.8775.8769.0763.6763.5Nodecode7397087067317591778704747690743694696σr/MPa759.3756.8755.9739.8739.1736.0734.3715.9706.4700.3700.1695.6SHUAICijun帅词俊etalStressAnalysisandOptimumDesignofHotExtrusionDies293TheinitialvalueofthedesignvariablesR1,R2,H,θ1,andθ2were75.000mm,88.000mm,80.000mm,30.000˚,and30.000˚,respectively,andthemaximumequivalentstressσmax1066.5MPa.Inthe21iterations,theoptimumiterationwastheeighteenth.ThedesignvariablevalueswereR165.048mm,R280.065mm,H89.596mm,θ130.642˚,θ220.045˚.Themaximumequivalentstressσmax723.1MPa,whichis27less.TheoptimumresultsareshowninTable4.Table4OptimizationprocessIterationtimes1234567891011R1/mm75.00081.94377.35880.85567.24980.44167.36565.59165.18465.17265.067R2/mm88.00088.22995.26190.47889.53589.98393.66182.79193.75380.60480.153H/mm80.00071.64060.10080.85489.68474.32781.40965.29761.47884.95588.627θ1/˚30.00033.84729.38221.40032.63336.08531.81637.64439.47433.86134.052θ2/˚30.00030.75126.40626.94623.01836.72921.26720.32524.74020.11320.058σmax/MPa1066.51167.41323.21229.7882.51241.7882.4866.8943.9756.0749.7Iterationtimes12131415161718192021R1/mm65.04865.04765.04865.04865.04765.04865.04865.04365.04265.042R2/mm80.07080.06393.50683.63384.98780.07080.06580.04580.04480.045H/mm65.80885.14188.11687.94588.97889.59889.59689.86766.84089.839θ1/˚30.58532.45635.41427.78633.23123.14430.64230.25027.55631.341θ2/˚23.47922.21420.04435.94120.04620.04520.04520.04220.04220.042σmax/MPa780.0769.6760.4788.0769.0795.8723.1741.3821.3751.34Conclusions1BasedonANSYSsoftware,itsseconddevelopmentlanguageAPDLwasusedtodevelopa3Dmodelofthehotextrusiondiethatextrudesaluminiumprofilehasbeenobtained.2The3Dstressdistributionwasveryuneven,withseverestressconcentrationsinthebridgeofthehotextrusiondie.Theoptimalgeometricdesignhad27lowermaximumstress,Abetterdiewillnotonlyreducedienumberbutalsoreducetimelostchangingdies,whichwillgreatlyheightenproductivity.References1YinJianhua.Structuraladjustmentorientationfordomesticlargescaledaluminumprocessingenterprisesintermsofimportsituationofaluminummaterialinrecentyears.TheWorldNonFerrousMetal,2001,103742.inChinese2LiYi.Forecastondomesticaluminummaterialconsumptionandadvicesonoptimizingdomesticaluminummaterialindustryconstitution.JournalofSouthernInstituteofMetallurgy,2002,4305308.inChinese3YiMiao,LiuFang.Thecontributingfactorsanalysisaboutthelifespanoftheextrusiondie.LightAlloyProcessTechnology,2000,283437.inChinese4NiZhengshun,ShuaiCijun,ZhongJue.SolidmodelingtechnologyanditsapplicationintheextrusiondiedesignbasedonANSYS.MechanicalScienceandTechnology,2003,221149150.inChinese5KaracsG.Computeraidedmethodsfordiedesign.ProceedingsoftheConferenceonMechanicalEngineering,1998,2463466.6MuellerG.DesignoptimizationwiththefiniteelementprogramANSYS.InternationalJournalofComputerApplicationsinTechnology,1994,7271277.7ChenJinyi,CaiGuozhong.TheComputerAidedEngineeringAnalysisANSYSUsersGuide.BeijingChinaRailwayPress,2001.inChinese8WangGuoqiang.PracticalEngineeringDigitalSimulationTechnologyandItsPracticeatANSYS.ShanxiWestnorthIndustrialUniversityPress,1999.inChinese9ZhangBaochang.NonferrousMetalandItsHeatTreatment.ShanxiWestnorthIndustrialUniversityPress,1993.inChinese10JiaXianan,HuJiuxi.HotExtrusionTechnicsandDieDesign.BeijingChinaMachinePress,1986.inChinese
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