1/11StressAnalysisandOptimumDesignofHotExtrusionDiesAbstract:Athree-dimensionalmodelofahotextrusiondiewasdevelopedbyusingANSYSsoftwareanditsseconddevelopmentlanguageANSYSparametricdesignlanguage.Afiniteelementanalysisandoptimumdesignwerecarriedout.Thethree-dimensionalstressdiagramshowsthatthestressconcentrationisrathersevereinthebridgeofthehotextrusiondie,andthatthestressdistributionisveryuneven.Theoptimumdimensionsareobtained.Theresultsshowthattheoptimumheightoftheextrusiondieis89.596mm.Theoptimumradiiofdiffluenceholesare65.048mmand80.065mm.Thestressconcentrationisreducedby27%.Keywords:three-dimensionalmethod；modeling；hotextrusiondie；optimumdesignIntroductionWiththecontinuousimprovementoflivingstandards,betterthermalconductivityofaluminumalloyprofiles.Aluminumcomponentswidelyusedineveryaspectoflife.Therefore,thealuminumalloyextrusionprofiles,profilesofvarioustypesofradiatorshavebeenwidelyusedinelectricalappliances,machinery,andotherindustries.Variableproductsandthegrowingdiversityandcomplexityofhigh-precision,theextrusionprocessisthebasisforextrusiondie.Itnotonlydeterminestheshape,size,accuracyandsurfacestate,butalsoaffecttheperformanceoftheproduct.Soextrusiondieextrusiontechnologyisthekey.Studiestoimproveextrusiondiequalityandprolongitslifespanusuallyattempttosimplify3-Dfiniteelementmodelto2-D,butitisonlyrightforsimplestructuralshapes.Withouta3-Dfiniteelementanalysis,theresultscannotgivepracticalmanufacturinghelpandofferusefulinformation3-5.Inthispaper,aluminiumprofileextrusiondiewasmodeledtogetinoptimumdesign6-8.1SolidModelingFigure1showsthemaledieofahotextrusionplanarcombineddie.Itsexternaldiameteris227.000mm,itsheightis80.000mm.OtherparametersareshowninFig.1.Themodelingmethodisasfollows.1.1CoordinatesofP1andP5ThecoordinatesofthepointofintersectionbetweenthebeelineL(y=kx+b)andthecirculararc(x2+y2=R2)are1.2CoordinatesofP2andP6Thecoordinatesoftheintersectionpoint(P2)betweenbeelineL1(y=kx+b)and2/11beelineL2(y=S1)areThecoordinatesoftheintersectionpoint(P6)betweenbeelineL3(y=kx+b)andbeelineL4(y=S1)are1.3CoordinatesofP3,P4,P7,andP8P3andP1aresymmetricaboutthey-axis.P4andP2arealsosymmetricaboutthey-axis.P7andP5aresymmetricaboutthex-axis.P8andP6arealsosymmetricaboutthex-axis.1.4VariablesintheequationsInEqs.(1)-(6),forpointsP1andP2,andR=R1.ForpointsP5andP6,andR=R2.R1,R2,T1,T2,S1,andS2arethechangerulealongtheheight(H)ofthedieexpressedasthefunctionsR1=f1(z),R2=f2(z),T1=f3(z),T2=f4(z),S1=f5(z),andS2=f6(z),z0,H.1.5SectionshapeatsomeheightWithlineslinkingP1-P4,P5-P8,withcirculararcfilletingatthepointofintersection(P1-P8),thesectionshapeatsomeheightisobtained.1.6SectionshapeateveryheightHisdividedtointerfacialnumber(INUM)equalparts(INUMisdecidedbytheprecision,iftheINUMishigher,theprecisionisbetter).ThesectionshapeisdrawnateveryheightasshowninFig.2.3/111.7SmoothcurvedsurfaceUsingSKINcommandinANSYS,smoothcurvedsurfaceswerebuiltalongthelines.Theyarethesurfacesoftheinfluencehole.UsingtheVA(itgeneratesavolumeboundedbyexistingarea)command,asolidwascreatedfromthosesurfaces.1.8SymmetryofthedieThemainbodyandkernelofthedieweredrawnusingtheBooleanoperationsofadd,subtract,etc.(Fig.3).Thesymmetryofthediewasusedtoacceleratethecomputationsusinga1/4-solidmodelforthefiniteelementanalysis(Fig.4).2ComputingModelAplanardiethatextrudesthealuminiumalloy(6063Al-Mg-Si)wasusedasanexample.TheliquidoidofAlis6579,andthemelttemperatureofAl+Mg2Siis558.Takingtheextrusionpressureandtheproductsqualityintoaccount,theworkingtemperaturewasdeterminedtobe450.Thediematerialis4Cr5MoSiV1(H13).Belowthe450,itsYoungmodulusandPossionratioare210GPaand0.25,respectively.Itsyieldstrengthis1200MPa.Thefrictioncoefficientis0.3.TheSolid923-Dsolidelementwasusedtocarrythroughthefreemesh.Inordertoloadthefrictionalforcewhileextruding,thesurfaceeffectelementSurf154wasusedtoproducetheregularquadrangles(Fig.5).Forthe1600t4/11extruder,theextrusionintensitywascomputedusingEq.(7)10.ThevaluesareshowninTable1.Thebridgecollapseoftentakesplaceinthedie.Anditsstrengthisdeterminedbytheheightandthedistributionofthediffluenceholes.Inthispaper,theheight(H)andtheradii(R1andR2)ofthediffluenceholeswereusedasdesignvariablesandthemaximumequivalentpressure(smax)wasusedasthegoalfunction.ThedesignvariablerangesarelistedinTable2.3ComputedResultsFigure6istheequivalentstressdiagram.FromFig.6wecanseethatthestressislargestatthebridge,asexpected24maximumequivalents