similar extrusion and mapping optimization of die cavity modeling for special-shaped products

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1、Similarextrusionandmappingoptimizationofdiecavitymodelingforspecial-shapedproductsSciencePressAvailableonlineatwww.sciencedirect.com●olEHoE]rans.NonferrousMet.Soc.China16(2006)587—592TransactionsofNonferrousMetalsSocietyofChinaWWW.CSU.edu.cn/ysxb/Similarextrusionandmappingoptimizationofdiecavity

2、modelingforspecial-shapedproductsQIHong-yuan(齐红元),WANGShuang?xinCv爽心),ZHUHeng-jun(朱衡君)SchoolofMechanicalandElectricControlEngineering,BeijingJiaotongUniversity,Beijing100044,ChinaReceived8October2005;accepted25March2006Abstract:Aimedatthemodelingissuesindesignandquickprocessingofextrudingdiefors

3、pecial?shapedproducts.withthehelpofConformalMappingtheory,ConformalMappingfunctionisdeterminedbythegivenmethodofnumericaltrigonometricinterpolation.Three—dimensionalformingproblemsaretransformedintotwo.dimensionalproblems.andmathematicalmodelofdiecavitysurfaceisestablishedbasedondifferentkindsof

4、verticalcurve,aswellasthemathematicalmodelofplasticflowinextrudingdeformationofspecial—shapedproductsgetscompleted.Byupperboundmethod,bothverticalcurvesofdiecavityanditsparametersareoptimized.Combiningtheoptimizedmodelwith山elatestNCtechnology,NCProgramofdiecavityanditsCAMcanberealized.Takingthes

5、imilarextrusionofsquare.shapedproductswitharcradiusasiustance.bothmetalplasticsimilarextrusionanddiecavityoptimizationarecarriedout.Keywords:extrusion;ConformalMapping;forming;diecavity;special?shapedproducts1IntroductionForspecia1.shapedproducts.similarextrusionisdefinedastheextrudingdeformatio

6、nprocesswhichcanmakegeometrica1profileofmetalarbitrarycross.sectionindeformingregionbemutuallysimilartothatofitsoriginalbillet.Duringthemetalforming,similarextrusionbecomesnon.axis.symmetrica1three.dimensionalproblemduetotheexistenceoftangentplasticflow,cannotbesimplydescribedbytwo.dimensionalth

7、eorem『1,21.Inaddition,onaccountofthedi~cultiesinmathematics,relatedanalysiswasrarelyreported,andnogeneralizedexpressionofthree?dimensionalanalysisexists[3,4】.Consequently,notonlysimilarextrudinganalysisbutalsoitsquickdieproc