擠壓模具概述外文資料翻譯

1、外文資料翻譯Overview of adaptable die design for extrusionsW.A. Gordon.C.J. Van Tyne.Y.H. MoonABSTRACTThe term “adaptable die design ” is used for the methodology inwhichthe tooling shape is determined or modified to produce someoptimalpropert y in either productor process. The adaptable diedesignmethod,

2、used in conjunction with an upper bound model,allowsthe rapid evaluation of a large number of die shapes and thedesired outcome. In order fordiscovery of the one that produces thethe adaptable di e designmethod to besuccessful,it is necessary tohave a realistic velocityfield for thedeformationproces

3、s throughextrusion dies of anyshape and the velocityfield must allowflexibility in material movement to achieve therequiredmaterialflow description. A variet y of criteria can be used in theadaptabledie design method. For example, dies which produceminimaldistortion in the product. A double optimiza

4、tion processis used todetermine the values for the flexible variables in the velocity fie ldand secondl y to determine the die shapethat best meets the givencriteria. The method has been extendedto the design of dies fornon-axisymmetric product shapes.? 2006 Elsevier B.V. All rights reserved.Keyword

5、s: Extrusion; Die design; Upperbound approach; Minimumdistortion criterion1. IntroductionNew metal alloysand composi tes are being developedto meetdemanding applications.Many of these new materials aswell astraditional materialshave li mited workability. Extrusionis ametalworking processthat can be

6、used to deform these diffi cultmaterials into the shapes needed for specific applications. For asuccessful extrusion proc ess, metalworking engineers and designersneed to know how the extrusion die shape can affectthe final product.The present work focuses on the design of appropriate extru sion die

7、shapes. A methodology is presented to determine dieshapes that meetspecific criteria: either shapes which pro -duce product withoptimalset of specified properties, such as minimum distortionin theextrudate, or shapes which produceproduct by an optimized process,adaptable die design ”pe is determined

8、 orsuch as minimum extrusion pressure. The term is used for the method nology in which the die shamodifiedto produce some optimal proper tyin either product orprocess.anupperThis adaptable die design method, used in conjunction with bound model, allows the rapid evaluation of a large num ber of die

9、shapes and the discove ry of the one that can optimize the desired outcome. There are sever al conditions that need to be met forFirst, a generalized butthe adaptable die design method to be viable.realistic velocit y field is needed for use in an upper bound model to mathematically describe the flo

10、w of the material during extrusion through dies of any shape. Second, a robust criteation of the die shape. Therion needs to be established for the optimiz criterion must be useable within an upper bound model. The full details of the method are presented elsewhere 1 -6. In the present paper, follow

11、ing a review of previous models for extrusion, the flexible velocit y field for the d eformation region in a direct extrusion will be briefl y pr esented. This velocity field is able to characterize the flow through a die of almost any config uration. The adaptableequation, which describes the die s

12、hape, is also presented. Theconstants in this die shape equation are optimized with respect to acriterion. The criterion, which canbe used to minimize distortion, ipresented. Finally, the shape of an adaptable die, which produces of an extruded product with minimal distortion, is presented. The obje

13、ctive of the present paper is to provide a brief overview of the adaptable die design method.2. Background2.1. Axisymmetric extrusionTO propo sedNumerous studies have anal yz ed the axisymmetric extrusion of a cylindrical product from a cylindrical billet. Avitzur7sion through conical dies.upper bou

14、nd models for axisymmetric extruZimerman and Avitzur 11 modeled extrusion using the upper boundmethod, but with generalized shearboundaries. Finite elementmethods were used by Chen et al. 12and Liu and Chung 13 tomodel axisymmetric extru sion throughconical dies. Chen and Ling14 and Nagpal 15 analyz

15、ed otherdie shapes. They developedvelocity fields for axisymmetric extrusion through arbitrarily shapeddies. Richmond16 was the first to propose the concept of astreamlined die shape as a die profile optimized for minimaldistortion. Yang et al. 17 as well as Yang and Han 18 developedupper bound mode

16、ls for streamlined dies. Srinivasan et al.19proposed a controlled strain rate die as a streamlined shape, whichimproved the extrusion process for materials with limited workability.Lu and Lo 2O proposed a die shape with an improved strain ratecontrol.2.2. Distortion and die shape analysisNumerous an

17、al ytical and experimental axisymmetric extru sioninvestigations have examined the die shape and resulting distortion.Avitzur 9 showed that distortionincreases with increasingreduction and die angle for axisymmetricextrusion through conicaldies. Zimerman and Avitzur 11 and Pan etal. 21 proposed furt

18、herupper bound models, including ones withflexibility in the velocityfield to allow the distorted grid to changewith friction. They foundthat increasing frictioncauses more distortion in the extrudedproduct. Chen et al.12con -firmed that distortion increases withincreasing reduction, dieangle, and f

19、riction. Other research work hasfocused on non-conicaldie shapes. Nagpal 15refined the upperbound approachto studyalter-native axisymmetricdie shapes. Chenand Ling 14used theupper bound approachto study the flowthrough cosine,ellip tic,and hyperbolic dies in an attempt to find adie shape, which mini

20、mized force and redundant st rain. Richmondand Devenpeck 16,22,23, instead of assuming a particular type ofdie shape, decided to design a die based upon some feature of theextrudedproduct. Using slip lineanalysis and assuming ideal andfrictionlessconditions, Richmond16 pro poseda stream-linedsigmoid

21、aldie, which has smooth transitions atthedie entrance andexit. Thestreamlined die shape is thebasisformany efforts inaxisymmetric extrusion die design. Yanget al.17, Yang and Han18 , and Ghulman et al. 24 deve lopedupperbound models usingstreamlined dies. Certain materials, such as metal matrix comp

22、osites,can be successfull yextruded only in a narrow effective strain rate reinforced composites decrease s when peak strain rate was min imized 25 . Initiall y developed by Srinivasan et al. 19 , the streamlined die shape attempts to produce a constant strain rate throughout a large region of the d

23、eformation zone. Lu and Lo 20 used a refinedrange, leadingto thedevelopment of controlled strain rate dies. Thecontrol of thest rainrate in the deformation zone came from stud iesthat showedfiberbreakage during the extrusion of whiskerslab method to accountfor friction and mate rial property changes

24、inthe deformation zone.Kim et al. 26 used FEM to designanaxisymmetric controlledstrain rate die. They used Bezier curvestodescribe the die shapeand minimized the volumetric effective strainrate deviation in the deformationzone.2.3. Three-dimensional non-axisymmetric extrusionanalysisBoth the upper b

25、ound and finite element techniques have beenused to anal yze three-dimensional non-axisymmetric extrusions.Nagpal 27 proposed one of the earliest upper bound analyses fornon-axisymmetric extrusion. Upper bound and finite element modelswere developed Bas ily and Sansome28 , Boer et al.29 , and Boeran

26、d Webster 30 . Kiuchi 31 studied non-axisymmetric extrusionsthrough straightconverging dies. Gunasekera and Hoshino 32 4used an upperbound model to studythe extrusion of polygonalshapes throughconverging dies as wellas through streamlined dies.Wu and Hsu 35 proposed a flexiblevelocity field toextrud

27、epolygonal shapes through straight convergingdies. Han etal. 36created a velocit y field from their previousaxisymmetricupperbound model 37 in order to study extrusionthrough streamlineddies that produced clover-shaped sections.Yang et al. 37 applied ageneral upper bound model to studyextrusion of e

28、lliptic andrectangular sections. Han and Yang 38modeled the extrusion oftrocoidalgears. Yang et al. 39 also used finite element analysis tocon-firmthe experimental and upper bound anal ysis of the cloversections.Non-axisymmetric three-dimensional extrusionshavebeenstudied further by usingupper bound

29、 elemental technique40andspatial elementary rigidzones 41,42 . Streamlined dieshavebeenthe proposed die shapefor most three-dimensional extrusion.Theshape of the die betweenthe entrance and exit has been selected byexperience and feel rather than rigorous engineering principles.Nagpal et al. 43 assu

30、medthat the final p ositi on ofa point that wasin itially on the billetis determ ined by en suri ng that area reducti on oflocal segments was the same as the overall area reduction.Once the1 of amaterialp oi ntwas assumed,a thirdwas fitbetwee nthedie entrance andexitet al.44refi nedthismetho d to al

31、lowfor rePon alagusamy etal. 45 proposed usingBezierfinalp ositi onorderpolyno mialp oi nts.Gun asekerageometries.curves-entrantfor designing streamlinedextrusiondies. Kang andYan g46usedfin ite eleme nt models to p redict the op timal beari ng len gth for ansha pe extrusi on. Studies on the desig n

32、 of three-dime nsio nal extrusi ondies have bee n limited. The con trolledstrain rate con cept has onlybee n app lied to axisymmetric extrusi ons and notto three-dime nsionalextrusi ons 19,20,26.3. The ada ptable die desig n methodThe adaptable die design methodhas been developedand isdescribed in d

33、etail in a series of papers1 -5. The method has beenexte nded to non-axisymmetric three-dime nsional extrusi onof a roundbar to a recta ngular sha pe 6. The major criteri onused in devel opingthe method was to mini mize the distortio n inthe p roduct. The p rese ntpaper pro vides a brief overview of

34、 themethod and results from thesep revious studies.Fig. 1. Schematic diagram of axisymme tric e xtrusion using sphericalcoord in ates yste m thro ugh a die of arbitrary shape3.1. Velocity fieldAn upper bound analysis of a metal formingp roblem requires akin matically admissi ble velocity field. Fig.

35、shows the processp arameters in a schematic diagram with a sp hericalcoord in ate system(r,0 , ) and the three velocityzones thatare used in the upperbound anal ysis of axisymmetricextru sion through a die with anarbitrary die sha pe. The material isassumed to be a p erfectly p lasticmaterial with f

36、low strength, b。.hefriction, which exists between thedeformation zone in he work piece and the die, is characterized by a frictional shear tress, t = mf % / J3 , where the constant friction factor,The materialstarts as acyli nderofinto a cylindricalp roduct ofradiusRf .zones I and III, with velociti

37、es ofvoandmf, can take values from 0 to 1.radius Ro and is extrudedRigid body flow occurs inVf, respectivel y. Zone II isthe deformationregion, where the velocity is fairl y compiex. Twospherical surfaces of velocit y discontinuityr 1 and r 2 separate thethree velo cit y zones. The surfacer is locat

38、ed a dista neero from theorig in and the surfacers located a dista neerf from the origin.The coord in atesystem is cen tered at the con verge neepoint ofthe die. The con verge neepoint is defi ned by the in tersecti onof the axis of symmetry with a line at angle a that goes through the pointwhere th

39、e die begi ns its deviati on from a cyli ndricalshape and the exit pointof the die. Fig. 1 showsthe positionof thecoord in atesystem orig in.The die surface, whichis labeled p (r) inFig. 1, is give n in the sp herical coord in ate system.(rs the angularpositionof the die surfaceas a fun cti onofthe

40、radial distanee fromthe origin. The die lengthfor the deformationregi on isgiven by thep arameter L.The best velocity field to describe theflow in thedeformati onfield uses aregion is the sine-1velocity field 1,2 . This velocitybase radial velocity,vr, which is modified by an additionaltermcomp rise

41、dto twofun cti onswith each function containingp seudo-i ndependentp arametersto determinethe radial velocit ycomponent in zone II:(1)The functionpermits flexibilityof flowin the radial,r, direct ion.and the 丫 functionpermitsflexib ility offlow in thean gular, 0 ,directi on.The value of vr is determ

42、 inedby assumingprop orti onaldista nces in a cyli ndricalsense from the cen treli ne:Vr = -Vo10 sin2 aThis velocit y field was found t o be the best rep rese ntatio n ofthe flowin the deformationregion of an extrusionprocess foranarbitraril ysha ped die.The function isrep rese ntedas a seriesofLege

43、 ndrepolyno mialsthat areorthog onaloverdeformati onzone. Therep rese ntati on of is:na名AiP (X )i z0Where2P (Rf / Ro ) 1X =with1-Rf/R0r。aibeingthe coefficientsof the LengendrepolynomialsPi(x)and n a be ingthe order of therep rese ntati on.Thereis a restrictionthat:na(odd )ng (evenThe remaininghigher

44、 ordercoefficie nts(A2to A na) arethep seudo-i ndependentp arameters,with valuesdeterm inedbyminimizationof thetotal po wer.Legendre polynomialsare usedsothat higher order terms can be added to the fun ction without causingp oly no mials.sig ni fica nt cha nges in the coefficie nts of the lower orde

45、rThis feature of the Legendre polynomialsoccurs because they are orthog onal over a fin ite dista nee.allowsThe 丫 function that satisfies the boundary conditions and the best descri pti on of the flow is:nby i ll-COS屮丿wherenb DBo-z旦y i+1andthe high order coefficients B1 to Brib are pseudo-independen

46、tparameterswith values determin ed byminimizationof the totalpower. The order of the representationisrib. It has been shown 3that n a= 6 and n b= 2 are usuall y sufficie nt to pro videreas on ableflexibility for the flow field in the deformati on regi on.3.2. Die sha peThe die shape is described by

47、the function(r). The adaptabledie sha pe is described by a set of Lege ndre polyno mials:nc屮=送Cj Pi ( X )i=0wherex/IRf/Ro)Twith丄 andro(Rf/Ro)c being thecoefficie ntsof theLegendre pol ynomialsPi(X). The order of theLege ndre polyno mialrep rese ntati onis nThe boundaryconditionsat the entrance andex

48、it of the deformati onregi on require that:At r = r0 , p = aAt r = rf , p = aIf a streamlineddie is used then this function must meet twoadditi onal boun dary con diti ons:屮At r =r0, r0 =ta nacr(8)At r = rf,&3.3. Distortio n criteriaThe criterion thatwas found to minimize thedistortionin theextrusi

49、on p roduct invo Ives mini miz ing the volumetric effectivestrainrate deviati on 4,5 . The volumetric effective stra in ratedeviatio n inthe deformati on zone is:Wherelsin OAOdp2 sin Gt值等）警）*（警y+（罟丁with:SII12/知說鳳Ofrqi罕+（T）“警y+涪”2血加蝕(10)and are the components of the strain rate field. ij3.4. Determi

50、ning the ada ptable die sha peThe search for the op timalcoefficie nts for the Lege ndrepolynomialsrepresentingthe die shape is not constrained.A nestedfor theoptimizationroutineis used with the velocity field (inside loop) being mini mized with res pect to the externally supp lied powerprocess, and

51、 the die shape (outside loop) being adapted to minimizethe distortioncriterion.The final shape is called an adaptable diesp ecified criterio n.adaptatio n in the rotationalsha pe, since the sha pe has ada pted to meet theFig. 2. Streamlinedadaptabledie shape with nodirectiowith red = 0.60, L/Ro= 1.0

52、,mf= 0.1,Rr/Ro= 0.1and= 1.5. The areareduction ratio is red, Rr is the corneredra diusof the rectangularproduct,and 1 is the height to width ratiooftherecta ngularp roduct.(Forinterpretation of the references to colourinthisfigure lege nd, the reader isreferred to the webve rsion of the article.)3.5

53、. Exte nsion to three-dime nsional non-axisymmetric sha pesIn exte nding the ada ptabi e die desig n method from axisymmetricflow to non-axisymmetricthree-dimensionalflow in the deformationregi on requires several sp ecial con siderati ons 6.First, the velocitfield needs to be modified to allowfor r

54、otationalmovement inthedeformati on regi on. Second, the beari ngregi on on the exit side of thedie needs to be analyzedproperly.Third, the functions usedtodescribe the die sha pe n eed to havesome flexibilit y in the rotati onaldirecti on(i.e. 書(r, ). This flexibility allows die sha pe ada ptati oncoordi