Computer Aids in Sheet Metal Engineering

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<ul><li><p>Key-Note- Papers </p><p>Computer Aids in Sheet Metal Engineering </p><p>J. L. Duncan (1) and R. Sowerby; Department of Mechanical Engineering, McMaster University, Hamilton, OntarioKanada </p><p>SUWItARY </p><p>Sheet metal par ts are character ized by a complicated shape; the s t ra ins involved i n forming r a r e l y exceed 20': but the displacements a re la rge . d i t i o n s can cause la rge changes i n f a i l u r e rates. </p><p>wh i le the l i m i t a t i o n o f useful s t ra in ing i n sheet mater ia ls can be reasonably modelled, the determinat ion o f s t r a i n d i s t r i - but ions i n complex par ts can no t y e t be determined i n an accurate and economic fashion. </p><p>gested t h a t the use o f these ideas leads to t rac tab le . approxiniate computer design aids fo r comp?ex shapes which can be used e f fec t i ve l y by experienced designers. </p><p>Sheet forming operations are conducted close t o a f a i l u r e l i m i t and there fore small changes i n con- </p><p>The various techniques employed as a basis fo r computer model l ing o f sheet forming are reviewed and i t i s concluded t h a t </p><p>The use o f i dea l i za t i ons o f deformation processes, mater ia ls , forming operat ions and shapes i s introduced and i t i s sug- </p><p>INTRODUCTION </p><p>Sheet metal engineering encompasses mater ia l se lec t ion , pro- cess design, t oo l design and the sett ing-up o f press l i n e s f o r h igh volume product ion o f sheet metal components. There are many spec ia l i zed branches o f sheet metal engineer ing bu t the areas con- s idered here are i n the automotive, appliance, and packaging i n - dus t r ies . Par ts are produced i n quan t i t i es greater than 5,000 per day and the p r i ce of the f i n i shed product i s t y p i c a l l y a few do l - l a r s per k i logram ra the r than many hundreds o f d o l l a r s per k i l o - gram as i s o f ten the case i n the a i r c r a f t and e lec t ron i c indus- t r i e s . </p><p>The forniing process i s character ized by a complicated f i n a l p a r t shape and although the sheet undergoes la rge displacements dur ing forming the deformation or s t r a i n imposed i s o f ten qu i te small. Studies a t Toyota [l], f o r example, show tha t most areas o f sheet i n an autobody are deformed less than a few percent and higher s t ra ins , which r a r e l y exceed 204, are conf ined t o r e l a t i v e - l y small volumes o f mater ia l . la rge amounts of money are expended on t o o l i n g wh i le o ther manu- fac tu r i ng costs per p a r t are qu i te small. </p><p>I t i s o f ten considered tha t there i s a h igh u t i l i z a t i o n of mater ia l i n forming processes. This i s no t always t rue and sheet metal p lan ts r a r e l y convert more than 70% o f the incoming sheet i n t o a f i n a l product. Most o f the scrap l oss comes from blanking and t r i sm ing around the f i n a l p a r t ra the r than breakage. Surpr is - i ng as i t may seem, however, the ob jec t i ve i n press forming i s no t t o avoid breakage a l together bu t ra the r t o run the process so c lose t o the l i m i t t h a t some breakages do occur. then c lea r l y , the mater ia l i s too good, the presses could be run fas te r , l ess l u b r i c a n t could be used o r var ious o ther savings achieved. The consequence o f operat ing very c lose t o f a i l u r e i s t h a t small mater ia l o r process changes can have very l a rge e f fec ts on scrap r a t e and f u r t h e r tha t f a i l u r e ana lys is must be conducted on a p r o b a b i l i s t i c basis. </p><p>The ex ten t t o which the workpiece i s con t ro l l ed dur ing form- i ng must a lso be considered. The too l designer aims a t maximum cont ro l bu t i nva r iab l y the sheet i s s l i d i n g over p a r t i a l l y l u b r i - cated surfaces, s t i c k i n g t o the too l i n some regions, constrained i n others and i n certa;n areas o f the d i e suspended f r e e l y i n a i r i n v i t i n g wr ink l i ng and o ther forms o f i n s t a b i l i t y . geometry i s changing a t every i ns tan t i n the forming s t roke and c l e a r l y one could no t expect t o develop a simple mathematical model o f such a process. </p><p>The fasc ina t ion o f sheet metal engineer ing l i e s i n the broad physical phenomena encountered, the inherent uncer ta in ty of the process and the f a c t t h a t i t cannot be reduced t o a simple set Of ru les . methods o f sheet metal engineer ing are being replaced on ly a t a gradual r a t e by computer-aided methods. no l ess computer-oriented than others and hopefu l l y they are j u s t as i n t e l l i g e n t , but the basic process depends c r i t i c a l l y on many var iab les and does no t i n v i t e simple mathematical so lu t ions . </p><p>There are enormous incent ives t o improve the e f f i c i e n c y Of sheet metal manufacture i n a l l areas - i n the design process, i n the u t i l i z a t i o n o f stronger bu t l ess formable mater ia ls , i n the lowering o f scrap ra tes and i n reducing manufacturing costs. I n t h i s paper we consider how computer-aided design and computer graphics a re con t r i bu t i ng towards t h i s improvement. t r o l o f presses and stamping p lan ts i s a lso important bu t i s no t discussed here because the fundamentals invo lved are no d i f f e r e n t from those i n o ther branches o f manufacturing. The discussion i s d iv ided i n t o three par ts ; two o f these concern ana lys is , one O f the forming process and the other o f the response o f sheet metals t o deformation. I n the f i n a l sec t ion we address the subject O f whether the ex i s t i ng concentrat ion on ana lys is i s r e a l l y appro- p r i a t e when i n f a c t the basic problem i s i n the area of design bo th o f the process and o f the d e t a i l s o f t oo l i ng . Various exam- p les a re presented where the i nves t i ga t i on o f idea l i zed processes has been more p r o f i t a b l e than the de ta i l ed ana lys is of e x i s t i n g forming operat ions. </p><p>ANALYSIS OF SHEET FORMING </p><p>From a process po in t o f view, very </p><p>I f no par ts f a i l , </p><p>The actual </p><p>These a t t r i b u t e s are a lso the reason why t r a d i t i o n a l </p><p>Sheet metal engineers a re </p><p>Computer Con- </p><p>There are two d i s t i n c t par ts t o the ana lys is o f a sheet form- </p><p>i ng process. The f i r s t i s t o p red ic t o r inodel the d i s t r i b u t i o n o f s t ra ins and show how these develop as forming proceeds. s t r a i n d i s t r i b u t i o n i s determined predominantly by the geometry o f the par t , the too l i ng and the blank and a lso by f r i c t i o n and the mechanical p roper t ies of the sheet. It i s required to determine the magnitude o f s t r a i n and the s t r a i n path. i ng o f an element i s considered to fo l l ow a simple p ropor t iona l o r l i n e a r path; t h i s i s n o t necessar i l y t rue bu t i n many cases the assumption i s reasonable. Figure 1 i s schematic representat ion o f successive s t r a i n envelopes, which have been exper imental ly de ter - mined from the defonnation o f selected elements i n a blank dur ing the deep drawing o f a square cup. </p><p>The second p a r t of the ana lys is i s t o determine the ex ten t t o which the mater ia l w i l l deform t .?fore i t s a b i l i t y t o d i s t r i b u t e the s t r a i n becomes exhausted. format ion h i s to ry . stresses, then the mater ia l l i m i t s can a lso be described i n the s t r a i n space. The we l l known forming l i m i t diagram, FLD, def ines the use fu l l i m i t s o f f o rmab i l i t y , as a func t ion o f s t r a i n i n g path, based on the c r i t e r i o n o f the onset of l oca l i zed necking. A form- i ng l i m i t curve i s shown schematical ly i n f i gu re 2. There are other competing modes o f f a i l u r e , which may in te rsec t the FLD, and these can a lso be p lo t ted on Figure 2. buck l ing f a i l u r e which can occur before the onset of l oca l i zed necking, o ther p o s s i b i l i t i e s are s t ress con t ro l l ed o r s t r a i n con- t r o l l e d f rac tu re l o c i . The l e f t hand hatched curve i s suggested from a maximum shear s t ress c r i t e r i o n , wh i l e the r i g h t hand locus i s based on a compet i t ion between the cont inu ing deformation o f a l oca l i zed groove and eventual f rac tu re o r f rac tu re preceding ( o r sometimes co inc id ing w i th ) t he development o f a l oca l i zed groove. </p><p>The combination o f the process and mater ia l diagrams i n Fig- ures 1 and 2 permit the p red ic t i on o f ove ra l l l i m i t s . the s t r a i n envelope i n Figure 1 cannot go beyond any l i m i t curve i n Figure 2 although there are exceptions. small rad ius bending, l oca l i zed necking i s prevented by t o o l i n g cons t ra in ts and the s t r a i n envelope can exceed the necking curve. The p r o b a b i l i s t i c nature o f sheet f o n i n g must a lso be remembered and the l i n e s i n Figure 2 should more proper ly be considered as mean curves. </p><p>This ove ra l l view o f sheet metal forming ana lys is was d is - cussed i n a previous con t r i bu t i on [2] and l i m i t curves are re- viewed more deeply i n a review o f f a i l u r e maps [3]. the numerical techniques which a re used t o de temine both the s t r a i n d i s t r i b u t i o n s dur ing forming and the s t r a i n l i m i t s which can be sustained by the mater ia ls are discussed. </p><p>The </p><p>Usual ly the s t r a i n - </p><p>This i s a lso dependent on the de- I f the sheet i s n o t subject t o l a rge surface </p><p>One i s a wr ink l i ng o r </p><p>I n general, </p><p>I n some cases, such as </p><p>I n t h i s paper, </p><p>ANALYTICAL TECHNIQUES FOR SHEET FORMING PROCESSES </p><p>The ana ly t i ca l study o f any forming operat ion requ i res a union o f a model o f the mater ia l behaviour and o f t he process: the model must a lso provide f o r r e a l i s t i c boundary cond i t ions and f r i c t i o n a l e f fec ts a t t he i n te r face o f t he too l s and mater ia l . Since the process may be performed hot o r cold, and a t e i t h e r a f a s t o r slow speed, these aspects must a lso be considered. t le ta l forming operat ions can be broadly c l a s s i f i e d i n t o two main groups: e i t h e r bu lk o r sheet forming processes. The former may be t r u e l y th ree dimensional i n character w i t h bo th the s t ress and s t r a i n components varying from po in t t o p o i n t throughout the body, wh i le i n the l a t t e r operat ions i t i s o f ten reasonable t o assume t h a t a t any l oca t i on there i s no v a r i a t i o n i n phys ica l quan t i t y across the thickness o f the sheet. </p><p>Due t o the complexity o f most forming processes an exact so- l u t i o n i s usua l ly unattainable. Therefore before embarking upon any ana ly t i ca l study o f a metal working operat ion i t i s prudent t o ask what i s required from the eventual so lu t ion . Often a r a t e i n - dependent, r i g i d - p l a s t i c ana lys is i s su i tab le i f the requirement i s a reasonable est imate o f a load o r pressure t o execute a form- ing operat ion, o r i f i t i s requ i red t o enquire how the load i s a f fec ted by changing c e r t a i n process parameters. I n add i t i on the actual process may fo l l ow c lose ly e i t h e r plane stress, plane s t r a i n o r axisynmetr ic deformation. modes, i n pa r t i cu la r , when coupled w i t h a r i g i d - p e r f e c t l y p l a s t i c mater ia l model have formed the basis o f many so lu t i on procedures f o r bu lk forming processes. lower and upper bound approaches [6, 7, 81 and s l i p l i n e f i e l d </p><p>The l a t t e r two deformation </p><p>Slab o r fo rce balance methods [4, 51, </p><p>Annals of the ClRP Vol. 30/2/1981 541 </p></li><li><p>(s.1. f . ) analyses, o r t he method of cha rac te r i s t i cs [7-111, have a l l been employed t o study such operat ions as drawing, extrusion, r o l l i n g . indent ing, upsett ing, fo rg ing and the l i k e . An overview of some o f these methods i s a lso t o be found i n Refs. [12, 131, and the b ib l iography t o each o f these a r t i c l e s c i t e s many app l i - cat ions. The ana ly t i ca l techniques mentioned above have been in- troduced i n ascending order o f mathematical soph is t i ca t ion , and w i t h i n the conf ines o f the assumed mater ia l model and plane s t r a i n deformation s.1.f. analysis i s mathematically r igorous and can a lso Drovide a qood reDresentat ion o f the deformation mode i n cer - </p><p>t e rna l force. Tension forces are t ransmi t ted through the sheet and the process can proceed provided the a b i l i t y o f the mater ia l t o sus ta in t h i s tension i s no t exceeded. the mater ia l may f a i l e i t h e r by necking o r by f rac tu re . Necking f a i l u r e may be approached by an i n s t a b i l i t y anal s i s If we con- s ide r the greatest tension ( force per u n i t widthf i n ' t h e sheet as </p><p>As already mentioned </p><p>T1 = 'lt (1 1 as i l l u s t r a t e d i n Fiqure 3 where l r i s the area tes t o r i nc ioa l . </p><p>I . tens i le , s t ress and t the cur ren t thickness;then the maximum ten- s ion occurs when </p><p>t a i n working process. ' The app l i ca t i on o f the same ana ly t i ca l techniques t o sheet </p><p>metal forming processes i s much less widespread. Reference [8] Drovides some simole examDles o f the o l a s t i c col laose o f f l a t A T p la tes by bending' i .e . the format ion o f a p l a s t i c hinge along cer - u'l uGl d t = t a i n l i n e s i n the surface o f a p l a t e t o form a mechanism. The 7 = T+F- same idea can be app l ied t o the p l a s t i c forming o f sheet metal , where a f i n a l shape can be achieved by bending along spec i f i ed curved o r s t r a i g h t l i n e s i n the surface o f t he sheet, see Refer- ences 114-161, and the discussion l a t e r i n t h i s tex t . S l i p l i n e f i e l d ana lys is can a i d i n the development o f t he best i n i t i a l blank shape when deep drawing i r r e g u l a r par ts [17]. symnetrical ear ing, which i s o f ten seen when drawing c y l i n d r i c a cups from s tee l d iscs. can be pred ic ted using an iso t rop ic s . l . f l [ l8] . Szczepinski [1...</p></li></ul>

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