Process and die design for square tube extrusion

Transcription

1 Indian Journal of Engineering & Maerials Sciences Vol. 16, February 2009, pp Process and die design for square ube exrusion K K Pahak a *, S Lomash b & A K Jha a a Advanced Maerials and Processes Research Insiue (CSIR, Bhopal , India b Bhara Heavy Elecricals Ld., New Delhi , India Received 9 July 2008; acceped 17 December 2008 In his sudy, die profile of he square ube exrusion process is opimized o produce microsrucuarlly sound produc a maximum producion speed and minimum lef ou maerial in he die. The design problem is formulaed as a nonlinear programming model, which is solved using geneic algorihms (GA. Selecion of he processing parameers is carried ou using dynamic maerial modeling (DMM. Using his approach a square ube exrusion process is successfully designed. Keywords: Microsrucure; Die profile; Simulaion, Processing parameers; Exrusion; Geneic algorihms Exrusion die profile plays an imporan role on maerial flow, microsrucural evoluion, speed of producion and lef ou maerial in he die. Conical dies, designed using convenional mehods, suffer from wo major drawbacks. Firs, he formaion of dead meal zone and secondly large amoun of lef ou maerial in he die caviy. Samana 1 proposed an approach for convex shape die profile for axisymmeric exrusion and drawing using upperbound heorem. Efficiencies of hese dies exceed hose of convenional conical dies. Reddy e al. 2,3 repored die profile design for ho and cold exrusion using upper bound mehod and FEM. Joun and Hwang 4 aemps shape opimal design of ube exrusion using sensiiviy and rigid visco-plasic finie elemen approach. Kim e al. 5 opimized die profile of axisymmeric exrusion of MMCs using FEM in order o obain uniform srain rae profile. Ponalagusamy e al. 6 aemps o design sreamlined dies using Bezier curve and upperbound heorem. Lee e al. 7 opimized he die profile using Bezier curve o ge uniform microsrucure in ho exrusion. Neural neworks are used in die profile design by Yan and Xia 8 and Meha 9. Geneic algorihms are also applied for die profile design by Wu and Hsu 10, Chung and Hwang 11 and Narayanasamy e al. 12 Alhough large amoun of lieraure is available on die profile design, i can be observed ha hey address specific aspec of manufacuring. I is very rare o find lieraure, which address meallurgical and *For correspondence ( kkpahak1@rediffmail.com manufacuring aspecs alogeher. To overcome his issue, a holisic approach of die profile design using power law equaion is proposed here. The imporan feaures of his are: (i selecion of processing parameers using DMM for microsrucurally sound produc and (ii maximizaion of he speed of producion a minimum lef ou maerial in he die caviy. The design problem is formulaed as a non-linear consrained programming problem, which is solved using geneic algorihms (GA. A ube exrusion process is successfully opimized using he proposed approach. Designed parameers are furher used for compuer simulaion. Dynamic Maerial Modeling (DMM DMM is based on relaionship beween he deformaion induced visco-plasic hea generaion and he energy dissipaion associaed wih he microsrucural mechanisms occurring during deformaion. DMM uses a non-dimensional iso-efficiency index (η and i is given as 13 η = m 1 + m (1 where m is he srain rae sensiiviy of he maerial. The plo of iso-efficiency (η values on he emperaure-srain rae axes wih he inerpreed deformaion mechanism mapped on o he plo consiue he processing map. The regions of high efficiency regime are he desirable region for he processing. The rue sress-plasic srain values, a

2 52 INDIAN J. ENG. MATER. SCI., FEBRUARY 2009 differen srain raes, are required for compuing he efficiency facor (η. The procedure of consrucing he map is presened elsewhere. 13 In Fig. 1, processing map of 304 LN is shown. I can be observed, maximum iso-efficiency is abou 29% and corresponding srain rae and emperaure are 0.1 and 1100 C respecively. The highes efficiency will correspond o dynamic recrysalizaion which in urn will ensure good workabiliy. DMM has been successfully used for designing of meal forming processes Geneic Algorihms Geneic algorihms are compuerized search and opimizaion algorihms based on he mechanics of naural geneics and naural selecion 16. The operaion of GA s begins wih a populaion of random srings or decision variables. Thereafer, each sring is evaluaed o he finess value. Three main operaors, viz., reproducion, crossover, and muaion are used o creae a new populaion of poins hen operae he populaion. The populaion is furher evaluaed and esed for erminaion. If he erminaion crierion is no me, he populaion is ieraively operaed by he above hree operaors and evaluaed. This procedure is coninued unil he erminaion crierion is me. One cycle of hese operaions and he subsequen evaluaion procedure is known as a generaion in GA s erminology. The basic difference of GA s wih mos of he radiional opimizaion mehods are ha GA use a coding of variables insead of variables direcly, a populaion of poins insead of a single poin, and sochasic operaors insead of deerminisic operaors. All hese feaures make GA search robus, allowing hem o be applied o a wide variey of problems. The advanage of using GA over oher gradien based mehods, is ha he laer can be mapped on local minima whereas, GA predics global minima which may be hidden beween several local minima (Fig. 2. In recen years GAs have been successfully applied o die design problems 10,11,17. Formulaion of Design Problem A schemaic of he die for square ube exrusion is shown in Fig. 3. Le D b, D e and D m be he dimensions of bille, exruded rod and mandrel respecively and Fig. 2 Local and Global Minima Fig. 1 Processing map of 304LN Fig. 3 Schemaic die for square ube exrusion

3 PATHAK e al.: PROCESS AND DIE DESIGN FOR SQUARE TUBE EXTRUSION 53 Maerial volume required o fill he die caviy is: {( Db De 3 Dm ( Db De } V = (2 6an ( α If v is he ram velociy hen ime o fill his volume will be T = V D D v ( b m Now srain rae can be calculaed by (3 ln R & ε = (4 T where R is he exrusion raio given by R= D D ( b m ( De Dm (5 Selecion of srain rae and emperaure can be carried ou via he processing map o mee ou meallurgical aspecs. Using hus seleced process parameers, raio of velociy o caviy volume can be maximized o resul in faser producion a minimum wasage of maerial. The whole design problem can be pu ino following opimizaion problem: Max v / V (6 Subjec o & ε ( v, α = c v min v v max α min v, α 0 α α max Here c is he srain rae obained from he processing map. Min and max are he limis of differen parameers. This consrained opimizaion problem is solved using GA. The flow char of he design process is shown in Fig. 4. Numerical Example A square ube exrusion process considering 304LN seel is designed using he proposed approach. Exernal and inernal dimensions of he ube are 20 and 16 mm. Ouer dimension of he bille is 80 mm and mandrel dimension is 16 mm. Exrusion raio is The minimum and maximum limis on velociy (v and die angle (α are 0 and 1 mm/s, 40 and 80 respecively. Processing map of 304L is shown in Fig. 1. The maximum iso-efficiency is abou 29% and corresponding srain rae and emperaure are 0.1 and 1100 C respecively. Using hese parameers he opimizaion of he above menioned objecive funcion is carried ou using GA. The GA parameers adoped in his sudy are given in Table 1. The Table 1 GA Parameers S. No. GA parameer Value 1. Populaion Generaions Reproducion ype 2 poins Crossover 4. Selecion ype Sigma Scaling 5. Muaion probabiliy Reproducion probabiliy Selecion probabiliy 0.85 Fig. 4 Flowchar of he proposed mehodology Fig. 5 Flow curve of 304 LN

4 54 INDIAN J. ENG. MATER. SCI., FEBRUARY 2009 Fig. 6 CAD Model Fig. 9 Srain rae Fig. 7 Effecive sress (MPa Fig. 8 Plasic srain Fig. 10 Load sroke curve opimized ram velociy and die angle come ou o be mm/s and respecively. Compuer simulaion on he opimized die is carried ou using MSC. Superforge sofware, which is based on conrol volume mehod 18. The maerial model is carried ou using rae power law: σ = K & ε (7 n where K and n are he coefficiens of rae dependen flow curve The flow daa for his maerial is given elsewhere 21. The coefficiens K and n of he rae flow curve for he given emperaure and srain rae are and 0.17 respecively. Yield sress is aken as MPa. Flow curve of 304 LN is shown in Fig. 5. The opimized die profile has been used for he compuer simulaion. A ypical CAD model showing die, punch and he mandrel is given in Fig. 6. Lengh

5 PATHAK e al.: PROCESS AND DIE DESIGN FOR SQUARE TUBE EXTRUSION 55 of he bille is 200 mm and Coulomb fricion is 0.1. Von mises sress, effecive plasic srain and srain rae conours obained from he simulaion are shown in Figs 7-9. Maximum sress is MPa, which indicae he yielding of he bille during deformaion. Maximum srain is 2.118, indicaing considerable deformaion during exrusion. Average srain rae in he deformaion zone is 0.1, which will ensure good microsrucure evoluion. The load sroke curve is shown in Fig. 10. I can be observed ha maximum load requiremen will be MN. Conclusions In his sudy, die and process for square ube exrusion is opimized o mee ou microsrucural crieria a maximum producion speed and minimum lef ou maerial in he die caviy. The exrusion process design is formulaed as a consrained nonlinear programming problem, which is solved using GA. An exrusion process is successfully design based on his approach. Compuer simulaion is also carried ou on he opimized design o obain sress, srain and srain rae disribuions and load requiremen. I can be observed ha proposed approach provides a oal soluion for exrusion process design of he square ube. Acknowledgemen Permission of ASM Inernaional o reproduce processing map of 304 LN is graefully acknowledged. References 1 Samana S K, Flow Turbulence Combus, 25(1 ( Venkaa Reddy N, Dixi P M & Lal G K, J Maer Process Technol, 55 ( Venkaa Reddy N, Dixi P M & Lal G K, In J Mach Tool Manufac, 37 (11 ( Joun M S & Hwang S M, In J Numer Mehods Eng, 41 ( Kim N H, Kang C G & Kim B M, In J Mech Sci, 43 ( } Ponalagusamy R, Narayanasamy R & Srinivasan P, J Maer Process Technol, 161 ( Lee S K, Ko D C, Kim B M, In J Mach Tool Manuf, 40 ( Hong Yan & Juchen Xia, Sci Technol Adv Maer, 7 ( Bhavin V Meha & Hamza Ghulman, J Maer, 51 ( Wu C Y & Hsu Y C, In J Adv Manuf Technol, 19 ( Chung J S & Hwang S M, J Maer Process Technol, 72 ( Narayanasamy R, Srinivasan P & Venkaesan R, J Maer Process Technol, 138(1-3 ( Prasad Y V R K & Sasidhara S, Ho working guide: A compendium of processing maps (ASM Inernaional Park, OH, USA, Srinivasan N, Ramakrishnan N, Venugopal Rao A & Swamy N, J Maer Process Technol, 124 (3 ( Venugopal S, Sivaparsad P V, J Maer Eng Perform, 12(6 ( Kalyanmoy Deb, Opimizaion for Engineering Design Algorihms and Examples, (Prenice Hall of India Privae Limied, New Delhi, India, Narayanasamy R, Venkaesan R & Ponalagusamy R, J Ins Eng, Singapore, 45( User s manual, MSC.Superforge, Dieer G.E, Mechanical meallurgy (McGraw Hill, Hosford W F & Caddell, R M, Meal forming: Mechanics and meallurgy. (Prenice-Hall,USA, Alan T, Oh S & Gegel H L, Meal forming: Fundamenals and applicaions, (ASM, Meals Park, OH, USA, 1983.