Analysis of wire-drawing process with friction and thermal conditions obtained by inverse engineering

Transcription

1 Journal o Mecanical Science and Tecnology 6 (9) () 93~9 OI.7/s6--7- Analysis o wire-drawing process wit riction and termal conditions obtained by inverse engineering Cangsun Moon and Naksoo Kim * epartment o Mecanical Engineering, Sogang University, -74, Korea (Manuscript Received September 3, ; Revised Marc 7, ; Accepted April 3, ) Abstract In cold wire-drawing process, wic is perormed at room temperature, eat is generated because o plastic work and riction at te workpiece-die interace. Temperature distribution in bot te workpiece and te die aects termal expansion, deormation pattern, and elastic recovery. Tese eects produce te inal dimension o te drawn products. We propose inverse engineering procedures to determine riction and termal conditions by comparing simple measurements wit te computational results o te drawing power and te temperature canges o te die. Te conditions were ten used to simulate numerically te deormation beavior o te wire and te temperature distribution in te die. Te termal eects on te quality o drawn products were investigated based on te prediction o te inal dimensions o te products. Tereore, termal eects sould not be ignored even in cold wire-drawing process because reasonable numerical results were acquired in comparing te experiments. Keywords: Wire-drawing; imensional cange; Quality o drawn product; Friction condition; Termal condition; Inverse engineering Introduction In wire-drawing process, te diameter o a wire is reduced by pulling te wire troug a conical die. Major variables in drawing process include reduction ratio, die angle, riction at te interace o te wire and te die, and drawing velocity. Plastic deormation o te wire and eat generation due to riction between te wire and te die increase te temperature o te die, wic results in termal expansion. Te trend o using ig speeds in te wire-drawing process to meet te demands o increasing productivity results in te diiculty o manuacturing drawn products wit a designated diameter because o te uncontrolled termal expansion o te die. Te magnitude and te distribution o temperature in te wire and te die depend on initial temperatures, eat generation due to plastic deormation in te wire, riction at te wire-die- interace as well as eat transer between te deorming wire, te die, and te surrounding environment, suc as ricants and te air. Heat generation in wire-drawing process was irst studied by Siebel and Kobitzsc []. In teir analysis, te plastic deormation work per unit volume was simply added to rictional work, and bot were converted to eat. Snidle urter expanded te teory o Siebel and Kobitzsc by considering * Corresponding autor. Tel.: , Fax.: address: nskim@sogang.ac.kr Recommended by Editor Sung-Lim Ko KSME & Springer te acceleration o te wire as it passes troug te die []. Lucca and Wrigt discussed te assumptions tat may be considered in predicting te increase in temperature due to rictional eating in te wire drawing [3]. Tey mentioned tat te coeicient o riction at te wire-die- interace is constant and independent o pressure and temperature. Tey also reported tat rictional eating is concentrated on te interace between te wire and te die, wic results in severe temperature gradient. Many process variables, besides eat rom drawing process, aect te quality o drawn products. U.S. ixit and P.M. ixit studied te eect o process variables, suc as reduction ratio, semi-angle o te die, and coeicient o riction o te interace, on te quality o te drawn product [4]. Castro et al. analyzed te eect o te die s semi-angle on te mecanical properties o annealed copper bars [5]. To identiy te eect o inclusion, Norasetasopon and Yosida studied te eect o inclusion size and parameters o te aspect ratio o drawing stress, te maximum ydrostatic stress, and te maximum die pressure during te single-ilament copper wire-drawing process [6]. Vega et al. measured te temperature and te drawing orce by canging te drawing velocity, wile te drawing orce was measured by using a wire-rolling gauge beind te die [7]. Furtermore, tey installed a termocouple to measure te temperature increase in te deormation zone. Tey conirmed rom teir experiment tat te temperature and te drawing orce were dependent on interace conditions. Leu evaluated

2 94 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 riction coeicient by using a model o plastic emisperical contact against a rigid lat [8]. To describe te deormed emisperical sape, e utilized te ractional proile o an ellipsoid and simultaneously deined te contact area ratio. To investigate dependence o te sear riction actor on d/t and L/, Ajiboye et al. conducted an ANOVA and compared two regression models [9]. Based on te statistical results o te investigation, te model tat used d/t as te independent variable was valid in successully predicting te sear riction actor at te punc interace compared wit oter models tat used tat use L/ kn. Obi and Oyinlola investigated attybased oils or metal-orming applications []. By measuring te coeicient o riction, grading tese oils according to teir ricating capabilities becomes possible since one o te qualities o a good ricant is te ability to reduce riction and applied to apply load. Luksza et al. ocused on te deormation beavior o te wires wile conducting experiments on bot te single- and te multi-pass- drawing processes []. Corrêa et al. analyzed te inluence o structural eatures o te drawn wire on te strain-sotening penomenon []. Tey also conducted micro-structural and X-ray diraction analyses to evaluate te drawing stress. Son et al. investigated te deormation beavior o surace deects wit a notc sape on te wire in a multi-pass ot-rolling process by using a inite element code called CAMProll [3]. Residual stress on te drawn products as a signiicant eect on post-deormation. Överstam examined te eect o bearing geometry o te die on residual stress o te drawn wire [4]. Atienza et al. studied te inluence o residual stresses on environmentally assisted cracking o te wire [5]. Carpinteri et al. investigated te eect o atigue crack propagation in a metallic-cracked round bar wit a V-saped circumerential notc on residual stresses [6]. Ripoll et al. proposed a reduction o circumerential residual stresses during wire drawing using advanced die geometry and perorming bending operations under avorable conditions [7]. El- omiaty and Kassab studied ways to minimize te energy required or te wire-drawing process [8]. To minimize te drawing orce, tey determined te reduction ratio and te coeicient o riction between te wire and te die. Sinoara and Yosida carried out a multi-pass drawing o stainless steel wire wit an artiicial crack, and ten investigated te growt and te disappearance o te crack rom bot sides troug experiments and te inite element analysis (FEA) [9]. Komori presented a new equation tat denoted a cange in te void volume raction suc racture deects in ig-carbonsteel wires can be investigated []. McAllen and Peland analyzed te ductile racture initiation and propagation by central bursting in Aluminium wire, wile te damage incurred beore te ductile racture was studied by using a modiied damage model []. Since te increase in temperature in te die aects te ricating condition, te equipment lie, and te quality o te drawn products, te accurate prediction o te temperature distribution in te die is crucial. Previous studies on temperature and products in te wire-drawing process primarily addressed te increase in temperature in te die because o deormation and generated rictional eating as te wire passes troug te die. Related literature also discussed te increase in temperature due to process variables suc as reduction ratio, reduction angle, and drawing velocity. In contrast, no inormation is available about FEA procedures or te conduct o practical analysis o temperature distribution in te die, wic considers riction condition and eat transer to te surroundings, suc as in te air. Tis study proposes a procedure tat utilizes measured drawing power and temperature curves o te die at a certain position in determining riction and termal conditions by inverse engineering. Te obtained process variables will be used to simulate numerically te deormation beavior o te workpiece and te die temperature distribution by FEA. Hence, te investigation on te eect o temperature distribution on te inal dimensions or quality o te drawn products can consequently proceed.. rawing conditions. Process parameters Fig.. Scematic outline o te model used in te experiments and in FEA; parameters tat deine te die geometry. Te dimensions o tooling tat is used in wire-drawing process are scematically illustrated in Fig.. As sown in Fig., te inlet and te outlet diameters o te die are =

3 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 95 Table. Termal properties o selected materials. Material S45CS WC AISI-H-3 Heat conductivity ( W / mk ) Heat capacity ( J / mmk ) Termal expansion coeicient (/ K ).397e-5 5e-5.7e-5 Fig.. True stress-strain curve o S45CS. mm and = 8. mm, respectively. Te eigt o te die and case assembly () is 3.95 mm and te widt o te case (w) is 35 mm. Te wire, te die, and te case were made o S45CS, WC, and AISI-H-3, respectively. Fig. sows te die geometry. Te parameters tat deined te die geometry include te back relie angle, te reduction angle, te entrance angle, and te bearing lengt. Fig. exibits te low stress o S45CS at C and C. Table displays te termal properties o te selected materials tat are used as workpieces or tools in te wire-drawing process. Te drawing velocity was 96 mm/s, te initial temperature o te tools was 3 C, and te environmental temperature was C.. Experiments In te wire-drawing process, wires were pulled out troug a die at constant drawing velocity. Friction acted on te interace between te wire and te die, and disrupted te relative motion o te wire. Te dierence in te drawing orce depended on te magnitude o te riction. To estimate riction stress, we used a simple riction model wit a constant riction actor. Te riction stress in te actual process can be inversely determined by measuring te drawing power using te drawing equipment []. Te drawing power was measured by using a wire-rolling gauge beind te die. Te drawing powers were measured by using several combinations o te diameter o te wires, te inner diameter o te die, and te reduction ratio. Fig. 3 contains te scematic diagram tat illustrates te measurement o temperature on te die in te wire-drawing process. A termocouple was installed to measure te die temperature at a certain position. For approximately 4 sec, te wire was pulled troug a die and te temperature at a speciic position was recorded. Fig. 3 sows te temperature curve measured or 4 sec. Te temperature reaced as ig as 7.4 C during te wire-drawing process. 3. Inverse engineering or determination o experimental conditions Friction conditions can be determined by comparing te drawing power obtained rom te experiments wit a calculated drawing power using FEA wit an assigned riction actor. Similar metods were employed to determine termal conditions by comparing te measured temperature curves o te die wit tose o te calculated ones tat will be described later. In FEA computations, we evaluated te eat transer coeicients or all parts. We used EFORM (ver. 9., Scientiic Forming Tecnologies Co., USA) or te wiredrawing process simulation. Te die and te case were assumed elastic, wile te wires exibited elastic-plastic deormation beavior. Te drawing analysis was conducted based on te two-dimensional axisymmetric model. 3. Friction conditions Fig. 3. Measurement o te die temperature during te wire-drawing process: experimental setup; temperature transition at cannel. Pressure and a sliding motion at te interace between te wire and te die resulted in wire deormation, and generated rictional eating tat led to an increase in temperature. Te elevated temperature aected te drawn products. Friction, wile by itsel inluenced te wire deormation pattern, and served as anoter important actor tat aected temperature.

4 96 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 Table. Friction actors calculated by Eq. (3) and a comparison o te drawing orces between te experiments and FEA ( m =.765). CASE V (mm/s) P (kw) (Experiment) F(N) (Experiment) m Eq. (3) F(N) (FEA) ierences (%) (Experiment vs FEA) CASE CASE CASE Average. Fig. 4. Temperature distribution o die ater.5 sec; temperature curves o nodes,, and 3. I a wire is pulled troug a die at a constant velocity in te wire-drawing process, te pulling orce varies depending on te rication status. rawing power, P drawing, drawing orce F drawing, and drawing stress σ d can be calculated using Eqs. ()-(3), respectively [3]. Pdrawing = Fdrawing Vdrawing velocity () F = σ A () drawing d m R σ d = Y + + sin α R 3 ( )ln tan α I we measure te drawing power P drawing at constant V drawing velocity, te drawing stress σ d can be easily estimated using Eqs. () and (). Ideally, te riction actor m is calculated by Eq. (3). However, since Eq. (3) does not consider excessive or redundant deormation and ignores temperature eects on yield stress Y, te estimated value o riction actor using Eq. (3) is expected to ave a discrepancy wit te actual value. We measured te drawing powers or tree cases wit te same materials and te same conditions o rication, except geometrical dimensions suc as te diameter o te wire, te inner diameter o te die, and te reduction ratio (Table ). We assumed tat te same riction condition applied to all tree cases, wic resulted in one value o riction actor m. Te dierence between experimental and calculated drawing orces can be expressed as a quadratic unction o m as expressed in Eq. (4). Multiple simulations o FEA wit dierent values o m near te minimum, obtained tis dierence. (3) E = m m + (4) error Te riction actor can be determined as a value tat is closest to te drawing orce obtained rom te experiments. Te value minimizing te dierence in te equation above was m =.765, wic gives a good correlation among te tree cases but te value is twice as muc as te value obtained using Eq. (3). Since Eq. (3) does not consider te decrease in low stress due to temperature rise, m is underestimated. In te cold wire-drawing process, termal eect sould tereore not be ignored. 3. Termal conditions 3.. Temperature at te wire-die interace Heat is generated by plastic deormation and riction in te wire-die interace. Ten, te eat is transerred to te die and to te environment. Te temperature at te wire-die interace becomes constant witin a sort time period. In oter words, a termally steady state at te interace is attained in te wiredrawing process. Te calculated riction actor ( m =.765) was used to obtain te temperature transition curve at te interace by carrying out a FEA simulation or deormation and to determine te temperature o te workpiece and te die. Fig. 4 sows te temperature distribution in te die and tree speciic points at te interace. Fig. 4 sows te increase in temperature at tree points. Temperature veriiably becomes constant in less tan.5 sec. Te temperature distribution along te wire-die interace, ater attaining a termally steady state condition, was used as a

5 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 97 Fig. 5. Model o eat transer on te surace during te FEA simulation in wire-drawing process. (c) Fig. 6. Two models: one-object model; two-object model, and te eects o interacial eat transer coeicient; (c) temperature curves wit dierent values. boundary condition o temperature in inverse engineering to identiy eat transer coeicients at te oter boundary. 3.. Boundary conditions or wire-drawing model For te relevant simulation o eat transer in wire-drawing process, appropriate eat transer coeicient at eac boundary o tool ragment needs is necessary to be applied, as sown in Fig. 5. Te interace o te wire and te die a-b in comparison wit te interace o te die and case c-g- as te same interace eat transer coeicient deined as. Tis assumption is reasonable considering tat te interaces are closely inluenced by ig pressure. Heat transer coeicient at te case boundary d-e to te support is deined as. b-c-d and e--a o te case tat comes in contact wit te air comprise te convective eat transer coeicient. Te support o te case is assumed to ave te same temperature as te air in te environment etermination o Te convective eat transer coeicient ( ) is between.-.5 kw / m K wen in contact wit air o atmospere pressure, wit te assumed value to be.5 kw / m K [4, 5]. As sown in Fig. 6, a simple metod was used to determine

6 98 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 Table 3. Levels o design variables. esign variables Initial value Level Level Level ( kw / m K ).... ( kw / m K ) Table 4. Ortogonal arrays or te optimization o te area. Fig. 7. Temperature transition curves obtained by experiment and computation.. Fig. 6 is a one-object model using two dierent materials, wereas Fig. 6 is a two-object model using two dierent materials. As sown in 6, te model was eated at a certain temperature, and te temperature at a certain position was measured. Te model in Fig. 6 was eated at te same temperature as te model in Fig. 6, but was canged to compare te temperature curve o te models in Fig. 6 and 6. As illustrated in Fig. 6(c), temperature curves coincided wit tat o te one-object model or o more tan kw / m K. Tus, o kw / m K can be reasonably assumed as applicable. Exp. No ( kw / m K ) ( kw / m K ) Object unction area ( mm ) 393,97 39,99 39,96 389,44 38,639 38, ,76 378,449 37,6 Error (%) etermination o and To obtain te appropriate values o and, te design o te experiments was applied to te unction o te area dierence under te temperature transition curves between te measurement and te computation, as sown in Fig. 7. Based on te study o Yen et al., initial assumptions o and were set as. and.5 kw / m K, respectively [4]. Te constraint condition o was set rom. to. kw / m K, wit te relative error set as less tan 4% in te range. Table 3 sows te initial value and te level o te design parameters. Te calculation results using FEA are summarized in Table 4. Te response surace metod was based on ortogonal arrays to obtain an objective unction tat comprises te design parameters. Te object unction or optimization is expressed in Eq. (5). c Φ =,4,88 + 8,48 35,74 5,4 + 4,57 +,8 BFGS was used to minimize te objective unction. Te metod is an optimization metodology tat directly updates a Hessian matrix. As a result, te design parameter was determined as. kw / m K, wile was.46 kw / m K. Te calculated parameters were compared wit te FEA results. and can be considered as appropriate since te comparison revealed less tan.5% margin o error. (5) Fig. 8. Measurement metod or dimensional cange troug: te experiment; FEA. 4. imensional canges o te drawn wire 4. einition o dimensional cange and numerical steady state As te wire passes troug te drawing die, te inal dimension o te drawn wire deviates rom te designated dimension or te inner diameter o te die. Te die wear is ignored due to elastic deormation o te die, elastic recovery o te workpiece, and termal expansion o bot te die and te workpiece. Te dimensional dierence between te drawn wire and te designated dimension is deined as te dimensional cange. In te experiment, dimensional cange is measured by subtracting te inner diameter o te die rom te average diameter o te drawn wire. Fig. 8 demonstrates tat te average diameter was calculated ater measuring diameters in te sample at tree points. Te size o te population was 5 wire samples, wit 3 m cut o ater drawing. Te standard deviation was.5%.

7 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 99 Table 5. Comparison o dimensional canges. CASE β L ω ( ) γ ( ) imensional canges, (eviation rom measurement, %) FEA wit termal Isotermal Experiment eect FEA CASE (%).(5%) CASE (5%).5(8%) CASE (%).(%) Te eects o termal deormation and elastic recovery o te workpiece and te die on te inal dimensional accuracy were investigated in oter metal-orming processes [6, 7]. In tis study, riction and termal conditions obtained rom inverse engineering were used to simulate numerically te deormation and te occurrence o eat transer during cold wire-drawing process using FEA. Te termal eect on te inal dimension o te drawn products is intended to be examined. Te inner diameter o te die wit termal eect was less tan tat o te isotermal case, wic resulted in te reduced dimensional cange o te wire by.3-.4 mm or tree cases o die geometry, as summarized in Table 5. Table 5 also sows te dimensional canges o te drawn wire wit tree cases o die geometry measured in te experiments, and computations wit and witout termal eect, respectively. Te computation results considering termal eect is twice closer tan tose calculations witout termal eect. Fig. 9. rawing orce in te steady state o wire-drawing process (FEA). Te calculation results o FEA or te wire-drawing process revealed tat te nodes, wic represent te surace o te wires, did not ave te same dimensions as sown in Fig. 8. Tereore, te numerical average diameter o te drawn wire must be deined. Te calculated diameter is deined as te volumetric average o te diameter wit a certain number, suc as 5 nodes, on te wire surace. Te calculated diameter is meaningul or te comparison wit experiments since te level o te computed deviation was less tan.%. In te wire-drawing process, te deormation pattern in te wire acieved a steady state ater te wire was drawn to a certain lengt. In te calculation, te steady state was attained ater te drawing orce became constant, as sown in Fig Termal eect on dimensional cange 5. Conclusions Inverse engineering procedures to determine riction and termal conditions in wire-drawing process are proposed by measuring te drawing orce and te transition curve o temperature at a certain position o te die assembly. Te analysis tool used in inverse engineering was a commercial FEA program based on elastic-plastic deormation and coupled eat transer algoritm. Comparison between te calculated results and te obtained measurements in te experiments, te ollowing conclusions are derived: () Wit te identiied riction actor via inverse engineering, te calculated drawing orces exibited a strong correlation. In addition, we obtained close temperature curves or te experiments wit known termal conditions or eat transer coeicients. Tereore, metodology o inverse engineering reasonably determines riction and termal conditions. Moreover, since te measurements include te drawing orce and te monitoring temperature at a convenient position, te metod is simple and useul to be applied in actual conditions. () Te calculated dimensional canges tat considered te termal eect were closer to te measurements tan tose tat did not consider te termal eect. Tus, simulation o cold wire-drawing process wit FEA sould always consider te termal eect. Correct values o riction and termal conditions sould be used to yield reliable calculation results. (3) Te calculated dimensional canges relect termal and elastic deormation o te die and elastic recovery o te workpiece. Since te FEA calculation results conormed to te experiments, we can utilize FEA to identiy te contribution o eac source to dimensional cange. We may control dimensional canges by varying process parameters, wic results in te enancement o quality o te drawn wire. Acknowledgements We would like to tank te members o te instrumentation and control team in ongbu Steel Co. Ltd. or teir supporting in tis researc. Tis work was also supported by te National Researc Foundation o Korea (NRF) wit te grant provided by te Korean government (MEST) (No. -35) and

8 9 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 by te Sogang University Researc Program wit Grant No. 4.. Nomenclature σ d : rawing stress Y : Yield stress m : Friction actor R : Wire radius beore drawing R : Wire radius ater drawing R e : Reduction ratio : Wire diameter beore drawing : Wire diameter ater drawing A : Wire area ater drawing F : rawing orce P : Power V : rawing velocity E error : Average error : Convective eat transer coeicient : Interace eat transer coeicient between wire and dies : Interace eat transer coeicient between dies and case Reerences [] E. Siebel and R. Kobitzsc, ie Erwarmung des Ziegutes beim ratzieen. Stal U. Eisen (63) (943) -3. [] R. W. Snidle, Contribution on te teory o rictional eating and te distribution o temperature in wire and strip drawing, Wear (44) (977) [3]. A. Lucca and R. N. Wrigt, Heating eect in te drawing o wire and strip under ydrodynamic rication conditions, Journal o Manuacturing Science and Engineering (88) (996) [4] U. S. ixit and P. M. ixit, An analysis o te steady-state wire drawing o strain-ardening materials, Journal o Materials Processing Tecnology (47) (995) -9. [5] A. L. R. de Castro, H. B. Campos and P. R. Cetlin, Inluence o die semi-angle on mecanical properties o single and multiple pass drawn copper, Journal o Materials Processing Tecnology (6) (996) [6] S. Norasetasopon and K. Yosida, Inluences o inclusion sape and size in drawing o copper saped-wire, Journal o Materials Processing Tecnology (7) (6) [7] G. Vega, A. Haddi and A. Imad, Temperature eects on wiredrawing process: experimental investigation, International Journal o Material Forming () (9) Suppl :9-3. [8]. K. Leu, Evaluation o riction coeicient using simpliied deormation model o plastic emisperical contact wit a rigid lat, Journal o Mecanical Science and Tecnology (4) () [9] J. S. Ajiboye, K. H. Jung and Y. T. Im, Sensitivity study o rictional beavior by dimensional analysis in cold orging, Journal o Mecanical Science and Tecnology (4) () 5-8. [] A. I. Obi and A. K. Oyinlola, Frictional caracteristics o atty-based oils in wire drawing, Wear (94) (996) [] J. Luksza, J. Majta, M. Burdek and M. Ruminski, Modelling and measurements o mecanical beaviour in multipass drawing process, Journal o Materials Processing Tecnology (8-8) (998) [] E. C. S. Corrêa, M. T. P. Aguilar and P. R. Cetlin, Te inluence o cyclic straining on te work ardening beavior o AISI 34 stainless steel bars in multiple-pass drawing, Materials Cemistry and Pysics (6) (7) 95-. [3] I. H. Son, J.. Lee, S. Coi,. L. Lee and Y. T. Im, eormation beavior o te surace deects o low carbon steel in wire rod rolling, Journal o Materials Processing Tecnology () (8) [4] H. Överstam, Te inluence o bearing geometry on te residual stress state in cold drawn wire analysed by te FEM, Journal o Materials Processing Tecnology (7) (6) [5] J. M. Atienza, M. Elices, J. R. Hervias, L. Caballero and A. Valiente, Residual stress and durability in cold drawn eutectoid steel wires, Metals and materials International (3) (7) [6] A. Carpinteri, R. Brigenti and S. Vantadori, Inluence o te cold-drawing process on atigue crack growt o a V- notced round bar, International Journal o Fatigue (3) () [7] M. R. Ripoll, S. M. Weygand and H. Riedel, Reduction o tensile residual stresses during te drawing process o tungsten wires, Materials Science and Engineering: A (57) () [8] A. El-omiaty and S. Z. Kassab, Temperature rise in wiredrawing, Journal o Materials Processing Tecnology (83) (998) [9] T. Sinoara and K. Yosida, eormation analysis o surace laws in stainless steel wire drawing, Journal o Materials Processing Tecnology (6-63) (5) [] K. Komori, Evolution o void volume raction or simulating inner racture deects related to in drawing o igcarbon steel wire rods, Teoretical and Applied Fracture Mecanics (5) (8) [] P. J. McAllen and P. Pelan, Numerical analysis o axisymmetric wire drawing by means o a coupled damage model, Journal o Materials Processing Tecnology (83) (7) -8. [] L. Lazzarotto, L. ubar, A. ubois, P. Ravassard and J. Oudin, Identiication o Coulomb's riction coeicient in real contact conditions applied to a wire drawing process, Wear () (997) [3] G. E. ieter, Mecanical metallurgy, SI Metric Ed. McGraw-Hill Book, UK (988). [4] Y. C. Yen, Soner, B. Lilly and T. Altan, Estimation o tool wear in ortogonal cutting using te inite element analysis, Journal o Materials Processing Tecnology (46) (4) 8-9. [5] P. P. Incropera,. P. ewitt, T. L. Bergman and A. S.

9 C. Moon and N. Kim / Journal o Mecanical Science and Tecnology 6 (9) () 93~9 9 Lavine, Introduction to eat transer, it Ed. Jon Wiley & Sons, USA (7). [6] H. Long and R. Balendra, FE simulation o te inluence o termal and elastic eects on te accuracy o cold-extruded components, Journal o Materials Processing Tecnology (84) (998) [7] Y. S. Lee, J. H. Lee, Y. N. Kwon and T. Isikawa, Analysis o te elastic caracteristics at die and work-piece to improve te dimensional accuracy or cold orged part, Journal o Materials Processing Tecnology (53-54) (4) Cangsun Moon is currently working or LG Electronics ater obtaining is Master s degree in te epartment o Mecanical Engineering, Sogang University. He received is B.S. degree rom te epartment o Mecanical Engineering, Inceon University, Inceon, Sout Korea in 9. His researc interests are in te areas o optimal design o orming process and metal-orming plasticity.