Skip to main content
SpringerLink
Log in

The optimal die semi-angle concept in wire drawing, examined using automatic optimization techniques

  • Original Research
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

Coupling of evolutionary algorithms (EA) with meta-models (MM) is used to investigate the concept of the optimal die semi-angle in wire drawing. Traditional process design by minimization of the wire drawing force highlights an optimal die angle which increases with friction factor and reduction ratio. When wire drawing optimization is applied on the Latham and Cockcroft damage criterion, an optimal die semi-angle no longer appears: in this mono-objective optimization, the lowest industrially achievable die angle is recommended. Thanks to EA-MM coupling, multi-objective optimizations have been performed and the Pareto optimal front has been precisely plotted so as to find the best compromise. Simultaneous optimization of damage and wire drawing force suggests a refined vision of the optimal die semi-angle concept. Choosing a lower angle than the traditional optimum allows damage to be decreased without a significant increase of the drawing force. However, it is shown that a die semi-angle slightly above the optimum should be selected, for fear of friction drift; this explains the rather high traditional value of the angle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

a :

Behaviour law parameter

D max :

Maximum value of the Latham and Cockcroft criterion

F :

Wire drawing force

K :

Behaviour law parameter

L :

Die length

\( \overline m \) :

Friction factor

N in :

Initial population of individuals (evolution strategy and genetic algorithm)

N FEM :

Number of processors

N max :

Maximum number of FEM simulations

N param :

Number of design variables

R :

Reduction ratio

R e :

Initial wire radius

R s :

Final wire radius

X :

Design variables vector (optimization)

α :

Die semi-angle

α opt :

Optimal die semi-angle

\( \varepsilon_{eq}^p \) :

Equivalent plastic strain

ϕ :

Objective function values

\( \widetilde{\phi } \) :

Metamodel-approximated values of ϕ

Δ\( \widetilde{\phi } \) :

Root mean square error of the Kriging approximation

λ :

Elongation ratio

λ GA :

Number of best individuals or parents (evolution strategy and genetic algorithm)

μ GA :

Children of λ best individuals after selection, combination and mutation (evolution strategy and genetic algorithm)

σ 0 :

Tensile yield stress

σ eq :

Equivalent stress

τ c :

Shear stress

References

  1. Wistreich JG (1955) Investigation of the mechanics of wire drawing. Proc Inst Mech Engrs (London) 169:654–665

    Article  Google Scholar 

  2. Evans W, Avitzur B (1968) Measurement of friction in drawing, extrusion and rolling. Trans ASME Series F, J Lub Tech 90(1):72–80

    Article  Google Scholar 

  3. Avitzur B (1963) Analysis of wire drawing and extrusion through conical dies of small cone angle. Trans ASME Series B, J Eng Ind 85:89–96

    Article  Google Scholar 

  4. Avitzur B (1964) Analysis of wire drawing and extrusion through dies of large cone angle. Trans ASME Series B, J Eng Ind 86:305–316

    Article  Google Scholar 

  5. Dixit US, Dixit PM (1995) An analysis of the steady-state wire drawing of strain-hardening materials. J Mater Process Technol 47:201–229

    Article  Google Scholar 

  6. Vega G, Haddi A, Imad A (2009) Investigation of process parameters effect on the copper-wire drawing. Material and Designs 30:3308–3312

    Article  Google Scholar 

  7. Luis CJ, León J, Luri R (2005) Comparison between finite element method and analytical methods for studying wire drawing processes. J Mater Process Technol 164–165:1218–1225

    Article  Google Scholar 

  8. Avitzur B (1968) Analysis of central bursting defects in extrusion and wire drawing. Trans ASME Series B, J Eng Ind 90:79–91

    Article  Google Scholar 

  9. Zimerman Z, Avitzur B (1970) Analysis of the effect of strain hardening on central bursting defects in drawing and extrusion. Trans ASME Series B, J Eng Ind 92:135–145

    Article  Google Scholar 

  10. Zimerman Z, Darlington H, Kottkamp HE (1979) Selection of operating parameters to prevent central bursting defects during cold extrusion. In: Hoffmanner AL (ed) Metal forming: interrelation between theory and practice. Plenum Press, New York, p 47

    Google Scholar 

  11. Chen CC, Oh SI, Kobayashi S (1979) Ductile fracture in axisymmetric extrusion and drawing. Trans ASME Series B, J Eng Ind 101(2):36–44

    Google Scholar 

  12. Chevalier L (1992) Prediction of defects in metal forming: application to wire drawing. J Mater Process Technol 32:145–153

    Article  Google Scholar 

  13. McAllen P, Phelan P (2005) A method for the prediction of ductile fracture by central bursts in axisymmetric extrusion. J Mech Eng Sci 219(C3):237–250

    Article  Google Scholar 

  14. McAllen P, Phelan P (2007) Numerical analysis of axisymmetric wire drawing by means of a coupled damage model. J Mater Process Technol 183:210–218

    Article  Google Scholar 

  15. Kuboki T, Abe M, Neishi Y, Akiyama M (2005) Design method of die geometry and pass schedule by void index in multi-pass drawing. J Manuf Sci Eng 127:173–182. doi:10.1115/1.1830490

    Article  Google Scholar 

  16. Campos HB, Cetlin PR (1998) The influence of die semi-angle and of the coefficient of friction on the uniform tensile elongation of drawn copper bars. J Mater Process Technol 80–81:388–391

    Article  Google Scholar 

  17. Mihelič Aand Štok B (1996) Optimization of single and multistep wire drawing processes with respect to minization of the forming energy. Struct Opt 12:120–126

    Article  Google Scholar 

  18. Roy S, Ghosh S, Shivpuri R (1997) A new approach to optimal design of multi-stage metal forming processes with micro genetic algorithms. Int J Mach Tools Manufact 37(1):29–44

    Article  Google Scholar 

  19. Celano G, Fichera E, Fratini E, Micari F (2001) The application of AI techniques in the optimal design of multi-pass cold drawing processes. J Mater Process Technol 113:680–685

    Article  Google Scholar 

  20. Van Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  21. Emmerich M, Naujoks B (2004) Metamodel-assisted multiobjective optimization with implicit constraints and its application in airfoil design. In: Proc. of Int. Conf. ERCOFTAC'04, Athens (CD-ROM), Barcelona, CIMNE

    Google Scholar 

  22. Kleijnen J, Sargent R (2000) A methodology for fitting and validating metamodels in simulation. Europ J Operat Res 120:14–29

    Article  MATH  Google Scholar 

  23. Myers R, Montgomery D (2002) Response surface methodology: process and product optimization using design experiments, 2nd edn. John Wiley and Sons, Inc., New York

    Google Scholar 

  24. Bonte MHA (2007) Optimisation strategies for metal forming processes, Ph. D. thesis, University of Twente

  25. Breitkopf P, Naceur H, Rassineux A, Villon P (2005) Moving least squares response surface approximation: formulation and metal forming applications. Comp & Struct 83:1411–1428

    Article  Google Scholar 

  26. Liszka T, Orkisz J (1980) The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comp Struct 11:83–95

    Article  MathSciNet  MATH  Google Scholar 

  27. Krok J (2002) An extended approach to error control in experimental and numerical data smoothing and evaluation using the meshless FDM. Comput Mech 11:913–945

    MATH  Google Scholar 

  28. Do MTT (2006) Optimisation de forme en forgeage 3D (shape optimization in 3D forging). Ph. D. thesis, Mines ParisTech(in French)

  29. Emmerich M, Giotis A, Ozdemir M, Bäck T, Giannakoglou K (2002) Metamodel-assisted evolution strategies, (2002) In: Proc. of the Int. Conf. on Parallel Problem Solving from Nature, Granada, Spain

  30. Bonte MHA, Fourment L, Do MTT, Van den Boogaard AH, Huétink J (2010) Optimization of metal forming processes using finite element simulations: a sequential approximate optimisation algorithm and its comparison to other algorithms by application to forging. Struct Multidisciplin Opt 42–5:797–810

    Article  Google Scholar 

  31. Fourment L, Massé T, Marie S, Ducloux R, Ejday M, Bobadilla C, Montmitonnet P (2009) Optimization of a range of 2D and 3D bulk forming processes by a meta-model assisted evolution strategy. Int J Mater Form 2–0:343–346

    Article  Google Scholar 

  32. Ejday M, Fourment L (2009) Meta-model assisted multi-objective optimization for non-steady 3D metal forming processes. Int J Mater Form 2–1:335–338

    Article  Google Scholar 

  33. Fourment L, Ducloux R, Marie S, Ejday M, Monnereau D, Masse T, Montmitonnet P (2010) Mono- and Multi-Objective optimisation techniques applied to a large range of industrial test cases using metamodel assisted evolutionary algorithms, 10th Int. NUMIFORM Conf. (Pohang, Korea, June 13–17, 2010), F Barlat, YH Moon, MG Lee (Editors). AIP Conf Proc, Mater Phys & Appl vol. 1252

  34. Ejday M, Fourment L (2010) Metamodel assisted evolutionary algorithm for multi-objective optimization of non-steady metal forming problems. Int J Mater Form 3–1:5–8

    Article  Google Scholar 

  35. Ducloux R, Fourment L, Marie S, Monnereau D (2010) Automatic optimization techniques applied to a large range of industrial test cases. Int J Mater Form 3–1:53–56

    Article  Google Scholar 

  36. Ejday M, Fourment L (2010) Optimisation multi-objectifs à base de métamodèle pour des applications en mise en forme des métaux. Mécanique & Industries 11:223–233 (in French)

    Article  Google Scholar 

  37. Bobadilla C, Persem N, Foissey S (2007) Modelling of the drawing and rolling of high carbon flat wires. In: Proc. Of the 10th ESAFORM Conference on Material Forming, Zaragoza, Spain, 18–20 April 2007, E Cueto, F Chinesta, (eds), Published by AIP Conf Proc 907:535–540

  38. Massé T (2010) Study and optimization of high carbon steel flat wires. Ph. D. Thesis, CEMEF, MinesParistech, Sophia-Antipolis, France

  39. Fereshteh-Saniee F, Pillinger I, Hartley P (2004) Friction modelling for the physical simulation of the bulk metal forming processes. J Mater Process Technol 153–154:151–156

    Article  Google Scholar 

  40. Deb K (2001) Multi-objective optimisation using evolutionary algorithms. John Wiley & Sons, Chichester

    Google Scholar 

  41. Emmerich M, Naujoks B (2004) Metamodel-Assisted multi-objective optimization with implicit constraints and its application in airfoil design. In International Conference & Advanced Course ERCOFTAC, Athens

    Google Scholar 

  42. Goal T, Vaidyanathan R, Haftka RT, Shyy W, Queipo NV, Tucker K (2007) Response surface approximation of Pareto optimal front in multi-objective optimization. Comput Methods Appl Mech Eng 196:879–893

    Article  Google Scholar 

  43. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGAII. IEEE Trans Evol Comp 6(2):182–197

    Article  Google Scholar 

  44. Komori K (2003) Effect of ductile fracture criteria on chevron crack formation and evolution in drawing. Int J Mech Sci 45:141–160

    Article  MATH  Google Scholar 

  45. Gurson AL (1997) Continuum theory of ductile rupture by void nucleation and growth—part 1: yield criteria and flow rules for porous ductile media. Trans ASME J Eng Mater Technol 99(1):2–15

    Article  Google Scholar 

  46. Reddy NV, Dixit PM, Lal GK (2000) Ductile fracture criteria and its prediction in axisymmetric drawing. Int J Mach Tools Manuf 40:95–111

    Article  Google Scholar 

Download references

Acknowledgments

The Research Centre of ArcelorMittal Gandrange and ArcelorMittal Wire Solutions are both gratefully acknowledged, for financial support as well as for generous access to their production and research facilities. The other part of this work has been carried out in the frame of the LOGIC ANR program, which support is gratefully acknowledged. The contribution of Stéphane Marie from Transvalor, for his help on the use of the optimization package, is also gratefully acknowledged.

Author information

Authors and Affiliations

  1. Mines ParisTech, CEMEF—Centre for Material Forming, CNRS UMR 7635, BP 207, 1 Rue C. Daunesse, 06904, Sophia-Antipolis Cedex, France

    T. Massé, L. Fourment & P. Montmitonnet

  2. ArcelorMittal Gandrange, Research and development—Long Carbon Bars & Wires, BP 3, 57360, Amnéville, France

    C. Bobadilla

  3. ArcelorMittal Bourg-en-Bresse, Wire Solutions, 25 Avenue de Lyon, 01000, Bourg-en-Bresse, France

    S. Foissey

  4. Laboratoire d’Étude et de Simulation des Systèmes, CEA Cadarache, DEN/DER/SESI/LE2S, Bât 212—P27, 13108, St Paul-Les-Durance, Cedex, France

    T. Massé

Authors
  1. T. Massé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Fourment
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Montmitonnet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Bobadilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. Foissey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Massé.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Massé, T., Fourment, L., Montmitonnet, P. et al. The optimal die semi-angle concept in wire drawing, examined using automatic optimization techniques. Int J Mater Form 6, 377–389 (2013). https://doi.org/10.1007/s12289-012-1092-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-012-1092-9

Keywords

Search

Navigation