Skip to main content
Log in

Optimization of stamping process parameters to predict and reduce springback and failure criterion

  • INDUSTRIAL APPLICATION
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Automotive manufacturers have been struggling with the big challenge of how to produce dimensionally acceptable stamped parts with minimal material cost. The thin nature of the sheet metal has always complicated the process and made the dimensional quality objectives difficult to achieve. The final layout quality is impacted by several fabrication flaws such as springback and failure. A possible approach to circumvent these unwanted process drawbacks consists in optimizing the process parameters with innovative methods. The aim of this paper is to introduce an efficient methodology to deal with complex, computationally expensive multicriteria optimization problems. Our approach is based on the combination of methods to capture Pareto Front, suitable surrogates (to save computational costs) and global optimizers. To illustrate the efficiency, we consider the stamping of an industrial workpiece as test-case. Our approach is applied to springback and failure criteria. To optimize these two criteria, a global approach was chosen. It is the Simulated Annealing algorithm hybridized with the Simultaneous Perturbation Stochastic Approximation in order to gain in time and in precision. The multicriteria concern amounts to the capture of the Pareto Front associated to the two criteria. Indeed, springback and failure are two conflicting criteria. Normal Boundary Intersection and Normalized Normal Constrained Method are considered for generating a set of Pareto-optimal solutions with the characteristic of uniform distribution of front points. The computational results are compared to those obtained with the well-known Non-dominated Sorting Genetic Algorithm II. The results show that our proposed approach is efficient to deal with the multicriteria parametric and shape optimization of highly non-linear mechanical systems.

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

Access this article

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

Instant access to the full article PDF.

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
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

References

  • Achatz S (2003) Higher order sparse grid methods for elliptic partial differential equations with variable coefficients. Comput 71(1):1–15

    Article  MATH  MathSciNet  Google Scholar 

  • Balder R, Rüde U, Schneider S et al (1994) Sparse grid and extrapolation methods for parabolic problems. In: Proceeding of international conference on computational methods in water ressources. Heidelberg Kluwer Academic, Dordrecht, pp 1383–1392

    Google Scholar 

  • Bungartz HJ, Dirnstorfer S (2003) Multivariate quadrature on adaptive sparse grids. Comput 71(1):89–114

    Article  MATH  MathSciNet  Google Scholar 

  • Bungartz H, Huber W (1995) First experiments with turbulence simulation on workstation networks using sparse grid methods. Comput Fluid Dyn Parallel Syst Notes Numer Fluid Mech (NNFM). Vieweg+ Teubner Verlag 50:36–48

    Google Scholar 

  • Cerny V, Gelatt CD, Vecchi MP (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51

    Article  MATH  MathSciNet  Google Scholar 

  • Col A (2010) L’emboutissage des aciers. Dunod, Paris

    Google Scholar 

  • Das I, Dennis JE (1998) Normal-boundary intersection, a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657

    Article  MATH  MathSciNet  Google Scholar 

  • Deb K (1999) Multiobjective genetic algorithms: Problem difficulties and construction of test problems. Evol Comput 8(2):205–230

    Article  Google Scholar 

  • Deb K, Partap A, Agarwal S, Meyarivan T (2002) A Fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • De Jong KA (1975) An analysis of the behavior of a class of genetic adaptive systems. University of Michigan, Doctoral Dissertation

    Google Scholar 

  • Dunne F, Petrinic N (2005) Introduction to computational plasticity. Oxford University Press Inc, New York

    MATH  Google Scholar 

  • Fabian V (1971) Stochastic approximation. Optimizing Methods in Statistics. Academic Press, New York, pp 439–470

    Book  Google Scholar 

  • Fonseca CM, Fleming PJ (1993) In Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, CA: Morgan Kauffman. In: Forrest S (ed) Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization, pp 416–423

  • Fonseca CM, Fleming PJ, Voigt H-M, Ebeling W, Rechenberg I, Schwefel H-P (1996) On the performance assessment and comparaison of stochastic multiobjective optimizers In parallel problems solving from nature IV, vol 1141. Springer, Berlin, Germany, pp 584–593

  • Fonseca CM, Fleming PJ (1998a) Multiobjective optimization and multiple constraint handling with evolutionary algorithms - Part I: A unified formulation. IEEE Trans Syst Man, Cybern A 28:26–37

    Article  Google Scholar 

  • Fonseca CM, Fleming PJ (1998b) Multiobjective optimization and multiple constraint handling with evolutionary algorithms - Part II: Application exemple. IEEE Trans Syst Man Cybern A 28:38–47

    Article  Google Scholar 

  • Garcke J, Griebel M (2002) Classification with sparse grids using simplicial basis functions. Intell data Anal 6(6):483–502

    MATH  Google Scholar 

  • Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc London 193:281–297

    Article  MATH  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Sci 220:671–680

    Article  MATH  MathSciNet  Google Scholar 

  • Klimke A, Wohlmuth B (2005) Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Transactions on Mathematical Software (TOMS) 31(4):561–579

    Article  MATH  MathSciNet  Google Scholar 

  • Klimke A (2007) Sparse grid interpolation toolboxusers guide. IANS report 17

  • Kursawe F (1990) In Parallel Problems Solving from Nature. In: Schwefel H-P, Männer R (eds) A variant of evolution strategies for vector optimization, vol 496. Springer, Berlin, Germany, pp 193–197

    Google Scholar 

  • Kushner HJ, Yin GG (1997) Stochastic approximation algorithms and applications. Springer, New York

    Book  MATH  Google Scholar 

  • Llewellyn DT, Hudd RC (1998) Steels: metallurgy and applications. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Marciniak Z, Duncan JL, Hu SJ (2002) Mechanics of sheet metal forming. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Marsden JE, Wiggins S, Hughes TJR, Sirovich L (1998) Computational Inelasticity. Springer, New York

    Google Scholar 

  • Messac A, Ismail-Yahaya A, Mattson CA (2003) The normalized normal constraint method for generating the pareto frontier. Struc Multidisc Optim 25(2):86–98

    Article  MATH  MathSciNet  Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E, Teller (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1090

    Article  Google Scholar 

  • Schaffer JD (1987) In Proceedings of the first international conference on genetic algorithms. In: Grefensttete JJ (ed) Multiple objective with vector evaluated genetic algorithms. Lawrence Erlbaum, Hillsdale, NJ, pp 93–100

    Google Scholar 

  • Smolyak SA (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR, 148:10421043, Russian, Engl. Transl.: Soviet Math. Dokl. 4, 240243

  • Spall JC (1998a) Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization. IEEE Trans Aerosp Electron Syst 34(3):817–823

    Article  Google Scholar 

  • Spall JC (1998b) An overview of the simultaneous perturbation method for efficient optimization. Johns Hopkins APL Tech Digest 19(4):482–492

    Google Scholar 

  • Spall JC (1998c) Introduction to stochastic search and optimization: estimation, simulation, and control. Jhon Wiley & Sons, Inc., Hoboken, New Jersey

    Google Scholar 

  • Van Veldhuizen D (1999) Multiobjective evolutionary algorithms: classifications, analyses and new innovations, doctoral dissertation air force inst. technol., Dayton, OH, Tech. Rep. AFIT/DS/ENG/ 99-01.

  • Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms - A comparative case study. In: Eiben AE, Bäck T, Schoenauer M, Schwefel H-P (eds) In Parallel problems solving from nature, V, vol 1498. Springer, Berlin, Germany, pp 292–301

    Chapter  Google Scholar 

  • Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications, doctoral dissertation ETH 13398, Swiss federal institue of technology (ETH). Zurich, Switzerland

    Google Scholar 

  • Zitzler E, Deb K, Thiele L (2000) Comparaison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

Download references

Acknowledgements

The present work was achieved within the framework of the OASIS Consortium, funded by the French FUI grant id. 1004009Z.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F.-Z. Oujebbour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Oujebbour, FZ., Habbal, A. & Ellaia, R. Optimization of stamping process parameters to predict and reduce springback and failure criterion. Struct Multidisc Optim 51, 495–514 (2015). https://doi.org/10.1007/s00158-014-1138-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-014-1138-3

Keywords

Navigation