Skip to main content
Log in

Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In a sheet forming process, drawbead plays an important role on the control of the material flow. In this paper, a numerical procedure for the design of forming processes is described. It is based on the coupling of an optimization technique and the simplified one step finite element method (also called inverse approach). The optimization technique allows adjustment of the process parameters so that specified criteria are fulfilled. Response surface methodology (RSM) is a global approximation method, which is ideally suited for solving highly nonlinear optimization problems. The finite element method, in addition to predicting the response of the process to certain parameters, allows assessment of the effect of a variation in these parameters on this response. The authors utilize the one step method at the preliminary design stage to supply stress or strain information for the following optimization using RSM. The procedure for this optimization process is fully described. The front fender for Numisheet 2002 is presented and the real defect free workpiece is produced to demonstrate the usefulness of the proposed optimization procedure. A comparison between the two forming limit curves (FLC) before and after optimization and results obtained using the precise incremental commercial software DYNAFORM based on the explicit dynamic approach verify that the optimization design method of drawbead could be successfully applied in designing actual tools of auto body cover panels.

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.

Similar content being viewed by others

Abbreviations

RSM:

Response surface methodology

FLC:

Forming limit curve

IA:

Inverse approach

SQP:

Sequential quadratic programming

PIA:

Pseudo inverse approach

AFSD:

Automatic forging sequence design

PVW:

Principle of virtual work

References

  1. Ghouati O, Lenoir H, Gelin JC (2000) Optimal design of forming processes using the finite element method. Adv Eng Mater 2(7):438–442

    Article  Google Scholar 

  2. Alberti N, Fratini L (2004) Innovative sheet metal forming processes: numerical simulations and experimental tests. J Mater Process Technol 150(1–2):2–9

    Article  Google Scholar 

  3. Erman Tekkaya A (2000) State-of-the-art of simulation of sheet metal forming. J Mater Process Technol 103(1):14–22

    Article  Google Scholar 

  4. Barlet O, Batoz JL, Guo YQ, Mercier F, Naceur H, Knopf-Lenoir C (1996) Optimum design of blank contours using the inverse approach and mathematical programming techniques. NUMISHEET’96, Michigan, USA, pp 178–185

  5. Barlet O, Naceur H, Batoz JL, Knopf-Lenoir C (1998) Shape optimum design of blank contours using a simplified inverse approach. NUMIFORM’98, Enschede, The Netherlands, pp 801–806

  6. Guo YQ, Batoz JL, Naceur H (2000) Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach. Comput Struct 78(1–3):133–148

    Article  Google Scholar 

  7. Park SH , Yoon JW, Yang DY, Kim YH (1999) Optimum blank design in sheet metal forming by the deformation path iteration method. Int J Mech Sci 41(10):1217–1232

    Article  MATH  Google Scholar 

  8. Luet D, Duval JL, Di Pasquale E (1998) Quality function approach to design and optimization of stamping process: application to an industrial case. International Congress and Exposition (SAE), Detroit, MI, USA

  9. Naceur H, Guo YQ, Batoz JL (2004) Blank optimization in sheet metal forming using an evolutionary algorithm. J Mater Process Technol 151(1–3):183–191

    Article  Google Scholar 

  10. Guo YQ , Li YM, Bogard F, Debray K (2004) An efficient pseudo-inverse approach for damage modeling in the sheet forming process. J Mater Process Technol 151(1–3):88–97

    Article  Google Scholar 

  11. Aivazi R, Yanagimoto J (2004) Automated sequence design for slab stretching with arbitrary height distribution using one-step FEM analysis. J Mater Process Technol 151(1–3):146–154

    Article  Google Scholar 

  12. Nine HD (1978) Drawbead forces in sheet metal forming. In: Koisinen DP, Wang NM, (ed) Mechanics of sheet metal forming. Plenum Press, New York, pp 179–211

    Google Scholar 

  13. Wang NM (1982) A mathematical model of drawbead forces in sheet metal forming. J Appl Metalwork 2:193–199

    Google Scholar 

  14. Ye Y, Hong PY, Yu RX (1998) Calculation of drawbead restraining forces associated with kinematics hardening rule. NUMIFORM’98, Balkema, The Netherlands, pp 905–910

  15. Carleer B (1996) Equivalent drawbead model in finite element simulations. NUMISHEET’96, Dearborn, USA, pp 25–31

  16. Levy BS (1998) Development of a predictive model for draw bead restraining force utilizing work of Nie and Wang. J Appl Metalwork 3(1):38–44

    Google Scholar 

  17. Hosford WF, Caddell RM (1983) Metal forming. Mechanics and metallurgy. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  18. Shi X, Wei Y, Ruan X (2001) Simulation of sheet metal forming by a one-step approach: choice of element. J Mater Process Technol 108(3):300–306

    Article  Google Scholar 

  19. Stoughton TB (1998) Model of drawbead forces in sheet metal forming. Proceedings of the 15th biennial IDDRG congress, Dearborn, USA, pp 205–215

  20. Schramm O, Pilke WD (1994) Optimal shape design for thin-walled beam cross-sections. Int J Num Meth Eng 37(23):4039–4058

    Article  MATH  Google Scholar 

  21. Kegl M, Butina BJ, Oblak MM (1995) Shape optimal design of elastic planar frames with non-linear response. Int J Num Meth Eng 38(19):3227–3242

    Article  MATH  Google Scholar 

  22. Barlet O (1998) PhD Thesis (in French), Université de Technologie du Compiègne

  23. Knabel J, Rojek J, Stocki R, Kleiber M (2002) Reliability analysis of sheet metal forming operations by response surface method. Reliability-based design and optimisation (RBO’02)conference proceedings 2, Warsaw

  24. Jansson T, Nilsson L, Redhe M (2003) Using surrogate models and response surfaces in structural optimization—with application to crashworthiness design and sheet metal forming. Struct Multidisc Optim 25:129–140

    Article  Google Scholar 

  25. Naceur H, Guo YQ, Batoz JL, Knopf-Lenoir C (2001) Optimization of drawbead restraining forces and drawbead design in sheet metal forming process. Int J Mech Sci 43(10):2407–2434

    Article  MATH  Google Scholar 

  26. Myers RH, Montgomery DC (1995) Response surface methodology: process and process optimization using design experiments. Wiley, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhen Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tang, B., Sun, J., Zhao, Z. et al. Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology. Int J Adv Manuf Technol 31, 225–234 (2006). https://doi.org/10.1007/s00170-005-0208-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-005-0208-5

Keywords

Navigation