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Multi-objective optimization of loading path design in multi-stage tube forming using MOGA

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Abstract

Pre-bending is a critical process required prior to hydroforming. The bending has an effect on the tube thickness and strain which will use up a portion of the formability of the as-received tube. To compensate for this loss of formability, a multi-objective optimization method was applied to improve the hydroforming process after pre-bending. A multi-objective genetic algorithm (MOGA) and Kriging surrogate model were used to optimize the loading path. The Kriging model was used to replace the finite element simulation in constraint handling. The optimal loading parameters in the hydroforming process were obtained for a tube that was previously bent 90°, and showed an improvement in reducing the corner radii of the part at the extrados and intrados of the bend (8.73 mm and 11.24 mm for the extrados and intrados of the bend, respectively). The corresponding corner fill expansion (CFE) was improved by 16.7% (or 1.79 mm) compared to the maximum expansion of 10.73 mm obtained experimentally.

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Abbreviations

σ 1 σ 2 :

True principal major and minor stresses

ε 1 ε 2 :

True principal major and minor strains

f 1 f 2, f 3, f 4 :

Objectives for forming severity evaluation

f 5 f 6 :

Objectives of corner fill radius

References

  1. Lee H, Van Tyne CJ, Field D (2005) Finite element bending analysis of oval tubes using rotary draw bender for hydroforming applications. J Mater Process Tech 168:327–335

    Article  Google Scholar 

  2. Oliveira DA, Worswick MJ, Grantab R (2005) Effect of lubricant in mandrel-rotary draw tube bending of steel and aluminum. Can Metall Q 44(1):71–78

    Article  Google Scholar 

  3. Green DE (2008) Formability Analysis for Tubular Hydroformed Parts. In: Koç M (ed) Hydroforming for advanced manufacturing (Chapter 5). Woodhead Publishing Ltd, Cambridge, England, ISBN 978-1-84569-328-2

    Google Scholar 

  4. Ahmetoglu M, Altan T (2000) Tube hydroforming: state-of-the-art and future trends. J Mater Process Tech 98:25–33

    Article  Google Scholar 

  5. Dyment J, Worswick MJ, Normani F, Oliveira D, Khodayari G (2003) Effect of endfeed on strains and thickness during bending and on the subsequent hydroformability of steel tubes. SAE Paper No. 2003-01-2837

  6. Bardelcik A, Worswick MJ (2005a) Numerical investigation into the effects of bending boost and hydroforming end-feed on the hydroformability of DP600 tube. 2005-01-0094, Proceedings of SAE Conference

  7. Bardelcik A, Worswick MJ (2005) The effect of element formulation on the prediction of boost in numerical tube bending. Proceedings of Numisheet 2005:775–780

    Google Scholar 

  8. Yang J, Jeon B, Oh S (2001) The tube bending technology of a hydroforming process for an automotive part. J Mat Process Tech 111:175–181

    Article  Google Scholar 

  9. Dyment J (2004) The Effect of Bending Process on the Hydroformability of Steel Tubes. MASc. Thesis, University of Waterloo

  10. Sorine M (2007) Formability of advanced high strength steel tubes in tube bending and hydroforming. MASc. Thesis, University of Waterloo

  11. Koc M, Altan T (2001) An overall review of the tube hydroforming (THF) technology. J Mater Process Tech 108:384–393

    Article  Google Scholar 

  12. Trana K (2002) Finite element simulation of the tube hydroforming process—bending, performing and hydroforming. J Mater Process Tech 127:401–408

    Article  Google Scholar 

  13. Bardelcik A (2006) Effect of pre-bending and hydroforming parameters on the formability of advanced high strength steel tubes. Master Thesis, University of Waterloo

  14. Bardelcik A, Sorine M, Oliveira D, Worswick M (2005) Tube Bending and Hydroforming of DP600, IF and AKDQ Steel Tube. AUTO21 Group Meeting

  15. Deb K, Pratap A, Agarwal S et al (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–19

    Article  Google Scholar 

  16. An H, Green DE, Johrendt J (2009) A global optimization of load path design for tube hydroforming applications using MOGA. Proceedings of IDDRG conference, June, Golden, CO, USA, 307–318

  17. An H, Green DE, Johrendt J (2010) Multi-objective optimization and sensitivity analysis of tube hydroforming simulations. Int J Adv Manufact Technol 50(1–4):67–84. doi:10.1007/s00170-009-2505-x

    Article  Google Scholar 

  18. An H, Green DE, Johrendt J (2009) Optimization of tube hydroforming using pulsating internal pressure. Proceedings of Materials Science & Technology (MS&T), October 25–29, Pittsburgh, Pennsylvania, USA, 2321–2332

  19. An H, Green DE, Johrendt J (2011) A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming. Int J Adv Manuf Tech. doi:10.1007/s00170-011-3648-0

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Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council (NSERC) and Ontario Graduate Scholarship for Science and Technology (OGSST) of Canada.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Oakland University, Rochester, MI, USA

    Honggang An & Lorenzo Smith

  2. Department of Mechanical, Automotive and Materials Engineering, University of Windsor, Windsor, ON, Canada

    Daniel Green & Jennifer Johrendt

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  1. Honggang An
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  2. Daniel Green
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  3. Jennifer Johrendt
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  4. Lorenzo Smith
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Correspondence to Honggang An.

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An, H., Green, D., Johrendt, J. et al. Multi-objective optimization of loading path design in multi-stage tube forming using MOGA. Int J Mater Form 6, 125–135 (2013). https://doi.org/10.1007/s12289-011-1079-y

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  • DOI: https://doi.org/10.1007/s12289-011-1079-y

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