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Optimization of variable blank holder force in deep drawing based on support vector regression model and trust region

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Abstract

Blank holder force (BHF) is one of the important process parameters for successful sheet metal forming. Variable blank holder force (VBHF) that the BHF varies through the forming process is recognized as one of the advanced manufacturing technologies. Therefore, optimization of VBHF trajectory is a crucial issue in industries. One of the effective approaches to determine the VBHF trajectory is to use the surrogate modeling techniques. However, it is very inaccurate and time-consuming to determine the VBHF trajectory for successful sheet forming through surrogate-based optimization methods. Therefore, this paper proposes an improved surrogate-based optimization method by integration of support vector regression (SVR) and trust region strategy to optimize VBHF in deep drawing. First, a random sampling test of VBHF in deep drawing is designed and a SVR approximate model of VBHF under random sampling is developed. Then, a trust region algorithm is adopted to predict and control the accuracy of the SVR approximate model of VBHF. Response surface is repeatedly constructed and optimized that is adopted to identify the Pareto-frontier of VBHF. The validity of the proposed approach is examined through the comparison of numerical and experimental results. The results of this research provide a reliable reference for future efforts to optimize VBHF in deep drawing.

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References

  1. Kitayama S, Yamada S (2017) Simultaneous optimization of blank shape and variable blank holder force of front side member manufacturing by deep drawing. Int J Adv Manuf Technol 91(1-4):1381–1390

    Article  Google Scholar 

  2. Feng YX, Zhang ZF, Tian GD, Lv ZH, Tian SX, Jia HF (2018) Data-driven accurate design of variable blank holder force in sheet forming under interval uncertainty using sequential approximate multi-objective optimization. Future Gener Comp Syst 86:1242–1250

    Article  Google Scholar 

  3. Tian GD, Zhang HH, Feng YX, Wang DQ, Peng Y, Jia HF (2018) Green decoration materials selection under interior environment characteristics: a grey-correlation based hybrid MCDM method. Renew Sustain Energ Rev 81(1):682–692

    Article  Google Scholar 

  4. Feng YX, Hong ZX, Tian GD, Li ZW, Tan JR, Hu HS (2018) Environmentally friendly MCDM of reliability-based product optimisation combining DEMATEL-based ANP, interval uncertainty and Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR). Inf Sci 442-443:128–144

    Article  Google Scholar 

  5. Feng YX, Gao YC, Tian GD, Li ZW, Hu HS, Zheng H (2019) Flexible process planning and end-of-life decision-making for product recovery optimization based on hybrid disassembly. IEEE Trans Autom Sci Eng 16(1):311–326

    Article  Google Scholar 

  6. Maeno T, Mori K, Nagai T (2014) Improvement in formability by control of temperature in hot stamping of ultra-high strength steel parts. CIRP Ann Manuf Technol 63(1):301–304

    Article  Google Scholar 

  7. Bardelcik A, Worswick MJ, Wells MA (2014) The influence of martensite, bainite and ferrite on the as-quenched constitutive response of simultaneously quenched and deformed boron steel-experiments and model. Mater Design 55:509–525

    Article  Google Scholar 

  8. Kotkunde N., Deole A. D., Gupta A. K., Singh S. K. 2014 Effect of process parameters on deep drawing of Ti-6Al-4V alloy using finite element analysis. NUMISHEET: The 9th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes: Part A Benchmark Problems and Results and Part B General Papers. American Institute of Physics.

  9. Sener B, Kurtaran H (2016) Optimization of process parameters for rectangular cup deep drawing by the Taguchi method and genetic algorithm. Materials Testing 58(3):238–245

    Article  Google Scholar 

  10. Li E (2013) Reduction of springback by intelligent sampling-based LSSVR met model-based optimization. Int J Mater Form 6(1):103–114

    Article  Google Scholar 

  11. Ma GY, Huang BB (2014) Optimization of process parameters of stamping forming of the automotive lower floor board. J Appl Math 2014:1–9

    Google Scholar 

  12. Kitayama S, Natsume S, Yamazaki K, Han J (2016) Numerical optimization of blank shape considering flatness and variable blank holder force for cylindrical cup deep drawing. Int J Adv Manuf Technol 85(9-12):2389–2400

    Article  Google Scholar 

  13. Obermeyer EJ, Majlessi SA (1998) A review of recent advances in the application of blank-holder force towards improving the forming limits of sheet metal parts. J Mater Process Technol 75(1-3):222–234

    Article  Google Scholar 

  14. Lin ZQ, Wang WR, Chen GL (2007) A new strategy to optimize variable blank holder force towards improving the forming limits of aluminum sheet metal forming. J Mater Process Technol 183(2-3):339–346

    Article  Google Scholar 

  15. Lo SW, Yang TC (2004) Closed-loop control of the blank holding force in sheet metal forming with a new embedded-type displacement sensor. Int J Adv Manuf Technol 24(7-8):553–559

    Article  Google Scholar 

  16. Sheng ZQ, Jirathearanat S, Altan T (2004) Adaptive FEM simulation for prediction of variable blank holder force in conical cup drawing. Int J Mach Tool Manuf 44(5):487–494

    Article  Google Scholar 

  17. Kitayama S, Hamano S, Yamazaki K et al (2010) A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing. Int J Adv Manuf Technol 51(5-8):507–517

    Article  Google Scholar 

  18. Endelt B (2013) Tommerup. S., Danckert, J. A novel feedback control system – controlling the material flow in deep drawing using distributed blank-holder force. J Mater Process Technol 213(1):36–50

    Article  Google Scholar 

  19. Kitayama S, Kenta K, Koetsu Y (2012) Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network. Int J Adv Manuf Technol 61(9-12):1067–1083

    Article  Google Scholar 

  20. Kakandikar G. M., Nandedkar V. M. 2005 Optimization of forming load and variables in deep drawing process for automotive cup using Genetic Algorithm. IISc Centenary-International Conference on Advances in Mechanical Engineering ICICAME, Bangalore Google Scholar.

  21. Manoochehri M, Farhad K (2014) Integration of artificial neural network and simulated annealing algorithm to optimize deep drawing process. Int J Adv Manuf Technol 73(1-4):241–249

    Article  Google Scholar 

  22. Tian Y, Xie YM, Sun XQ, He YJ (2014) Process parameters optimization of deep drawing based on fish RBF neural network and improved ant colony algorithm. Forg Stamp Technol 39(12):129–136

    Google Scholar 

  23. Chen L, Yang JC, Zhang LW et al (2007) Finite element simulation and model optimization of blankholder gap and shell element type in the stamping of a washing-trough. J Mater Process Technol 182(1-3):637–643

    Article  Google Scholar 

  24. Hosseini A, Kadkhodayan M (2014) A hybrid NN-FE approach to adjust blank holder gap over punch stroke in deep drawing process. Int J Adv Manuf Technol 71(1-4):337–355

    Article  Google Scholar 

  25. Feng YX, Hu BT, Hao H, Gao YC, Li ZW, Tan JR (2018) Design of distributed cyber-physical systems for connected and automated vehicles with implementing methodologies. IEEE Trans Ind Inform 14(9):4200–4211

    Article  Google Scholar 

  26. Feng YX, Zhou MC, Tian GD, Li ZW, Zhang ZF, Zhang Q, Tan JR (2018) Target disassembly sequencing and scheme evaluation for CNC machine tools using improved multiobjective ant colony algorithm and fuzzy integral. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2847448

    Article  Google Scholar 

  27. Wang K, Li HN, Feng YX, Tian GD (2017) Big data analytics for system stability evaluation strategy in the energy Internet. IEEE Trans Ind Inform 13(4):1969–1978

    Article  Google Scholar 

  28. Jakumeit J, Herdy M, Nitsche M (2005) Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm. Struct Multidiscipl Opt 29(6):498–507

    Article  Google Scholar 

  29. Kitayama S, Huang SS, Yamazaki K (2013) Optimization of variable blank holder force trajectory for springback reduction via sequential approximate optimization with radial basis function network. Struct Multidiscipl Opt 47(2):289–300

    Article  Google Scholar 

  30. Kitayama S, Jirasak S (2013) Sequential approximate multi-objective optimization using radial basis function network. Struct Multidiscipl Opt 48(3):501–515

    Article  MathSciNet  Google Scholar 

  31. Di Lorenzo R, Ingarao G, Micari F, Chinesta F (2009) A Pareto optimal design approach for simultaneous control of thinning and springback in stamping processes. Int J Mater Form 2:801–804

    Article  Google Scholar 

  32. Hu W, Yao LG, Hua ZZ (2008) Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Process Technol 197(1-3):77–88

    Article  Google Scholar 

  33. Zhang WF, Shivpuri R (2008) Investigating reliability of variable blank holder force control in sheet drawing under process uncertainties. J Manuf Sci Eng 130(4):1–8

    Article  Google Scholar 

  34. Bonte MHA, Fourment L, Do TT, van den Boogaard AH, Huetink J (2010) Optimization of forging processes using finite element simulations. Struct Multidiscipl Opt 42(5):797–810

    Article  Google Scholar 

  35. Srirat J, Kitayama S, Yamazaki K (2012) Optimization of initial blank shape with a variable blank holder force in deep-drawing via sequential approximate optimization. J Adv Mech Des Syst Manuf 6(7):1093–1106

    Article  Google Scholar 

  36. Jiang C, Han X, Liu GR, Li GY (2007) The optimization of the variable binder force in U-shaped forming with uncertain friction coefficient. J Mater Process Technol 182(1-3):262–267

    Article  Google Scholar 

  37. Wang H, Li EY, Li GY (2010) Parallel boundary and best neighbor searching sampling algorithm for drawbead design optimization in sheet metal forming. Struct Multidiscipl Opt 41(2):309–324

    Article  Google Scholar 

  38. Sun GY, Li GY, Chen T, Zhang Y (2009) Application of multi-objective particle swarm optimization in sheet metal forming. J Mech Eng 45(5):153–159

    Article  Google Scholar 

  39. Li EY (2013) Reduction of springback by intelligent sampling-based LSSVR metamodel-based optimization. Int J Mater Form 6(1):103–114

    Article  Google Scholar 

  40. Hong WC, Pai PF (2007) Potential assessment of the support vector regression technique in rainfall forecasting. Water Resour Manag 21(2):495–513

    Article  Google Scholar 

  41. Wang XX, Chen S, Lowe D, Harris CJ (2006) Sparse support vector regression based on orthogonal forward selection for the generalised kernel model. Neurocomputing 70(1-3):462–474

    Article  Google Scholar 

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Acknowledgments

Sincere appreciation is extended to the reviewers of this paper for their helpful comments.

Funding

This work was supported by Zhejiang Provincial Natural Science Foundation of China (No. LZ18E050001) and the National Natural Science Foundation of China (No. 51775489).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Yixiong Feng, Zhaoxi Hong, Yicong Gao, Runjie Lu & Jianrong Tan

  2. Hefei Metalforming Machine Tool Co., Ltd., Hefei, 230001, People’s Republic of China

    Yushan Wang

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  1. Yixiong Feng
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  2. Zhaoxi Hong
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  3. Yicong Gao
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  4. Runjie Lu
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  5. Yushan Wang
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  6. Jianrong Tan
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Correspondence to Yixiong Feng.

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Feng, Y., Hong, Z., Gao, Y. et al. Optimization of variable blank holder force in deep drawing based on support vector regression model and trust region. Int J Adv Manuf Technol 105, 4265–4278 (2019). https://doi.org/10.1007/s00170-019-04477-5

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  • DOI: https://doi.org/10.1007/s00170-019-04477-5

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