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

  • Yixiong FengEmail author
  • Zhaoxi Hong
  • Yicong Gao
  • Runjie Lu
  • Yushan Wang
  • Jianrong Tan


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.


Deep drawing Variable blank holder force Support vector regression model Trust region 



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

Funding information

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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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Yixiong Feng
    • 1
    Email author
  • Zhaoxi Hong
    • 1
  • Yicong Gao
    • 1
  • Runjie Lu
    • 1
  • Yushan Wang
    • 2
  • Jianrong Tan
    • 1
  1. 1.State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhouPeople’s Republic of China
  2. 2.Hefei Metalforming Machine Tool Co., Ltd.HefeiPeople’s Republic of China

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