Optimization of Variable Blank Holder Force Trajectory Using Multi-objective Sequential Approximate Optimization

在板料成形过程中，压边力的调整非常重要。低BHF会导致起皱，而高BHF会导致撕裂。变压边力（VBHF）是指压边力随冲程变化而变化的一种成形技术。不幸的是，VBHF是事先未知的，用数值模拟确定VBHF是有效的。板料成形过程的数值模拟成本很高，因此采用顺序近似优化（SAO）方法是有益的。在本研究中，为了确定VBHF轨迹，构造了一个优化问题。为避免方杯拉深时的撕裂和起皱，确定了最佳的VBHF轨迹。为此，构建了多目标优化（MOO）模型。提出了一种序列近似多目标优化方法，并将其应用于MOO问题。通过数值仿真，证明了该方法的有效性。

In sheet metal forming, it is important to adjust the blank holder force (BHF). Low BHF causes wrinkling, whereas high BHF result in tearing. Variable BHF (VBHF) approach that the BHF varies through the punch stroke is one of the attractive forming techniques. Unfortunately, the VBHF is unknown in advance, and the determination of the VBHF using numerical simulation is valid. Numerical simulation in sheet forming is so expensive that a sequential approximate optimization (SAO) is beneficial.In this research, in order to determine the VBHF trajectory, an optimization problem is constructed. We determine the optimal VBHF trajectory to avoid the tearing and wrinkling for square cup deep drawing. Thus, a multi-objective optimization (MOO) is constructed for this purpose. A sequential approximate multi-objective optimization method is developed and applied to the MOO problem. Through numerical simulation, the proposed approach is so effective.