Optimization of initial blank shape for square cup deep drawing using variable blank holder force

In deep drawing, area above the trimmed line is called earing. Reduction of the earing in deep drawing is one of the major issues for cost reduction. In addition, a high BHF causes tearing while a low BHF leads to wrinkling. Therefore it is important to determine an appropriate BHF through drawing. Recently, variable BHF (VBHF) approach which varies through the punch stroke has received a lot of attention, and its validity is discussed. In this study, both initial blank shape minimizing the earing and VBHF trajectory are simultaneously determined under tearing/wrinkling constants. Our design problem is formulated as a multi-objective design optimization for evaluation the earing. First objective function is the area above the trimmed line, and second one is the area below the trimmed line. In general, numerical simulation in sheet forming is so expensive that a sequential approximate optimization (SAO) using the radial basis function (RBF) network is adopted to identify the Pareto-frontier. The validity of the proposed approach is examined through numerical simulation. It can be found from the numerical result that earing is drastically reduced by the proposed approach.