2102 Optimization of Initial Blank Shape and Variable Blank Holder Force for Square Cup Deep Drawing

In deep drawing, area above the trimmed line is called earing. Reduction of the earing is one of the major issues for cost reduction. In addition, it is well known that blank holder force (BHF) has a direct influence on the product quality. 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. In particular, two objective functions are defined for evaluation the earing. In other words, our design problem is formulated as a multi-objective design optimization. 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.