Numerical optimization of blank shape considering flatness and variable blank holder force for cylindrical cup deep drawing

Both blank shape minimizing earing and blank holder force (BHF) have an influence on the product quality as well as product cost. Recently, variable blank holder force (VBHF) that the BHF varies through the punch stroke is an attractive approach for improving the product quality as well. This paper proposes a method to simultaneously determine both optimal blank shape minimizing earing and the optimal VBHF trajectory for a cylindrical cup deep drawing. In this paper, the earing is separately evaluated as (1) the area above the trimmed line, and (2) the area below the trimmed line, and both are then minimized. The distance between the trimmed line and the cup height is also considered in the objective functions for the flatness of earing. Therefore, a multi-objective optimization problem is formulated. Numerical simulation in sheet metal forming is so numerically intensive that response surface approach is used. In particular, a sequential approximate optimization (SAO) using a radial basis function (RBF) network is used to determine the optimal blank shape and VBHF trajectory. In the numerical simulation, a cylindrical cup deep drawing based on NUMISHEET 2011(BM1) is considered, and the validity of the proposed approach is examined.