Optimum Trajectory of the Variable Blank Holder Force in the Square Cup Deep Drawing

Abstract

In deep drawing, a low blank holder force (BHF) will cause wrinkling, while a high BHF will lead to tearing. The Variable Blank Holder Force (VBHF) is an attractive approach in the industries, and it is important to determine the VBHF trajectory. In this paper, a sequential approximate optimization (SAO) approach is employed for determining the VBHF trajectory. The objective is taken as the minimization of the deviation of whole thickness. The constraint is quantitatively defined with the Forming Limit Diagram (FLD), in which no wrinkling and tearing can be observed. The blank holder forces are taken as the design variables. Two constraints in which wrinkling and tearing are avoided are employed in this paper. The Radial Basis Function (RBF) network is employed for constructing the response surface to capture the non-linear phenomena. In the proposed SAO approach, the optimum BHF is added to refine the VBHF trajectory, while some data points are also added to cover the entire design variable space. The result of the VBHF trajectory with the proposed SAO approach is compared with the one of the closed-loop type algorithm.