Optimization of Variable Blank Holder Force Trajectory for Springback Reduction

Abstract

Springback is one of the major defects in sheet metal forming. Numerical simulation based on finite element analysis is a powerful tool for springback prediction. Variable blank holder force (VBHF) approach is one of the effective ways for the springback reduction. In this paper, the VBHF trajectory is optimized by a sequential approximate optimization (SAO) with radial basis function network. U-shaped forming is handled for determining an optimum VBHF trajectory. In general, three objective functions are formulated in the springback reduction. These objective functions are not considered the state of the blank. In this paper, the residual bending moment is taken as the objective function. In order to evaluate the constraint quantitatively, the forming limit diagram (FLD) is employed. In particular, the tearing is considered as the constraint. It can be found from numerical results that the residual bending moment is more effective than the maximum nodal displacement for the springback reduction. In addition, the forming by VBHF trajectory can drastically reduce the springback in comparison with the forming with the constant blank holder force.