Optimum Springback Compensation for Hat-Shaped Beam Forming

Abstract

A new method of springback compensation for a hat-shaped beam based on finite element (FE) simulation and the optimization technique is presented, in which the objective function to be minimized is the shape error of the press-formed beam after springback and the design variables are the geometrical parameters for defining the die shape. This method starts with rough die compensation based on empirical knowledge and springforward analysis, and then optimization is carried out. To reduce the computation time in optimization, the idea of two-step optimization is presented, where the die cross-sectional shape and longitudinal die curvature are determined separately. In addition, a partial FE model, which is less expensive computationally, is used in die cross-sectional shape optimization, instead of a full FE model. In this paper, we describe the general method of die compensation, the formulation of the optimization problem, details of the numerical technique, and the verification of this method by solving a springback problem for the beam model.