An inverse technique on the optimization of rolling and drawing process parameters

Abstract

An optimal process design in steady-state metal plastic forming is proposed using an inverse problem solving technique and a finite element based approach. In particular, the method is applied to the problem of optimization of rolling and drawing process parameters. The goals of the two shape optimization problems are to specify the state variable distribution in the final product. A general formulation based on the minimization of a quadratic functional of nodal state variables is proposed. The rolling design variables are the roll radius, the reduction coefficient, the initial thickness, the rolling speed and the front and/or back tension. The drawing design parameters are the geometric die shape variables and the reduction coefficient. The optimization algorithm is based on the sequential unconstrained minimization technique and a gradient method. The sensitivities are obtained using a discrete formulation of the adjoint variable method.