A multilevel approach to optimization of bulk forming processes

Abstract

An optimal process design in metal plastic forming is proposed using an inverse solving technique and a finite element based approach. The goal of the shape optimization problem is 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 optimization algorithm is based on a modified sequential unconstrained minimization technique and a gradient method. The sensitivities are obtained using a discrete formulation of the direct differentiation method. The constitutive model assumes a rigid, isotropic, strain hardening viscoplastic incompressive deformation. Friction and contact are modeled by interface elements of zero thickness, formulated on the basis of local normal and tangential relative displacements. It is recognized that the optimization of bulk forming processes is an important task to minimize the energy consumption, to avoid forming defects and to improve the microstrutural properties of the final part. In open die forging and under manufacturing conditions, these goals may be reached through a multilevel sequence of preforms before the final form. The approach is based on the finite element inverse technique with the problem being solved in the following manner: The forging code is considered a black box and is inserted into an optimization algorithm. The information obtained from the direct problem solution is combined with the sensitivity analysis and a sequential unconstrained minimization technique to achieve the optimal design of the preforms. The method is applied to a forging example demonstrating the applicability and efficiency of the proposed algorithm.