Forging tool shape optimization using pseudo inverse approach and adaptive incremental approach
Abstract
This paper presents a simplified finite element method called "Pseudo Inverse Approach" (PIA) for tool shape design and optimization in multi-step cold forging processes. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without contact treatment. A robust direct algorithm of plasticity is implemented by using the equivalent stress notion and tensile curve. Numerical tests have shown that the PIA is very fast compared to the incremental approach. The PIA is used in an optimization procedure to automatically design the shapes of the preform tools. Our objective is to find the optimal preforms which minimize the equivalent plastic strain and punch force. The preform shapes are defined by B-Spline curves. A simulated annealing algorithm is adopted for the optimization procedure. The forging results obtained by the PIA are compared to those obtained by the incremental approach to show the efficiency and accuracy of the PIA.