Optimized Tooling Design Algorithm for Sheet Metal Forming over Reconfigurable Compliant Tooling

Abstract

New forming technologies based on compliant “discrete‐die” reconfigurable tooling are available for production of sheet metal parts, but there is a need for a formalism that can accurately predict the three‐dimensional shape of the required tooling, a priori. An optimized tooling design algorithm has been developed based on a methodology that uncouples the effects due to springback and those due to the compliance of the polymeric layer. A springback compensated die shape is initially predicted for the case of stretch forming over smooth rigid dies based on an iterative approach using the finite element method. The tooling design algorithm is based on an inverse springback approach that uses the elastic‐plastic stress state prior to unloading to elastically deform the sheet in a direction opposite to springback. A procedure has been developed to improve the convergence behavior of the inverse springback approach utilizing an interpolation scheme. The interpolation scheme uses prior iterations to predict the desired die shape by fitting spatially varying quadratic relationships between the tool shape and the part shape error histories. The optimized tooling design algorithm is extended to compliant dies by developing a method that corrects the die shape for polymer through the thickness compression. The algorithm is applied to stretch forming of large‐scale airframe skin parts commonly found in aerospace structures. Two shapes are investigated, a 90‐inch radius cylindrical cap and a 90‐inch radius spherical cap.