A new mapping technique to consider intermediate stages in multistep deep drawing

The inverse solution is helpful to determine the drawability of a part and drawing parameters at the initial design stage. The usual inverse algorithms consider the drawing process that occurs in one step and therefore they are not able to analyze the processes which need more than one drawing step. Therefore, multistep inverse solution has been used for such problems. The multistep inverse solution deals with finding the initial guesses of nodal positions on intermediate stages and solving inverse equations between two consecutive steps. In this paper, a new mapping method has been developed to find the initial nodal positions on intermediate stages and the unfolding technique has been applied to find the final nodal positions on the blank sheet. The proposed method would obtain a system of equations without convergence problems. Two examples have been considered to demonstrate the capability of the proposed modeling technique. First, a two-stage drawing process of a circular cup has been analyzed and the results have been compared with the experiment results. Second, in order to apply the technique on a non-axisymmetric part, a multistage drawing of a square cup has been examined and the results have been reported.