An algorithm for determining the optimal blank shape for the deep drawing of aluminum cups

In the deep drawing of cups, the earing defect is caused by planar anisotropy in the sheet and friction between the blank and punch/die. In the past, several incomplete research efforts have been directed toward predicting an optimal blank shape that will avoid the formation of ears. In this paper, we consider the problem of optimal blank design for deep drawing, including the effects of anisotropy and friction. The material considered for the simulations is aluminum 2048. A planar anisotropic yield function proposed by Barlat is used. The initial blank shape chosen is circular. A finite element analysis is performed to simulate the deep-drawing process. An error metric, to measure the amount of earing, is constructed for the resulting cup. This error metric is then used to re-design the initial blank shape. The cycle is repeated until the error metric satisfies a preset convergence criterion. This iterative design process leads to an optimal blank shape. Several different test problems are considered, including flanged and flangeless circular and square cups. Simulation results are very encouraging with reasonable number of iterations to arrive at the optimal blank shape.