The determination of optimum blank shapes when deep drawing prismatic cups

The article discusses some techniques for the determination of ideal (or optimum) blank contours when deep drawing prismatic cups. The ideal contours are designed to produce essentially flat topped cups and thus trimming of excess material is minimized. The techniques lend themselves to such processes where the cups are drawn from initially flat blanks in the presence of a blank holder. Tooling which involves lock beads or draw beads is not considered.Attention is devoted to two techniques developed by the authors; each method is based on the solution of Laplace’s equation. One technique is experimental and uses an electrostatic analogue, the second is numerical and the solution procedure employs the boundary element method. Neither method attempts a rigorous analysis of the actual drawing operation. They are intended as a means of producing near-net shaped blanks with little computational effort. Since material costs usually represent a major portion of the overall cost of a sheet metal part, the theme of the paper has immediate practical significance.