A Method for evaluating limiting drawing ratios

Abstract

Sufficient data have now been generated to assess the influence of material, process, and tooling variables on the limiting drawing ratio, when deep drawing cylindrical cups from circular blanks. The influence of these parameters is less well understood in the deep drawing of nonaxisymmetric cups, and the data that exist have generally been collected from drawing tests. A theoretical approach is presented for predicting the limiting drawing ratio when deep drawing prismatic cups. For a given blank geometry, the drawing load is calculated to plastically deform the flange, overcome friction between the flange and the blank holder, and to bend the material over the die radius. Deformation in the cup wall is ignored. The onset of yielding in the flange is determined using a finite-element code. The calculated drawing load is compared to a theoretical maximum, and when the two values coincide, this yields the limiting blank size under the assumed processing conditions, i.e., blank holder force, die radius, blank shape, and coefficient of friction. The theoretical predictions were compared with experimental results when deep drawing square cups from optimum blank shapes, and the correspondence was found to be acceptable.