Optimum Blank Shapes for Prismatic Cup Drawing—Consideration of Friction and Material Anisotropy

Abstract

A theory employing the concept of potential flow and an easily implemented numerical method are developed. It can offer a preliminary prediction of the optimum blank shape with a little computational effort. The effects of the material anisotropy and the interfacial friction between the workpiece and blank holder on the material flow can be modeled by superimposing a “sink” or “source” term in the potential field. Variations in the cup wall thickness are considered. Both convex and non-convex punch profiles are studied. Generally speaking, the contours of the present theory are smoother than the solutions from the slip-line method. The discrepancy of the optimum blank contours between the plane strain and anisotropic cases is more significant for polygon and irregular cup drawing. The influence of friction on the optimum blank contour is not negligible.