A Simplified Approach to Estimate Limiting Drawing Ratio and Maximum Drawing Load in Cup Drawing

Abstract

A new and practically applicable equation, including the normal anisotropy R, the strain hardening exponent n, the friction coefficient μ, and the bending factor t0/rd for estimating the limiting drawing ratio LDR (a measure of drawability of sheet metal) in cup drawing of a cylindrical cup with a flat-nosed punch is derived by an elementary theory of plasticity in an explicit form. Whiteley’s and Leu’s equations for estimating the LDR, and Hill’s upper limit value of LDR, all are the special cases of the derived equation. The estimation of LDR agrees well with the experiment. It is shown that the most important parameters for LDR are the normal anisotropy R and friction coefficient μ, however the strain hardening exponent n has little effect on the LDR. On the other hand, a new and simple equation, incorporating the derived LDR and the critical drawing load Pc, for estimating the maximum drawing load Pd at a certain drawing ratio is derived. It also agrees well with the experiment. It is thereby possible to better understand and control the drawing limit of sheet metal in industry necessity.