Evaluation of Limiting Drawing Ratio (LDR) in deep drawing process

Abstract

Part production by deep drawing technology brings important economic advantages. Cupping test is used to determine material suitability for deep drawing. The main principle of the test is redrawing of cylinder metal test piece to the cup. The result of the test is calculation of limiting drawing ratio (LDR) whichstates the ratio betweenthe largest blank diameter and final cup diameter. Many cupping tests for various materials were performedin order to determine maximal value of LDRthatwould still allow deep drawing without failure of material integrity. Limiting drawing ratio (LDR)converges to Euler’s number (e) for high test piece depth and final cup diameter ratio values. Theoretical analysis of the cupping on drawing die with tractrix curve shows that maximal value of LDR may achieve value LDR>e. This is possible at lower values of test piece depth to final cup diameter ratio.Evaluated values of LDR published in reference literature do not include description ofstrict test conditions. Coefficient of friction has determining influence on LDR value. The theory of limiting drawing ratio(LDR)evaluation described in this paper regards the influence of coefficient of friction between drawing die and drawing cup.