EVALUATION OF LIMITING DRAWING RATIO (LDR) IN DEEP DRAWING PROCESS
Keywords:deep drawing, differential equations, relative radial stress, cup, limiting drawing ratio, LDR
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) which states the ratio between the largest blank diameter and final cup diameter. Many cupping tests for various materials were performed in order to determine maximal value of LDR that would still allow deep drawing without failure of material integrity.Paper presents the theoretical determination of the limiting drawing ratio (LDR) in dependence on d0/t0 ratio and friction coefficient between blank and punch.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. Coefficient of friction has determining influence on LDR value.
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