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) 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.
Highlights
Deep drawing technology is used to produce metal parts from various materials such as steel, copper, aluminum and their alloys [1,2,3]
2 Experimental Material and Methods This paper is aimed at materials that are processed by deep drawing technology
3 Results and Discussion 3.1 Drawing die with tractrix curve The tractrix curve is defined as evolvent upon general catenary curve and it is described by the function (8)
Summary
Deep drawing technology is used to produce metal parts from various materials such as steel, copper, aluminum and their alloys [1,2,3]. The technology is used to make car body parts in automotive industry, cartridges in armament industry, mining blasting cups and various boxes and complex shaped parts [4]. Materials given for deep drawing must be tested for capability to be deep drawn and to determine limit condition for deep drawing [5, 6]. Testing is performed by the cupping test. Cupping is performed without blank holder by two tools – drawing die and punch. Cylinder metal piece (roundel) with diameter D0 and thickness t0 is drawn by punch with diameter d0. Outer diameter of final cup dk is determined by the formula dk d0 2t0
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