A Mathematical Model for Calculating the Limiting Drawing Ratio of Cylindrical Parts Drawn from Sheet Blanks of Variable Thickness

This paper presents a solution to a topical problem of determining the limit deformation capability of sheet metal when forming cylindrical parts. This solution is further used to develop methodological recommendations to control the quality as well as technical and economic indicators of the manufactured products. By solving a differential equilibrium equation for a workpiece flange of variable thickness described by the power rule, analytical and graphic dependencies are obtained for evaluating the limiting drawing ratio with and without taking into account flange displacement. The influence patterns of the workpiece edge thickness and the power of the thickness variation law on the drawing ratio are revealed. It is shown that the largest value of the limiting drawing ratio is provided by the parabolic law of thickness variation. Based on the calculation results, it is established that for drawing parts with a constant wall thickness, the largest limiting drawing ratio can be obtained using disk workpieces with a thickness that changes following the linear law in the radial direction. Efficient technologies for manufacturing workpieces of variable thickness and features of subsequent drawing of cylindrical parts are analysed.

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