Performance evaluation of analytical expressions for cylindrical and rectangular deep drawing force estimation

The deep drawing force (DDF) is defined as the maximum force required to perform a given deep drawing operation. The DDF is needed to design the drawing tools, to define the press capacity and to estimate the drawing work and process efficiency. Although several expressions to estimate the DDF have been proposed in the literature, particularly for cylindrical parts, very few research works have focused on their evaluation in terms of prediction performance. Moreover, a limited number of expressions to estimate the DDF of rectangular parts have been reported in the literature. In this paper, an investigation to evaluate and compare different analytical expressions to estimate the DDF of cylindrical and rectangular parts is presented. The aim of this investigation is twofold: first, to propose new expressions to estimate the DDF of rectangular parts, and second, to evaluate the prediction performance of the DDF expressions for cylindrical and rectangular parts. Initially, several DDF expressions for cylindrical parts are identified and analysed. These expressions are then transformed into equivalent expressions for rectangular parts by using the equivalent diameter concept. The prediction performance of these DDF expressions for cylindrical and rectangular deep drawing is then quantified and analysed based on experimental data from the literature. Finally, the influence of the deep drawing parameters on the DDF is also presented and analysed.