Development of a CAD/CAM system for the drawing of hemispherical cups using flexible tools

Abstract

This paper discusses the development of a CAD/CAM system for the drawing of hemispherical cups using a flexible urethane pad as the punch. It performs the prediction of strains across the cup, the geometric modelling of the drawing of hemispherical cups and the sizing of equipment, components, blank material and the generation of the machining part programme for the machining of the die. Approximate empirical models for the variation of thickness, circumferential and meridional strains at different portions of the cup are proposed. The model was developed based on the observation that the thickness of the sheet metal at the “equator” of the cup remains unchanged, thinning according to an exponential function of the arc-length towards the crown and thickening also according to an exponential function of the arc-length until the annulus. The thickness at the straight flange is relatively constant. The proposed model is augmented by incorporating the capability of predicting the strain gradients as functions of such factors as the cup radius, thickness, blank size and the die radius. The results obtained using the proposed model agree well with experimental results. The profile of the uncompleted cups is observed to be approximately spherical during the early stages of the deformation process, and ellipsoidal towards the later stage of the deformation process. The partially drawn cup has a curvilinear shape that is congruent with the urethane pad being in full contact with the sheet metal throughout the deformation process. The pressure exerted on the cup by the urethane pad eliminates the puckering problem. To prevent wrinkling at the flange, a sufficiently high blank force is required, whilst to prevent tearing at the hemispherical portion of the cup the blank-holding force has to be limited: dimensions of the urethane pad to satisfy these conditions are proposed. A special custom-macro program has been written for the computer numerical control (CNC) machining of the die, with the cup radius, die (corner) radius and cup height as parameters.