The hydrodynamic deep-drawing process for blanks of non-uniform thickness

Abstract

The process of hydrodynamic deep-drawing (HDD) has been modified to draw tapered blanks of small angles. This option, unattainable in classical deep-drawing processes, has its applications in producing specially-dedicated products. But, more generally, this process is aimed at decreasing the demand for a strict uniformity of blank thickness and thus relaxing the costly tight tolerances on the preformed blanks. The idea rests on changing the customary clamped die to a self-aligned die by letting it be semi-spherical with rotational degrees of freedom. The automatic self-alignment of the die to the current angle of the blank arises from the very nature of the hydrodynamic fluid pressure beneath the blank. The solution for the statically admissible stresses throughout the flange is produced in an asymptotic-expansion fashion, with the inclusion of thickness variation, interfacial friction and exponential hardening of the material. Consequently, the apparently ‘bizarre’ phenomenon of rupture initiating at the thickest portion of the blank (rather than at the thinnest portion) is revealed. Expressions for the limit drawing ratio (LDR) as a function of the angle of the tapered blank (beside other relevant parameters) are developed. They are compared favourably with experiments produced on a specially built apparatus.