On the hydrodynamic deep-drawing process

Abstract

The feasibility of deep-drawing aided by hydrodynamic flow beneath the blank is demonstrated. The analytical background for directing the design of the process is based on the limit analysis in plasticity theory coupled with flow analysis of viscous, non-inertial fluid. It is done for isotropic non-hardening material with inclusion of constant friction coefficient as an additional parameter acting on plastic/rigid interfaces. The main attention is focused on approximating the Limit Drawing Ratio (LDR) via upper and lower bound and comparing the conventional process to the suggested hydrodynamic-aided process. The unique features of the process along with its limitations (geometrical and material-wise) are exhibited. The prominent role of the die curvature with regard to LDR is emphasized. A non-dimensional number combining fluid viscosity, punch speed, material strength and a characteristic length of the process (identified as Sommerfeld Number) appears as a useful measure for the clearance height through which the fluid flows. The study is corroborated with experiments.