Investigation of lubricated die/billet interface in hydrostatic extrusion process using upper bound theorem

The objective of this paper is to investigate numerically the existence of thermal minimum film thickness at the die-billet interface in the inlet in the hydrostatic extrusion of aluminum alloy by incorporating the viscous heat dissipation in the lubricating film. Governing equations (Reynolds equation, energy equation, Roelands viscosity relation, and film thickness geometry relation) have been solved herein using lobatto quadrature technique. Predicted minimum film thickness, temperature, and pressure at the exit of inlet zone have been used as boundary conditions in the work zone analysis. In the proposed work zone analysis, heat transfer by convection along the lubricating film, conduction across the film, uniform billet heating by plastic deformation and strain hardening of billet material have been accounted. Drastic reduction in thermal minimum film thickness has been observed in the inlet zone with respect to the isothermal minimum film thickness of inlet zone. However, about 4 to 5 times less thermal minimum film thickness has been achieved respect to the corresponding isothermal minimum film thickness at the exit of the inlet zone. (C) 2017 The Authors. Published by Elsevier Ltd.