An Upper Bound Solution for the Extrusion of Square Section from Round Bar through Converging Dies

Abstract

This paper presents a theoretical solution obtained for the extrusion of square sections from round bar through converging dies. A new upper bound solution is proposed for the solution of three dimensional metal flow through converging dies formed by an envelope of straight lines drawn from points on the perimeter of the circular, entry section to corresponding points on the square, exit shape. For a given extrusion ratio, material properties, and frictional condition the method can be used to determine the upper bound extrusion force and the optimum die geometry in order to minimise this extrusion force. This investigation is one part of an overall research programme into CAD/CAM of shaped extrusion dies.