A Class of Solutions for Extrusion through Converging Dies

Abstract

Extrusion, as a metal forming process, has definite advantages over rolling for production of three-dimensional section shapes. The very large reductions achieved in this process, even at high strain rates, have made it one of the fastest growing metal forming methods. With the increasing demand for sections of different shapes, it has become essential to develop analytical methods for their solution.The present investigation is a sincere attempt to develop a class of solutions for extrusion of different sections from round and square billet through converging dies by three-dimensional upper bound method as well as Finite element method. Three dimensional upper bound solutions are based on both continuous velocity field and discontinuous velocity field. The continuous velocity fields are based on dual stream function method. The discontinuous velocity fields are based on SERR (spatial elementary rigid region) technique.Upper bound method based on SERR technique is used for analysis of extrusion of pentagon, octagon, triangular and rhomboidal sections from round billet using linear converging die. The constant friction factor is assumed at the die billet interface. The single point formulation has been used keeping the die orifice in the centroid of billet axis so that product emerges straight. The extrusion pressure and die profile has been determined for different reductions and friction factors.