Finite element analysis of steady-state three-dimensional helical extrusion of twisted sections using recurrent boundary conditions

Abstract

In metal-forming, there are problems with recurrent shapes and without explicitly prescribed boundary conditions. In such problems, so-called recurrent boundary conditions must be introduced. The present study is concerned with three-dimensional finite element analysis for helical extrusion of twisted sections. A finite element analysis is carried out for steady-state three-dimensional helical extrusion of noncircular twisted sections, such as clover and trocoidal gear sections, through curved dies. The curved die profiles are described by continuous functions by which smooth transitions of the die surface from the entrance to the exit are obtained. The work-hardening effect is considered by integrating the effective strain rate along each stream line through interpolation by the least-square method. The computed extrusion pressures by the finite element method are compared with the experimental results. The extrusion pressure, as well as the twist angle of working material, is compared for several friction factors. Distorted flow patterns in the three-dimensional space and the distribution of the final effective strain are also obtained.