Numerical analysis of three-dimensional extrusionof sections through curved dies by the method of weighted residuals

Abstract

The importance of analysis for the extrusion process lies in the determination of forming load, flow characteristics and state of stress and strain. They provide the necessary design specifications and data for the dies, punches, press and die setup etc., and provide the informations to control the material properties of products effectively. For extrusion of complicated sections the acquisition of detailed informations is possible by resorting to the numerical methods of analysis, such as the finite element method or the method of weighted residuals. Despite increasing demand for the analysis of three-dimensional extrusion of sctions through continuous dies, so far there has been few systematic and general analysis by using such numerical methods of anlysis. Due to the use of continuous global functions in the deformation region and the reduced computation time the method of weighted residuals shows some advantages in its own right. In the present study, by using a method of numerical analysis based on the method of weighted residuals, axisymmetric extrusion and three-dimensional extrusion of various sections through contiunous curved dies are analyzed to provide a theoretical bais for the optimal die design and process control in the extrusion technology. The study is categorized into the following three parts depending on the products shapes and the techniques of the analysis. (1) Analysis of axisymmetric extrusion of rods using the finite difference method based on body-fitted coordinate transformation. (2) Analysis of three-dimensional extrusion of elliptic sections by flow functions (3) Analysis of three-dimensional extrusion of arbitrarily-shaped sections by assuming the velocity components as global functions For steady-state three-dimensional extrusion of sections, the rigid-plastic finite element analysis by penalty constraint method is caried out to verify the results by the method of weighted residuals. The analysis has been shown to render the resu...