A universal formulation for the extrusion of sections with no axis of symmetry

摘要

The subject of theoretical analysis for the extrusion of profiled sections has been heavily worked on by many researchers. However most of these have concentrated on the extrusion of sections with some axes of symmetry. This paper aims to provide a new formulation for the analysis of the extrusion process for non symmetric profiled sections with no axis of symmetry. The upper bound theorem has been used to obtain an approximate solution. Both flat faced dies and bilinear dies were used in the present work. In fact this formulation could be applied to the extrusion process of hollow sections as well as solid parts. The advantage of the proposed method is the new way of discretizing the deforming region in the extrusion of shaped sections based on which a generalized kinematically admissible velocity field was formulated. For a given extruded profiled section this method employs fewer number of sub-divisions than before, giving a lower upper bound value for the extrusion power. The generality, easy application to different sections, short computing time and fairly realistic outcomes of the analysis could be regarded as other strengths of the present method. The lack of incorporation of temperature effects for hot extrusion processes could be mentioned as one of the disadvantages of the present method. The position of the die cavity was also optimized using the new method. A design map for the extrusion die geometry was also given as a graph of extrusion pressure versus the optimum die length for the bilinear dies with different frictional conditions and reductions of area. The extrusion of L-shape profiled section was chosen as a sample since it had no axis of symmetry. Extrusion dies were also manufactured and experiments carried out to verify the theoretical results. Finite element simulation for the extrusion of U, T and I-shape profiled sections was also carried out using ABAQUSCAEExplicit commercial software.