Upper Bound Solution For Forward Conical And Spiral Extrusion Of Hardening Material

Plastic forming technolog is one of the basic and the most important solution methods of manufacturing industry,which has excellent properties,such as large-yield,low-consumption,high-quality.It is an important direction of the development of modern manufacturing technology.With important research and application value,it is meaningful to study the mechanical properties of hardening material forming process by use of appropriate theory.The upper bound theory is one of the important solution methods of plastic forming problems,which has a certain reference value for engineering practice.By use of the upper bound theory,the objective of this paper is to study the plastic deformation problem in the processes of the conical extrusion,forward spiral extrusion and variable spiral extrusion for linear hardening material,power hardening material and perfectly plastic material.The specific contents are as follows:1.The upper bound theory and basic principle are briefly introduced and the theory application to hardning material plastic deformation has been presented.2.The upper bound solutions of conical squeeze pressure for linear hardening materials,perfectly plastic materials and the linear strain hardening material have been obtained by use of admissible velocity field in cone-die direct extrusion.Meanwhile,we obtained the curve of extrusion pressure change with haif cone angle in cone-die direct extrusion and the curve of extrusion pressure change with haif cone angle variation in cone-die direct under the condition of various friction values(in cone wall of cone-die ?(28)0.1 and ?(28)0.5)for perfectly plastic materials and linear hardening materials.Further,the effects of the hardening property of material,concave conical die wall friction coefficient and cross section contraction rate,die half cone angle on extrusion deformation have been analyzed.3.The upper bound solution of forward spiral extrusion for power hardening materials has been obtained by use of admissible velocity field,and the difference between the upper bound result and experimental data has been conducted.Reasonability of velocity field and the preciseness of upper bound solution are verified.4.Two design schemes of spiral have been proposed and the upper bound solution of variable spiral extrusion for power hardening materials has been achieved.