Upper-bound analysis of axi-symmetric forward spiral extrusion

Abstract

An axi-symmetric forward spiral extrusion process, AFSE, has been analyzed using the principle of the virtual work rate. Based on an existing kinematically admissible velocity field, an upper bound solution has been developed for the new forming process. The solution also provides estimation of the die reaction torque during the process. AFSE experiments were conducted with lead specimens in order to verify the upper-bound solution. A reasonable agreement between experimental results and the upper bound solution was observed. The upper bound analysis indicated that both deformation in a small zone next to the velocity discontinuity plane and the frictional power constitute the most significant parts of the consumed power, respectively, during AFSE. As a result, reduction in friction will lead to a dramatic decrease in the total forming force in AFSE while maintaining a circumferentially slippage free flow of material during the process. It was shown that by increasing the die helix angle above a critical value, the rate of growth in the die reaction torque and extrusion load with the helix angle increases dramatically.