A study of the effect of the process variables in unsymmetrical single-hole and multi-hole extrusion processes

A plane-strain upper-bound analysis of eccentric single-hole extrusion and unsymmetrical multi-hole extrusion is presented using analytical and semi-analytical expressions. Expressions for the following dependent process parameters have been developed: the extrusion pressure, exit angle and velocity of the emerging product. The given relationships may be applied to an extrusion die with any number of aligned orifices. The analytical or numerical optimization of the upper-bound expression for the power allowed a study of the dead-zone angles of the assumed pattern of deformation. The results are given as a function of the independent process parameters, such as the eccentricity of the holes, the distance between the holes, the shear factor coefficient, the fractional reduction and the ram position. To verify the accuracy of the present results, quantitative and qualitative comparisons are made with published works from the literature and with finite-element results. (C) 1998 Elsevier Science S.A.