A UBET analysis of non-axisymmetric forward and backward extrusion

In this study, UBET is used to analyze the forward and backward extrusion of hexagonal- and trochoidal-shaped wrench bolts. For the UBET analysis, the extrusion process is assumed to have two stages. In the first stage, axisymmetric forward extrusion and non-axisymmetric backward extrusion simultaneously take place until the backward extrusion of a wrench socket is completed. In the second stage, only the cylindrical forward extrusion process takes place. New kinematically admissible velocity fields are proposed to determine the forming load, the extruded length and the deformation pattern with respect to the punch stroke. From the proposed velocity fields, the upper-bound load and the average length of the extruded billet are determined by minimizing the total energy consumption rate with respect to chosen parameters. Experiments are carried out with antimony–lead billets at room temperature using hexagonal- and trochoidal-shaped punches. The forming load and the extruded length with respect to the punch stroke are compared with the theoretical predictions, good agreement being found.