AN UPPER-BOUND ANALYSIS OF THE BACKWARD EXTRUSION OF TUBES OF COMPLICATED INTERNAL SHAPES FROM ROUND BILLETS

Abstract

A new kinematically-admissible velocity field is proposed to determine the final-stage extrusion load and the average extruded height in the backward extrusion of internally non-axisymmetric tubes from round billets. The proposed velocity field is applied to the backward extrusion of internally trochoidal gear-shaped tubes and rounded rectangular-shaped tubes, the profile function of a rounded rectangle being approximated by using a Fourier series. Experiments are carried out with fully-annealed commercial aluminum-alloy billets at room temperature using various shaped punches. The theoretical predictions of the extrusion load are in good agreement with the experimental results and there is generally reasonable agreement in average extruded height between theory and experiment.