A generalised CAD/CAM solution to the three-dimensional off-centric extrusion of shaped sections: analysis

In analytical method based on the upper-bound theory is proposed to investigate the three-dimensional off-centric extrusion of arbitrarily shaped sections from arbitrarily shaped billets through linearly converging and smooth curved dies. A set of generalised kinematically admissible velocity fields are derived on the assumption of Bezier-type streamlines that provide compatibility of surface representation with most CAD/CAM systems. To obtain a more realistic non-uniform metal flow, a special velocity function was also incorporated into the derived velocity fields and work hardening effect of the material considered. Based on the method presented, for a given reduction in area, material property, friction condition and off-centric positioning of the exit cross-section, predictions of the deforming grid pattern, curvature of the extruded product as well as upper-bound to the extrusion pressures may be obtained. The above procedure is highlighted and commented upon.