Application of an upper bound method to off-centric extrusion of square sections, analysis and experiments

In the present study, previously developed analytical approach (Chitkara and Celik) which was based on the upper-bound theory, for the design of three dimensional off-centric extrusion of arbitrarily shaped dies was applied to the off-centric extrusion of square sections from initially round billets with experimental verifications. A computer program was written to obtain optimum die design which yield the lowest upper-bound for a given reduction in area, die length, off-centric positioning and frictional conditions. Computations were carried out both for the converging (ruled-surface) and smooth curved (advancedsurface) dies. Curvature of the extruded product and simulated deforming grid pattern were also predicted. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to manufacture the streamlined dies for the off-centric extrusion of square section rods. The theoretical predictions were observed to be in good agreement with the experimental results.