This paper presents an upper bound approach to analyze axisymmetric extrusion processes. A cylindrical and a spherical coordinate system are defined to represent the die geometry and the velocity field, respectively. For various curved dies, minimized upper bound results can be obtained by relating these two coordinate systems. Based on this modeling technique, the effects of die geometry, reduction ratio, and friction are investigated. Axisymmetric extrusion through various curved dies can be easily optimized with the proposed methodology.

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