An approximate three-dimensional metal flow analysis for shape rolling is developed. The analysis, which is presently applicable to rod rolling, is based on an upper-bound approach in which an iterative numerical procedure is used to minimize the energy dissipation rate to obtain kinematically admissible velocity field solutions of the rolling problem. Once the velocity field and the final shape of the plastically deforming body are known, then elementary stress analysis techniques are used to determine the force related aspects of the rolling problem. It is assumed that the rolled material is rigid perfectly plastic, and only the purely mechanical aspects of the metal deformation problem in rolling are considered assuming isothermal conditions. The analysis shows good agreement with elongation and roll separating force measurements in the hot rolling of mild carbon steel for a variety of workpiece and roll cross-section geometries commonly used in rod rolling.

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