A Method for Analyzing Spread, Elongation and Bulge in Flat Rolling

A method for analyzing spread, elongation, and bulge in flat rolling is developed. The analysis is based on an upper-bound approach in which an iterative numerical procedure is used to minimize the energy dissipation rate for kinematically admissible velocity field solutions for 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 spread, elongation, roll separating force, and roll torque measurements in the hot rolling of mild carbon steel. Discussion of the factors which lead to single-bulge or double-bulge deformation in flat rolling, and a suggested technique for estimating the interface friction conditions in rolling, the Flat Bar Test, are also included.