An Upper-Bound Approach to Cold-Strip Rolling

Abstract

The operation of cold-strip rolling is treated under the assumption of “Mises” material. A lower upper bound on energy consumption is computed. Then, assuming constant shear between strip and rolls, an approximate value of the actual energy is determined. Another value is arrived at by assuming Coulomb friction between strip and rolls. An efficiency factor is determined through the ratio of required to ideal energy, the former being the combined energy of deformation and friction losses on the strip surface. The total deformation energy includes the internal strain energy (ideal energy) associated with an assumed strain field and the energy along the surfaces of velocity discontinuities. The roll torque, minimum required friction (or maximum possible reduction), and efficiency are determined as functions of the other process variables. Results are presented graphically and as mathematical expressions. This study is a direct sequel to an earlier paper [6], in which velocity discontinuities were disregarded.