Shear Plane Theories of Hot and Cold Flat Rolling

Abstract

The shear plane theory of hot rolling of thick stock, due to Green and Wallace, is extended to hot and cold flat rolling. Values calculated from the hot rolling theory compared satisfactorily with the theory of Sims and the experimental results of Wallquist. The cold rolling theory is similarly satisfactory in comparison with the experimental results of Ford and it is anticipated that the theory will be more accurate than that of Bland and Ford for small R/h ratios and large reductions. Examples of calculation of load and torque for rolling are given in Appendixes for both Coulomb friction and sticking and shearing at the metal surface and it is shown that both conditions may occur and be taken into account concurrently. A method of determining the total torque is given which is derived from an upper bound to the work done on shear planes which are shown to have the same configuration as that chosen in the analysis of forces.