The Evaluation of Load and Torque in Hot Flat Rolling from Slip Line Fields

Abstract

This paper presents a computer evaluation of slip line fields for rolling with medium arc of contact to thickness ratios for conditions of sticking throughout the arc of contact. The results of load and torque evaluations using a computer version of the Prager geometrical method are combined with the results obtained by Dewhurst, Collins and Johnson for the classes of slip line fields with shorter arc of contact to thickness ratios. The two methods of slip line field evaluation by the Prager and the matrix methods are shown to give load and torque functions which give a smooth transition over the boundary. The load and torque functions are presented in the form suitable for use with the yield stress functions of Cook and McCrum (BISRA method). The computer evaluation of slip line fields by the Prager method lacks elegance by comparison with the matrix method, but is the only method at present available for the evaluation of slip line fields for rolling where two rigid metal zones occur on the surface of the rolls. It is also believed that the computerized Prager method for slip line field evaluation is more readily adapted to the evaluation of slip line fields for conditions of mixed sticking and sliding friction.