Considering the Shape of the Deformation Region when Defining Contact Stresses and Cold Rolling Force for a Plate of Strengthened Material

Abstract

The influence of the mechanical performance of a workpiece material and the shape of the contact surface of a deformation region on the change in the yield point along the arc of roll contact under cold bar rolling is considered. The error in calculating the equivalent yield point during the replacement of a hardening curve with a linear and an exponential dependence is estimated. A hardening curve approximation is suggested the parameters of which depend on power n of the hardening curve, the initial deformation degree, and the equivalent yield point. This approximation is used to derive the analytical solutions of the von Karman equation for replacing the arc of roll contact and define the contact stresses and the roll effort. We compare the already known and new solutions by analysis. In particular, it is established that the replacement of an arc of roll with a chord at n = 1 weakens the design roll effort by 20% and greater.