DISTRIBUTION NORMAL CONTACT STRESSES IN THE ROLL GAP AT A CONSTANT SHEAR STRESS

Abstract

Differential equation describing stress state in the rolling gap was derived first time by Karman. Since the solution of the differential equation is not easy many authors try to simplify of entry conditions. Some authors have replaced the circular arch of the contact zone of rolls by straight line, polygonal curve or parabola for simplifications of solution. These simplifications allow to obtain analytical solution differential equation but with acceptation some inaccuracy of the final results. Another solution of the differential equation was focused on the substitution of the analytical solution by the numerical solution, but should also expect some uncertainty of the final results. A more sophisticated solution was given by Gubkin is based on defining a constant shear stress and the approximation of the circular arch through the straight line. Gubkin for analytic solution of differential equation used one constant that includes the friction coefficient and second constant which is including the geometry of the rolling gap. The contribution of this paper is an original analytical solution of the differential equation based on the description of the contact arc by the equation of a circle. The proposed solution for the calculation of normal stress distribution is described by two constants. The first constant is describing the geometry of the rolling gap and the second describes friction coefficient. The final solution of differential equation is sum of two independent functions involving the shear stress as a variable value. The proposed solution does not consider with material work hardening during processing.