Calculation of rolling pressure distribution and force based on improved Karman equation for hot strip mill

An improved Karman equation for hot-rolled strip was deduced to generate a new rolling pressure formula, based on comprehensive consideration of the slipping and sticking friction on the contact arc between hot-rolled strip and work rolls. The Runge-Kutta method was applied to solve the improved differential equation, and then the distribution of rolling pressure on the contact arc was obtained. The roll force in the roll-bite can be calculated by integrating the vertical component of positive pressure and friction shear stress of every slice. This paper also analyzed the influence of friction condition, flow stress, roller distortion and other factors on the results of rolling pressure and force per unit width. Using 7 stands of hot strip mills as an example, this paper conducted actual industrial application verification. The computational results demonstrate that the proposed new model improves the setting precision of roll force and can be applied to online control of hot rolled strip.