An analytical model for dependence of force and forward slip on speed in cold rolling

An explicit analytical method for determining approximations for roll force and forward slip for strip rolling is introduced. It reproduces all main predictions of classical strip theory, but is completely free of any numerical algorithms. Nevertheless, for extreme cases of cold rolling, like foil or skin pass rolling, more sophisticated algorithms are still needed. For the friction coefficient in the roll gap and its increase from the entry to the neutral point also explicit relations are proposed. In the framework of this analysis, they are sufficiently precise for cold rolling with one-phase lubricants and stochastic surfaces. Only a single parameter of adaptation is needed, the microscopic friction coefficient μ micro The quality of the total model is illustrated by means of the dependence of roll force and forward slip on rolling speed. For this purpose measured process data (four different pass-schedules, seven to ten coils each) for cold rolling of copper with rolling oil is analyzed.