Dynamic characteristics of a rolling mill drive system with backlash in rolling slippage

According to the rolling slippage of a rolling mill drive train with backlash, the present authors have established a universal non-linear mathematical model for the drive system and used the Krilov–Bogolubov method to solve it, having ascertained the conditions of the self-excited vibration being aroused such as the relationship of rolling normal force and rolling speed, and also presenting the method of calculating the minimal rolling normal force required to arouse the self-excited vibration and the limit rolling speeds in which the self-excited vibration of the main drive train arises. The relationship of rolling normal force, rolling speed and torque amplification factor associated with the self-excited vibration is also derived. The research may provide a valuable way to avoid self-excited vibration and thus prevent the system from instantaneous breakage.