Vertical vibration analysis of rolling interface based on dynamic rolling force with variable friction characteristics

This study investigates the impact of variable friction characteristics at the rolling interface on the vertical vibration of plate and strip rolling mills. Based on the optimized Karman equilibrium theory, a dynamic rolling force model considering the front and back tension, elastic stretching, and rolling speed was established. The amplitude-frequency response equation of rolling mill system is solved by multi-scale method, and the influence of main parameters on vertical vibration of rolling mill system is analyzed. The results show that the increase of the first stiffness coefficient of dynamic rolling force leads to the decrease of the principal common amplitude of the system. On the contrary, when the third stiffness coefficient increases, the system exhibits a jump phenomenon. When the third stiffness coefficient of dynamic rolling force is reduced within a certain range, a stable and unique solution is obtained without jumping phenomenon. Moreover, the smaller the damping coefficient of the upper and lower roller system is, the larger the vibration amplitude is and the jump phenomenon occurs. Decreasing the external disturbance force can effectively reduce the system’s vertical vibration amplitude and suppress the resonance. In addition, with the change of external disturbance force, the roll system of the rolling mill shows a variety of complex motion states, such as periodic motion, double-periodic motion, and chaotic motion. The research results provide an effective theoretical reference for the suppression of vertical vibration of rolling mill.