A Nonlinear Research on Coupled Vibration of Strip Steel with the Impact of the Main Drive System of Tandem Mill

Based on the movement mechanism of strip steel and main drive system during the continuous rolling process, the main drive system of each frame was simplified into a two-degree-of-freedom discrete model and the strip steel was simplified into an axially moving Euler beam. Then, the coupled mechanical model of transverse and longitudinal vibrations of the strip steel with torsional vibration of the main drive system was established. Meanwhile, the nonlinear vibration differential equations of the coupled model were derived with Hamilton's principle, and the solution method of the mathematical model was studied. In fact, the solution method of the mathematical model was a joint solution process of discrete matrix differential equations and continuous nonlinear differential equations. Therefore, the established model could be called the discrete-continuous coupled nonlinear vibration model. Then, the discrete-continuous coupled differential equations were jointly solved with the modified iteration method and the Kantorovich averaging method. Finally, by using the MATLAB simulation, the amplitude-frequency response curves of strip steel vibrations coupled with torsional vibration of main drive system were obtained to explore the influences of axial velocity and tension of strip steel on coupled vibration characteristics. The results improve the theoretical study on the vibration of rolling mill for engineering applications.