Analysis of Dynamic Characteristics of Forced and Free Vibrations of Mill Roll System Based on Fractional Order Theory

In this paper, the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill, mainly including the study of forced vibration and free vibration of the roller. Firstly, the nonlinear damping parameters and nonlinear stiffness parameters within interface of the rolling mill are both considered, and a fractional-order differential term is also introduced to model the horizontal nonlinear vibration. Secondly, the averaging method is introduced to solve the forced vibration system of the mill roll system, and the amplitude-frequency characteristic curves of the system are obtained for different orders, external excitation amplitudes, stiffness and fractional order coefficients. Thirdly, the amplitude-frequency and phase-frequency characteristics of the free vibration of the mill roll system are investigated at different fractional orders. Then, the accuracy of the averaging method for solving the dynamic characteristics of the system is verified by numerical analysis, and the effect of the fractional differential term coefficients and order on the dynamic characteristics of the roll system are investigated. Finally, the time-frequency characteristics and phase-frequency characteristics of free vibration systems at different fractional orders are studied. The validity of the theoretical study is also verified through experiments.