Nonlinear dynamic rolling forces in the vertical and horizontal directions are, respectively, established, considering the impact of vertical and horizontal directions vibration of rolls. Then a vertical-horizontal coupling nonlinear vibration dynamic model of rolling mill rolls is proposed, based on the interactions between this dynamic rolling force and mill structure. The amplitude-frequency equations of the main resonance and inner resonance are carried out by using multiple-scale method. The characteristics of amplitude frequency under nonlinear stiffness, damping, and amplitude of the disturbance are obtained by adopting the actual parameters of 1780 rolling mills. Finally, the bifurcation behavior of the system is studied, and it is found that many dynamic behaviors such as period, period-3 motion, and chaos exist in rolling mill, and this behavior could be restrained effectively by choosing proper system parameters. 1. Introduction The vibration of rolling mill often occurs in rolling process. The occurrence of vibration not only affects the quality of rolling products, but also leads to breakdown of the rolling equipment. In order to understand the vibration behaviors of mills, a number of models have been developed during the past few decades [1–5]. However, in most open literatures, the vibrations in the horizontal direction and in the vertical direction are studied separately. In recent years, the coupling relationship in rolling mill is proposed; Hu et al. studied the linear vibration characteristics in vertical and horizontal direction . Yang et al. studied the stability of coupling dynamic vertical model of cold rolling mill, which consists of the rolling process model, the mill roll stand structure model, and the hydraulic servo system model . In the process of studying rolling mill vibration, modeling of rolling force directly determines the accuracy of vibration model. In the early years, the rolling force in the rolling process is quasistatic, which assumes that only dynamic variations in roll spacing produce variations in force, strip speed, and strip thickness to those occurring under steady-state conditions [8–10]. Yun et al. proposed a dynamic model of rolling mill, which considers the rate variation of change of the roll spacing. But in order to simplify calculation, he only selected the linear section of rolling force by using Taylor formula . In fact, most of the literatures adopted the method of Yun, by taking the rolling force as a linear factor and neglecting nonlinear section. In this paper, nonlinear dynamic
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