Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area, nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directions were obtained based on the Karman’s balance theory. Based on these dynamic rolling forces and the mechanical vibration of the rolling mill, a vertical–horizontal coupling nonlinear vibration dynamic model was established. The amplitude–frequency equation of the main resonance was derived by using the multiple-scale method. At last, the parameters of the 1780 rolling mill were used for numerical simulation, and the time-domain response curves of the system's vibration displacement and lubricating film thickness under the steady and unsteady conditions were analyzed. The influences of parameters such as interface contact ratio, nonlinear parameters and external disturbances on the primary resonance frequency characteristics were obtained, which provided a theoretical reference for the suppression of rolling mill vibration.

考虑到轧辊振动对轧制变形区域中润滑剂膜厚度的动态影响，基于卡尔曼平衡理论，获得了与垂直和水平方向上的膜厚度有关的非线性动态轧制力。基于这些动态轧制力和轧机的机械振动，建立了垂直-水平耦合非线性振动动力学模型。主共振的振幅-频率方程是通过使用多尺度方法得出的。最后，利用1780轧机的参数进行了数值模拟，分析了系统在稳态和非稳态条件下的振动位移和润滑膜厚度的时域响应曲线。参数的影响，例如界面接触率，