中文摘要：

以四辊板带轧机为例，分析液压压下缸及弯辊缸在轧机辊系振动时表现出的分段弹性力和摩擦力两种非线性约束，建立液压缸非线性约束作用下的轧机辊系振动模型，并采用平均法求得振动系统的幅频响应。通过比较两种非线性作用下辊系振动速度和振动幅值的仿真曲线，研究辊系受分段弹性力和摩擦力影响时的行为特性。取不同分段弹性力和摩擦力，仿真分析两种非线性因素分别对轧机辊系幅频特性的影响规律。结果表明，轧机辊系振动速度受分段弹性力大小影响，系统不稳定频率区域随分段弹性力增大而变宽；摩擦力较小时，对辊系振动行为影响表现为阻尼特性，较大时，摩擦力的非线性成为影响辊系振动行为的主要特性。该结论为轧机辊系振动控制提供了理论参考。

英文摘要：

With four-high plate mill as an example, two nonlinear constraints that are segmented elastic force and friction force of hydraulic screw-down cylinders and bending cylinders in rolling mill roll system vibration are analyzed, the model that nonlinear roll system vibration under the nonlinear constraint action from hydraulic cylinder is established, and amplitude-frequency response of the vibration system is obtained by using average method. The behavior characteristic of roll system under the action of segment elastic force and friction force is studied by analysis of vibration curves under the function produced by two kinds of nonlinear factors. The law of amplitude-frequency characteristics of roll system influenced by two kinds of nonlinear factors respectively is studied by taking different segmented elastic force and friction force. The results show that vibration speed is affected by the magnitude of elastic force, the instability frequency area is wider with increases of segmented elastic force increasing, and the influence on the vibration behavior of the roll system turns damping into nonlinear with friction force increasingly. This conclusion provides a theory reference for roll system vibration control.