中文摘要：

考虑上下工作辊之间以及上下支撑辊与机架之间的非线性刚度和非线性阻尼,建立了四辊轧机辊系四自由度参激垂直耦合振动模型。运用多尺度法求解了该系统在主共振和1∶1内共振情形下的解析近似解,得到了幅频特性曲线方程。分析了轧机主要参数对主共振的影响,通过分析1∶1内共振幅频特性曲线,发现内共振和主共振一样存在幅值跳跃现象。通过数值仿真验证了模型及分析结果的有效性,并分析了参激耦合振动系统随参数变化时的局部分岔现象。研究结果可为轧机辊系垂直颤振机理分析及抑制提供参考。

英文摘要：

A vertical nonlinear parametrically exited coupling vibration model of 4-h rolling system was established,which considered the nonlinear damping and nonlinear stiffness between working rolls and supporting rolls to rolling mill＇s frame,The parse approximation solution were carried out by using multiple-scale method,under main frequency,1∶1 inner resonance,and the curve equations of amplitude-frequency were obtained.The vibration characteristics of the system under nonlinear stiffness and nonlinear damping were analyzed.With the changes of nonlinear stiffness,the amplitude appears the jumping phenomenon.It leads instability of the system.The numerical simulation indicates that the solution is validated.Local bifurcation was studied with parameter transform.It can offer some theoretic guidance on vibration mechanism and control in rolling mills.