中文摘要：

基于Roberts摩擦因数公式和Hill轧制力公式,建立能够表征不同摩擦状态下的动态轧制力模型;在此基础上进一步考虑轧机结构的振动和轧件振动之间的相互影响,提出轧件-轧辊耦合振动模型。根据广义耗散的Lagrange原理,分别沿轧制方向和垂直于轧制方向建立动力学平衡方程;采用多尺度法求解出考虑系统内共振的幅频特性方程,并仿真分析不同外部激励和非线性参数作用下的轧机振动规律。研究结果表明：滑动摩擦状态下耦合系统对内部非线性参数变化和外部扰动变化的敏感程度远远高于静摩擦状态下的情况;适当选取耦合三次项非线性参数,可以将系统不稳定振动的出现控制在一个较小的频率区间,削弱轧件-轧辊耦合振动对板带轧机振动的影响。

英文摘要：

Based on the Roberts friction factor formula and the Hill rolling force formula,a kind of dynamic rolling force model was established.The model might characterize different friction states.On the basis of further consideration of the interaction between the structure of rolling mill vibrations and rolled piece vibrations,a coupling vibration model of rolled piece-roll was proposed.According to the Lagrange principle of generalized dissipation,a dynamic equilibrium equation was established respectively both of in rolling direction and in vertical direction.Then by using the method of multiple scales,the amplitude-frequency characteristic equation of the system was solved.The law of mill vibration influenced by different internal nonlinear parameters and external excitations was analyzed.Research results show that when rolled piece is slided,the coupling system is far more sensitive to the change of internal nonlinear parameters and external excitation than static state.If the coupling cube nonlinear parameters are reasonable,the occurance of system unstable vibration may be controlled in a small frequency range,which may weaken the impacts from rolled piece-roll coupling system on the vibration of strip mill.