中文摘要：

基于热连轧机的机械结构和工艺结构,考虑态轧制力对轧机振动的影响,建立了轧机辊系的非线性动态轧制振动模型。根据Lagrange原理,得到了轧机辊系的动力学方程,应用多尺度法求解了系统的分岔响应方程,采用奇异性理论分析得到了系统稳态响应的转迁集及其相应的分岔曲线拓扑结构,利用Melnikov函数法研究了系统发生分岔与混沌的参数临界条件。最后进行数值仿真,通过分岔混沌图、最大Lyapunov指数、相轨迹和Poincare截面验证了理论的有效性,这为抑制和控制轧机系统非线性振动提供了理论参考和借鉴。

英文摘要：

Based on the mechanical structure and the process structure of the hot continuous rolling mills, considering the influence of the dynamic rolling farce on the rolling mill vibration, a nonlinear dynamic rolling process vibration model of the rolling system was established, and the dynamic equation of the rolling mill system was obtained according to Lagrange theory. The bifurcation response equation was obtained by the multiple-scale method, the static response transition sets of the system was analyzed to get by the singulary theory, and the topology structure of the correspnding the bifurcation cure was obtained. The critical condition of chaotic and bifurcation motion was obtained by Melnikov function method. Finally, using the numerical simulation, the effectiveness of the theoretical was proved by the biftrcation chaotic map, the top Lyapunov exponent map, the phase plane plots and the Poincare section maps, which provides the theoretical reference for suppressing and controlling the nonlinear vibration of the rolling system.