中文摘要：

根据4200立辊轧机的实测参数，采用理论分析和数值计算相结合的方法建立了中厚板立辊轧机主传动系统的4自由度非线性振动模型，通过对该模型的简化求解，得到系统线性振动下的全部响应．采用Matlab软件编程求出了非线性振动方程的数值解，并采用相图、庞加莱映射图和时间历程图等方法，分析讨论参激角频率靠近线性振动固有角频率时振动系统的运动状态．为进一步讨论系统的稳定性，分析了参激角频率在固有频率间变动时的运动现象．结果表明：当参激角频率从接近一阶固有频率开始逐渐增大时，系统的运动是不稳定的，其运动状态由周期运动逐渐过渡到准周期运动，乃至混沌运动．

英文摘要：

According to the testing parameters of a 4200 vertical mill and by using the numerical calculation com- bined with theoretical analysis, this paper proposes a nonlinear vibration model with four degrees of freedom for the main transmission system of the vertical medium plate mill. The model is simplified and is then used to obtain the responses of the linear vibration system. The numerical solutions to the nonlinear vibration equations are obtained by means of Matlab. Afterwards, the motion state of the vibration system with a vibrating angular frequency approaching to the natural one is analyzed by means of phase graph, Poincare mapping graph and time＇history curve. Finally, the motion state of the system with a vibrating angular frequency varying in the natural frequency range is analyzed to further reveal the system stability. The results indicate that, when the angular frequency increases from the first-order natural frequency, the system is instable, with a motion state changing from a periodical mode to a quasi-periodical and even a chaotic one.