中文摘要：

以Orowan单位压力微分方程为基础,考虑轧制过程轧辊纵向和横向振动的影响,建立了轧件的动态轧制力模型。在此基础上,考虑轧机结构的影响,建立了轧机辊系的耦合振动动力学模型。运用多尺度法求解了该系统在主共振和内共振情形下的解析近似解,得到了幅频特性曲线方程,同时采用奇异性理论分析了系统的分岔行为,得到了系统的转迁集及在不同区域中分岔曲线的拓扑结构。最后以轧机实际参数为例,分析了不同参数对系统振动特性的影响,发现主共振与内共振都存在着跳跃现象,且耦合项参数对内共振影响颇大,适当选取系统参数可有效减小这种振动行为,这为抑制轧机辊系振动提供了理论参考。

英文摘要：

A dynamic rolling force model of workpiece was established,which considered the impact of the longitudinal and transversal vibration in the rolling process,based on the Orowan unit pressure differential equation. Then considering the influence of the mill structure, the coupling vibration dynamic model of rolling mill rolls was proposed, the parse approximation solu tion of resonance was carried out by using multiple-scale method under the main resonance and inner resonance,and the equations of amplitude frequency were obtained. At the same time,the singularity theory was applied to analyze the bifurcation behaviors and then obtain the transition set and topological structure of bifurcation curve in different regions. Finally,according to the actual parameters of rolling mill,the different parameters was analyzed which had the impact on vibration characteristics of this system,then the results was got that the main resonance and inner resonance appeared the jumping phenomenon,and coupling parameters effected the inner resonance heavily,so choosing proper system parameter can restrain this behavior effectively,which provided a theoretical reference to suppress vibration of rolling mill rolls.