转子-弹性机壳系统碰摩的分段光滑模型分析

Analysis to a Piecewise-Smooth Model of Rub-Impacting Rotor Systems with Elastic Cases

分别采用两种不同的截面建立 Poincaré映射 ,对转子 -弹性机壳系统的碰摩运动进行了研究 ,得到了该类分段光滑系统运动的一般特点和转子碰摩运动随碰撞刚度变化发生分岔的规律。研究表明 ,该系统的碰摩运动主要以混沌形式出现 ,但不同的周期窗口按一定规律嵌入混沌区内。随着定子碰撞刚度增加 ,碰摩运动将会加剧。然后由该系统导出了刚性转子碰摩的约束微分系统 ,从而将碰摩转子系统的两种不同描述形式统一起来 。

This paper deals with rub impacts of a rotor system with elastic case by using the method of Poincaré map. Two kinds of Poincaré map are constructed in order to study different characters of rub impacting motions, including the numbers of period and impact. It is found that the non smooth feature of piecewise smooth vector fields is very rich and complex. The rub impacting motions of the system are mainly chaotic, but periodic motions are also possible for parameters properly chosen, and various period windows are embedded in the chaotic region. The bifurcating rule of the system with the variation of case stiffness is also obtained through numerical simulations. It is shown that the rub impacts of the rotor system become even voilent as the case stiffness increases. As a special and simplified model, a constrained differential system describing rigid impacts of rotor systems are studied and some new results are shown.