转子系统碰摩行为的研究

应用非线性动力学现代理论对一个带间隙转子系统的数学模型进行了研究 ,通过以转速比变化为参数的分岔图发现 :在超临界转速下存在完整的间隔混沌、周期加分岔序列 ,即系统在周期运动与混沌运动之间交替 ,且周期加一、周期数与临界转速的倍数对应相等 ;在转速小于临界转速时 ,各个连续阶次谐运动的转换区分别都出现了经由一个倍周期分岔直接导致的混沌频带 ,后又直接由一个逆倍周期分岔转化为周期一的现象。同时还揭示了阻尼对系统谐波振动幅值和转换区混沌频带宽的抑制作用 ,以及非线性刚度对混沌频带的抑制和对谐波响应幅值的促进作用。提出设计转子系统时应适当增加阻尼和选材时综合考虑系统的动力学特性 ,系统提高转速时 ,转速不要在转换区滞留太长及工作转速尽量不要选在系统的临界转速的倍频上等建议 ,这些都对减小系统故障发生率和提高系统动力学特性有重要意义

Study on Dynamic Characteristics of a Rotor System with Clearance

The mathematic model of the rotor with clearance is analyzed by applying modern nonlinear dynamics theory. By the bifurcation diagrams of the change of rotating speed, it is discovered that the motions of the system alternates between periodic vibration and chaos in the supercritical wheeling speed, and the period of vibration will add one after a region of chaos. In the same time, the number of the period is equal to the whole number multiples of critical wheeling speed. In the subcritical wheeling speed, it is discovered that chaotic vibration bands of transition zones between successive orders of subharmonic responses as a result of a period-doubling bifurcation returns to the period-one through an inverse period-doubling bifurcation. It is shown that an increase of damping may cause a gradual reduction of the chaotic bands and amplitude of subharmonic response, nonlinear factor leads to reduction of chaotic vibration bands also, but make amplitude of subharmonic response increase. So it is suggested that proper increase of damping should reduce ratio of incident and advance dynamic characteristics when designing the rotor system, in addition to proper material selected by compromising dynamic characteristics, that wheeling speed goes through the transition zones of any subharmonic response as fast as possible during a course of increasing the wheeling speed and working speed had better not select N times its natural frequency.