理想转子的碰摩周期运动分析

ANALYSIS OF PERIODIC RUB-IMPACT MOTION OF IDEAL ROTOR

应用poincare映射方法对理想转子碰摩运动的单碰运动进行分析,通过严格的理论推导,得出了理想转子单点刚性碰摩的存在条件,并指出当激振力的频率(ω)与系统的固有频率(ω0)比值(ω)为无理数时,周期性的单碰运动是不存在的;导出了判断理想转子周期性碰摩运动稳定性的特征方程。通过数值模拟验证了理论结果的正确性,发现理想转子发生周期性单碰时,轴心轨迹可呈现丰富的运动形式,且与周期单碰运动条件ω=n/m中的m值有关,并得到了周期1的擦边碰摩运动。

Rub-impact movement of a ideal rotor is under consideration based on the Poicare map in the paper.Due to complexity of rub-impact movement in a rotor sysem,it is difficult to give a satisfied analysis on the issues of periodic rub-impact motion of rotor system.Here our attention is paid to single impact period-n motion of the ideal rotor which has an impact to occur after a time of n times of the external excitation period.We demonstrate the existence of single impact periodic motion by means of the strict theoretical derivation,meanwhile we obtain the nonexistence criterion of single impact periodic motion,which is that the ratio(ω)of the frequency of external excitation((ω))to the natural frequency(ω_0) of rotor system is irrational number.Moreover,the stability of periodic motion is studied and the corresponding characteristic equation is derived.By numerical simulation,it is show that the conclusion is valid.The complex characteristic of the rotor centerline orbit is seen,and is relaed to m(ω =n/m).The edge rub-impact in single impact period-1 motion is obtained.