光滑时变约束转子动力特性分析

光滑时变约束是转静子碰摩所产生的一种力学效果，指静子与转子发生持续接触，静子对转子产生周期时变的约束作用，转子在该约束下的附加刚度曲线是一条光滑可导的函数。根据试验转子在光滑时变约束下的附加刚度曲线建立一种光滑时变约束模型，基于Hill行列式理论分析光滑时变约束转子的模态频率、稳定性及响应，为碰摩转子故障识别和稳定性分析提供一种分析途径。结果表明:光滑时变约束下转子具有频率耦合、多频、失稳特性。失稳转速区中，转子的幅值随时间逐渐增大，引起转子失稳的频率成分即为转子模态分析中特征值实部大于0的频率成分；非失稳转速区中，转子的频率成分主要为转速频率和波动频率构成的频率组合。 

Dynamic characteristics of smooth time-varying constrained rotor

The smooth time-varying constraint is a mechanical effect of continuous contact produced by the rubbing between rotor and stator, in which the periodic time-varying constraint is applied to the rotor. The additional stiffness curve caused by contact between the stator and the rotor is a smooth and derivable function with time. A smooth time-varying constraint model is established based on the orbit of rotor in experiment, and the modal frequency, stability and response of rotor system with smooth time-varying constraint are analyzed based on the Hill method, which provides an analysis frame for the fault identification and stability analysis of the rubbing rotor. The research results show that the rotor with smooth time-varying constraint has the characteristics of frequency coupling, multi-frequency and instability. In the unstable speed region, the amplitude of the rotor gradually increases with time. The frequency component that causes the instability of the rotor system is the frequency component whose real part of eigenvalue is greater than 0 in the rotor modal analysis. In the stable speed region, the rotor's frequency response is mainly the frequency combination composed of speed frequency and contact frequency.