具有初始热变形的转子系统振动响应分析

航空发动机热起动时的温度分布不均会使转子产生初始热变形，进而引起发动机振动过大，甚至导致起动失败。针对此问题，以航空发动机中的典型转子为对象，根据初始热变形对转子振动的影响建立相应的动力学方程，并通过模态坐标变换分析初始热变形对转子系统振动响应的影响。结果表明，初始热变形相当于对转子作用了附加激励，包括转轴初始弯曲激励、附加不平衡激励和附加陀螺力矩激励，上述激励均与转速同步。其中，附加不平衡激励和附加陀螺力矩激励大小与转速有关，对转子通过各阶临界转速的振动响应均有较大影响；转轴初始弯曲激励大小与转速无关，主要影响低阶临界转速的振动响应。 

Vibration response analysis of rotor system with initial thermal deformation

Uneven temperature distribution of an aero-engine during hot restart can lead to initial thermal deformation of its rotors, which causes excessive engine vibration, or even a start-up failure. In view of the problem, this paper takes a typical rotor in aero-engines as an object, establishes its dynamic equation based on the effects of thermal deformation on vibration, and analyzes the effects of thermal deformation on vibration response of rotor system through modal coordinate transformation. The results show that thermal deformation is equivalent to additional excitations acting on the rotor, that is, initial shaft bow excitation, additional unbalance excitation and additional gyroscopic moment excitation, all of which are synchronous with the rotating speed. Moreover, the amplitude of unbalance and gyroscopic moment excitation is related to the rotating speed, therefore influencing rotor vibration response at different critical speeds to an equivalent extent, while that of initial shaft bow excitation is not related to the rotating speed and the response of low-order critical rotating speeds is more affected.