光滑时变约束转子动力特性分析

刘棣，李超，马艳红，洪杰

（北京航空航天大学 能源与动力工程学院，北京 100083）

Abstract：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.

Keywords：smooth time-varying；rotor；modal characteristics；stability；response

碰摩是转子系统中一种常见故障，可以根据转子的碰摩形式分为全周碰摩［1-2］、局部碰摩［3-5］及干摩擦反向涡动［6-8］。其中，全周碰摩、局部碰摩在航空发动机转子系统中最为常见。

Muszynska［9］指出，碰摩发生时转静子之间同时存在摩擦、冲击、扭转和刚度耦合4种效应。当发生全周碰摩时，摩擦效应占主导地位；而发生局部碰摩时，冲击效应占主导地位。全周碰摩状态下，转子与静子始终保持接触状态，且一般静子对转子的约束作用是恒定的。Choi［10］通过建立碰摩试验装置分析了全周碰摩的产生机理。局部碰摩状态下，转子的部分弧段与静子发生碰摩，对转子产生复杂的力学效果，包括冲击、摩擦及静子对转子产生附加刚度，使转子系统高度非线性［11］。Sinha［12］通过显示积分算法研究了叶尖与机匣发生局部碰摩所产生的周期冲击载荷对悬臂Timoshenko梁的响应特性。Dai等［13］通过数值方法研究了飞轮转子与制动装置发生碰摩所产生的非线性振动响应，通过简谐激励模拟碰摩时静子对转子产生的低频扰动，利用库伦摩擦模型和分段线性弹簧来模拟转静子之间的接触状态，研究表明随着激振力的增加，局部碰摩会发展为反向涡动，降低制动装置的效果。Wang等［14］以悬臂转子为研究对象，分析了局部碰摩转子运动过程，建立了对应的周期时变系数方程并通过试验研究了局部碰摩转子的响应特性。Abuzaid等［15］通过实验和数值分析的方法研究了局部碰摩下不同碰摩程度对转子动力特性的影响，轻微碰摩使转子出现1倍、2倍、3倍转速频率，严重碰摩使转子出现1／3、2／3转速频率，同时碰摩使得转子的固有频率增加。……