非线性转子-机匣系统碰撞稳定性分析

转子与机匣的碰撞在一定条件下可能诱发转子失稳。以转子．机匣系统为研究对象，将转子和机匣视为弹性体并考虑了阻尼的效应，建立了非线性转子一机匣系统的碰磨模型和动力学方程。利用Lyapunov运动稳定性理论和Routh—Hurwitz稳定性准则分析了系统的碰撞和失稳条件，通过数值方法和Matlab程序得到了碰撞和失稳的临界转速以及系统参数对临界转速的影响。理论分析和实例计算表明，转子及机匣的刚度和阻尼对临界转速的影响较大，增大机匣刚度和转子的阻尼可以增大碰撞的临界转速，失稳发生在转速较高时，且失稳的临界转速比碰撞得临界转速高的多。具有重要的工程实用价值，为旋转机械的设计和参数优化提供了理论基础。

Research on Collision Stability of Nonlinear Rotor-stator Box System

The collision between rotor and stator box may cause rotor instability under certain condition, considering the elasticity and damping of rotor-stator box system, we propose its collision rubbing model and dynamic equation. The collision and instability conditions of the system are analyzed based on Lyapunov theory about kinematical stability and Routh-Rurwitz stability criteria. Using the mathematic method and Matlab program, the critical speed of collision and instability and the influence of system parameters on the critical speed are obtained. Theoretical analysis and practical calculation indicate that the rigidity and damping of rotor and stator have great impact on critical speed. With increasing the rigidity of stator and damping of rotor, the collision critical speed can be increased. The instability occurs at the high speed, and the instability critical speed is higher than the collision critical speed. The results are practical which provide the theory foundation of rotary machines design and optimization of parameters.