部分充有粘性流体的转子系统稳定性的理论分析

Stability of a Rotor Partially Filled with a Viscous Incompressible Fluid

在直接对二维 Navier- Stokes方程进行线性化的基础上 ,详细分析了二维粘性旋转流体模型 ,得到了旋转流体对转子作用力的表达式 ,然后研究了部分充液转子系统的稳定性问题 。

On the basis of the linearized fluid forces acting on the rotor system for the 2D-case, we directly use the full Navier - Stokes equation to investigate the stability of a symmetrical flexible rotor partially filled with a viscous incompressible fluid and to analyse the effects of the parameters of the rotor system on the stability of the rotor fluid system. We draw the following conclusions: (1) for isotropic rotor systems, the viscous fluid model may predict two unstable regions, the upper one is generally above the critical speed of empty rotor system and the lower one is below the critical speed. The lower instability boundary of the upper unstable region may also be less than the critical speed in some cases. (2) Adding external damping makes the system more stable and may be an effective method to suppress the unstable motion in certain cases. (3) The influence of the rotor system parameters on the instability boundaries are more complex. For different regions of the system parameters and their com binations, the effects of the system parameters on the instability are different.