Stability of a Clamped-Free Rotor Partially Filled With Liquid

Abstract

When a flexible rotor is partially filled with liquid, the motion is unstable over some operating range. The extent of this operating range depends on various system parameters such as rotor damping, fluid viscosity, the amount of fluid present, etc. If the rotor is arranged so that it must tilt as it vibrates (as in the clamped-free configuration) then the tilt of the rotor greatly complicates the stability analysis. The source of the complication is that the fluid motion becomes three-dimensional. A three-dimensional stability theory is developed here and applied to a simple clamped-free rotor. The results show that the stability boundaries are influenced by both rotor and fluid “gyroscopic stiffening” effects. Brief experimental results are also reported.