The Effects of Gas Bubbles on the Rotordynamic Forces in Finite-Length Bearings

This paper presents an analytical study of the effects of dispersed gas bubbles on the unsteady rotordynamic forces on a shaft rotating and whirling with constant speed and eccentricity in a finite-length journal bearing or a squeeze-film damper. A linearized analysis which includes the dynamic effects of the bubble response is used to determine the rotordynamic forces caused by a small-amplitude whirl motion of the rotating shaft both in the viscosity-dominated regime and at intermediate values of the Reynolds number, where the inertia of the lubricant is no longer negligible. The classical Reynolds lubrication equation for the liquid velocity is modified to include flow acceleration effects and used together with the continuity and Rayleigh-Plesset equations to account for the presence of the bubbles. A number of additional nondimensional parameters is introduced by the two-phase nature of the flow and the inertia of the liquid. Depending on the values of these parameters, the rotordynamic forces on whirling shafts exhibit significant deviations from their classical behavior in single-phase flows and appreciably modify the stability of the rotor. Examples are presented to illustrate the effects of the relevant flow parameters. Despite its inherent limitations, the present analytical solution clearly highlights the importance of the complex interactions of the dynamics of the bubbles with the average flow and provides useful insight on the influence of the various flow phenomena occurring in whirling bearings or squeeze-film dampers operating under bubbly ventilated cavitation conditions.