On Hydrodynamic Instability of Gas-Lubricated Journal Bearings

Paper starts with a study of static stability response of gas-lubricated bearing, followed by a general small perturbations theory of the dynamic stability of journal bearings. Then the pressure equation for bearings subjected to variable forces and velocities is analyzed, by pointing out the existence of a limiting solution which can occur both for high speeds or for high frequency of the bearing eccentricity. At the same time the squeeze effect can be strongly altered by the lubricant compressibility so that, for motions with high tangential speeds or with high frequencies, the pressures depend only on the thickness h and not on the derivative with respect to time h˙ as is the case of incompressible films. Finally, the analysis of the stability conditions reveals that bearings operating at low numbers H are unstable according to the small perturbations theory. The same situation occurs to the bearings operating with small eccentricity ratios, for any number H. The frequency of undamped oscillations is proportional to the shaft angular speed ω for low numbers H but tends to a bounded value ω₀* for high number H. Quasi-resonant conditions may also occur when the number H is increasing, a fact which allows the deduction of a simple half-empirical stability condition.