Analysis of Tangential-Against-Rotation Injection Lomakin Bearings

This work presents a thin film flow model for analyzing the static and dynamic characteristics of centered, eccentric or misaligned tangential-against-rotation injection Lomakin bearings. The Lomakin bearing is a recent device intended for use in modern turbomachinery and having characteristics similar to hybrid bearings. It can be described as an ensemble of two opposing straight annular seals separated by a circumferential feeding groove. The fluid is supplied to the groove via orifice restrictors. Their tangential inclination generates an against-rotation circumferential flow in the groove that further penetrates into the thin film. This effect, known from annular seals as the pre-rotation speed, improves the dynamic characteristics of the bearing. The zero and first order analyses are carried out by recognizing the crucial importance of taking into account the interaction between the flow in the thin film lands, the circumferential groove and the supply orifices. Due to the high Reynolds number regime, the land flow is governed by the two dimensional thin film inertia equations (the “bulk flow” model). A one-dimensional circumferential flow dominated by inertia forces is assumed to take place in the groove and is described by an appropriate bulk flow equation. The flows in the supply orifices, the groove and the thin film lands are linked together by the same mass flow rate balance algorithm as used for hydrostatic and hybrid bearings analysis. The algorithm is extended to Lomakin bearings by considering the groove areas surrounding each orifice as a row of intercommunicating feeding pockets. This approach enables the analysis of centered, eccentric or misaligned Lomakin bearings. Comparisons with water-lubricated test results are used to validate the present model. For the zero eccentricity case a good agreement is obtained for the cross-coupled stiffness and for the whirl frequency ratio. A parametric study shows the variation of the bearing characteristics with increasing static eccentricity or misalignment. The limits of the developed thin film model are further estimated by comparing the static and zero eccentricity thin film results with a full Navier Stokes calculation.