An Extended Reynolds Equation Development with Applications to Fixed Geometry Bearings and Squeeze Film Dampers

Water lubricated bearings and squeeze film dampers exhibit large lubricant inertia forces on the order of viscous forces. To model these bearings, the traditional Reynolds equation is not adequate. An extended Reynolds equation is developed in this study which takes into account the turbulence and inertia effects: both convective and temporal. The most complete form of the temporal inertia effect model is developed and applies to the turbulent regime, consisting of primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu's approach. The turbulence model is also based on Constantinescu's model and is tuned using CFD analysis.

To apply the proposed model to fixed geometry cylindrical water bearings, a computer code named SLEEVEBRG is developed. This program is also capable of satisfying the circumferential periodicity constraint associated with cylindrical bearings. The numerical results show significant convective and temporal inertia effects in water bearings. Convective inertia effects increase the load capacity of the bearing. The temporal inertia, resulting in effective added mass coefficients, exhibits destabilizing effects, while the convective inertia effects serve to improve stability of the bearing. The secondary temporal inertia reduces the added mass terms, thus increasing the stability of the bearing.

Squeeze film dampers are designed with numerous different configurations. Features such as supply and discharge holes, end seals, and grooves contribute into the dynamic characteristics of squeeze film dampers. Grooves are shown, contrary to previous perceptions, to generate a considerable amount of dynamic pressure. To capture their effects, an effective groove depth approach is adopted in this work. Additionally, an applicable extended Reynolds equation is developed which includes temporal inertia and also takes into account the contribution of the holes. A computer code named MAXSFD is developed accordingly. Four different configurations are analyzed and results are compared against experimentally obtained data. It is found that in general two distinct effective groove depths are required to match the experimental added mass and damping values. This indicates that different amounts of lubricant trapped in the groove contribute to the added mass and damping characteristics of squeeze film dampers. In open end squeeze film dampers, the ratio of the two effective grooves is nearly two, and for sealed squeeze film dampers the ratio is approximately one long and one and half for short SFD. The numerical observations prove that secondary temporal inertia plays a minor role in the determination of the added mass coefficients. The results are compared against an older squeeze film damper code SQFDAMP [1], which underpredicts the damping values and lacks the added mass prediction capability.