A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Oil Seal Rings

Squeeze film damper (SFD) designs typically implement supply grooves to ensure adequate lubricant flow into the film lands. Oil seal rings, of land film clearance $c$⁠, also incorporate short and shallow grooves $(length≤30c,depth≤15c)$ to reduce cross-coupled stiffnesses, thus promoting dynamic stability without a penalty in increased leakage. However, extensive experimental results in the archival literature demonstrate that grooves do not reduce the force coefficients as much as theory predicts. A common assumption is that deep grooves do not influence a damper or oil seal ring forced response. However, unexpected large added mass coefficients, not adequately predicted, appear to be common in many tested SFD and oil seal configurations. In the case of oil seals, experiments demonstrate that circumferential grooves do reduce cross-coupled stiffnesses but to a lesser extent than predictions would otherwise indicate. A linear fluid inertia bulk-flow model for analysis of the forced response of SFDs and oil seal configurations with multiple grooves is advanced. A perturbation analysis for small amplitude journal motions about a centered position yields zeroth and first-order flow equations at each flow region (lands and grooves). At a groove region, a groove effective depth $dη$⁠, differing from its actual physical value, is derived from qualitative observations of the laminar flow pattern through annular cavities. The boundary conditions at the inlet and exit planes depend on the actual seal or SFD configuration. Integration of the resulting first-order pressure fields on the journal surface yields the force coefficients (stiffness, damping, and inertia). Current model predictions are in excellent agreement with published test force coefficients for a grooved SFD and a grooved oil seal. The results confirm that large added mass coefficients arise from the flow interactions between the feed/discharge grooves and film lands in the test elements. Furthermore, the predictions, benchmarking experimental data, corroborate that short length inner-land grooves in an oil seal do not isolate the pressure fields of adjacent film lands and hence contribute greatly to the forced response of the mechanical element.