Effect of fluid inertia on squeeze film damper force response

Abstract

The effect of fluid inertia on the force response of Squeeze Film Dampers (SFD) is a subject of great importance since most existent damper applications operate with Reynolds numbers in the range of one to ten. For small amplitude off centered motions, linear flow equations are solved by finite differences. Approximate force coefficients for finite length open ends SFDs are determined and shown to have excellent agreement with the numerical predictions. For a squeeze film Reynolds number of order 1, fluid inertia forces are one order of magnitude lower than the purely viscous forces. For Reynolds numbers larger than 10, fluid inertia forces dominate the damper force response. An analysis for circular centered motions of arbitrary amplitude reveals the importance fluid advection has on the film forces. For the long and short SFD models, the flow equations are solved using a regular perturbation approach valid for small Reynolds numbers. For finite length SFDs, integro-differential equations in terms of mean flow velocity components are solved using the finite element method. It is found that the relative strength of fluid inertia is larger at small rather than at large orbit radii. For a Reynolds number of order 1, fluid inertia forces are one order of magnitude lower than the purely viscous forces and decreasing as the orbit radius increases. In a cavitated damper, the net effect of inertia is to increase the damping force and decrease the radial force, thus reducing the possibilities of rotor bi-stable operation. A controlled orbit test rig is used for the experimentation. Measured film pressures and forces for different film geometries and Reynolds numbers ranging from 2 to 12 are reported and discussed. A tremendous fluid inertia effect is measured for all Reynolds numbers tested, and it is observed the film geometry has a large influence on the measured forces. Comparison with analytical predictions is good for the simplest geometry tested, and for the more complicated film geometries the measured forces show fluid inertia to dominate the damper force response even for low Reynolds numbers.