A Study of the Effect of Fluid Inertia and End Leakage in the Finite Squeeze Film Damper

A modified form of Reynolds’ equation is obtained by integrating the thin film equations across the film and approximating the nonlinear inertia terms using the lubrication theory velocity field. The resulting nonhomogeneous partial differential equation is tackled by the classical separation of variables technique, and the corresponding eigenvalue problem solved by a computer library routine. The end boundary condition is that the local exiting flow rate is proportional to the pressure difference across the end seal. The results show a large effect of inertia in terms of pressure amplitude and phase shift, but the phase shift is reduced at large eccentricity. End leakage and bearing length change the pressure amplitude for the inertialess and inertia cases, but in equal measure. Hence conclusions reported in the literature regarding the effect of inertia in long or short dampers generally hold for finite bearings.