Finite length Squeeze Film Dampers with air entrainment, non-dimensional maps and their applicability

Squeeze Film Dampers (SFDs) are bearings that support large motion amplitudes when traversing rotor-bearing systems critical speeds. Actual practice demands bearings with operating conditions of low oil supply pressure and high frequency. In open-ended SFDs, large amplitudes of journal motion draw air into the film gap. The air ingested and entrapped results in a bubbly mixture that affects the dynamic performance and the overall damping capability of the SFDs. Diaz and San Andrés [11] developed a model to predict the amount of air ingested into SFDs with open-ends. They proposed an innovative nondimensional number to estimate the amount of air entrapped in the film gap, but their analytical results are limited to short length bearings. Mendez et al. [13] extended the results of Diaz and San Andrés to finite length bearings, devising a Finite Volume Method (FVM) scheme. Even though their research presented new and significant results, they lack wider applicability that includes different geometries or boundary conditions. The present research proposes the solution of the Reynolds equation by the finite element method. Results computed by this formulation explore non-dimensional maps for determination of the amount of entrapped air. The results show that for fixed lubricant properties the amount of entrapped air depends exclusively on three dimensionless parameters: feedsqueeze flow number, length to diameter ratio, and dimensionless orbit radius.