The Gaseous Squeeze-Film at Moderately Large Squeeze Numbers

Abstract

The asymptotic analysis of the gaseous squeeze-film bearing has been extended to obtain 0 {σ−1/2 } effects in accordance with the isothermal gas lubrication theory and the method of singular perturbation. 0 {σ−1/2 } corrections are identified to contain not only edge effects (inner problem) but also edge-interior interactions which are analogous to the boundary layer displacement effects in aerodynamics. The latter features can further be recognized to be related to mean-gap taper, squeeze taper, and cross-edge sliding. These results are discussed from the point of view of “global bearing properties” including the temporal mean as well as the in-phase and quadrature synchronous components of the fluid film force and moment. The edge effects are presented in terms of universal functions which can be used directly as corrections in the global properties. The edge-interior interactions must be determined by solving the asymptotic p.d.e. with boundary condition also expressed in terms of universal functions. Formulations applicable to cylindrical, conical, and spherical bearing geometries are outlined. Illustrative numerical examples are provided. Conditions affecting the validity of the isothermal gas lubrication theory (neglecting inertia effects) as related to the magnitude of the squeeze number are discussed.