Perturbation Solutions for Gas-Lubricating Films

Abstract

Perturbation solutions for large and for small bearing numbers are developed and applied to steady, self-acting, infinitely long, journal and plane wedge films. Bearing films of this type develop load capacity as a consequence of relative surface motion. The solutions given here have validity for all ranges of geometrical parameters. Four-place accuracy in determining the load carried by a journal bearing is achieved. The plane wedge film solution for large bearing numbers is complicated by the reduction in order of the limiting equation. A boundary-layer type analysis yields fairly accurate results.

The two-dimensional, finite, gas lubricated, slider bearing in slip flow

“…Early calculations [2] indicate that the solution of the reduced equation satisfies the boundary condition at x = 0 ; but not the boundary conditions at the trailing edge x = 1 and the side edges z = ± boundary layers occur, where the pressure corrects rapidly from the solution of the reduced equation to the prescribed boundary conditions. To analyze these layer solutions, local variables are introduced, and the limit Λ, B → ∞ considered in terms of these variables.…”

“…Thus a perturbation analysis of the problem (1), (2) and (3) based on the limits B → ∞ , Λ → ∞ for given O(1) values of k is indicated. Since two large parameters are involved, B and Λ, and since, in the most general situation, they may become infinitely large independently, we place a restriction on the limiting process.…”

“…Thus, the problem (1), (2) and (3) is a singular perturbation problem as Λ, B → ∞ ; and appropriate methods of analysis are needed.…”

“…P a is the pressure external to the bearing, assumed constant. Thus the boundary conditions (2) and (3) signify the pressure returning to ambient at the boundaries. H 0 is a characteristic (constant) value of the function H(X, Z).…”

Comparison between Different Supply Port Configurations in Gas Journal Bearings

“…Researchers have studied this problem using different methods since the '60s. Gross first applied a perturbation method to evaluate the stability of an infinitely long journal bearing (Gross & Zachmanaglou, 1961). Galerkin's method was used by others to calculate rotor speed and mass at the stability threshold (Cheng & Pan, 1965).…”