This paper describes a theory of liquid lubrication applicable to parallel surfaces, such as the surfaces of a rotary-shaft face seal. The lubrication mechanism presented is based on surface microirregularities and associated film cavities. Closed-form analytical solutions are obtained giving load capacity as a function of speed, viscosity, and surface-asperity dimensions. The theoretical results agree qualitatively with load capacity determined experimentally for three asperity distributions.

This work is concerned with an evaluation of the performance of a gas journal bearing using a spring supported compliant foil as the bearing surface. The analysis, conducted for both single and multipad configurations, is concerned with the effects that the various structural, geometric, and operational variables have on bearing behavior. Following the solution of the relevant differential equation, tabular or graphical solutions are provided for a range of relevant geometric and operational parameters. The solutions include values of the colinear and cross-coupled spring coefficients due to both structural and hydrodynamic stiffness. Desirable design features with regard to start of bearing arc, selection of load angle, number of pads and degree of compliance are discussed.

The stability of Couette flow and flow due to an azimuthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces is investigated. The stability problems are solved by using the Galerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on the stability of Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing, respectively.

This work is concerned with an evaluation of the performance of a gas thrust bearing using what amounts to a spring supported compliant foil as the bearing surface. To enhance the load capacity of such a device, the leading portion of the foil is given an appropriate converging geometry. The paper offers an analytical investigation of the elastohydrodynamics of the compliant foil bearing, and the effects that the various structural and operational variables have on bearing behavior. Following the solution of the relevant differential equation, the geometry of the thrust sector is first optimized, then solutions are provided for a range of relevant geometrical and operational parameters. The parametric study shows that the optimum geometry for a bearing with the common OD to ID ratio of 2 is β=45deg,b=0.5,h¯1>10 In addition to the geometric parameters, there are also the structural parameters of the foil. The load capacity is shown to increase as the compliance of the bearing rises. While at moderate Λ’s high values of compliance yield the highest load capacity, at high Λ, the optimum compliance is some intermediate value, in our case, α* = 1. Since the stiffness of the bearing is a function of both the structural and hydrodynamic film stiffnesses, high loads tend to flatten the values of K for the softer bearings, leaving essentially the structural stiffness as the dominating spring constant.

The generalized plane strain problem of the contact of layered elastic solids is reduced to an integral equation using Green’s function approach. Approximate numerical solutions are obtained by replacing the integral equation by a matrix inversion when the trapezoidal rule is used to represent the integral. Results for determining the actual contact pressure at the center of the contact zone and size of contact zone for a wide range of layer thicknesses are presented for two most practical cases, (i) when the indenter is rigid, and (ii) when the indenter is elastic having a modulus of elasticity equal to that of the substrate of the indented body. When the layer is softer than the substrate it is found that the actual contact pressure distribution is very closely determined by a weighted sum of elliptic and parabolic functions. For a substrate softer than the layer the pressures substantially deviate from an elliptical or parabolic behavior, for the cases when the layer thickness is finite. The analysis checks with the Hertzian solution in the extreme cases when the layer thickness either tends to zero or approaches infinity.