The objective of this paper is to study the effect of molecular mean free path on the steady-state performance characteristics of a spiral-grooved thrust bearing operating in extremely thin film and/or low ambient pressure environments. Numerical results for the most popular three versions of the spiral-grooved designs are presented. These results reveal that the effect of slip boundary conditions could contribute substantial reduction, in performance. Helium is the worst gas lubricant in this sense because of its high Knudsen number. The slip-flow corrected results check well with recently published experimental data [11].

The well-established narrow groove theory for spiral groove gas bearings [1] has been generalized to include the effects of rarefied gas and turbulence. The slip flow effect was considered locally depending upon gaseous density and molecular mean free path [2] while the local turbulence effect was introduced by a set of viscosity modification functions [3, 4]. For transition flow, the concept of “mean” local Reynolds number may be adapted [5]. The fundamental governing equation was derived in terms of a generalized coordinate for bodies of rotational symmetry and valid for both incompressible and compressible bearings or seals.

The pulsating flows in both infinite and finite conical nozzles were analyzed theoretically. Sinusoidal pressure disturbances were impressed at the nozzle exit for the infinite nozzle and at either the inlet or at the exit for the case of a finite nozzle. The results have been calculated in terms of mass-flux response. The parameters involved are the Mach number and the modified Strouhal number; the inlet and exit radii ratio enters as an additional parameter for a finite nozzle. The results for an infinite conical nozzle indicate that, when the frequency is low, the quasistatic relationship between the pressure and mass-flux fluctuations holds; the same was reported in reference [1]. But, as the frequency increases, the dynamic characteristics of the pulsating flow become important. And, at high frequencies, the mass-flux response is less than the quasistatic value by an amount depending on the Mach number. For a finite conical nozzle the quasistatic condition is still valid if the frequency is low. However, at higher frequencies, the dynamic behavior becomes critically dependent on the frequency expressed in terms of w, for a given nozzle geometry and exit Mach number.

The work presented here is a preliminary study of the Mach number effect based on the usual lubrication assumptions except, for the retention of convective terms in the equations of motion. The essential step in this analysis is to adopt the momentum integral method, i.e., to assume a velocity profile satisfying the prescribed boundary conditions. The first attempt is to assume a second-order polynomial for the velocity profile. Although this may not be able to give a sufficient detail of the velocity field. Nevertheless, the results should, hopefully, give us some more insight into this problem. Analytical results based on perturbation theory are presented for journal, slider, and step bearings. Numerical results for a plane slider are also presented here. All results indicate that when a dimensionless mean speed parameter, namely, the modified Mach number, approaches to unity the pressrue field converges very quickly to the limiting solution ph = constant even at moderate values of the compressibility number. In addition, both small perturbation analysis and numerical results reveal that under some circumstances, e.g., in a plane slider, the pressure boundary condition at the trailing edge should be modified in order to obtain a physically meaningful solution.

Exact solutions for a class of incompressible spiral-grooved viscous pumps were obtained by solving the dynamic perturbation equations based on the governing equations of the well-known narrow groove theory. The resulting closed-form analytical expressions contain two integration constants which can be determined by appropriate boundary conditions pertinent to a specific application and design. A flat thrust bearing was chosen to illustrate the application of these results. The load-carrying capacity calculated from present theory was compared with those obtained by other investigator [2]. The agreement is extremely good. No attempt was made to generate design charts for various designs since the resulting expressions obtained in this work can be used quite easily in a straightforward fashion.