On Slip Flow Considerations in Gas-Lubricated Porous Bearings

1984 ◽  
Vol 106 (4) ◽  
pp. 484-491 ◽  
Author(s):  
M. Malik ◽  
Cz. M. Rodkiewicz
Keyword(s):  
Free Path ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Mean Free Path ◽  
Journal Bearings ◽  
Numerical Results ◽  
Static Characteristics ◽  
Flow Conditions ◽  
Porous Shell ◽  
Sliding Surfaces

A modified form of Reynolds equation is derived for the compressible lubrication of porous bearings. The analysis takes into account two kinds of nonadherence conditions on the sliding surfaces, namely, the slip flow under the influence of molecular mean free path and the slip flow at gas film-porous shell interface. Numerical results are presented to illustrate the relative effects of the two kinds of slip flow conditions on static characteristics of self acting journal bearings.

The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings

1959 ◽  
Vol 81 (1) ◽  
pp. 94-98 ◽  
Author(s):  
Albert Burgdorfer
Keyword(s):  
Free Path ◽  
Reynolds Equation ◽  
Perturbation Technique ◽  
Slip Flow ◽  
Mean Free Path ◽  
Arbitrary Form ◽  
Flow Conditions ◽  
Slider Bearing ◽  
Parameter Perturbation ◽  
Two Dimensional Flow

A modified Reynolds equation is derived for gas-lubricated hydrodynamic bearings operating under “slip flow” conditions. Closed analytical solutions are given for a Rayleigh type step-bearing and an inclined plane slider bearing for the case of two-dimensional flow. The influence of the molecular mean free path on the performance of bearings of arbitrary form is obtained by means of a small parameter, perturbation technique.

Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

2017 ◽  
Vol 232 (8) ◽  
pp. 927-939 ◽  
Author(s):  
Shitendu Some ◽  
Sisir K Guha
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Journal Bearings ◽  
Static Characteristics ◽  
Governing Equations ◽  
Modified Reynolds Equation ◽  
Film Interface ◽  
Coupled Stress ◽  
Steady State Performance

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

Static Characteristics of Gas-Lubricated Slider Bearings Operating in a Helium-Air Mixture

1989 ◽  
Vol 111 (4) ◽  
pp. 620-627 ◽  
Author(s):  
T. Ohkubo ◽  
S. Fukui ◽  
K. Kogure
Keyword(s):  
Reynolds Equation ◽  
Mean Free Path ◽  
Linear Interpolation ◽  
Numerical Results ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Static Characteristics ◽  
Slider Bearings ◽  
Lubrication Equation ◽  
Modified Reynolds Equation

This paper outlines experimental investigations of the static characteristics of self-acting gas-lubricated slider bearings operating in a helium-air mixture. The experimental results are compared with numerical results obtained by solving a modified Reynolds equation and a generalized lubrication equation based on an equivalent molecular mean free path (MMFP) and on an equivalent viscosity derived from molecular gas dynamics. At any mole ratio of air α, the values of the equivalent MMFP are generally expected to be smaller than those of the MMFP derived from linear interpolation, whereas the values of equivalent viscosity are expected to be larger. The numerical results agree well with the experimental results within the range of α from 1.0 to 0.6. Lower values of α give a bigger difference between numerical and experimental results, and make the experimental results lower than the numerical results. Moreover, results of a generalized lubrication equation based on the Boltzmann equation give a closer prediction or qualitative tendency to the experimental results than do those based on the modified Reynolds equation.

On the linear stability analysis of finite-hydrodynamic porous journal bearings under coupled stress lubrication

2007 ◽  
Vol 221 (7) ◽  
pp. 831-840 ◽  
Author(s):  
S. K. Guha ◽  
A. K. Chattopadhyay
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Tangential Velocity ◽  
Continuum Theory ◽  
Transient State ◽  
Velocity Slip ◽  
Journal Bearings ◽  
The Stability ◽  
Coupled Stress

The objective of the present investigation is to study theoretically, using the finite-difference techniques, the dynamic performance characteristics of finite-hydrodynamic porous journal bearings lubricated with coupled stress fluids. In the analysis based on the Stokes micro-continuum theory of the rheological effects of coupled stress fluids, a modified form of Reynolds equation governing the transient-state hydrodynamic film pressures in porous journal bearings with the effect of slip flow of coupled stress fluid as lubricant is obtained. Moreover, the tangential velocity slip at the surface of porous bush has been considered by using Beavers-Joseph criterion. Using the first-order perturbation of the modified Reynolds equation, the stability characteristics in terms of threshold stability parameter and whirl ratios are obtained for various parameters viz. permeability factor, slip coefficient, bearing feeding parameter, and eccentricity ratio. The results show that the coupled stress fluid exhibits better stability in comparison with Newtonian fluid.

Performance of Lightly Loaded Gas Journal Bearings in the Slip-Flow and Turbulent-Flow Regimes

1968 ◽  
Vol 10 (4) ◽  
pp. 363-366
Author(s):  
M. D. Wood
Keyword(s):  
Steady State ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Flow Regimes ◽  
Journal Bearings ◽  
Performance Parameters ◽  
Existing Data

The note compares recently published versions of the governing gas film equations for slip-flow and turbulent flow with Reynolds equation for laminar flow. The comparison shows how approximate values of steady-state and dynamic performance parameters may be deduced for the new conditions from existing data.

Theoretical Considerations of Molecular Mean Free Path Influenced Slip in Self-Acting Gas-Lubricated Plain Journal Bearings

1984 ◽  
Vol 198 (1) ◽  
pp. 25-31 ◽  
Author(s):  
M Malik
Keyword(s):  
Steady State ◽  
Beneficial Effect ◽  
Free Path ◽  
Dynamic Performance ◽  
Mean Free Path ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Wide Range ◽  
Theoretical Investigations ◽  
Theoretical Considerations

The purpose of this paper is to study the effect of slip under the influence of molecular mean free path on the steady state and dynamic performance characteristics of plain gas journal bearings. The theoretical investigations have been made over a wide range of compressibility number. It is found that slip usually impairs the bearing performance, particularly at low compressibility numbers, A; the effect of slip, however, diminishes with increasing values of A. In fact at high compressibility numbers, theory suggests that slip has a beneficial effect of improving the dynamic performance of the bearing.

Design of Pivoted-Pad Journal Bearings

1969 ◽  
Vol 91 (1) ◽  
pp. 87-103 ◽  
Author(s):  
R. C. Elwell ◽  
J. A. Findlay
Keyword(s):  
Numerical Solution ◽  
Incompressible Flow ◽  
Digital Computer ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Numerical Results ◽  
Load Direction ◽  
Numerical Examples ◽  
Calculated Load

Calculated load capacity and friction for complete pivoted-pad journal bearings are presented, for use in design computations. Dimensionless numerical results are given for the following variations in bearing geometry: 3 and 5 pads, L/D ratios of 1/2 to 1, pivot locations of 40, 50, and 60 percent, on pivot and between pivot loading, and ratios of “assembled” to “ground” clearance of 0.6, 0.8, and 1.0. The numerical results are an extension of the work of Castelli, et al., reference [1],1 and were generated in the same manner i.e., numerical solution of Reynolds’ equation by digital computer. Laminar, incompressible flow, and subambient pressures in diverging portions of the films were assumed. Illustrative numerical examples are included and significant conclusions with respect to major variables (L/D ratio, number of pads, clearances, pivot location, load direction) are drawn from the range of data produced.

High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads

1987 ◽  
Vol 109 (2) ◽  
pp. 276-282 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Ambient Air ◽  
Mean Free Path ◽  
Lubricating Film ◽  
Modified Reynolds Equation ◽  
Air Film ◽  
Rarefaction Effects

This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

Elastohydrodynamic Analysis of an Offset Journal Bearing Lubricated with Couple Stress Fluid

2010 ◽  
Vol 2 ◽  
pp. 53-62
Author(s):  
B. Chetti
Keyword(s):  
Elastic Deformation ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Load Carrying Capacity ◽  
Static Characteristics ◽  
Large Molecules ◽  
Couple Stresses ◽  
Load Carrying

This work is an investigation of the performance characteristics of an offset journal bearing lubricated with a fluid with couple stresses taking into consideration the elastic deformation of the liner. The couple stresses might be expected to appear in noticeable magnitudes in liquids containing additives with large molecules. The modified Reynolds equation has been solved using the finite difference method. Load carrying capacity, attitude angle, side leakage and friction coefficients are determined for various values of couple stress parameter of a rigid and deformable bearing. It is found that, the static characteristics of journal bearings lubricated with couple stress fluids are improved compared to journal bearings lubricated with Newtonian fluids. It is concluded that, the elastic deformation of the bearing has significant influence on the bearing characteristics.

Elastohydrodynamic Lubrication of Air-Lubricated Rollers

1996 ◽  
Vol 118 (3) ◽  
pp. 623-628 ◽  
Author(s):  
Y. B. Chang ◽  
F. W. Chambers ◽  
J. J. Shelton
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Free Path ◽  
Close Contact ◽  
Slip Flow ◽  
Elastohydrodynamic Lubrication ◽  
Mean Free Path ◽  
Pressure Profiles ◽  
The Mean ◽  
Air Film

The lubricating air film between two rotating rollers in close contact was studied numerically. The numerical model used in this study accounts for the effects of air compressibility, material deformation, and the slip flow which occurs when the air film thickness is not much larger than the mean-free-path of the air molecules. The air film profiles and the pressure profiles for the nip region between the rollers were calculated. It was found that the calculated air film thicknesses are lower than predicted by the liquid elastohydrodynamic calculation. From this study, equations for the minimum air film thickness, the air film thickness at the center of contact, and the amount of air that passes through the nip were obtained. This study has application to the prediction of the amount of air entrained in a winding roll.

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