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.

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.

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.

Tribological Study of a Slider Bearing in the Supersonic Regime

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Florence Dupuy ◽  
Benyebka Bou-Saïd ◽  
Mathieu Garcia ◽  
Grégory Grau ◽  
Jérôme Rocchi ◽  
...  
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Navier Stokes Equations ◽  
Supersonic Regime ◽  
Two Dimensional Flow ◽  
Modified Reynolds Equation ◽  
The One

Aerodynamic slider bearings are currently used in various types of turbomachinery. Many such systems perform at increasingly faster speeds and may operate in the supersonic regime. Although there is extensive research on compressible lubrication extrapolated to high-speeds, very little of it addresses the potential supersonic nature of the flow. It is well known in compressible flow that many of the tendencies of subsonic flow actually reverse themselves as the singularity at Mach one is traversed. Thus, examination of this high-speed regime may yield some unanticipated results. The behavior of a thin film of air in the supersonic regime is studied in the two-dimensional flow case with rigid sliding surfaces. The one-dimensional bearing studied has a dual profile consisting of an inlet region converging wedge of constant slope and an exit region of constant gap. Two approaches are compared: the solution of a modified Reynolds equation, and the solution to a version of Navier–Stokes equations adapted to thin films. The results show that the modified Reynolds equation approach, which is useful to describe the behavior of lubricating fluids at high subsonic speeds may be inadequate in the supersonic regime. The present studies show the absence of shock and expansion wave phenomena for cases in which the film thickness ratio does not exceed 0.01.

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.

Low-Speed Slip Flow Over a Wedge

1970 ◽  
Vol 37 (2) ◽  
pp. 454-460 ◽  
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Free Path ◽  
Asymptotic Method ◽  
Slip Velocity ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Low Speed ◽  
Boundary Layer Equations

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

scholarly journals Prediction of Windage Losses of an Enclosed High Speed Composite Rotor in Low Air Pressure Environments

2003 ◽  
Author(s):  
Hsing-Pang Liu ◽  
Mike Werst ◽  
Jonathan J. Hahne ◽  
David Bogard
Keyword(s):  
Free Path ◽  
High Speed ◽  
Rarefied Gas ◽  
Flow Instability ◽  
Slip Flow ◽  
Mean Free Path ◽  
Air Gap ◽  
Air Pressure ◽  
General Interest ◽  
Continuum Flow

The frictional windage losses associated with non-ventilated airflows in the air gaps between the rotor and stator of a high speed rotating machine can greatly influence the rotor outer and stator inner surface temperatures. The characteristics of the radial and axial air-gap flows have been of general interest in many engineering applications. A rotating air gap flow is very complex, and in general, can be categorized as a continuum flow, slip flow, and free molecule flow, depending on the ratio of its mean free path to the air gap dimension. For a continuum flow between concentric rotating cylinders, secondary flow of rows of circumferential Taylor vortices in the air gap due to centrifugal flow instability of a curved flow at relatively high rotating speeds will typically be formed. As the air pressure in the air gap drops significantly, rarefied gas flow, departure from continuum flow, occurs when the mean free path becomes relatively large compared to the air gap dimension. This paper has developed and summarized an analytical approach to predict high speed windage losses (rotor tip velocities up to 900 m/s) at low rotor cavity air pressures (0.1 torr to 10 torr). The predicted transient windage losses at various air pressures and high rotor speeds are compared with measured windage losses generated in continuum and slip flow regimes. The agreements between the predicted and measured windage losses are relatively well.

An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances

1983 ◽  
Vol 105 (1) ◽  
pp. 120-129 ◽  
Author(s):  
Y.-T. Hsia ◽  
G. A. Domoto
Keyword(s):  
Experimental Investigation ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slider Bearing ◽  
Interferometric Technique ◽  
Slip Boundary ◽  
Knudsen Numbers ◽  
Theoretical Predictions ◽  
Rarefaction Effects

The experimental investigation discussed here gives experimental confirmation of the slip-flow theory for modeling hydrodynamic gas bearings with clearances below 0.25 microns. An interferometric technique employing two CW lasers is used to measure the small clearances with an accuracy of 0.025 microns. The effects of molecular rarefaction are studied by operating the slider bearing in different gas media of different mean free paths. Bearings operating at extremely high local Knudsen numbers are studied without approaching excessively high bearing numbers. Experimentally measured trailing edge clearances and pitch angles are compared with theoretical predictions using the modified Reynolds equation with velocity slip boundary conditions. Excellent agreement between experiment and theory is found for clearances as high as 1.60 microns to as low as 0.075 microns with corresponding ambient Knudsen numbers of 0.04 and 2.51, respectively.

scholarly journals Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Nishanth Dongari ◽  
Yonghao Zhang ◽  
Jason M Reese
Keyword(s):  
Free Path ◽  
Flow Behavior ◽  
Constitutive Relations ◽  
Slip Flow ◽  
Theoretical Models ◽  
Mean Free Path ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Gas Flows ◽  
Planar Wall

We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.

New First and Second Order Slip Models for the Compressible Reynolds Equation

2003 ◽  
Vol 125 (3) ◽  
pp. 558-561 ◽  
Author(s):  
Lin Wu ◽  
D. B. Bogy
Keyword(s):  
Free Path ◽  
Reynolds Equation ◽  
Mean Free Path ◽  
Second Order ◽  
Surface Element ◽  
Length Scale ◽  
Mean Velocity ◽  
First Order ◽  
Lubrication Equation ◽  
The Mean

In the original derivations of the first order and the second order slip models of the generalized Reynolds equation in the literature [3,4], a length scale equal to the mean free path of the gas molecules was used in a Taylor series expansion of the mean velocity field. The coefficients of the correction terms in the derived lubrication equation depend on that length scale. This choice of the length scale is arbitrary to some extent. In this paper, new first order and the second order slip models are derived using a somewhat more physical approach, in which the requirement that the expansion length scale be the mean free path is relaxed. In this approach the momentum transfer rate across each surface element is obtained by summing up the contributions from each group of molecules impinging on the surface at an angle θ to the surface normal within a solid angle dω. The new second order slip lubrication equation appears to be preferable to the original one when the inverse Knudsen number is small, and it is free of any contact pressure singularity, whereas the new first order slip model continues to contain the unacceptable pressure singularity in the limit as the spacing approaches zero, as does the original first order model.

Mean Free Path Effect in Spiral-Grooved Thrust Bearings

1969 ◽  
Vol 91 (1) ◽  
pp. 69-78 ◽  
Author(s):  
F. C. Hsing ◽  
S. B. Malanoski
Keyword(s):  
Free Path ◽  
Thrust Bearing ◽  
Ambient Pressure ◽  
Slip Flow ◽  
Substantial Reduction ◽  
Mean Free Path ◽  
Slip Boundary Conditions ◽  
Thrust Bearings ◽  
Slip Boundary ◽  
Steady State Performance

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].

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