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.

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.

scholarly journals Slip Flow of Kerosene Oil Based SWCNT Nanofluid over Stretching Sheet with Radiation and Suction/Injection Effects

2021 ◽  
Vol 6 (3) ◽  
pp. 860-877
Author(s):  
Susheela Chaudhary ◽  
Kiran Kunwar Chouhan ◽  
Santosh Chaudhary
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Skin Friction Coefficient ◽  
Single Wall Carbon Nanotubes ◽  
Local Skin ◽  
Slip Boundary ◽  
Similarity Transformations

Present study numerically investigates a two dimensional steady laminar boundary layer nanofluid flow of single-wall carbon nanotubes (SWCNTs) immersed into kerosene oil, due to a linearly stretched sheet. Flow is subjected to the slip boundary condition and suction/injection effects. Employing suitable similarity transformations, governing PDEs of the arising problem are converted into coupled nonlinear non-dimensional ordinary differential equations. A set of obtained ODEs with assisting boundary conditions is solved numerically by applying finite element method (FEM). Effect of pertinent factors, velocity slip parameter, suction/injection parameter and solid volume fraction parameter on non-dimensional velocity and temperature profiles are characterized graphically. In addition, physical emerging parameters, local Nusselt’s number and local skin friction coefficient are computed and presented via table. Furthermore, derived numerical values of shear stress and heat flux at the surface are compared with previously published results.

Experimental Investigation of Slider Gas Bearings With Ultra-Thin Films

1979 ◽  
Vol 101 (4) ◽  
pp. 510-515 ◽  
Author(s):  
Aron Sereny ◽  
Vittorio Castelli
Keyword(s):  
Experimental Investigation ◽  
Mean Free Path ◽  
Compressible Fluids ◽  
Flying Height ◽  
Gas Bearings ◽  
Slip Boundary ◽  
Light Interference ◽  
Theoretical Predictions ◽  
Surface Irregularities ◽  
Gas Bearing

The experimental investigation described here involves the highly accurate measurement of bearing clearances on the order of 0.25 μm in self-acting, pivoted, narrow-slider gas bearings. The experimental measurements are based on light interferometry using a variable-wavelength pulsed dye laser and a CW HeNe laser as monochromatic sources. The light interference in the gas bearing is obtained by flying the slider on a very precise, optically flat quartz disk through which the light beam is transmitted. The combined effect of high Knudsen numbers and surface irregularities on the flying height of narrow gas bearings is observed by varying the load on the bearing and the ambient molecular mean free path. The experimentally measured bearing clearances are compared quantitatively with theoretical predictions obtained by numerical solution of Reynolds differential equation for compressible fluids with slip boundary conditions.

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.

Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow

1988 ◽  
Vol 110 (2) ◽  
pp. 253-261 ◽  
Author(s):  
S. Fukui ◽  
R. Kaneko
Keyword(s):  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Thermal Creep ◽  
Creep Flow ◽  
Slip Boundary ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Knudsen Numbers ◽  
Bearing Number ◽  
Thermal Creep Flow

A generalized Reynolds-type lubrication equation valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, is derived from a linearized Boltzmann equation by semi-numerically calculating the flow rates of fundamental flows in the lubrication film: Poiseuille flow, Couette flow, and thermal creep flow. Numerical analysis of the equation for high Knudsen numbers reveals three principal results. First, Burgdorfer’s modified Reynolds equation featuring the first-order velocity slip boundary condition overestimates load carrying capacities, while the approximation equation including both the first- and second-order velocity slip boundary condition underestimates them. Second, since the flow rate of the Couette flow, which is independent of Knudsen numbers, becomes dominant as the bearing number increases, all the lubrication equation results tend toward the same asymptotic value for an infinite bearing number. Third, a new kind of load carrying capacity caused by thermal creep flow occurs if temperature gradients at the boundaries exist in the flow direction.

Effect of Slip-Flow in Narrow Porous Bearings

1973 ◽  
Vol 95 (4) ◽  
pp. 518-523 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Friction Force ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Flow ◽  
Velocity Slip ◽  
Low Permeability ◽  
Eccentricity Ratio ◽  
Porous Bearing ◽  
Thin Walled

The experimental work of Beavers, et al., established that velocity slip takes place over a permeable boundary. The presence of slip flow is taken into account while deriving the appropriate modified Reynolds equation that governs the flow of lubricant in a finite porous bearing. The performance of a thin-walled bearing is then analyzed making use of the narrow bearing approximation. It is found that slip flow adversely affects the load capacity and reduces the friction force on the journal; the attitude angle, however, is not significantly affected. Also the analysis indicates that the effects of velocity slip are prominent when the bearing operates at a lower eccentricity ratio and/or the bearing-matrix has a low permeability.

Rayleigh Problem in Slip Flow With Modified Initial Conditions

1967 ◽  
Vol 34 (4) ◽  
pp. 833-836 ◽  
Author(s):  
K. C. Reddy
Keyword(s):  
Temperature Jump ◽  
Initial Conditions ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Conditions ◽  
Flow Conditions ◽  
Slip Boundary ◽  
Rayleigh Problem ◽  
Molecule Flow ◽  
The Continuum

The initial conditions of the linearized Rayleigh problem in slip flow are modified so as to satisfy the free molecule flow conditions at the start of the motion. Approximate initial profiles for velocity and temperature are chosen which would yield correct values of velocity slip, temperature jump, and so on, at the start of the motion. The continuum solutions with the modified initial conditions and slip boundary conditions are found to be uniformly valid for all times of motion and agree well with the results of the kinetic theory analyses of the problem.

Rarefaction Effects of Gas-Lubricated Bearings in a Magnetic Recording Disk File

1975 ◽  
Vol 97 (4) ◽  
pp. 624-629 ◽  
Author(s):  
R. C. Tseng
Keyword(s):  
Magnetic Recording ◽  
Numerical Solutions ◽  
Velocity Slip ◽  
Disk File ◽  
Ambient Conditions ◽  
Slider Bearing ◽  
Slip Boundary ◽  
Lubrication Equation ◽  
Wide Range ◽  
Bearing Number

The load versus spacing characteristics of a self-acting, gas-lubricated slider bearing similar to that used in a magnetic recording disk file have been investigated experimentally under sub-atmospheric ambient conditions. Interferometric techniques are used to measure the steady spacing between a rotating glass disk and the slider over a wide range of ambient pressures and disk speeds. For local Knudsen number less than 0.1, excellent agreement is found to exist between experimental data and numerical solutions of the Reynolds lubrication equation taking into account the velocity-slip boundary conditions. Effects of rarefaction on the bearing performance for a range of pertinent bearing parameters (i.e., bearing number and inlet-to-outlet ratio) are presented.

scholarly journals Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017 ◽  
Vol 818 ◽  
pp. 68-99 ◽  
Author(s):  
N. Y. Bailey ◽  
S. Hibberd ◽  
H. Power
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Slip Length ◽  
Velocity Slip ◽  
Structural Equations ◽  
Force Balance ◽  
Slip Boundary Conditions ◽  
Inertia Effects ◽  
Navier Slip ◽  
Slip Boundary

A gas lubricated bearing model is derived which is appropriate for a very small bearing face separation by including velocity slip boundary conditions and centrifugal inertia effects. The bearing dynamics is examined when an external harmonic force is imposed on the bearing due to the bearing being situated within a larger complex dynamical system. A compressible Reynolds equation is formulated for the gas film which is coupled to the bearing structure through an axial force balance where the rotor and stator correspond to spring–mass–damper systems. Surface slip boundary conditions are derived on the bearing faces, characterised by the slip length parameter. The coupled bearing system is analysed using a stroboscopic map solver with the modified Reynolds equation and structural equations solved simultaneously. For a sufficiently large forcing amplitude a flapping motion of the bearing faces is induced when the rotor and stator are in close proximity. The minimum bearing gap over the time period of the external forcing is examined for a range of bearing parameters.

Subsonic gas flow in a straight and uniform microchannel

2002 ◽  
Vol 472 ◽  
pp. 125-151 ◽  
Author(s):  
YITSHAK ZOHAR ◽  
SYLVANUS YUK KWAN LEE ◽  
WING YIN LEE ◽  
LINAN JIANG ◽  
PIN TONG
Keyword(s):  
Gas Flow ◽  
Theoretical Calculations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Perturbation Expansions ◽  
Slip Boundary ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
Flow Effects

A nonlinear equation based on the hydrodynamic equations is solved analytically using perturbation expansions to calculate the flow field of a steady isothermal, compressible and laminar gas flow in either a circular or a planar microchannel. The solution takes into account slip-flow effects explicitly by utilizing the classical velocity-slip boundary condition, assuming the gas properties are known. Consistent expansions provide not only the cross-stream but also the streamwise evolution of the various flow parameters of interest, such as pressure, density and Mach number. The slip-flow effect enters the solution explicitly as a zero-order correction comparable to, though smaller than, the compressible effect. The theoretical calculations are verified in an experimental study of pressure-driven gas flow in a long microchannel of sub-micron height. Standard micromachining techniques were utilized to fabricate the microchannel, with integral pressure microsensors based on the piezoresistivity principle of operation. The integrated microsystem allows accurate measurements of mass flow rates and pressure distributions along the microchannel. Nitrogen, helium and argon were used as the working fluids forced through the microchannel. The experimental results support the theoretical calculations in finding that acceleration and non-parabolic velocity profile effects were found to be negligible. A detailed error analysis is also carried out in an attempt to expose the challenges in conducting accurate measurements in microsystems.

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