Effect of Slip Flow in Narrow Porous Bearings With Arbitrary Wall Thickness

1975 ◽  
Vol 42 (2) ◽  
pp. 305-310 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Wall Thickness ◽  
Reynolds Equation ◽  
Bessel Functions ◽  
Load Capacity ◽  
Slip Flow ◽  
Velocity Slip ◽  
Low Permeability ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

The experimental work of Beavers, et al., established that velocity slip takes place over a permeable boundary. The Reynolds equation governing the flow of lubricant in a finite porous bearing is appropriately modified to include the effect of velocity slip at the permeable boundary. The performance of a bearing with arbitrary wall thickness is then analyzed adopting the narrow bearing approximation. An exact solution is given for the pressure of the lubricant in the bearing material using modified Bessel functions and the modified Reynolds equation for the problem is solved by the Galerkin method. Numerical results obtained with a digital computer indicate 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 higher eccentricity ratio and/or the bearing matrix has a low permeability. The results are presented in graphical and tabular forms and guidelines are outlined to enable designers in assessing bearing performance using the results.

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.

Hydrodynamic Lubrication of Partial Porous Metal Bearings

1966 ◽  
Vol 88 (1) ◽  
pp. 53-60 ◽  
Author(s):  
C. A. Rhodes ◽  
W. T. Rouleau
Keyword(s):  
Series Solution ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Metal ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

Partial porous metal bearings are analyzed to determine their performance during steady-state operating conditions with a full film of lubricant. The pressure distribution is determined by a simultaneous solution of the two-dimensional Reynolds equation in the film region and the Laplace equation within the porous bearing material. An infinite-series solution is obtained for pressure utilizing the Galerkin method to determine coefficients. Numerical values of load capacity and coefficient of friction are presented for bearing arcs of 180, 150, and 120 deg.

Lubrication of Narrow Porous Bearings With Arbitrary Wall Thickness

1973 ◽  
Vol 95 (4) ◽  
pp. 511-517 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Reynolds Equation ◽  
Bessel Functions ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Metal ◽  
Progressive Reduction ◽  
Bearing Material ◽  
Permeability Parameter ◽  
The Galerkin Method ◽  
Side Result

An analysis is given for the hydrodynamic lubrication of short porous metal bearings that are press-fitted into a solid housing. An exact solution is given for the pressure of the lubricant in the bearing material using modified Bessel functions and the modified Reynolds equation for the problem is solved by the Galerkin method. Numerical results obtained on a digital computer indicate a progressive reduction in the load capacity and increment in the friction parameter and attitude angle as the permeability parameter is increased. These results are presented in graphical and tabular forms. A side result of this analysis is the emergence of a new permeability parameter and its convenience in bearing selection is discussed.

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.

Hydrodynamic Behaviors of the Gas-Lubricated Film in Wedge-Shaped Microchannel

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Xueqing Zhang ◽  
Qinghua Chen ◽  
Juanfang Liu
Keyword(s):  
Wall Temperature ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Hydrodynamic Properties ◽  
Obvious Effect ◽  
Navier Stokes Equations

As for the micro gas bearing operating at a high temperature and speed, one wedge-shaped microchannel is established, and the hydrodynamic properties of the wedge-shaped gas film are comprehensively investigated. The Reynolds equation, modified Reynolds equation, energy equation, and Navier–Stokes equations are employed to describe and analyze the hydrodynamics of the gas film. Furthermore, the comparisons among the hydrodynamic properties predicted by various models were performed for the different wedge factors and the different wall temperatures. The results show that coupling the simplified energy equation with the Reynolds or modified Reynolds equations has an obvious effect on the change of the friction force acting on the horizontal plate and the load capacity of the gas film at the higher wedge factor and the lower wall temperature. The velocity slip weakens the squeeze of the gas film and strengths the gas backflow. A larger wedge factor or a higher wall temperature leads to a higher gas film temperature and thus enhances the rarefaction effect. As the wall temperature is elevated, the load capacity obtained by the Reynolds equation increases, while the results by the Navier–Stokes equations coupled with the full energy equation rapidly decrease. Additionally, the vertical flow across the gas film in the Navier–Stokes equations weakens the squeeze between the gas film and the tilt plate and the gas backflow.

Lubrication of a Porous Bearing—Reynolds’ Solution

1966 ◽  
Vol 33 (4) ◽  
pp. 761-767 ◽  
Author(s):  
C. C. Shir ◽  
D. D. Joseph
Keyword(s):  
Mass Transfer ◽  
Shear Stress ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Radius Ratio ◽  
Total Load ◽  
Porous Bearing ◽  
Stress Resultant

The problem of lubrication of a journal in a porous bearing is considered. A Reynolds equation modified to accommodate mass transfer with the fluid-saturated bearing is solved, and the influence of the permeability and radius ratio of the bearing is examined. The effects of the bearing flow are such as to reduce the magnitude of the pressure and shift the maximum away from the position of minimum gap. In extreme cases, the integrated resultant of the pressure forces is so reduced as to become comparable in magnitude with the normally negligible shear stress resultant. This latter resultant has an opposing sense so that the total load capacity of the bearing is greatly reduced as a result of bearing flow.

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Loading Capacity ◽  
Global Approach ◽  
Pressure Flow ◽  
Stiffness Coefficients ◽  
Porous Bearing ◽  
Bearing Load ◽  
Modified Reynolds Equation ◽  
Precision Machines

Aerostatic porous bearings are becoming important elements in precision machines due to their inherent characteristics. The mathematical modeling of such bearings depends on the pressure-flow assumptions that are adopted for the flow in the porous medium. In this work, one proposes a nondimensional modified Reynolds equations based on the quadratic Forchheimer assumption. In this quadratic approach, the nondimensional parameter Φ strongly affects the bearing load capacity, by defining the nonlinearity level of the system. For values of Φ>10, the results obtained with the modified Reynolds equation with quadratic Forchheimer assumption tend to those obtained with the linear Darcy model, thus showing that this is a more robust and global approach of the problem, and can be used for both pressure-flow assumptions (linear and quadratic). The threshold between linear and quadratic assumptions is numerically investigated for a bronze sintered porous bearing, and the effects of bearing geometry are discussed. Numerical results show that Φ strongly affects the bearing loading capacity and stiffness coefficients.

An Analytical Study of Starved Porous Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 38-47 ◽  
Author(s):  
C. Cusano
Keyword(s):  
Analytical Study ◽  
Load Capacity ◽  
Porous Wall ◽  
Velocity Slip ◽  
Diameter Ratio ◽  
Radial Clearance ◽  
Oil Film ◽  
Porous Bearing ◽  
Inside Radius ◽  
Outside Diameter

An analytical solution for the performance characteristics of starved porous bearings is obtained. The solution is based on a finite bearing with an arbitrary wall thickness. The Reynolds equation is modified to include the effect of velocity slip at the interface between the oil film and porous wall. The data presented are for a bearing with a length-to-diameter ratio of 1.0, an outside diameter-to-inside diameter ratio of 1.25 and a radial clearance-to-inside radius ratio of 0.0015. The data are presented in a form such that by knowing the oil supplied externally to the porous bearing or by knowing the active oil film arc, the load capacity and coefficient of friction of the bearing can be obtained for given eccentricity ratios and permeability parameters.

Hybrid Porous Gas Journal Bearings: Steady State Solution Incorporating the Effect of Velocity Slip

1984 ◽  
Vol 106 (3) ◽  
pp. 322-328 ◽  
Author(s):  
K. C. Singh ◽  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Steady State Solution ◽  
Static Characteristic ◽  
Journal Bearings ◽  
Mass Rate ◽  
Modified Reynolds Equation

A theoretical analysis is presented to predict the steady state performance characteristics of externally pressurized rotating gas journal bearings incorporating the effect of velocity slip at the porous interface. The governing equation for flow in the porous media and the modified Reynolds equation derived from the Navier-Stokes equations satisfying the velocity slip boundary condition, are solved simultaneously for film pressure distribution. Due to the nonlinearity of modified Reynolds equation the solution is obtained by perturbation method using finite difference technique. The dimensionless load capacity, attitude angle and mass rate of flow are computed numerically for different operating parameters. The effect of slip on the static characteristic is discussed. Comparison of the results with similar available solution for the no-slip case shows good agreement.

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.

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