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.

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.

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.

Hydrodynamic Lubrication of Narrow Press-Fitted Porous Metal Bearings

1963 ◽  
Vol 85 (1) ◽  
pp. 123-128 ◽  
Author(s):  
W. T. Rouleau
Keyword(s):  
Coefficient Of Friction ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Practical Importance ◽  
Porous Metal ◽  
Length Ratio ◽  
Eccentricity Ratio ◽  
Bronze Powder ◽  
Permeability Parameter ◽  
Sintered Bronze

An analysis is made of the performance of narrow porous metal bearings (e.g., sintered bronze powder) which operate with a full film of lubricant. The configuration considered is that in which the bearings are pressed tightly into housings with their ends remaining open to the atmosphere. A solution for the lubricant pressure is obtained which satisfies Reynolds’ equation in the film and Laplace’s equation in the porous metal. Expressions are developed which give the Sommerfeld and Ocvirk numbers, attitude angle, and coefficient of friction as functions of eccentricity ratio, permeability parameter, and thickness-to-length ratio. The results are shown graphically for situations of practical importance.

A Contribution to the Analysis of the Thermo-Hydrodynamic Lubrication of Porous Self-Lubricating Journal Bearings

2010 ◽  
Vol 297-301 ◽  
pp. 618-623 ◽  
Author(s):  
S. Boubendir ◽  
Salah Larbi ◽  
Rachid Bennacer
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Matrix ◽  
Journal Bearings ◽  
Governing Equations ◽  
Hydrodynamic Analysis ◽  
Result Show

In this work the influence of thermal effects on the performance of a finite porous journal bearing has been investigated using a thermo-hydrodynamic analysis. The Reynolds equation of thin viscous films is modified taking into account the oil leakage into the porous matrix, by applying Darcy’s law to determine the fluid flow in the porous media. The governing equations were solved numerically using the finite difference approach. Obtained result show a reduction in the performance of journal bearings when the thermal effects are accounted for and, this reduction is greater when the load capacity is significant.

Squeeze-Film Behavior in Porous Circular Disks

1974 ◽  
Vol 96 (2) ◽  
pp. 206-209 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Adverse Effect ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Finite Time ◽  
Reynolds Equation ◽  
Load Capacity ◽  
The Other ◽  
Squeeze Film ◽  
Permeability Parameter ◽  
Circular Disks

The squeeze film behavior between two circular disks is analyzed when one disk has a porous facing and approaches the other disk with uniform velocity. The modified Reynolds equation governs the pressure in the film region while the pressure in the porous facing satisfies the Laplace equation. These equations are solved in a closed form and expressions are derived for pressure distribution, load capacity, and time of approach for the plates in terms of Fourier-Bessel series. It is found that an enhanced value for the permeability parameter diminishes the pressure over the entire disk and also evens out the pressure distribution; however, there is an adverse effect on the load capacity and time of approach. Unlike in the nonporous case, the entire fluid can be squeezed out in a finite time resulting in actual contact of the disks. The porous effects are shown to predominate at very low film thickness values.

Evaluation on Applicability of Reynolds Equation for Squared Transverse Roughness Compared to CFD

2007 ◽  
Vol 129 (4) ◽  
pp. 963-967 ◽  
Author(s):  
Jiang Li ◽  
Haosheng Chen
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Roughness Height ◽  
Obvious Effect ◽  
Disk Interface ◽  
Transverse Roughness ◽  
The Difference ◽  
Cfd Method

A discrete probability distribution function is used to represent the squared transverse roughness effect in a modified Reynolds equation, and the Reynolds equation is used to calculate the hydrodynamic lubrication in a slider-disk interface compared to the CFD method. When the roughness height is below 1% of the film thickness, the results acquired by the two methods are the same and the surface roughness does not show obvious effect on the lubrication results compared to that on the smooth surface. The load capacity and friction force increase as the roughness height increases when the roughness height exceeds 1% of the film thickness. Moreover, the forces acquired by Reynolds equations are smaller than those acquired by CFD, and the difference between them exceeds 10% when the roughness height is higher than 10% of the film thickness. Sidewall effect is considered to be the main reason for the difference, and the Reynolds equation is believed not suitable for calculating the effect of the squared transverse roughness in the hydrodynamic lubrication.

A Theoretical Analysis Considering Cavitation Occurrence in Oil-Lubricated Spiral-Grooved Journal Bearings With Experimental Verification

2004 ◽  
Vol 126 (3) ◽  
pp. 490-498 ◽  
Author(s):  
Tomoko Hirayama ◽  
Takeo Sakurai ◽  
Hiroshi Yabe
Keyword(s):  
Reynolds Equation ◽  
Flow Model ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Theoretical Studies ◽  
Bearing Stiffness ◽  
Hydrodynamic Lubrication Theory ◽  
The Difference ◽  
Theoretical Results

Performances of an oil-lubricated spiral-grooved journal bearing are investigated in this paper with special attention paid to cavitation occurrence. The “equivalent flow model,” which is a theoretical scheme for taking the cavitation occurrence into hydrodynamic lubrication theory, is applied to the analyses by a finite difference treatment of the Reynolds equation that deals with the geometry of a finite number of grooves. The calculated results are compared with experimental results under eccentric states, and verified in terms of cavitation map and pressure distribution. The cavitated area ratio, load capacity and bearing stiffness are also theoretically calculated. The difference between the theoretical results with and without consideration of the cavitation occurrence is considerable, and thus the influence of cavitation occurrence should not be ignored in theoretical studies on bearing characteristics.

Analysis of a Hydrodynamic Spiral Grooved Upstream Pumping Face Seal Considering Cavitation

2015 ◽  
Vol 799-800 ◽  
pp. 671-680
Author(s):  
Ding Hua Liu ◽  
Bin Zhang ◽  
Juan Zhao ◽  
Kai Ge ◽  
Shun Zhang
Keyword(s):  
Boundary Condition ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Logarithmic Spiral ◽  
Groove Depth ◽  
Frictional Torque ◽  
Face Seal ◽  
The Difference ◽  
Rotary Speed

A numerical analysis of an oil-lubricated spiral grooved upstream pumping face seal, accounting for the occurrence of cavitation, have been performed in this paper. The “equivalent flow model”, which is a theoretical scheme for taking the JFO boundary condition into hydrodynamic lubrication theory, was applied to the analyses by a finite difference treatment of the Reynolds equation that dealt with the geometry of logarithmic spiral groove. The calculated results were compared respectively based on Reynolds model and JFO model. The load capacity, cavitation ratio, frictional torque and leakage rate were also theoretically calculated. The difference between the theoretical results based on two boundary conditions for cavitation occurrence is considerable. The JFO boundary condition should be used in theoretical studies on sealing characteristics rather than Reynolds equation, especially in the conditions of less groove depth and high rotary speed.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Hydrodynamic Lubrication of Pocket Bearings and Effect of Contouring the Inner and Outer Regions, and Optimum Design Data

1989 ◽  
Author(s):  
C. Bagci ◽  
C. J. McClure ◽  
S. K. Rajavenkateswaran
Keyword(s):  
Optimum Design ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Load Flow ◽  
Temperature Dependent Viscosity ◽  
Design Data ◽  
Planar Surfaces ◽  
Friction Factors ◽  
The Coefficient Of Friction ◽  
Dependent Viscosity

Abstract The article investigates pocket bearings with contoured profiles of exponential forms on both surfaces inside and outside of the step boundary forming hydro-dynamic action surfaces, and develops optimum design data yielding efficient slider bearings with small pockets with higher load capacities than conventional pocket bearings. In the case of a pocket bearings, in addition to the Reynolds equation used for the regions inside and outside the pocket, the continuity equation along the pocket boundary is satisfied to form the complete model of the bearing. The optimum design data includes dimensionless load-, flow-, temperature rise-, power loss-, stiffness-, and the coefficient of friction factors. Incompressible lubricant with temperature dependent viscosity is considered. Detailed study of conventional pocket bearings with planar surfaces is included. Some optimum exponential pocket bearings yield up to 561 percent increase in load capacity as compared to the conventional tapered bearings.

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