Analysis of Short Journal Bearings With New Upstream Boundary Conditions

1974 ◽  
Vol 96 (3) ◽  
pp. 489-496 ◽  
Author(s):  
I. Etsion ◽  
O. Pinkus
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
General Analysis ◽  
New Approach ◽  
Starting Condition ◽  
Lubricating Film ◽  
Limiting Case

The Reynolds equation, for short journal bearings, is treated with a new approach to the boundary condition at the beginning of the lubricating film. The nondimensional hydrodynamic side leakage and other performance characteristics of the bearing are shown to be a function not only of Sommerfeld number and width over diameter ratio but also of another parameter which depends on the starting condition at the film inlet. The results obtained by other investigators till now are shown to be only a limiting case of the more general analysis given here. This work is the first part of a larger work embracing the analysis of finite bearings.

On the Performance of Journal Bearings Under Conditions of Film Rupture, Part II

1975 ◽  
Vol 97 (4) ◽  
pp. 591-598
Author(s):  
W. A. Crosby ◽  
E. M. Badawy
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Length ◽  
Infinite Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Operating Characteristics ◽  
Film Rupture ◽  
Rupture Part

An analytical analysis of journal bearing performance under conditions of film rupture by separation and by cavitation is performed. The ruptured region is considered to have an infinite number of cavities. The boundary condition of Reynolds’ equation at the trailing edge is influenced by the bearing’s operating characteristics and the method of oil admission. A variational solution is given in order to extend the applicability of the boundary conditions to bearings of finite length.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

Solutions of Finite Journal Bearings With Incomplete Films

1975 ◽  
Vol 97 (1) ◽  
pp. 89-93 ◽  
Author(s):  
I. Etsion ◽  
O. Pinkus
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Operating Parameters ◽  
Previous Theory ◽  
Feed Pressure ◽  
Theory And Experiment

The Reynolds equation is here solved for journal bearings using new upstream boundary conditions which reflect the fact that starting films in these bearings are often incomplete. The work is an extension of previously published results for short bearings to the case of finite bearings of arbitrary width and arbitrary extent of inlet film. An expression is also derived relating the width of the inlet film with the lubricant feed pressure and the bearing operating parameters, when the lubricant is fed through a hole. The results provide an explanation for the profound lack of agreement between previous theory and experiment with regard to side leakage in journal bearings.

Behavior of Finite Journal Bearings Under Dynamic Loading Conditions

1980 ◽  
Vol 102 (3) ◽  
pp. 333-338 ◽  
Author(s):  
G. S. A. Shawki ◽  
M. O. A. Mokhtar ◽  
Z. S. Safar
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variational Methods ◽  
Axial Length ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
The Third ◽  
Dynamic Loading Conditions ◽  
Generalized Reynolds Equation

Performance characteristics for a complete journal bearing of finite axial length are obtained analytically using a new set of boundary conditions. The generalized Reynolds equation is transformed, in the present analysis, into three ordinary differential equations, two of which being readily integrable while the third is solved by variational methods. By the aid of a specially devised computer program, the validity of the analysis has been assured when applied to prescribed journal loci including stationary, circular, elliptical, and linear harmonic journal oscillation.

Journal Bearings With Arbitrary Position of Source—II

1961 ◽  
Vol 83 (4) ◽  
pp. 572-578 ◽  
Author(s):  
J. V. Fedor
Keyword(s):  
Point Source ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Vertical Plane ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Source Parameter ◽  
Rapid Rise ◽  
Finite Form ◽  
Arbitrary Position

A complete oil film solution of Reynolds equation is found that takes into account the presence of a point source. The solution gives integrated journal bearing characteristics in finite form. With the load in a vertical plane and the source at the top or bottom of the bearing, two simple universal relationships have emerged between the angle indicating the line of centers (α) and the eccentricity (b). With the source at the base of the bearing and −cos α = b, the plot of coefficient of friction versus the Sommerfeld variable goes through the origin and is essentially independent of bearing length to diameter ratio. Also, lubricant end flow becomes vanishingly small as the Sommerfeld variable approaches zero. With the source at the top of the bearing a friction axis intercept can be obtained depending upon a source parameter, q. With cos α ≈ b/2, a rapid rise in the co-efficient of friction can also be simulated by properly varying the source parameter. Also, lubricant end flow increases monotonically as the Sommerfeld variable approaches zero.

Numerical Solution to Reynolds Equation for Micro Gas Journal Bearings

2012 ◽  
Vol 466-467 ◽  
pp. 991-994
Author(s):  
Qin Yang ◽  
Hai Jun Zhang
Keyword(s):  
Boundary Condition ◽  
Reynolds Equation ◽  
Effective Means ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
First Order ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
The Finite Difference Method ◽  
Modified Reynolds Equation

Reynolds equation for gas bearings is a nonlinear partial differential one and its analytical solution usually is difficult to obtain. Therefore numerical method is an effective means to investigate the performance of gas-lubricated journal bearings. In this paper, firstly the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution for micro gas journal bearings under different reference Knudsen numbers. Numerical analysis shows that the pressure profiles for micro gas journal bearings decrease obviously with the reference Knudsen number increasing.

Study on the Performance of Gas Journal Bearings for Power MEMS

2011 ◽  
Vol 483 ◽  
pp. 635-639
Author(s):  
Hai Jun Zhang ◽  
Qin Yang
Keyword(s):  
Boundary Condition ◽  
Knudsen Number ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Slip Boundary ◽  
Attitude Angle ◽  
Pressure Profiles ◽  
Power Mems ◽  
Modified Reynolds Equation

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

scholarly journals About boundary conditions for kinetic equations in metal

2021 ◽  
Vol 2056 (1) ◽  
pp. 012019
Author(s):  
F Karimov ◽  
T N Lam ◽  
A A Yushkanov
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Kinetic Equations ◽  
Limiting Case

Abstract Boundary conditions for kinetic equations describing the dynamics of electrons in the metal were analyzed. The boundary condition of the Fuchs and the boundary condition of Soffer were considered. The Andreev conditions for almost tangential moving electrons were taken into account. It is shown that the Soffer boundary condition does not satisfy this condition. The boundary condition was proposed that satisfies the Andreev condition. It is shown that this boundary condition passes in the limiting case into the mirror–diffuse Fuchs boundary condition.

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