Reynolds Equation for Spherical Bearings

2002 ◽  
Vol 125 (1) ◽  
pp. 203-206 ◽  
Author(s):  
Donna Meyer
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Horizontal Position ◽  
Hemispherical Shell ◽  
Pressure Distributions ◽  
Spherical Bearing ◽  
Classical Paper ◽  
Fluid Film Thickness ◽  
Generalized Reynolds Equation

Osborne Reynolds’ classical paper on the theory of lubrication Reynolds (1886) produced the generalized Reynolds equation. For spherical bearing applications, the generalized Reynolds equation is transformed in order to obtain useful results when the hemispherical shell is not in a horizontal position. A new film thickness expression is also presented. These transformations permit the determination of pressure distributions and fluid film thickness for any orientation of the hemispherical shell including the horizontal position, for which the conventional description of Reynolds equation is well suited. The resulting equation in two-dimensional form, for an incompressible, variable viscosity fluid, with upper and lower sliding surfaces, in spherical coordinates, contains the inclination angle β, which accounts for non-horizontal positions of the shell.

Effects of Surface Roughness and Additives in Lubrication: Generalized Reynolds Equation and its Application to Elastohydrodynamic Film

1987 ◽  
Vol 201 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P Sinha ◽  
J S Kennedy ◽  
C M Rodkiewicz ◽  
P Chandra ◽  
R Sharma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Molecular Size ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Minimum Film Thickness ◽  
Porous Matrices ◽  
The Mean ◽  
Generalized Reynolds Equation

To study the effects of surface roughness and additives in lubrication, a generalized form of Reynolds equation is derived by taking into account the roughness interaction zones adjacent to the moving rough surfaces as sparsely porous matrices and purely hydrodynamic film of micropolar fluid characterizing the lubricant with additives. A particular, one-dimensional form of this equation is used to study these effects on the elastohydrodynamic (EHD) minimum film thickness at the inlet, between two rough rollers. It is shown that for the low permeability of the roughness zone, the EHD film thickness increases as the mean height of the asperities increases, whereas for the high permeability it decreases. The EHD film thickness is also found to increase with the concentration of the additives and the molecular size of the particles. These results are in conformity at least qualitatively, with various experimental and theoretical investigations, cited in the paper.

Theoretical Studies of a Continuously Adjustable Hydrodynamic Fluid Film Bearing

2001 ◽  
Vol 124 (1) ◽  
pp. 203-211 ◽  
Author(s):  
J. K. Martin ◽  
D. W. Parkins
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Solution Procedure ◽  
Fluid Film ◽  
Theoretical Studies ◽  
Analysis Model ◽  
Operating Characteristics ◽  
Hydrodynamic Bearing ◽  
Wide Range ◽  
Fluid Film Thickness

Principles of a continuously adjustable hydrodynamic bearing are described together with an analysis model for studying its theoretical performance. The model included an expanded form of the governing Reynolds equation which took account of non-uniform variations in the fluid film thickness. A solution procedure was devised whereby for a given set of adjustment conditions, simultaneously converged fields of fluid film thickness, temperature, viscosity and pressure would result, together with oil film forces. A wide range of operating characteristics were studied with results predicting advantages and benefits over conventional hydrodynamic bearings.

Vibration Analysis of High Speed Stepped Thrust Gas Film Bearings With Inertia Effects

1997 ◽  
Author(s):  
Masayuki Ochiai ◽  
Hiromu Hashimoto
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Reynolds Equation ◽  
Dynamic Pressure ◽  
Mechanical Energy ◽  
Inertia Effects ◽  
Pressure Distributions ◽  
Load Carrying ◽  
Inertia Forces ◽  
Generalized Reynolds Equation

Abstract Stepped thrust gas film bearings are widely used for high speed rotating machinery because of their simple structure, relatively high load carrying capacity and stability. In such bearings, the gas film inertia forces may play an important role under high speed conditions. In this paper, the vibration analysis of high speed, stepped thrust gas film bearings considering the inertia effects is described. In the numerical analysis, the static and dynamic pressure distributions in pocket and land regions are evaluated from the generalized Reynolds equation considering the centrifugal force. The pressure values at the step are calculated by considering the conservation of mechanical energy and the continuity of gas film flow in pocket and land regions. Moreover, the dynamic response of bearings subjected to impulsive and sinusoidal excitations are analyzed for different values of film thickness ratios. From the numerical results, the effects of gas film inertia on the vibration characteristics of bearings are clarified.

Surface Roughness Effects on Fluid Flow between Two Rotating Cylinders

2015 ◽  
Vol 642 ◽  
pp. 275-280
Author(s):  
Sutthinan Srirattayawong ◽  
Shian Gao
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Profile ◽  
Fluid Film ◽  
Real Surface ◽  
Contact Center ◽  
Roughness Effects ◽  
Fluid Film Thickness ◽  
Lubricant Viscosity

In general, the thin fluid film problems are explained by the classical Reynolds equation, but this approach has some limitations. To overcome them, the method of Computational Fluid Dynamics (CFD) is used in this study, as an alternative to solving the Reynolds equation. The characteristics of the two cylinders contact with real surface roughness are investigated. The CFD model has been used to simulate the behavior of the fluid flows at the conjunction between two different radius cylinders. The non-Newtonian fluid is employed to calculate the lubricant viscosity, and the thermal effect is also considered in the evaluation of the lubricant properties. The pressure distributions, the fluid film thickness and the temperature distributions are investigated. The obtained results show clearly the significance of the surface roughness on the lubricant flow at the contact center area. The fluctuated flow also affects the pressure distribution, the temperature and the lubricant viscosity in a similar pattern to the rough surface profile. The surface roughness effect will decrease when the film thickness is increased.

Theoretical Pressure Distribution in Journal Bearings

1961 ◽  
Vol 28 (4) ◽  
pp. 497-506 ◽  
Author(s):  
Kichiye Habata
Keyword(s):  
Reynolds Equation ◽  
Variable Viscosity ◽  
Slenderness Ratio ◽  
Approximate Solutions ◽  
Journal Bearings ◽  
Oil Viscosity ◽  
Pressure Distributions ◽  
Hill’S Method ◽  
Ritz’S Method ◽  
Theoretical Pressure

By assuming oil viscosity constant, Reynolds’ equation for journal bearings has been solved in a manner similar to Hill’s method. Two approximate solutions using E. O. Waters’ method and Ritz’s method have been added. Numerical computations have been carried out for a centrally supported 120-deg bearing with a unity slenderness ratio. Isobarriers have been determined from the pressure distributions. In order to show a justification for assuming the viscosity constant, the Reynolds equation was solved for the infinitely long bearing with variable viscosity, and the solution compared with that of Sommerfeld.

The Piezo-Viscous Fluid, Rigid Solid Regime of Lubrication

1983 ◽  
Vol 197 (1) ◽  
pp. 43-52 ◽  
Author(s):  
D Dowson ◽  
J F Dunn ◽  
C M Taylor
Keyword(s):  
Viscous Fluid ◽  
Film Thickness ◽  
Variable Viscosity ◽  
Point Contact ◽  
Hydrodynamic Performance ◽  
Pressure Distributions ◽  
Principal Directions ◽  
Physical Effects ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A general analysis of the lubrication of rigid-ellipsoidal solids by a piezo-viscous fluid is reported. Solutions based upon the Reynolds cavitation boundary condition are presented and details are given of the resulting pressure distributions and film thickness predictions. Four distinct forms of the fluid film lubrication of a general curved solid near a plane have previously been noted and described as: (i) rigid-isoviscous, (ii) elastic-isoviscous, (iii) elastic-variable viscosity (piezo-viscous), (iv) rigid-variable viscosity (piezo-viscous). Solutions already exist for the first three forms of lubrication for conjunctions formed between solids having curvatures in two principal directions, but the rigid-variable viscosity regime has not previously been analysed within the same general set of conditions. The results not only enable the film thickness between curved solids in nominal point contact to be predicted with reasonable confidence, but they indicate quite clearly the dominant physical effects governing the hydrodynamic performance of such conjunctions.

Non-Newtonian Thermal Elastohydrodynamic Lubrication

1991 ◽  
Vol 113 (2) ◽  
pp. 390-396 ◽  
Author(s):  
P. C. Sui ◽  
F. Sadeghi
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Simultaneous System ◽  
Energy Equations ◽  
Rheology Model ◽  
Generalized Reynolds Equation

A numerical solution to the problem of thermal and non-Newtonian fluid model in elastohydrodynamic lubrication is presented. The generalized Reynolds equation was modified by the Eyring rheology model to incorporate the non-Newtonian effects of the fluid. The simultaneous system of modified Reynolds, elasticity and energy equations were numerically solved for the pressure, temperature and film thickness. Results have been presented for loads ranging from W = 7 × 10−5 to W = 2.3 × 10−4 and the speeds ranging from U* = 2 × 10−11 to U* = 6 × 10−11 at various slip conditions. Comparison between the isothermal and thermal non-Newtonian traction force has also been presented.

DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

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