Generalized Reynolds Equation for Stochastic Lubrication and its Application

1975 ◽  
Vol 17 (5) ◽  
pp. 262-270 ◽  
Author(s):  
H. Christensen ◽  
J. B. Shukla ◽  
S. Kumar
Keyword(s):  
Stochastic Process ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Roughness Parameter ◽  
Slider Bearing ◽  
Hydrostatic Bearing ◽  
Force Increase ◽  
Thickness Function ◽  
Generalized Reynolds Equation ◽  
Good Agreement

By using the theory of a stochastic process, a generalized form of Reynolds equation applicable to rough bearings is derived by assuming the fluxes to be represented by power series of a stochastic film-thickness function. In the case of a step slider bearing, it is shown that load capacity and friction force increase but that coefficient of friction decreases as roughness parameter increases. Similar results are true in the case of a hydrostatic bearing. Further, in this case, good agreement between this theory and the sinusoidal approach is illustrated by suitably choosing the roughness parameter.

On the granular lubrication theory

2005 ◽  
Vol 461 (2062) ◽  
pp. 3255-3278 ◽  
Author(s):  
J.Y Jang ◽  
M.M Khonsari
Keyword(s):  
Granular Material ◽  
Reynolds Equation ◽  
Three Dimensional ◽  
Lubrication Theory ◽  
Slider Bearing ◽  
Governing Equations ◽  
Three Dimensional Flow ◽  
Generation Capacity ◽  
Side Flow ◽  
Generalized Reynolds Equation

The governing equations for the flow of a granular material within the context of the lubrication theory are derived. The resulting analysis gives a generalized Reynolds equation that predicts the pressure generation capacity in a bearing with consideration of side flow. A series of simulations are presented that characterize the three-dimensional flow behaviour of powder in a slider bearing.

Analysis of Thermal Effects in Hydrodynamic Bearings

1986 ◽  
Vol 108 (2) ◽  
pp. 219-224 ◽  
Author(s):  
R. Boncompain ◽  
M. Fillon ◽  
J. Frene
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Thermal Effects ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Heat Transfer Equation ◽  
Reversed Flow ◽  
Theoretical Results ◽  
Generalized Reynolds Equation ◽  
Good Agreement

A general THD theory and a comparison between theoretical and experimental results are presented. The generalized Reynolds equation, the energy equation in the film, and the heat transfer equation in the bush and the shaft are solved simultaneously. The cavitation in the film, the lubricant recirculation, and the reversed flow at the inlet are taken into account. In addition, the thermoelastic deformations are also calculated in order to define the film thickness. Good agreement is found between experimental data and theoretical results which include thermoelastic displacements of both the shaft and the bush.

Generalized Reynolds Equation for Micropolar Lubricants and its Application to Optimum One-Dimensional Slider Bearings: Effects of Solid-Particle Additives in Solution

1975 ◽  
Vol 17 (5) ◽  
pp. 280-284 ◽  
Author(s):  
J. B. Shukla ◽  
M. Isa
Keyword(s):  
Calculus Of Variations ◽  
Solid Particle ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slider Bearing ◽  
One Dimensional ◽  
Slider Bearings ◽  
Generalized Reynolds Equation

The effects of solid-particle additives in the lubricant are considered by characterizing this suspension as a micropolar fluid. The generalized Reynolds equation for this case has been derived and the optimum one-dimensional slider bearing is studied by using the techniques of the calculus of variations.

Forced Cooling of a Slider Bearing With Wedge Film

1968 ◽  
Vol 90 (1) ◽  
pp. 297-304 ◽  
Author(s):  
H. Tahara
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Flow ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Heat Flow Rate ◽  
Slider Bearing ◽  
The Mean ◽  
Forced Cooling ◽  
Generalized Reynolds Equation

This paper deals with the forced cooling problem of a slider bearing with wedge film of finite length, where most of the heat generated in the lubricant film is removed by a coolant which flows under the surface of the bearing pad. Analysis was made on the generalized Reynolds’ equation, including viscosity variations with temperature throughout the film and the energy equation. Simultaneous solutions of these equations seemed to be supported by experiments. From the analysis, calculations were made on the heat flow rate into the coolant, the temperature difference between slider and pad surfaces, bearing characteristics using the representative viscosity, and the mean heat transfer coefficient of the wedge film.

A Thermohydrodynamic Coupling Model of Oil Aeration Turbulent Lubrication for Journal Bearing With Interface Effect

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Xiaohui Lin ◽  
Shuyun Jiang ◽  
Chengyu Hua ◽  
Feng Cheng
Keyword(s):  
Velocity Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Coupling Model ◽  
Wall Turbulence ◽  
Volume Distribution ◽  
Bubble Volume ◽  
Coupled Equations ◽  
Generalized Reynolds Equation

Oil aeration lubricant in high-speed journal bearing is composed of mixture of continuous phase liquid and discrete phase bubbles. This work establishes a thermohydrodynamic (THD) coupling model for this lubrication condition. The generalized Reynolds equation is derived by the continuity equation, Navier–Stokes equation, law of wall turbulence model, and bubble volume distribution function, and then a THD oil aeration turbulent lubrication model is established by coupling the generalized Reynolds equation, energy equation, force equilibrium equation of bubble, and population balance equations (PBEs). The coupled-equations are solved numerically to obtain the pressure distribution under oil aeration lubrication state, the equilibrium distribution of bubble volume, the turbulent velocity distribution, the bubble velocity distribution, and the temperature rise. The results show that the load capacity of a bearing with oil aeration lubrication model is higher than that of the same bearing with a pure oil lubrication model, and heat dissipation performance of the bearing under the oil aeration lubrication state is superior.

Thermal-EHD contacts lubricated with oil/refrigerant solutions: a new cavitation modeling approach based on refrigerant solubility

2022 ◽  
pp. 1-19
Author(s):  
Fan Zhang ◽  
Nicolas Fillot ◽  
Rudolf Hauleitner ◽  
Guillermo Morales Espejel
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Conservation Equation ◽  
Point Contacts ◽  
Energy Conservation Equation ◽  
Cavitation Region ◽  
Cavitation Intensity ◽  
Thickness Prediction ◽  
Generalized Reynolds Equation ◽  
Good Agreement

Abstract A first cavitation modeling with thermal effects for oil/refrigerant solutions lubricated ElastoHydroDynamic (EHD) point contacts is reported in this work. The solubility of the oil/refrigerant system is introduced into the Generalized Reynolds equation coupled with the elasticity equation and the energy conservation equation. The numerical results show a very good agreement with the published experimental results concerning film thickness prediction. Moreover, the present model describes the cavitation region on a physical basis. A discussion with other cavitation models from the literature is proposed. It puts into light the necessity of taking into account the solubility of the refrigerant into oil for such problems. Compared to pure oil, oil/refrigerant solutions can potentially reduce the amount of liquid oil for the next contact due to its higher cavitation intensity.

Spiral Bearing Lubrication with Viscosity Variation And Thermal Effect of Two Layer Fluid

2017 ◽  
Vol 6 (5) ◽  
Author(s):  
M. Ganapathi ◽  
S. Vijayakumarvarma ◽  
K.R.K. Prasad ◽  
Bharath Kumar
Keyword(s):  
Thermal Effect ◽  
Layer Thickness ◽  
Coefficient Of Friction ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Load Factor ◽  
Load Pressure ◽  
Viscosity Variation ◽  
Generalized Reynolds Equation

In this paper a fluid film equation for two layer fluids and generalized Reynolds equation for convergent and divergent spiral bearing is derived with thermal effect. It is applied to see the effect of pre-load factor, viscosity variation, eccentricity, peripheral layer thickness. Expressions for load, pressure and coefficient of friction are derived and are analyzed numerically. The effect of pre-load factor analyzed for convergent and divergent spiral bearings. When pre-load factor is zero then both convergent and divergent spiral bearings are becomes journal bearing. It is observed the dimensionless load capacity values form the tables. The spiral bearing bears more load capacity than journal bearing. The effects of viscosity variation and thermal effect on these parameters are also analyzed.

A Simplified One-Dimensional Thermal Model for Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Daquan Liu ◽  
Wen Zhang ◽  
Tiesheng Zheng
Keyword(s):  
Thermal Effects ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Computing Time ◽  
One Dimensional ◽  
Lubricating Film ◽  
Direct Solution Method ◽  
The One ◽  
Generalized Reynolds Equation ◽  
Good Agreement

The variational approach, which is used to solve the Reynolds equation based on the assumption of constant temperature, is extended to the generalized Reynolds equation calculation. The direct solution method of the generalized Reynolds equation is presented, where the pressure of the nodal points and the cavitation zone boundary of the film can be determined without iterating. A simplified one-dimensional thermal model is built on the basis of the original two-dimensional thermal model. The model not only concerns the thermal effects of the lubricating film, but also offers a direct and rapid numerical algorithm for solving lubricating film temperature field. The numerical results of the temperature distributions for the one model are in good agreement with experiment, and less computing time is needed.

scholarly journals Numerical Solution of the MHD Reynolds Equation for Squeeze-Film Lubrication between Porous and Rough Rectangular Plates

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
N. Murulidhara ◽  
H. P. Patil
Keyword(s):  
Pressure Distribution ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Roughness Parameter ◽  
Transverse Magnetic ◽  
Couple Stress Fluid ◽  
Squeeze Film ◽  
Physical Parameters ◽  
Rectangular Plates

The present theoretical study investigates the effects of surface roughness and couple-stress fluid between two rectangular plates, of which an upper rough plate has a roughness structure and the lower plate has a porous material in the presence of transverse magnetic field. The lubricant in the gap is taken to be a viscous, incompressible, and electrically conducting couple-stress fluid. This gap is separated by a film thickness H which is made up of nominal smooth part and rough part. The modified Reynolds equation in the film region is derived for one-dimensional longitudinal roughness structure and solved numerically using multigrid method. The numerical results for various physical parameters are discussed in terms of pressure distribution, load capacity, and squeeze film time of the bearing surfaces. Our results show that, the pressure distribution, load capacity and squeeze film time are predominant for larger values of Hartman number and roughness parameter, and for smaller values of couple-stress parameters when compared to their corresponding classical cases.

The Influence of Fluid Inertia in Steady Laminar Lubrication

1983 ◽  
Vol 105 (1) ◽  
pp. 77-83 ◽  
Author(s):  
R. Malvano ◽  
F. Vatta
Keyword(s):  
Load Capacity ◽  
Inertial Forces ◽  
Fluid Inertia ◽  
Slider Bearing ◽  
Minimum Thickness ◽  
Approximate Methods ◽  
Friction Forces ◽  
Lubricant Flow ◽  
Simplifying Assumptions ◽  
Good Agreement

In this work the authors give a method to determine the influence of the inertial terms, in the case of a lubricated slider bearing, based on the solution of the “inverse problem.” That is to determine the geometry of a slider bearing given the pressure distribution, the lubricant flow rate and the slider velocity. Unlike other methods till now proposed (i.e., the Slezkin and Targ, Kahlert, Constantinescu methods), in this work no simplifying assumptions have been made. A sensible influence of the inertial forces, already at the value of the modified Reynolds number Re* = 0.1, has been shown. At the same load capacity, the minimum thickness of the film decreases because of the inertia (at values of the parameters Re* = 0.1 and a = 0.2 the decreasing is about five percent). At a given geometry of the lubricant film, the inertial forces increase the load capacity, the friction forces and the friction coefficient if they are compared with the linear case. A comparison between the results of the present study and the results obtained solving the “direct problem” with approximate methods shows a good agreement relating to quality.

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