On the Mean Reynolds Equation in the Presence of Homogeneous Random Surface Roughness

1982 ◽  
Vol 49 (3) ◽  
pp. 476-480 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Spectral Density ◽  
Small Amplitude ◽  
Random Function ◽  
Reynolds Equation ◽  
Random Surface ◽  
Dimensionless Amplitude ◽  
The Mean

Assuming that the surface roughness is of small amplitude and can be modeled by a homogeneous random function in space, the classical Reynolds equation is averaged using a method due to J. B. Keller. The mean Reynolds equation is accurate up to terms of 0(ε2), where ε is the dimensionless amplitude of the surface roughness and has a nonlocal character. Furthermore, by exploiting the slowly varying property of the mean film thickness, this nonlocal character is eliminated. The resulting mean Reynolds equation depends on the surface roughness via its spectral density and, in the limits of either parallel or transverse surface roughness, it reduces to Christensen’s theory.

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.

On the Mean Reynolds Equation in the Presence of Surface Roughness: Squeeze-Film Bearing

1981 ◽  
Vol 48 (4) ◽  
pp. 717-720 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Flow Field ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Homogeneous Surface ◽  
Parallel Surface ◽  
Mean Pressure ◽  
The Mean

The mean Reynolds equation in the presence of surface roughness is derived using the techniques developed by Keller. This mean equation is nonlocal in the sense that the mean pressure at all points in the flow field has some effect on the mean pressure at any particular point. The performance of a two-dimensional squeeze film bearing with homogeneous surface roughness is considered next showing that the load is enhanced by a factor of 1 + ε2a2S/h2, where εa is the amplitude of the roughness, h is the film thickness, and S varies between −3 〈m2〉, for parallel surface roughness, to 6 〈m2〉 for transverse surface roughness. Here, the bearing surfaces are described by εam1 and h + εam2 and m = m2 − m1.

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.

Analysis of Oil Film Thickness on a Piston Ring of Diesel Engine: Effect of Oil Film Temperature

2001 ◽  
Author(s):  
Yasuo Harigaya ◽  
Michiyoshi Suzuki ◽  
Masaaki Takiguchi
Keyword(s):  
Diesel Engine ◽  
Temperature Distribution ◽  
Heat Flow ◽  
Film Thickness ◽  
Piston Ring ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Two Dimensional ◽  
Oil Film ◽  
The Mean

Abstract This paper describes that an analysis of oil film thickness on a piston ring of diesel engine. The oil film thickness has been performed by using Reynolds equation and unsteady, two-dimensional (2-D) energy equation with a heat generated from viscous dissipation. The temperature distribution in the oil film is calculated by using the energy equation and the mean oil film temperature is computed. Then the viscosity of oil film is estimated by using the mean oil film temperature. The effect of oil film temperature on the oil film thickness of a piston ring was examined. This model has been verified with published experimental results. Moreover, the heat flow at ring and liner surfaces was examined. As a result, the oil film thickness could be calculated by using the viscosity estimated from the mean oil film temperature and the calculated value is agreement with the measured values.

scholarly journals Hydrodynamic lubrication of rough surfaces

1982 ◽  
Vol 383 (1785) ◽  
pp. 439-446 ◽  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Homogenization Method ◽  
Squeeze Film ◽  
Spatial Average

Using the two-space homogenization method we derive an averaged Reynolds equation that is correct to O (< H 6 > — < H 3 > 2 ), where H is the total film thickness and the angle brackets denote a spatial average. Applications of this mean Reynolds equation to a squeeze-film bearing with a sinusoidal or an isotropic surface roughness are discussed.

Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Masjedi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Material Surface ◽  
Line Contact ◽  
Wide Range ◽  
Minimum Film Thickness

Three formulas are derived for predicting the central and the minimum film thickness as well as the asperity load ratio in line-contact EHL with provision for surface roughness. These expressions are based on the simultaneous solution to the modified Reynolds equation and surface deformation with consideration of elastic, plastic and elasto-plastic deformation of the surface asperities. The formulas cover a wide range of input and they are of the form f(W, U, G, σ¯, V), where the parameters represented are dimensionless load, speed, material, surface roughness and hardness, respectively.

On the Effects of Homogeneous Reynolds Roughness in a Two-Dimensional Slider Bearing With Exponential Film Thickness

1982 ◽  
Vol 104 (2) ◽  
pp. 220-226 ◽  
Author(s):  
N. Phan-Thien ◽  
J. D. Atkinson
Keyword(s):  
Surface Roughness ◽  
Aspect Ratio ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Perturbation Approach ◽  
Mean Square ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Characteristic Frequencies ◽  
Parallel Surface

The effects of rough surfaces on the performance of a two-dimensional slider bearing with a mean exponential film thickness is investigated using the Reynolds equation, whose application requires the aspect ratio of the bearing to be large and the amplitude and the characteristic frequencies of the roughness to be considerably smaller than a representative film thickness (all are dimensionless). This problem has been previously considered by Sun using a straightforward perturbation approach; here, a formulation due to Keller is adopted and we make explicit use of h0/l<<1, where l is the bearing length and h0 is a representative film thickness. It is shown that neglecting terms of 0(h0/l), the load enhancement is maximum and positive for a transverse surface roughness; and it is minimum and negative for a parallel surface roughness. In these two extreme cases, both load enhancements depend on the statistics of the surface only through its mean square and are exactly predicted by Christensen’s theory.

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.

Thermal Resistance of Pressed Contacts between Steel Surfaces: Influence of Oxide Films

1979 ◽  
Vol 21 (3) ◽  
pp. 159-166 ◽  
Author(s):  
M. N. Mian ◽  
F. R. Al-Astrabadi ◽  
P. W. O'Callaghan ◽  
S. D. Probert
Keyword(s):  
Surface Roughness ◽  
Statistical Analysis ◽  
Film Thickness ◽  
Thermal Resistance ◽  
Applied Load ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Experimental Measurements ◽  
The Mean ◽  
Steel Surfaces

Flat, rough surfaces of steel specimens were oxidized and subsequently pressed into contact. From a statistical analysis of the experimental measurements for freshly-assembled contacts, an expression has been established relating the loading pressure, mean roughness of the two surfaces and oxide film thicknesses to the thermal resistance of the contacts in high vacua. The thermal contact resistance increased with (i) the film thickness and (ii) the ratio of the total film thickness to the mean surface roughness, and decreased with the loading pressure and the mean surface roughness. Increasing and decreasing the applied load revealed a slight hysteresis effect.

On the effects of the Reynolds and Stokes surface roughnesses in a two-dimensional slider bearing

1981 ◽  
Vol 377 (1770) ◽  
pp. 349-362 ◽  
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Flow Direction ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Homogeneous Surface ◽  
Parallel Surface ◽  
The Mean ◽  
The Stokes Equation

Perturbation solutions are presented to the Reynolds and the Stokes equations for a two-dimensional slider bearing with homogeneous surface roughness. In the Reynolds equation the surface roughness has a general two-dimensional form, and in the Stokes equation the surface roughness is parallel to the flow direction. For the parallel surface roughness, if the surface corrugations on two bearing plates are uncorrelated then an error of order 10% is made when using the Reynolds equation to correct for the surface roughness provided that λh ≼ 0.5. Here λ is a characteristic frequency of the corrugation and h is the mean film thickness. Furthermore, if λh ≽ 1.91 then the Stokes solution demands a positive load enhancement, whereas the Reynolds equation predicts a negative load enhancement that depends on λ through terms of order O ( h / L ), where 2 L is the bearing length.

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