Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces

1969 ◽  
Vol 184 (1) ◽  
pp. 1013-1026 ◽  
Author(s):  
H. Christensen
Keyword(s):  
Surface Roughness ◽  
Stochastic Models ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Type Equation ◽  
Mathematical Form ◽  
Slider Bearing ◽  
Operating Characteristics ◽  
Different Types

This paper deals with hydrodynamic aspects of rough bearing surfaces. On the basis of stochastic theory two different forms of Reynolds-type equation corresponding to two different types of surface roughnesses are developed. It is shown that the mathematical form of these equations is similar but not identical to the form of the Reynolds equation governing the behaviour of smooth, deterministic bearing surfaces. To illustrate the functional effects of surface roughness the influence on the operating characteristics of a plane pad, no side leakage slider bearing is analysed. It is shown that surface roughness may considerably influence the operating characteristics of bearings and that the direction of the influence depends upon the type of roughness assumed. The effects are not, however, critically dependent upon the detailed form of the distribution function of the roughness heights.

The Effect of Surface Roughness on the Average Film Thickness Between Lubricated Rollers

1976 ◽  
Vol 98 (1) ◽  
pp. 117-124 ◽  
Author(s):  
L. S. H. Chow ◽  
H. S. Cheng
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Stochastic Models ◽  
Hydrodynamic Lubrication ◽  
Elastohydrodynamic Lubrication ◽  
Type Equation ◽  
Slider Bearing ◽  
Reduced Pressure ◽  
Average Film Thickness ◽  
Effect Of Surface

The Christensen theory of stochastic models [7] for hydrodynamic lubrication of rough surfaces is extended to elastohydrodynamic lubrication between two rollers. The Grubin-type equation including asperity effects in the inlet region is derived. Solutions for the reduced pressure at the entrance as a function of the ratio of the average nominal film thickness to the r.m.s. surface roughness (in terms of standard deviation σ), have been obtained numerically. Results were obtained for purely transverse as well as purely longitudinal surface roughness for cases with or without slip. The reduced pressure is shown to decrease slightly by considering longitudinal surface roughness. The transverse surface roughness, on the other hand, has a slight beneficial effect on the average film thickess at the inlet. The same approach was used to study the effect of surface roughness on lubrication between rigid rollers and lubrication of an infinitely-wide slider bearing. Results of these two cases show that the effects of surface roughness are similar to those found in elastohydrodynamic contacts.

Lubrication of a Porous Bearing With Surface Corrugations

1982 ◽  
Vol 104 (1) ◽  
pp. 127-134 ◽  
Author(s):  
J. Prakash ◽  
K. Tiwari
Keyword(s):  
Surface Roughness ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Stochastic Theory ◽  
Circular Plates ◽  
Operating Characteristics ◽  
Roughness Effects ◽  
Porous Bearing

The paper considers the surface roughness effects in hydrodynamic porous bearings. On the basis of stochastic theory of hydrodynamic lubrication of rough surfaces developed by Christensen, different forms of Reynolds type equations, as applicable to a general porous bearings are derived for various types of surface roughness pattern. To illustrate the functional effects of surface roughness on the operating characteristics of a porous bearing, the case of nonrotating circular plates in normal approach is analyzed. It is shown that surface roughness may considerably influence the operating characteristics of porous bearings. The direction of the influence, however, depends upon the type of roughness assumed.

A Comparison of Porous Structures on the Performance of a Slider Bearing with Surface Roughness in Couple Stress Fluid Film Lubrication

2015 ◽  
Vol 813-814 ◽  
pp. 921-937
Author(s):  
P.S. Rao ◽  
Santosh Agarwal
Keyword(s):  
Surface Roughness ◽  
Carrying Capacity ◽  
Couple Stress ◽  
Type Equation ◽  
Random Variable ◽  
Couple Stress Fluid ◽  
Load Carrying Capacity ◽  
Porous Structures ◽  
Slider Bearing ◽  
Load Carrying

This paper presents the theoretical study and analyzes the comparison of porous structures on the performance of a couple stress fluid based on rough slider bearing. The globular sphere model of Kozeny-Carman and Irmay’s capillary fissures model have been subjected to investigations. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The stochastically averaged Reynolds type equation has been solved under suitable boundary conditions to obtain the pressure distribution in turn which gives the expression for the load carrying capacity, frictional force and coefficient of friction. The results are illustrated by graphical representations which show that the introduction of combined porous structure with couple stress fluid results in an enhanced load carrying capacity more in the case of Kozeny-Carman model as compared to Irmay’s model.

On the effects of two-dimensional Reynolds roughness in hydrodynamic lubrication

1978 ◽  
Vol 364 (1716) ◽  
pp. 89-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Numerical Computation ◽  
Autocorrelation Function ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
The Other ◽  
Roughness Height ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Dimensional Surface

The hydrodynamic lubrication of rough surfaces is analysed with the Reynolds equation, whose application requires the roughness spacing to be large, and the roughness height to be small, compared with the thick­ness of the fluid film. The general two-dimensional surface roughness is considered, and results applicable to any roughness structure are obtained. It is revealed analytically that two types of term contribute to roughness effects: one depends on the shape of the autocorrelation function and the other does not. The former contribution was neglected by previous workers. The numerical computation of an example shows that these two contributions are comparable in magnitude.

scholarly journals SPH modelling of hydrodynamic lubrication: laminar fluid flow–structure interaction with no-slip conditions for slider bearings

2020 ◽  
Author(s):  
Marco Paggi ◽  
Andrea Amicarelli ◽  
Pietro Lenarda
Keyword(s):  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Flow Direction ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Fluid Films ◽  
Slip Conditions ◽  
Application Fields ◽  
New Research

Abstract The FOSS CFD-SPH code SPHERA v.9.0.0 (RSE SpA) is improved to deal with “fluid–solid body” interactions under no-slip conditions and laminar regimes for the simulation of hydrodynamic lubrication. The code is herein validated in relation to a uniform slider bearing (i.e. for a constant lubricant film depth) and a linear slider bearing (i.e. for a film depth with a linear profile variation along the main flow direction). Validations refer to comparisons with analytical solutions, herein generalized to consider any Dirichlet boundary condition. Further, this study allows a first code validation of the “fluid–fixed frontier” interactions under no-slip conditions. With respect to the most state-of-the-art models (2D codes based on Reynolds’ equation for fluid films), the following distinctive features are highlighted: (1) 3D formulation on all the terms of the Navier–Stokes equations for incompressible fluids with uniform viscosity; (2) validations on both local and global quantities (pressure and velocity profiles; load-bearing capacity); (3) possibility to simulate any 3D topology. This study also shows the advantages of using a CFD-SPH code in simulating the inertia and 3D effects close to the slider edges, and it opens new research directions overcoming the limitations of the codes for hydrodynamic lubrication based on the Reynolds’ equation for fluid films. This study finally allows SPHERA to deal with hydrodynamic lubrication and improves the code for other relevant application fields involving fluid–structure interactions (e.g. transport of solid bodies by floods and earth landslides; rock landslides). SPHERA is developed and distributed on a GitHub public repository.

Hydrodynamic Lubrication of Finite Slider Bearings: Effect of One Dimensional Film Shape, and Their Computer Aided Optimum Designs

1983 ◽  
Vol 105 (1) ◽  
pp. 48-63 ◽  
Author(s):  
C. Bagci ◽  
A. P. Singh
Keyword(s):  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Design Data ◽  
Slider Bearings ◽  
Load Carrying ◽  
Computer Aided

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

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.

Squeeze film behavior in porous transversely circular stepped plates with a couple stress fluid

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Santhana Krishnan Narayanan ◽  
A Chamkha ◽  
Sundarammal Kesavan
Keyword(s):  
Surface Roughness ◽  
Couple Stress ◽  
Design Methodology ◽  
Reynolds Equation ◽  
Closed Form Solution ◽  
Stochastic Theory ◽  
Classical Case ◽  
Form Solution ◽  
Couple Stress Fluid ◽  
Squeeze Film

Purpose The purpose of this work is to carry our a study of the effect of surface roughness on squeeze film behavior between two transversely circular stepped plates with couple stress lubricant when the upper circular stepped plate has porous facing which approaches the lower plate with uniform velocity. Design/methodology/approach The modified Stochastic Reynolds equation is derived for Christensen Stochastic theory for the rough surfaces. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier-Bessel series. Findings It is found that the effect of couple stress fluid and surface roughness is more pronounced compared to classical case. Originality/value The problem is original that it consider a couple stress fluid in this type of applications.

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.

scholarly journals Estimation of Random Friction Forces on the Microbearing Cooperating Surfaces

2019 ◽  
Vol 26 (2) ◽  
pp. 167-174
Author(s):  
Krzysztof Wierzcholski ◽  
Andrzej Miszczak
Keyword(s):  
Dynamic Viscosity ◽  
Apparent Viscosity ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Superficial Layer ◽  
Mathematical Form ◽  
Friction Forces ◽  
Random Roughness ◽  
Load Carrying ◽  
Gap Height

Abstract Presented paper concerns a new mathematical form of stochastic theory of hydrodynamic friction forces occurring on the real cooperating surfaces in computer micro bearing fan and computer microbearing in hard disc driver HDD. This paper presents particularly a new-review of stochastic analytical considerations realized by the authors for friction forces estimation during hydrodynamic lubrication performed on the ground of the measurements of the gap height between two roughness surfaces. After numerous experimental measurements directly follows that the random unsymmetrical increments and decrements of the gap height of computer microbearings have important influence on the load carrying capacities and finally on the friction forces and wear of cooperating surfaces. The main topic demonstrates the influence of the variations of expectancy values and standard deviation of the computer microbearing gap height on the friction forces occurring in the HDD and microbearing fan. Moreover, it is observed the evident connection between the apparent dynamic viscosity and the features of the microbearing superficial surface. Hence after abovementioned remarks follows the corollary that the influence of the microbearing gap height stochastic variations connected with the surface roughness tend moreover indirect from the apparent viscosity into the friction forces variations. The synthetic, complex elaboration of obtained results indicates finally the influence of the random roughness in micro and nano level of microbearing surfaces on the friction forces distribution. A new results contained in this paper are obtained taking into account 3D variations of dynamic viscosity of the non-Newtonian lubricant, particularly variations crosswise the film thickness and influences of surface superficial layer features on the lubricant apparent viscosity.

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