Micropolarity—Roughness Interaction in Hydrodynamic Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 368-372 ◽  
Author(s):  
J. Prakash ◽  
K. To̸nder ◽  
H. Christensen
Keyword(s):  
Surface Roughness ◽  
Theoretical Analysis ◽  
Micropolar Fluid ◽  
Hydrodynamic Lubrication ◽  
Type Equation ◽  
Pressure Level ◽  
Surface Forces ◽  
Direction Transverse ◽  
One Dimensional ◽  
Fluid Theory

The paper describes a theoretical analysis of micropolarity-roughness interaction. A modified Reynolds’ type equation for a rough surface based on micropolar fluid theory is developed and is applied to the case of a fixed inclined slider, having a one-dimensional roughness pattern in the direction transverse to sliding. The analysis shows that the inclusion of surface roughness in the theory causes an increase in the pressure level, over and above the micropolar level. However, these additional increases are of a smaller order and are not likely to mask the increases caused by additives and surface forces (characterized by micropolarity) as is conjectured by some earlier workers.

The Hydrodynamic Lubrication of Rough Bearing Surfaces of Finite Width

1971 ◽  
Vol 93 (3) ◽  
pp. 324-329 ◽  
Author(s):  
H. Christensen ◽  
K. Tonder
Keyword(s):  
Surface Roughness ◽  
Theoretical Analysis ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Finite Width ◽  
Operational Factors ◽  
Effect Of Surface

The paper describes a theoretical analysis of the effects of surface roughness in a finite width bearing. The analysis is based upon a stochastic theory of hydrodynamic lubrication developed previously. It is shown how the effect of surface roughness on the bearing characteristics is closely tied up with features of nominal geometry as well as with operational factors.

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.

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.

Homogenization of a compressible cavitation model

2015 ◽  
Vol 26 (3) ◽  
pp. 383-399 ◽  
Author(s):  
JOHN FABRICIUS ◽  
AFONSO TSANDZANA ◽  
PETER WALL
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Dimensional Problem ◽  
Cavitation Model ◽  
One Dimensional

We develop a mathematical model in hydrodynamic lubrication that takes into account three phenomena: cavitation, surface roughness and compressibility of the fluid. Like the classical Reynolds equation, the model is mass preserving. We compute the homogenized coefficients in the case of unidirectional roughness. A one-dimensional problem is also solved explicitly.

PHOTOINDUCED NONLINEAR OCTUPOLAR POLARIZATION: TRANSIENT AND PERMANENT REGIMES

1996 ◽  
Vol 05 (04) ◽  
pp. 653-670 ◽  
Author(s):  
CÉLINE FIORINI ◽  
JEAN-MICHEL NUNZI ◽  
FABRICE CHARRA ◽  
IFOR D.W. SAMUEL ◽  
JOSEPH ZYSS
Keyword(s):  
Theoretical Analysis ◽  
Second Harmonic ◽  
Experimental Results ◽  
Polar Field ◽  
Rotational Spectrum ◽  
Dual Frequency ◽  
One Dimensional ◽  
Ethyl Violet ◽  
Disperse Red 1 ◽  
Good Agreement

An original poling method using purely optical means and based on a dual-frequency interference process is presented. We show that the coherent superposition of two beams at fundamental and second-harmonic frequencies results in a polar field with an irreducible rotational spectrum containing both a vector and an octupolar component. This enables the method to be applied even to molecules without a permanent dipole such as octupolar molecules. After a theoretical analysis of the process, we describe different experiments aiming at light-induced noncentrosymmetry performed respectively on one-dimensional Disperse Red 1 and octupolar Ethyl Violet molecules. Macroscopic octupolar patterning of the induced order is demonstrated in both transient and permanent regimes. Experimental results show good agreement with theory.

scholarly journals How Should We Categorize Approaches to the History of Political Thought?

2020 ◽  
Vol 83 (1) ◽  
pp. 91-114
Author(s):  
Adrian Blau
Keyword(s):  
Theoretical Analysis ◽  
Political Theory ◽  
Political Thought ◽  
Two Dimensional ◽  
History Of Political Thought ◽  
One Dimensional ◽  
History Of ◽  
New Framework

AbstractThis paper proposes a new framework for categorizing approaches to the history of political thought. Previous categorizations exclude much research; political theory, if included, is often caricatured. And previous categorizations are one-dimensional, presenting different approaches as alternatives. My framework is two-dimensional, distinguishing six kinds of end (two empirical, four theoretical) and six kinds of means. Importantly, these choices are not alternatives: studies may have more than one end and typically use several means. Studies with different ends often use some of the same means. And all studies straddle the supposed empirical/theoretical “divide.” Quentin Skinner himself expertly combines empirical and theoretical analysis—yet the latter is often overlooked, not least because of Skinner's own methodological pronouncements. This highlights a curious disjuncture in methodological writings, between what they say we do, and what we should do. What we should do is much broader than existing categorizations imply.

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

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.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

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