Different averaging techniques have proved to be useful for analyzing the effects of surface roughness in hydrodynamic lubrication. This paper compares two of these averaging techniques, namely the flow factor method by Patir and Cheng (P&C) and homogenization. It has been rigorously proved by many authors that the homogenization method provides a correct solution for arbitrary roughness. In this work it is shown that the two methods coincide if and only if the roughness exhibits certain symmetries. Hence, homogenization is always the preferred method.

References

1.
Almqvist
,
T.
, and
Larsson
,
R.
, 2004, “
Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale
,”
J. Tribol.
,
126
(
4
), pp.
703
710
.
2.
Cioranescu
,
D.
, and
Donato
,
P.
, 1999,
An Introduction to Homogenization, of Oxford Lecture Series in Mathematics and its Applications
,
Clarendon, Oxford, Oxford University
,
New York
,
Vol. 17
.
3.
Patir
,
N.
, and
Cheng
,
H. S.
, 1978 “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
Trans. ASME, J. Tribol.
,
100
, pp.
12
17
.
4.
Patir
,
N.
, and
Cheng
,
H. S.
, 1979, “
Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces
,”
Trans. ASME, J. Tribol.
,
101
, pp.
220
230
.
5.
Bayada
,
G.
, and
Faure
,
J.
, 1989, “
A Double Scale Analysis Approach of the Reynolds Roughness; Comments and Application to the Journal Bearing
,”
Trans. ASME, J. Tribol.
,
111
(
2
), pp.
323
330
.
6.
Almqvist
,
A.
,
Larsson
,
R.
, and
Wall
,
P.
, 2007, “
The Homogenization Process of the Time Dependent Reynolds Equation Describing Compressible Liquid Flow
,”
Tribol. – Finn. J. Tribol.
,
26
(
4
), pp.
30
44
.
7.
Bayada
,
G.
,
Ciuperca
,
I.
, and
Jai
,
M.
, 2006, “
Homogenized Elliptic Equations and Variational Inequalities with Oscillating Parameters. Application to the Study of Thin Flow Behavior With Rough Surfaces
,”
Nonlinear Anal.: Real World Appl.
,
7
(
5
), pp.
950
966
.
8.
Kane
,
M.
, and Bou-
Said
,
B.
, 2004, “
Comparison of Homogenization and Direct Techniques for the Treatment of Roughness in Incompressible Lubrication
,”
Trans. ASME, J. Tribol.
,
126
(
4
), pp.
733
737
.
9.
Kane
,
M.
, and Bou-
Said
,
B.
, 2005, “
A Study of Roughness and Non-Newtonian Effects in Lubricated Contacts
,”
Trans. ASME, J. Tribol.
,
127
, pp.
575
581
.
10.
Martin
,
S.
, 2008, “
Influence of Multiscale Roughness Patterns in Cavitated Flows: Applications to Journal Bearings
,”
Math. Probl. Eng.
,
2008
, pp.
1
26
.
11.
Almqvist
,
A.
,
Essel
,
E. K.
,
Fabricius
,
J.
, and
Wall
,
P.
, 2008, “
Reiterated Homogenization Applied in Hydrodynamic lubrication
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
222
(
7
), pp.
827
841
.
12.
Almqvist
,
A.
,
Essel
,
E. K.
, Persson, L.-E., and
Wall
,
P.
, 2007, “
Homogenization of the Unstationary Incompressible Reynolds Equation
,”
Tribol. Int.
,
40
(
9
), pp.
1344
1350
.
13.
Almqvist
,
A.
, and
Dasht
,
J.
, 2006, “
The Homogenization Process of the Reynolds Equation Describing Compressible Liquid Flow
,”
Tribol. Int.
,
39
(
9
), pp.
994
1002
.
14.
Sahlin
,
F.
,
Larsson
,
R.
,
Marklund
,
P.
,
Lugt
,
P. M.
, and
Almqvist
,
A.
, 2010, “
A Mixed Lubrication Model Incorporating Measured Surface Topography. Part 1: Theory of Flow Factors
,”
Proc. Inst. Mech. Eng., Part J:J. Eng. Tribol.
,
224
(
4
), pp.
335
351
.
15.
Sahlin
,
F.
,
Larsson
,
R.
,
Marklund
,
P.
,
Lugt
,
P. M.
, and
Almqvist
,
A.
, 2010, “
A Mixed Lubrication Model Incorporating Measured Surface Topography. Part 2: Roughness Treatment, Model Validation, and Simulation
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
224
(
4
), pp.
353
365
.
16.
Tripp
,
J. H.
, 1983, “
Surface Roughness Effects in Hydrodynamic Lubrication: The Flow Factor Method
,”
Trans. ASME, J. Tribol.
,
105
(
3
), pp.
458
465
.
17.
Lunde
,
L.
, and
Tonder
,
K.
, 1997, “
Pressure and Shear Flow in a Rough Hydrodynamic Bearing Flow Factor Calculation
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
119
(
3
), pp.
549
555
.
18.
Harp
,
S. R.
, and
Salant
,
R. F.
, 2001, “
An Average Flow Model of Rough Surface Lubrication With Inter-Asperity Cavitation
,”
Trans. ASME, J. Tribol.
,
123
(
1
), pp.
134
143
.
19.
Kim
,
T. W.
, and
Cho
,
Y. J.
, 2008, “
The Flow Factors Considering the Elastic Deformation for the Rough Surface with a Non-Gaussian Height Distribution
,”
Tribol. Trans.
,
51
(
2
), pp.
213
220
.
20.
Meng
,
F.
,
Wang
,
Q. J.
,
Hua
,
D.
, and
Liu
,
S.
, 2010, “
A Simple Method to Calculate Contact Factor used in Average Flow Model
,”
Trans. ASME, J. Tribol.
,
132
(
2
), p
p.
024505
.
21.
Reynolds
,
O.
, 1886, “
On the Theory of Lubrication and Its Application to Mr. Beauchamps Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,”
Philos. Trans. R. Soc. London A
,
177
, pp.
157
234
.
22.
Hamrock
,
B. J.
, 1994,
Fundamentals of Fluid Film Lubrication
,
McGraw-Hill
,
New York
.
23.
Almqvist
,
A.
, 2009,
On the Effects of Roughness in Lubrication
,
Lambert Academic Publishing
, Saarbrücken.
You do not currently have access to this content.