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.
Issue Section:
Hydrodynamic Lubrication
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
), pp.
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. Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.