This article is concerned with the simulation of a lubricated contact considering the fluid to be non-Newtonian of the Maxwell type. Severe operating conditions lead to very small surface-to-surface distances. In this situation it is necessary to take roughness effects into account. A popular method consists in averaging the film thickness following Patir and Cheng (ASME J. Lubr. Technol., 100, pp. 12–17, 1978), or more recently Wang et al. (Tribol. Trans., 45(1), pp. 1–10, 2000), with good reported results compared with experimental data. To overcome certain limitations that become apparent at very small film thickness, notably when the roughness is two-dimensional, in 1995 Jai (Math. Modell. Numer. Anal., 29(2), pp. 199–233, 1995) introduced a new technique based on a rigorous homogenization theory in the case of compressible fluid flow. This procedure was further mathematically developed by Buscaglia and Jai (Math. Probl. Eng., 7(4), pp. 355–377, 2001) and applied to tribological problems by Jai and Bou-Saı¨d (ASME J. Tribol., 124, pp. 327–355, 2002). In this paper, we propose a similar homogenized approach in the case of non-Newtonian fluids to avoid numerical problems which are often encountered in other approaches. Results in the homogenized roughness case are obtained and compared with direct numerical solutions.

1.
Elrod
,
H. G.
,
1979
, “
A general theory for laminar lubrication with Reynolds Roughness
,”
ASME J. Lubr. Technol.
,
101
, pp.
2
9
.
2.
Tichy, J., and Bou-Saı¨d, B., “On the transition from Reynolds to stokes equation,” Proceedings of the Leeds-Lyon symposium, to be published.
3.
Bushan, B., 1990, Tribology and Mechanics of Magnetic Storage Devices, Springer Verlag New York.
4.
Patir
,
N.
, and
Cheng
,
H. S.
,
1978
, “
An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication
,”
ASME J. Lubr. Technol.
,
100
, pp.
12
17
.
5.
Bushan
,
B.
, and
Tonder
,
K.
,
1989
, “
Roughness-induced shear and squeeze film effects in magnetic recording. Part. ii. Applications
,”
ASME J. Tribol.
,
111
, pp.
228
237
.
6.
Christensen, H., and Tonder, K., 1969 “Tribology of rough surfaces, stochastic models of hydrodynamic lubrication,” Technical Report, SINETF Report N 10/69-18, University of Tronhein, Norway.
7.
Mitsuya
,
Y.
, and
Fukui
,
S.
,
1986
, “
Stokes roughness effects on hydrodynamic lubrication, Part. i. comparison between incompressible and compressible lubricating films
,”
ASME J. Tribol.
,
108
, pp.
151
158
.
8.
Patir
,
N.
, and
Cheng
,
H. S.
,
1979
, “
Application of average flow model to lubrication between rough sliding surfaces
,”
ASME J. Tribol.
,
101
, pp.
220
230
.
9.
Mitsuya
,
Y.
,
Ohkybo
,
T.
, and
Ota
,
H.
,
1989
, “
Averaged Reynolds equation extended to gas lubricant possessing surface roughness in the slip flow regime: Approximate method and confirmation experiments
,”
ASME J. Tribol.
,
111
, pp.
495
503
.
10.
Bushan
,
B.
,
1992
, “
Magnetic slider/rigid disk substrate materials and disk texturing techniques—status and future outlook
,”
Adv. Inf. Storage Syst.
,
5
, pp.
175
209
.
11.
Najji
,
B.
,
Bou-Saı¨d
,
B.
, and
Berthe
,
D.
,
1989
, “
New formulation for lubrication with non-newtonian fluids
,”
ASME J. Tribol.
,
111
(
1
), p.
29
29
.
12.
Bou-Saı¨d, B., 1993, “Habilitation a` diriger des recherches, spe´cialite´ Me´canique,” Institut Nationale des Sciences Applique´es de Lyon, Universite´ Claude Bernard, Lyon 1.
13.
Najji, B., 1989, “Effets Non-Newtonien dans les paliers: Etudes statique et dynamique par e´le´ments finis,” The`se de doctorat d’e`s science, Ecole Mohammedia D’inge´nieurs, Universite´ Mohammed 5.
14.
Jaı¨
,
M.
,
1995
, “
Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface
,”
Math. Modell. Numer. Anal.
,
29
(
2
), pp.
199
233
.
15.
Buscaglia
,
G.
, and
Jaı¨
,
M.
,
2001
, “
A new numerical scheme for non uniform homogenized problems: Application to the non linear Reynolds compressible equation
,”
Math. Probl. Eng.
,
7
(
4
), pp.
355
377
.
16.
Jaı¨
,
M.
, and
Bou-Saı¨d
,
B.
,
2002
, “
A comparison of homogenization and averaging techniques for treatment of roughness in Boltzmann flow modified Reynolds equation
,”
ASME J. Tribol.
,
124
, pp.
327
355
.
17.
Kane, M., 2003, “Contribution a` l’e´tude de l’influence de la rugosite´ et des effets non-newtonien dans les contact se´ve`res lubrifies,” The`se de doctorat, Institut Nationale des Sciences Applique´es de Lyon.
18.
Wang
,
P.
,
Keith
,
T. G.
, and
Vaidyanathan
,
K.
,
2000
, “
Combined surface roughness pattern and non-Newtonian effects on the performance of dynamically loaded journal bearings
,”
Tribol. Trans.
,
45
(
1
), pp.
1
10
.
You do not currently have access to this content.