Combining the contact model of elastic-layered solid with the concept of asperity contact in elastohydrodynamic lubrication (EHL), a mixed-lubrication model is presented to predict friction coefficient over rough surfaces with/without an elastic-layered medium under entire lubrication regimes. Solution of contact problems for elastic-layered solids is presented based upon the classical model of Greenwood and Williamson (GW) in conjunction with Chen and Engel's analysis. The effects of the Young's modulus ratio of the layer to substrate and the thickness of the layer on the elastic real area of contact and contact load for a fixed dimensionless separation are studied using the proposed method, which is used for the asperities having contact with an elastic coating. Coefficient of friction with elastic-layered solids in boundary lubrication is calculated in terms of Rabinowicz's findings and elastic-layered solutions of Gupta and Walowit. The effect of rough contacts with an elastic layer on friction coefficient in lubrication regimes has been analyzed. Variations in plasticity index ψ significantly affect friction coefficients in boundary and mixed lubrications. For a large value of ψ, the degree of plastic contact exhibits a stronger dependence of the mean separation or film thickness than the roughness, and for a small value of ψ, the opposite result is true. The effect of governing parameters, such as inlet oil viscosity at ambient pressure, pressure–viscosity coefficient, combined surface roughness, and El/E2 on friction coefficient, has been investigated. Simulations are shown to be in good agreement with the experimental friction data.

References

References
1.
Holmes
,
M. J. A.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
2005
, “
Analysis of Mixed Lubrication Effects in Simulated Gear Tooth Contacts
,”
ASME J. Tribol.
,
127
(
1
), pp.
61
69
.
2.
Johnson
,
K. L.
,
Greenwood
,
J. A.
, and
Poon
,
S. Y.
,
1972
, “
A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication
,”
Wear
,
19
(
1
), pp.
91
108
.
3.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. (London), Ser. A
,
295
(
1442
), pp.
300
319
.
4.
Gelinck
,
E. R. M.
, and
Schipper
,
D. J.
,
2000
, “
Calculation of Stribeck Curves for Line Contacts
,”
Tribol. Int.
,
33
(3–4), pp.
175
181
.
5.
Liu
,
Z.
,
Sun
,
J.
, and
Shen
,
W. D.
,
2002
, “
Friction of Lubricated Layered Surfaces
,”
STLE Tribol. Trans.
,
45
(
2
), pp.
153
160
.
6.
Akbarzadeh
,
S.
, and
Khonsari
,
M. M.
,
2010
, “
On the Prediction of Running-In Behavior in Mixed-Lubrication Line Contact
,”
ASME J. Tribol.
,
132
(
3
), p.
032102
.
7.
Akbarzadeh
,
S.
, and
Khonsari
,
M. M.
,
2013
, “
On the Optimization of Running-In Operating Conditions in Applications Involving EHL Line Contact
,”
Wear
,
303
(1–2), pp.
130
137
.
8.
Sojoudi
,
H.
, and
Khonsari
,
M. M.
,
2010
, “
On the Behavior of Friction in Lubricated Point Contact With Provision for Surface Roughness
,”
ASME J. Tribol.
,
132
(
1
), p.
012102
.
9.
Masjedi
,
M.
, and
Khonsari
,
M. M.
,
2012
, “
Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness
,”
ASME J. Tribol.
,
134
(
1
), p.
011503
.
10.
Masjedi
,
M.
, and
Khonsari
,
M. M.
,
2014
, “
Theoretical and Experimental Investigation of Traction Coefficient in Line-Contact EHL of Rough Surfaces
,”
Tribol. Int.
,
70
(2), pp.
179
189
.
11.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1987
, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
ASME J. Tribol.
,
109
(
2
), pp.
257
263
.
12.
Kogut
,
L.
, and
Etsion
,
I.
,
2002
, “
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
,”
ASME J. Appl. Mech.
,
69
(
5
), pp.
657
662
.
13.
Jackson
,
R. L.
, and
Green
,
I.
,
2005
, “
A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat
,”
ASME J. Tribol.
,
127
(
2
), pp.
343
354
.
14.
Beheshti
,
A.
, and
Khonsari
,
M. M.
,
2014
, “
On the Contact of Curved Rough Surfaces: Contact Behavior and Predictive Formulas
,”
ASME J. Appl. Mech.
,
81
(
11
), p.
111004
.
15.
Bush
,
A. W.
,
Gibson
,
R. D.
, and
Keogh
,
G. P.
,
1976
, “
The Limit of Elastic Deformation in the Contact of Rough Surfaces
,”
Mech. Res. Commun.
,
3
(
3
), pp.
169
174
.
16.
McCool
,
J. I.
,
1988
, “
The Distribution of Microcontact Area, Load, Pressure, and Flash Temperature Under the Greenwood-Williamson Model
,”
ASME J. Tribol.
,
110
(
1
), pp.
106
111
.
17.
Chen
,
W.
, and
Engel
,
P.
,
1972
, “
Impact and Contact Stress Analysis in Multilayer Media
,”
Int. J. Solids Struct.
,
8
(
11
), pp.
1257
1281
.
18.
McCool
,
J. I.
,
2000
, “
Extending the Capability of the Greenwood Williamson Microcontact Model
,”
ASME J. Tribol.
,
122
(
3
), pp.
496
502
.
19.
Komvopoulos
,
K.
,
Saka
,
N.
, and
Suh
,
N. P.
,
1985
, “
The Mechanism of Friction in Boundary Lubrication
,”
ASME J. Tribol.
,
107
(
4
), pp.
452
462
.
20.
Komvopoulos
,
K.
,
Saka
,
N.
, and
Suh
,
N. P.
,
1986
, “
The Significance of Oxide Layers in Boundary Lubrication
,”
ASME J. Tribol.
,
108
(
4
), pp.
502
513
.
21.
Komvopoulos
,
K.
,
Saka
,
N.
, and
Suh
,
N. P.
,
1987
, “
The Role of Hard Layers in Lubricated and Dry Sliding
,”
ASME J. Tribol.
,
109
(
2
), pp.
223
231
.
22.
Liu
,
Z.
,
Hua
,
M.
, and
Reuben
,
R. L.
,
1999
, “
Three-Dimensional Contact Model for Numerically Analyzing Pressure Distribution in Wear
,”
Tribol. Lett.
,
7
(
4
), pp.
183
197
.
23.
Jacobson
,
B. O.
,
1991
,
Rheology and Elastohydrodynamic Lubrication
(Tribology Series), Vol.
19
,
Elsevier
,
Amsterdam, The Netherlands
, pp.
1
380
.
24.
Bair
,
S.
, and
Winer
,
W. O.
,
1982
, “
Some Observations in High Pressure Rheology of Lubricants
,”
ASME J. Lubr. Technol.
,
104
(
3
), pp.
357
364
.
25.
Dowson
,
D.
,
1995
, “
Elastohydrodynamic and Micro-Elastohydrodynamic Lubrication
,”
Wear
,
190
(
2
), pp.
125
138
.
26.
Rabinowicz
,
E.
,
1980
, “
Friction-Especially Low Friction
,”
Fundamentals of Tribology
,
N. P.
Suh
and
N.
Saka
, eds.,
The MIT Press
,
Cambridge, MA
, pp.
351
364
.
27.
Nijenbanning
,
G.
,
Venner
,
C. H.
, and
Moes
,
H.
,
1994
, “
Film Thickness in Elastohydrodynamically Lubricated Elliptic
,”
Wear
,
176
(
2
), pp.
217
229
.
28.
Khonsari
,
M. M.
, and
Booser
,
E. R.
,
2008
,
Applied Tribology
,
2nd ed.
,
Wiley
,
West Sussex, UK
.
29.
Lubrecht
,
A. A.
,
Ten Napel
,
W. E.
, and
Bosma
,
R.
,
1988
, “
The Influence of Longitudinal and Transverse Roughness on the Elastohydrodynamic Lubrication of Circular Contacts
,”
ASME J. Tribol.
,
110
(
3
), pp.
421
446
.
30.
Schipper
,
D. J.
,
Vroegop
,
P. H.
,
de Gee
,
A. W. J.
, and
Bosma
,
R.
,
1990
, “
Micro-EHL in Lubricated Concentrated Contacts
,”
ASME J. Tribol.
,
112
(
2
), pp.
392
397
.
31.
Hoglund
,
E.
,
1999
, “
Influence of Lubricant Properties on Elastohydrodynamic Lubrication
,”
Wear
,
232
(
2
), pp.
176
184
.
32.
Komvopoulos
,
K.
,
1991
, “
Sliding Friction Mechanisms of Boundary-Lubricated Layered Surfaces—Part II: Theoretical Analysis
,”
STLE Tribol. Trans.
,
34
(
2
), pp.
281
291
.
33.
Dawson
,
P. H.
,
1962
, “
Effect of Metallic Contact on the Pitting of Lubricated Rolling Surfaces
,”
J. Mech. Eng. Sci.
,
4
(
1
), pp.
16
21
.
34.
Johnson
,
K. L.
, and
Tevaarwerk
,
J. L.
,
1977
, “
Shear Behavior of Elastohydrodynamic Oil Film
,”
Proc. R. Soc. (London), Ser. A
,
356
(
1685
), pp.
215
236
.
35.
Whitehouse
,
D. J.
, and
Archard
,
J. F.
,
1970
, “
The Properties of Random Surfaces of Significance in Their Contact
,”
Proc. R. Soc. (London), Ser. A
,
316
(
1524
), pp.
97
121
.
36.
Gupta
,
P. K.
, and
Walowit
,
J. A.
,
1974
, “
Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid
,”
ASME J. Lubr. Technol.
,
96
(
2
), pp.
250
257
.
37.
Roelands
,
C. J. R.
,
1966
, “Correlation Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils,” Ph.D. thesis, Technical University of Delft, Delft, The Netherlands.
You do not currently have access to this content.