A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, “A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with experimentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication problems in which the load is mainly carried by the fluid pressure and the total area of asperity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques.

References

References
1.
Bell
,
J. C.
,
Dyson
,
A.
, and
Hadley
,
J. W.
,
1974
, “
The Effects of Rolling and Sliding Speeds on the Scuffing of Lubricated Steel Discs
,”
ASLE Trans.
,
18
, pp.
62
73
.10.1080/05698197508982748
2.
Tomaru
,
M.
,
Hironaka
,
S.
, and
Sakurai
,
T.
,
1977
, “
Effects of Some Chemical Factors on Film Failure Under EP Conditions
,”
Wear
,
41
, pp.
141
155
.10.1016/0043-1648(77)90197-1
3.
Yamanoto
,
Y.
,
1983
, “
The Effect of Surface Hardness of Carbon Steels on Scuffing Resistance in Rolling-Sliding Contacts
,”
Wear
,
89
, pp.
225
234
.10.1016/0043-1648(83)90246-6
4.
Jeng
,
Y. R.
,
1990
, “
Experimental Study of the Effects of Surface Roughness on Friction
,”
Tribol. Trans.
,
33
, pp.
402
410
.10.1080/10402009008981970
5.
Jackson
,
A.
,
Webster
,
M. N.
, and
Enthoven
,
J. C.
,
1994
, “
The Effect of Lubricant Traction on Scuffing
,”
Tribol. Trans.
,
37
, pp.
387
395
.10.1080/10402009408983307
6.
Britton
,
R. D.
,
Elcoate
,
C. D.
,
Alanou
,
M. P.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
2000
, “
Effect of Surface Finish on Gear Tooth Friction
,”
ASME J. Tribol.
,
122
(
1
), pp.
354
360
.10.1115/1.555367
7.
Evans
,
H. P.
,
Snidle
,
R. W.
,
Sharif
,
K. J.
,
Shaw
,
B. A.
, and
Zhang
,
J.
,
2013
, “
Analysis of Micro Elastohydrodynamic Lubrication and Prediction of Surface Fatigue Damage in Micropitting Tests on Helical Gears
,”
ASME J. Tribol.
,
135
(
1
), p.
011501
.10.1115/1.4007693
8.
Hu
,
Y. Z.
and
Zhu
,
D.
,
2000
, “
A Full Numerical Solution to the Mixed Lubrication in Point Contacts
,”
ASME J. Tribol.
,
122
(
1
), pp.
1
9
.10.1115/1.555322
9.
Holms
,
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
.10.1115/1.1828452
10.
Ren
,
N.
,
Zhu
,
D.
,
Chen
,
W. W.
,
Liu
,
Y.
, and
Wang
,
Q. J.
,
2009
, “
A Three-Dimensional Deteministic Model for Rough Surface Line-Contact EHL Problems
,”
ASME J. Tribol.
,
131
(
1
), p.
011501
.10.1115/1.2991291
11.
Zhu
,
D.
and
Wang
,
Q. J.
,
2013
, “
Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness
,”
ASME J. Tribol.
,
135
(
3
), p.
031501
.10.1115/1.4023250
12.
Li
,
S.
,
Kahraman
,
A.
,
Anderson
,
N.
, and
Wedeven
,
L. D.
,
2013
, “
A Model to Predict Scuffing Failures of a Ball-on-Disk Contact
,”
Tribol. Int.
,
60
, pp.
233
245
.10.1016/j.triboint.2012.11.007
13.
Ren
,
N.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2011
, “
Three-Dimensional Plasto-Elastohydrodynamic Lubrication (PEHL) for Surfaces With Irregularities
,”
ASME J. Tribol.
,
133
(
3
), p.
031502
.10.1115/1.4004100
14.
Johnson
,
K. L.
,
Greenwood
,
J. A.
, and
Poon
,
S. Y.
,
1972
, “
A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication
,”
Wear
,
19
, pp.
91
108
.10.1016/0043-1648(72)90445-0
15.
Gelink
,
E.
and
Schipper
,
D.
,
2000
, “
Calculation of Stribeck Curves for Line Contacts
,”
Tribol. Int.
,
33
, pp.
175
181
.10.1016/S0301-679X(00)00024-4
16.
Akbarzadeh
,
S.
and
Khonsari
,
M. M.
,
2008
, “
Performance of Spur Gears Considering Surface Roughness and Shear Thinning Lubricant
,”
ASME J. Tribol.
,
130
(
2
), p.
021503
.10.1115/1.2805431
17.
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
.10.1115/1.1490373
18.
Zhao
,
Y.
,
Maietta
,
D. M.
, and
Chang
,
L.
,
2000
, “
An Asperity Micro-Contact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow
,”
ASME J. Tribol.
,
122
(
1
), pp.
86
93
.10.1115/1.555332
19.
Chang
,
L.
and
Zhang
,
H.
,
2007
, “
A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient
,”
ASME J. Appl. Mech.
,
74
(
1
), pp.
100
106
.10.1115/1.2178838
20.
Chang
,
L.
and
Zhang
,
H.
,
2012
, “
Modeling and Parametric Study of Fatty Acids Boundary Lubrication in Nominally Flat Contacts of Metallic Surfaces
,”
Tribol. Trans.
,
55
, pp.
376
386
.10.1080/10402004.2012.661523
21.
Chang
,
L.
,
Webster
,
M. N.
, and
Jackson
,
A.
,
1993
, “
On the Pressure Rippling and Roughness Deformation in Elastohydrodynamic Lubrication of Rough Surfaces
,”
ASME J. Tribol.
,
115
(
3
), pp.
439
444
.10.1115/1.2921656
22.
Chang
,
L.
and
Zhao
,
W.
,
1995
, “
Wavelength Dependence of Micro-EHL Pressure Rippling With Random Surface-Roughness Profiles
,”
Tribol. Trans.
,
38
, pp.
389
395
.10.1080/10402009508983419
23.
Dowson
,
D.
and
Toyoda
,
S.
,
1977
, “
A Central Film Thickness Formula for Elastohydrodynamic Line Contacts
,”
Proceedings of the 5th Leads/Lyon Symposium
, pp.
60
67
.
24.
Greenwood
,
J. A.
and
Kauzlarich
,
J. J.
,
1973
Inlet Shear Heating in Elastohydrodynamic Lubrication (Discussion by K. L. Johnson)
,”
ASME J. Lubr. Technol.
,
95
(
4
), pp.
417
425
.10.1115/1.3451844
25.
Johnson
,
K. L.
and
Tevaarwerk
,
J. L.
,
1977
, “
Shear Behavior of Elastohydrodynamic Oil Films
,”
Proc. R. Soc. London, Ser. A
,
356
, pp.
215
236
.10.1098/rspa.1977.0129
26.
Khonsari
,
M. M.
and
Booser
,
E. R.
,
2008
,
Applied Tribology
,
2nd ed.
,
John Wiley and Sons
,
West Sussex, UK
.
27.
Chang
,
L.
,
2006
, “
A Parametric Analysis of Thermal Shear Localization in Elastohydrodynamic Lubrication Films
,”
ASME J. Tribol.
,
128
(
1
), pp.
79
84
.10.1115/1.2125968
28.
Chang
,
L.
,
Jeng
,
Y. R.
, and
Huang
,
P. Y.
,
2013
, “
Modeling and Analysis of the Meshing Losses of Involute Spur Gears in High-Speed and High-Load Conditions
,”
ASME J. Tribol.
,
135
(
1
), p.
011504
.10.1115/1.4007809
29.
Greenwood
,
J. A.
and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
295
, pp.
300
319
.10.1098/rspa.1966.0242
30.
Tian
,
X.
and
Kennedy
,
F. E.
,
1994
, “
Maximum and Average Flash Temperatures in Sliding Contacts
,”
ASME J. Tribol.
,
116
(
1
), pp.
167
174
.10.1115/1.2927035
31.
Tabor
,
D.
,
1981
, “
Friction—The Present State of Our Understanding
,”
ASME J. Lubr. Techno.
,
103
(
2
), pp.
169
179
.10.1115/1.3251622
32.
Bowden
,
F. P.
and
Tabor
,
D.
,
1954
,
The Friction and Lubrication of Solids
, Part I,
Oxford University Press
,
London
.
33.
Ludema
,
K.
,
1984
, “
A Review of Scuffing and Running-in of Lubricated Surfaces, With Asperities and Oxides in Perspective
,”
Wear
,
100
, pp.
315
331
.10.1016/0043-1648(84)90019-X
34.
Hirst
,
W.
,
1974
, “
Scuffing and Its Prevention
,”
Chart. Mech. Eng.
,
21
, pp.
88
92
.
35.
Hirst
,
W.
and
Hollander
,
A. E.
,
1974
, “
Surface Finish and Damage in Sliding
,”
Proc. R. Soc. London, Ser. A.
,
337
, pp.
379
394
.10.1098/rspa.1974.0056
36.
Hiratsuka
,
K.
and
Kajdas
,
C.
,
2013
, “
Mechanochemistry as a Key to Understanding the Mechanisms of Boundary Lubrication, Mechnolysis and Gas Evolution During Friction
,”
Proc. Inst. Mech. Eng., Part J
,
227
, pp. 1191–1203.
37.
Johnson
,
K. L.
,
Contact Mechanics
,
1985
,
Cambridge University Press
,
Cambridge, UK
.
38.
Zhang
,
H.
,
Chang
,
L.
,
Webster
,
M. N.
, and
Jackson
,
A.
,
2003
, “
Effects of Friction on the Contact and Deformation Behavior in Sliding Asperity Contacts
,”
Tribol. Trans.
,
46
, pp.
514
521
.10.1080/10402000308982658
39.
Tabor
,
D.
,
1959
, “
Junction Growth in Metallic Friction: the Role of Combined Stresses and Surface Contamination
,”
Proc. R. Soc. London, Ser. A.
,
251
, pp.
378
393
.10.1098/rspa.1959.0114
40.
Kayaba
,
T.
and
Kato
,
K.
,
1978
, “
Theoretical Analysis of Junction Growth
,”
Technol. Rep. Tohoku Univ.
,
43
, pp.
1
10
.
41.
McCool
,
J. I.
,
1986
, “
Comparison of Models for the Contact of Rough Surfaces
,”
Wear
,
107
, pp.
37
60
.10.1016/0043-1648(86)90045-1
42.
Nayak
,
P. R.
,
1971
, “
Random Process Model of Rough Surface
,”
ASME J. Lubr. Technol.
,
93
(
3
), pp.
398
407
.10.1115/1.3451608
43.
Chang
,
L.
,
2009
, “
Determination of the Sampling Interval in Surface Roughness Measurements With Implications to Engineering Tribo-Surface Characterization and Evaluation
,”
Proc. Inst. Mech. Eng., Part J
,
223
, pp.
675
681
.10.1243/13506501JET466
44.
Bell
,
J. C.
and
Dyson
,
A.
,
1972
, “
The Effect of Some Operating Factors on the Scuffing of Hardened Steel Disks
,”
Proceedings of the Institution of Mechanical Engineers, Symposium on EHL
, Paper No. C11/72, pp.
61
72
.
45.
Chang
,
L.
,
Hall
,
P. B.
,
Thom
,
R.
,
Zhao
,
Y.
, and
Moore
,
C.
,
2000
, “
On Heat Generation in Rolling Contacts Under Boundary and Mixed Lubrication
,”
ASME J. Tribol.
,
123
(
1
), pp.
61
66
.10.1115/1.1330733
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