The “Stribeck curve” is a well-known concept, describing the frictional behavior of a lubricated interface during the transition from boundary and mixed lubrication up to full-film hydrodynamic/elastohydrodynamic lubrication. It can be found in nearly every tribology textbook/handbook and many articles and technical papers. However, the majority of the published Stribeck curves are only conceptual without real data from either experiments or numerical solutions. The limited number of published ones with real data is often incomplete, covering only a portion of the entire transition. This is because generating a complete Stribeck curve requires experimental or numerical results in an extremely wide range of operating conditions, which has been a great challenge. Also, numerically calculating a Stribeck curve requires a unified model with robust algorithms that is capable of handling the entire spectrum of lubrication status. In the present study, numerical solutions in counterformal contacts of rough surfaces are obtained by using the unified deterministic mixed elastohydrodynamic lubrication (EHL) model recently developed. Stribeck curves are plotted in a wide range of speed and lubricant film thickness based on the simulation results with various types of contact geometry using machined rough surfaces of different orientations. Surface flash temperature is also analyzed during the friction calculation considering the mutual dependence between friction and interfacial temperature. Obtained results show that in lubricated concentrated contacts, friction continuously decreases as speed and film thickness increase even in the full-film regime until extremely high speeds are reached. This is mainly due to the reduction of lubricant limiting shear stress caused by flash temperature rise. The results also reveal that contact ellipticity and roughness orientation have limited influence on frictional behaviors, especially in the full-film and boundary lubrication regimes.

References

References
1.
Stribeck
,
R.
,
1902
, “
Die Wesentlichen Eigenschaften der Gleit und Rollenlager
,”
Z. Ver. Dtsch. Ing.
,
36
, pp.
1341
1348
; 46, pp. 1432–1438; 46, pp. 1463–1470.
2.
Hersey
,
M. D.
,
1914
, “
The Laws of Lubrication of Horizontal Journal Bearings
,”
J. Washington Acad. Sci.
,
4
, pp.
542
552
.
3.
Luengo
,
G.
,
Israelachvili
,
J.
, and
Granick
,
S.
,
1996
, “
Generalized Effects in Confined Fluids: New Friction Map for Boundary Lubrication
,”
Wear
,
200
(
1–2
), pp.
328
335
.10.1016/S0043-1648(96)07248-1
4.
Crook
,
A. W.
,
1963
, “
The Lubrication of Rollers—IV. Measurements of Friction and Effective Viscosity
,”
Phil. Trans. R. Soc. London A
,
255
(
1056
), pp.
281
312
.10.1098/rsta.1963.0005
5.
Plint
,
M. A.
,
1967–1968
, “
Traction in Elastohydrodynamic Contacts
,”
Proc. Inst. Mech. Eng.
,
182
(
1
), pp.
300
306
.10.1243/PIME_PROC_1967_182_028_02
6.
Johnson
,
K. L.
, and
Cameron
,
R.
,
1967–1968
, “
Shear Behavior of Elastohydrodynamic Oil Films at High Rolling Contact Pressures
,”
Proc. Inst. Mech. Eng.
,
182
(
1
), pp.
307
319
.10.1243/PIME_PROC_1967_182_029_02
7.
Johnson
,
K. L.
, and
Tevaarwerk
,
J. L.
,
1977
, “
Shear Behavior of EHD Oil Films
,”
Proc. Royal Soc., London A
,
356
(1685), pp.
215
236
.10.1098/rspa.1977.0129
8.
Bair
,
S.
, and
Winer
,
W. O.
,
1978
, “
Rheological Response of Lubricants in EHD Contacts
,”
Proceedings of the 5th Leeds-Lyon Symposium on Tribology
, pp.
162
169
.
9.
Zhu
,
D.
,
2013
, “
Elastohydrodynamic Lubrication (EHL)
,”
Encyclopedia of Tribology
,
Q. J.
Wang
and
Y. W.
Chung
, eds.,
Springer Science and Business Media
,
New York
, pp.
874
889
.
10.
Lu
,
X. B.
,
Khonsari
,
M. M.
, and
Gelinck
,
E. R. M.
,
2006
, “
The Stribeck Curve: Experimental Results and Theoretical Prediction
,”
ASME J. Tribol.
,
128
(
4
), pp.
789
794
.10.1115/1.2345406
11.
Wang
,
Y. S.
,
Wang
,
Q.
,
Lin
,
C.
, and
Shi
,
F. H.
,
2006
, “
Development of a Set of Stribeck Curves for Conformal Contacts of Rough Surfaces
,”
Tribol. Trans.
,
49
(
4
), pp.
526
535
.10.1080/10402000600846110
12.
de Kraker
,
A.
,
van Ostayen
,
R. A. J.
, and
Rixen
,
D. J.
,
2007
, “
Calculation of Stribeck Curves for (Water) Lubricated Journal Bearings
,”
Tribol. Int.
,
40
(
3
), pp.
459
469
.10.1016/j.triboint.2006.04.012
13.
Guangteng
,
G.
, and
Spikes
,
H. A.
,
1997
, “
The Control of Friction by Molecular Fractionation of Base Fluid Mixtures at Metal Surfaces
,”
Tribol. Trans.
,
40
(
3
), pp.
461
469
.10.1080/10402009708983681
14.
Zhu
,
D.
, and
Wang
,
Q.
,
2012
, “
On the λ Ratio Range of Mixed Lubrication
,”
Proc. Inst. Mech. Eng., Part J
,
226
(
12
), pp.
1010
1022
.10.1177/1350650112461867
15.
Gelinck
,
E. R. M.
, and
Schipper
,
D. J.
,
2000
, “
Calculation of Stribeck Curves for Line Contacts
,”
Tribol. Int.
,
33
(
3–4
), pp.
175
181
.10.1016/S0301-679X(00)00024-4
16.
Faraon
,
I. C.
, and
Schipper
,
D. J.
,
2007
, “
Stribeck Curves for Starved Line Contacts
,”
ASME J. Tribol.
,
129
(
1
), pp.
181
187
.10.1115/1.2404964
17.
Redlich
,
A. C.
,
Bartel
,
B.
, and
Deters
,
L.
,
2003
, “
Calculation of EHL Contacts in Mixed Lubrication Regime
,” Tribological Research and Design for Engineering Systems,
Proceedings of 29th Leeds-Lyon Symposium on Tribology
,
D.
Dowson
,
M.
Priest
,
G.
Dalmaz
, and
A.
Lubrecht
, eds.,
Elsevier B. V.
, New York, Vol. 41, pp.
537
547
.10.1016/S0167-8922(03)80168-2
18.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London A
,
295
(
1442
), pp.
300
319
.10.1098/rspa.1966.0242
19.
Moes
,
H.
,
1992
, “
Optimum Similarity Analysis with Applications to Elastohydrodynamic Lubrication
,”
Wear
,
159
(
1
), pp.
57
66
.10.1016/0043-1648(92)90286-H
20.
Masjedi
,
M.
, and
Khonsari
,
M. M.
,
2014
, “
Theoretical and Experimental Investigation of Traction Coefficient in Line-Contact EHL of Rough Surfaces
,”
Tribol. Int.
,
70
, pp.
179
189
.10.1016/j.triboint.2013.10.004
21.
Chang
,
L. M.
, and
Jeng
,
Y. R.
,
2014
, “
A Mathematical Model for the Mixed Lubrication of Non-Conformable Contacts With Asperity Friction, Plastic Deformation, Flash Temperature, and Tribo-Chemistry
,”
ASME J. Tribol.
,
136
(
2
), p.
022301
.10.1115/1.4026589
22.
Wang
,
Q.
,
Zhu
,
D.
,
Yu
,
T.
,
Cheng
,
H. S.
,
Jiang
,
J.
, and
Liu
,
S.
,
2004
, “
Mixed Lubrication Analyses by a Micro-Macro Approach and a Full-Scale Micro EHL Model
,”
ASME J. Tribol.
,
126
(
1
), pp.
81
91
.10.1115/1.1631017
23.
Zhu
,
D.
, and
Hu
,
Y. Z.
,
1999
, “
The Study of Transition from Full Film Elastohydrodynamic to Mixed and Boundary Lubrication
,”
The Advanced Frontier of Engineering Tribology
, STLE, pp.
150
156
.
24.
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
25.
Ai
,
X.
,
1993
, “
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods
,” Ph.D. dissertation, Northwestern University, Evanston, IL.
26.
Wang
,
W. Z.
,
Wang
,
H.
,
Liu
,
Y. C.
,
Hu
,
Y. Z.
, and
Zhu
,
D.
,
2003
, “
A Comparative Study of the Methods for Calculation of Surface Elastic Deformation
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
2
), pp.
145
153
.10.1243/13506500360603570
27.
Liu
,
Y. C.
,
Wang
,
Q.
,
Wang
,
W.
,
Hu
,
Y.
, and
Zhu
,
D.
,
2006
, “
Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts
,”
ASME J. Tribol.
,
128
(
3
), pp.
641
653
.10.1115/1.2194916
28.
Zhu
,
D.
,
2007
, “
On Some Aspects in Numerical Solution of Thin-Film and Mixed EHL
,”
Proc. Inst. Mech. Eng., Part J
,
221
(
5
), pp.
561
579
.10.1243/13506501JET259
29.
Wang
,
W. Z.
,
Wang
,
S.
,
Shi
,
F. H.
,
Wang
,
Y. C.
,
Chen
,
H. B.
,
Wang
,
H.
, and
Hu
,
Y. Z.
,
2007
, “
Simulations and Measurements of Sliding Friction Between Rough Surfaces in Point Contacts: From EHL to Boundary Lubrication
,”
ASME J. Tribol.
,
129
(
3
), pp.
495
501
.10.1115/1.2736432
30.
Liu
,
Y. C.
,
Wang
,
Q.
,
Zhu
,
D.
,
Wang
,
W.
, and
Hu
,
Y.
,
2009
Effects of Differential Scheme and Viscosity Model on Rough-Surface Point-Contact Isothermal EHL
,”
ASME J. Tribol.
,
131
(
4
), p.
044501
.10.1115/1.2842245
31.
Wang
,
W. Z.
,
Hu
,
Y. Z.
,
Liu
,
Y. C.
, and
Zhu
,
D.
,
2010
, “
Solution Agreement Between Dry Contacts and Lubrication System at Ultra-Low Speed
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
224
(
10
), pp.
1049
1060
.10.1243/13506501JET774
32.
Zhu
,
D.
, and
Wang
,
Q.
,
2011
, “
Elastohydrodynamic Lubrication (EHL): A Gateway to Interfacial Mechanics―Review and Prospect
,”
ASME J. Tribol.
,
133
(
4
), p.
041001
.10.1115/1.4004457
33.
Zhu
,
D.
, and
Wang
,
Q.
,
2013
, “
Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness
,”
ASME J. Tribol.
,
135
(
3
), p.
031501
.10.1115/1.4023250
34.
Ren
,
N.
,
Zhu
,
D.
,
Chen
,
W. W.
,
Liu
,
Y.
, and
Wang
,
Q. J.
,
2009
, “
A Three-Dimensional Deterministic Model for Rough Surface Line Contact EHL Problems
,”
ASME J. Tribol.
,
131
(
1
), p.
011501
.10.1115/1.2991291
35.
Martini
,
A.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2007
, “
Friction Reduction in Mixed Lubrication
,”
Tribol. Lett.
,
28
(
2
), pp.
139
147
.10.1007/s11249-007-9258-1
36.
Zhu
,
D.
, and
Hu
,
Y. Z.
,
2001
, “
A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3-D Surface Roughness
,”
Tribol. Trans.
,
44
(
3
), pp.
383
390
.10.1080/10402000108982471
37.
Zhu
,
D.
, and
Cheng
,
H. S.
,
1989
, “
An Analysis and Computational Procedure for EHL Film Thickness, Friction and Flash Temperature in Line and Point Contacts
,”
Tribol. Trans.
,
32
(
3
), pp.
364
370
.10.1080/10402008908981901
38.
Liu
,
Y. C.
,
Wang
,
H.
,
Wang
,
W. Z.
,
Hu
,
Y. Z.
, and
Zhu
,
D.
,
2002
, “
Method Comparison in Computation of Temperature Rise on Frictional Interface
,”
Tribol. Int.
,
35
(
8
), pp.
549
560
.10.1016/S0301-679X(02)00062-2
39.
Liu
,
S. B.
,
Wang
,
Q.
, and
Liu
,
G.
,
2000
, “
A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,”
Wear
,
243
(
1–2
), pp.
101
111
.10.1016/S0043-1648(00)00427-0
40.
Chen
,
W. W.
,
Liu
,
S. B.
, and
Wang
,
Q.
,
2008
, “
Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Nominally Flat Surface
,”
ASME J. Appl. Mech.
,
75
(
1
), p.
011022
.10.1115/1.2755158
41.
Zhu
,
D.
,
Liu
,
Y.
, and
Wang
,
Q.
,
2014
, “
On the Numerical Accuracy of Rough Surface EHL Solution
,”
Tribol. Trans.
,
57
(
4
), pp.
570
580
.10.1080/10402004.2014.886349
You do not currently have access to this content.