The Stribeck curve is an important means to demonstrate the frictional behavior of a lubricated interface during the entire transition from boundary and mixed to full-film lubrication. In the present study, a new test apparatus has been built that can operate under rolling–sliding conditions at a continuously variable speed in an extremely wide range, approximately from 0.00006 to 60 m/s, covering six orders of magnitude. Hence, a complete Stribeck curve can be measured to reveal its basic characteristics for lubricated counterformal contacts. The measured curves are compared with numerical simulation results obtained from an available unified mixed elastohydrodynamic lubrication (EHL) model that is also capable of handling cases during the entire transition. A modified empirical model for the limiting shear stress of lubricant is obtained, and a good agreement between the measured and calculated Stribeck curves is achieved for the tested base oils in all the three lubrication regimes, which thus well validates the simulation methods employed. Both the experimental and numerical results indicate that the Stribeck curves for counterformal contact interfaces behave differently from those for conformal contacts. When the rolling speed increases at a fixed slide-to-roll ratio, the friction continuously decreases even in the full-film lubrication regime due to the reduction of the lubricant limiting shear stress caused mainly by the rise of the surface flash temperature. In addition, the test results indicate that the boundary additives in a commodity lubricant may have considerable influence on the boundary lubrication friction but that on the friction in the mixed and full-film lubrication appears to be limited.

References

References
1.
Stribeck
,
R.
,
1902
, “
Die Wesentlichen Eigenschaften der Gleit und Rollenlager, Part 1
,”
Z. Ver. Dtsch. Ing.
,
46
(37), pp.
1341
1348
.
2.
Stribeck
,
R.
,
1902
, “
Die Wesentlichen Eigenschaften der Gleit und Rollenlager, Part 2
,”
Z. Ver. Dtsch. Ing.
,
46
(38), pp.
1432
1438
.
3.
Stribeck
,
R.
,
1902
, “
Die Wesentlichen Eigenschaften der Gleit und Rollenlager, Part 3
,”
Z. Ver. Dtsch. Ing.
,
46
(39), pp.
1463
1470
.
4.
Hersey
,
M. D.
,
1914
, “
The Laws of Lubrication of Horizontal Journal Bearings
,”
J. Wash. Acad. Sci.
,
4
, pp.
542
552
.
5.
Luengo
,
G.
,
Israelachvili
,
J.
, and
Granick
,
S.
,
2002
, “
Generalized Effects in Confined Fluids: New Friction Map for Boundary Lubrication
,”
Wear
,
200
(
1–2
)., pp.
328
335
.
6.
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
.
7.
Crook
,
A. W.
,
1963
, “
The Lubrication of Rollers—IV. Measurements of Friction and Effective Viscosity
,”
Philos. Trans. R. Soc., London A
,
255
(
1056
), pp.
281
312
.
8.
Plint
,
M. A.
,
1967–1968
, “
Traction in Elastohydrodynamic Contacts
,”
Proc. Inst. Mech. Eng.
,
182
(
1967
), pp.
300
306
.
9.
Johnson
,
K. L.
, and
Cameron
,
R.
,
1967–1968
, “
Shear Behavior of Elastohydrodynamic Oil Films at High Rolling Contact Pressures
,”
Proc. Inst. Mech. Eng.
,
182
(
1967
), pp.
307
319
.
10.
Johnson
,
K. L.
, and
Tevaarwerk
,
J. L.
,
1977
, “
Shear Behavior of EHD Oil Films
,”
Proc. R. Soc. London, Ser. A
,
356
(
1685
), pp.
215
236
.
11.
Bair
,
S.
, and
Winer
,
W. O.
,
1978
, “
Rheological Response of Lubricants in EHD Contacts
,”
5th Leeds-Lyon Symposium on Tribology
, pp.
162
169
.
12.
Zhu
,
D.
,
2013
, “
Elastohydrodynamic Lubrication (EHL)
,”
Encyclopedia of Tribology
,
Q. J.
Wang
and
Y. W.
Chung
, eds.,
Springer Science+Business Media
,
New York
, pp.
874
889
.
13.
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
.
14.
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
.
15.
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
.
16.
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
.
17.
Gelinck
,
E. R. M.
, and
Schipper
,
D. J.
,
2000
, “
Calculation of Stribeck Curves for Line Contacts
,”
Tribol. Int.
,
33
(3–4), pp.
175
181
.
18.
Faraon
,
I. C.
, and
Schipper
,
D. J.
,
2007
, “
Stribeck Curves for Starved Line Contacts
,”
ASME J. Tribol.
,
129
(
1
), pp.
181
187
.
19.
Redlich
,
A. C.
,
Bartel
,
B.
, and
Deters
,
L.
,
2003
, “
Calculation of EHL Contacts in Mixed Lubrication Regime
,”
Tribol. Ser.
,
41
, pp.
537
547
.
20.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Philos. Trans. R. Soc. London, Ser. A
,
295
(
1442
), pp.
300
319
.
21.
Moes
,
H.
,
1992
, “
Optimum Similarity Analysis With Applications to Elastohydrodynamic Lubrication
,”
Wear
,
159
(
1
), pp.
57
66
.
22.
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
.
23.
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
.
24.
Björling
,
M.
,
Habchi
,
W.
,
Bair
,
S.
,
Larsson
,
R.
, and
Marklund
,
P.
,
2013
, “
Towards the True Prediction of EHL Friction
,”
Tribol. Int.
,
66
, pp.
19
26
.
25.
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
.
26.
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, Proceedings of the 199 STLE/ASME H.S. Cheng Tribology Surveillance, pp.
150
156
.
27.
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
.
28.
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.
29.
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
.
30.
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
.
31.
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
.
32.
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
.
33.
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
.
34.
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
,
224
(
10
), pp.
1049
1060
.
35.
Zhu
,
D.
, and
Wang
,
Q.
,
2011
, “
Elastohydrodynamic Lubrication (EHL): A Gateway to Interfacial Mechanics―Review and Prospect
,”
ASME J. Tribol.
,
133
(
4
), p.
041001
.
36.
Zhu
,
D.
, and
Wang
,
Q.
,
2013
, “
Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness
,”
ASME J. Tribol.
,
135
(
3
), p.
031501
.
37.
Zhu
,
D.
,
Wang
,
J. X.
, and
Wang
,
Q.
,
2015
, “
On the Stribeck Curves for Lubricated Counterformal Contacts of Rough Surfaces
,”
ASME J. Tribol.
,
137
(
2
), p.
021501
.
38.
Martini
,
A.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2007
, “
Friction Reduction in Mixed Lubrication
,”
Tribol. Lett.
,
28
(
2
), pp.
139
147
.
39.
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 3D Surface Roughness
,”
Tribol. Trans.
,
44
(
3
), pp.
383
390
.
40.
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
.
41.
Dyson
,
A.
,
1970
, “
Frictional Traction and Lubricant Rheology in Elastohydrodynamic Lubrication
,”
Philos. Trans. R. Soc. London, A
,
266
(
1170
), pp.
1
33
.
42.
Houpert
,
L.
,
Flamand
,
L.
, and
Berthe
,
D.
,
1981
, “
Rheological and Thermal Effects in Lubricated E.H.D. Contacts
,”
ASME J. Lubr. Technol.
,
103
(
4
), pp.
526
532
.
43.
Hsiao
,
H.-S. S.
, and
Hamrock
,
B. J.
,
1992
, “
A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model
,”
ASME J. Tribol.
,
114
(
3
), pp.
540
551
.
44.
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
.
45.
Trachman
,
E. G.
, and
Cheng
,
H. S.
,
1973
, “
Rheological Effects on Friction in Elastohydrodynamic Lubrication
,” NASA Technical Report No. CR-2206.
46.
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
.
47.
Pu
,
W.
,
Wang
,
J. X.
, and
Zhu
,
D.
,
2016
, “
Progressive Mesh Densification (PMD) Method for Numerical Solution of Mixed Elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
138
(
2
), p.
021502
.
48.
Zhu
,
D.
,
Liu
,
Y.
, and
Wang
,
Q.
,
2014
, “
On the Numerical Accuracy of Rough Surface EHL Solution
,”
Tribol. Trans.
,
57
(
4
), pp.
570
580
.
49.
Bair
,
S.
, and
Winer
,
W. O.
,
1992
, “
The High Pressure High Shear Stress Rheology of Liquid Lubricants
,”
ASME J. Tribol.
,
114
(
1
), pp.
1
9
.
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