Abstract

Mixed lubrication is a major lubrication regime in the presence of surface roughness. A deterministic model is established to solve mixed lubricated point contact in this paper, using a new method to solve the asperity contact region in mixed lubrication. Treatment of pressure boundary conditions between elastohydrodynamic lubrication region and asperity contact region is discussed. The new model is capable of calculating the typical Stribeck curve and analyzing the transition of lubrication regime, from full film lubrication to boundary lubrication. Moreover, the final result of the model is independent of pressure initialization. High performance in accuracy and convergence has been achieved, which is of great importance for further lubrication modeling with consideration of nano-scale roughness, intermolecular, and surface forces.

References

1.
Ranger
,
A.
,
Ettles
,
C.
, and
Cameron
,
A.
,
1975
, “
The Solution of the Point Contact Elasto-Hydrodynamic Problem
,”
Proc. R. Soc. London A. Math. Phys. Sci.
,
346
(
1645
), pp.
227
244
. 10.1098/rspa.1975.0174
2.
Hamrock
,
B. J.
, and
Dowson
,
D.
,
1976
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 1—Theoretical Formulation
,”
ASME J. Lubr. Tech.
,
98
(
2
), pp.
223
228
. 10.1115/1.3452801
3.
Evans
,
H. P.
, and
Snidle
,
R. W.
,
1981
, “
Inverse Solution of Reynolds-Equation of Lubrication Under Point-Contact Elastohydrodynamic Conditions
,”
ASME J. Lubr. Tech
,
103
(
4
), pp.
539
546
. 10.1115/1.3251733
4.
Okamura
,
H.
,
1982
, “
A Contribution to the Numerical Analysis of Isothermal Elastohydrodynamic Lubrication, Tribology of Reciprocating Engines
,”
Proceedings of the 9th Leeds-Lyon Symposium on Tribology
,
London
,
Sept. 7–10
, pp.
313
320
.
5.
Lubrecht
,
A. A.
,
1987
, “
The Numerical Solution of the Elastohydrodynamically Lubricated Line and Point Contact Problem Using Multigrid Techniques
,”
Ph. D. thesis
,
University of Twente
,
Enschede, The Netherlands
.
6.
Venner
,
C. H.
,
1991
, “
Multilevel Solution of the EHL Line and Point Contact Problems
,”
Ph. D. Thesis
,
Univ. Twente
,
Enschede, The Netherlands
.
7.
Ai
,
X.
,
1993
,
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-system and Multigrid Methods (Volumes 1 and 2)
,
Northwestern University
,
Evanston, IL
.
8.
Patir
,
N.
, and
Cheng
,
H.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Lubr. Tech.
,
100
(
1
), pp.
12
17
. 10.1115/1.3453103
9.
Zhu
,
D.
,
Cheng
,
H. S.
,
Arai
,
T.
, and
Hamai
,
K.
,
1992
, “
A Numerical-Analysis for Piston Skirts in Mixed Lubrication .1. Basic Modeling
,”
ASME J. Tribol.
,
114
(
3
), pp.
553
562
. 10.1115/1.2920917
10.
Hu
,
Y. Z.
,
Cheng
,
H. S.
,
Arai
,
T.
,
Kobayashi
,
Y.
, and
Aoyama
,
S.
,
1994
, “
Numerical Simulation of Piston Ring in Mixed Lubrication—A Nonaxisymmetrical Analysis
,”
ASME J. Tribol.
,
116
(
3
), pp.
470
478
. 10.1115/1.2928867
11.
Wang
,
Y. C.
,
Liu
,
Y.
,
Wang
,
Z. C.
, and
Wang
,
Y. M.
,
2017
, “
Surface Roughness Characteristics Effects on Fluid Load Capability of Tilt pad Thrust Bearings with Water Lubrication
,”
Friction
,
5
(
4
), pp.
392
401
. 10.1007/s40544-017-0153-y
12.
Fang
,
Y.
,
Ma
,
L.
, and
Luo
,
J.
,
2020
, “
Modelling for Water-Based Liquid Lubrication with Ultra-low Friction Coefficient in Rough Surface Point Contact
,”
Tribol. Int.
,
141
, p.
105901
. 10.1016/j.triboint.2019.105901
13.
Almqvist
,
A.
,
Lukkassen
,
D.
,
Meidell
,
A.
, and
Wall
,
P.
,
2007
, “
New Concepts of Homogenization Applied in Rough Surface Hydrodynamic Lubrication
,”
Int. J. Eng. Sci.
,
45
(
1
), pp.
139
154
. 10.1016/j.ijengsci.2006.09.005
14.
Almqvist
,
A.
,
Fabricius
,
J.
,
Spencer
,
A.
, and
Wall
,
P.
,
2011
, “
Similarities and Differences Between the Flow Factor Method by Patir and Cheng and Homogenization
,”
ASME J. Tribol.
,
133
(
3
), p.
031702
. 10.1115/1.4004078
15.
Jiang
,
X.
,
Hua
,
D.
,
Cheng
,
H.
,
Ai
,
X.
, and
Lee
,
S. C.
,
1999
, “
A Mixed Elastohydrodynamic Lubrication Model with Asperity Contact
,”
ASME J. Tribol.
,
121
(
3
), pp.
481
491
. 10.1115/1.2834093
16.
Liu
,
S.
,
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
17.
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.: J. Eng. Tribol.
,
217
(
2
), pp.
145
154
. 10.1243/13506500360603570
18.
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
19.
Hu
,
Y. Z.
,
Wang
,
H.
,
Wang
,
W. Z.
, and
Zhu
,
D.
,
2001
, “
A Computer Model of Mixed Lubrication in Point Contacts
,”
Tribol. Int.
,
34
(
1
), pp.
65
73
. 10.1016/S0301-679X(00)00139-0
20.
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
21.
Venner
,
C. H.
,
2005
, “
EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling
,”
Proc. Inst. Mech. Eng. Part J.-J. Eng. Tribol.
,
219
(
J4
), pp.
285
290
. 10.1243/135065005X33928
22.
Zhu
,
D.
,
2007
, “
On Some Aspects of Numerical Solutions of Thin-Film and Mixed Elastohydrodynamic Lubrication
,”
Proc. Inst. Mech. Eng. Part J.-J. Eng. Tribol.
,
221
(
J5
), pp.
561
579
. 10.1243/13506501JET259
23.
Zhang
,
S. W.
,
Zhang
,
C. H.
,
Hu
,
Y. Z.
, and
Ma
,
L. R.
,
2019
, “
Numerical Simulation of Mixed Lubrication Considering Surface Forces
,”
Tribol. Int.
,
140
, p.
105878
. 10.1016/j.triboint.2019.105878
24.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge
.
25.
Barus
,
C.
,
1893
, “
Isothermals, Isopiestics and Isometrics Relative to Viscosity
,”
Am. J. Sci.
,
s3-45
(
266
), pp.
87
96
. 10.2475/ajs.s3-45.266.87
26.
Bair
,
S.
, and
Winer
,
W. O.
,
1979
, “
A Rheological Model for Elastohydrodynamic Contacts Based on Primary Laboratory Data
,”
ASME J. Lubr. Tech.
,
101
(
3
), pp.
258
264
. 10.1115/1.3453342
27.
Wang
,
S.
,
Hu
,
Y. Z.
,
Wang
,
W. Z.
, and
Wang
,
H.
,
2008
, “
Transition of Frictional States and Surface Roughness Effects in Lubricated Contacts
,”
Proc. Inst. Mech. Eng. Part J.-J. Eng. Tribol.
,
222
(
J3
), pp.
407
414
. 10.1243/13506501JET346
28.
Dowson
,
D.
, and
Higginson
,
G.
,
1966
,
Elastohydrodynamic Lubrication
,
Pergamon Press
,
Oxford, UK
.
29.
Luo
,
J. B.
,
Wen
,
S. Z.
, and
Huang
,
P.
,
1996
, “
Thin Film Lubrication .1. Study on the Transition Between EHL and Thin Film Lubrication Using a Relative Optical Interference Intensity Technique
,”
Wear
,
194
(
1–2
), pp.
107
115
. 10.1016/0043-1648(95)06799-X
30.
Han
,
T.
,
Zhang
,
C.
, and
Luo
,
J.
,
2018
, “
Macroscale Superlubricity Enabled by Hydrated Alkali Metal Ions
,”
Langmuir
,
34
(
38
), pp.
11281
11291
. 10.1021/acs.langmuir.8b01722
31.
Bett
,
K. E.
, and
Cappi
,
J. B.
,
1965
, “
Effect of Pressure on Viscosity of Water
,”
Nature
,
207
(
4997
), pp.
620
621
. 10.1038/207620a0
32.
Hu
,
Y.
, and
Tonder
,
K.
,
1992
, “
Simulation of 3-D Random Rough Surface by 2-D Digital Filter and Fourier Analysis
,”
Int. J. Mach. Tools Manuf.
,
32
(
1–2
), pp.
83
90
. 10.1016/0890-6955(92)90064-N
33.
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
34.
Polonsky
,
I. A.
, and
Keer
,
L. M.
,
1999
, “
A Numerical Method for Solving Rough Contact Problems Based on the Multi-level Multi-summation and Conjugate Gradient Techniques
,”
Wear
,
231
(
2
), pp.
206
219
. 10.1016/S0043-1648(99)00113-1
You do not currently have access to this content.