Abstract

Studying elastohydrodynamic lubrication (EHL) of line contacts involving micro-cavitations, this paper examines various numerical solutions with a focus on their explicit flow continuities from inlet to exit. For the first time, influences of relaxation details, error controls, differential schemes, and mesh densities on flow continuity in EHL are revealed systemically. Furthermore, hybrid relaxation factors are introduced, the line relaxation is enabled with earlier boundary-condition enforcement, and a typical iteration process is updated with a three-in-one iteration control. Such a process is further integrated with two different starvation/cavitation treatments: one explicitly adjusts reformation locations, and the other uses a fractional film content parameter to adjust the Couette term originated by Bayada et al. The mass conservation results for problems with multiple micro-cavitations occurring inside the lubrication region are compared, and flow curves clearly demonstrate satisfactory continuities. These insights are beneficial for EHL simulations.

References

References
1.
Zhu
,
D.
, and
Jane Wang
,
Q.
,
2011
, “
Elastohydrodynamic Lubrication: A Gateway to Interfacial Mechanics—Review and Prospect
,”
Tribol. Trans.
,
133
(
4
), p.
041001
. 10.1115/1.4004457
2.
Dowson
,
D.
, and
Higginson
,
G. R.
,
1959
, “
A Numerical Solution to the Elasto-hydrodynamic Problem
,”
J. Mech. Eng. Sci.
,
1
(
1
), pp.
6
15
. 10.1243/JMES_JOUR_1959_001_004_02
3.
Rohde
,
S. M.
, and
Oh
,
K. P.
,
1975
, “
A Unified Treatment of Thick and Thin Film Elastohydrodynamic Problems by Using Higher Order Element Methods
,”
Proc. R. Soc. London. A. Math. Phys. Sci.
,
10
, pp.
315
331
.
4.
Hamrock
,
B. J.
, and
Dowson
,
D.
,
1976
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 1—Theoretical Formulation
,”
ASME J. Tribol.
,
98
(
2
), pp.
223
228
. 10.1115/1.3452801
5.
Oh
,
K. P.
, and
Rohde
,
S. M.
,
1977
, “
Numerical Solution of the Point Contact Problem Using the Finite Element Method
,”
Int. J. Numer. Methods Eng.
,
11
(
10
), pp.
1507
1518
. 10.1002/nme.1620111003
6.
Hamrock
,
B. J.
, and
Jacobson
,
B. O.
,
1984
, “
Elastohydrodynamic Lubrication of Line Contacts
,”
ASLE Trans.
,
27
(
4
), pp.
275
287
. 10.1080/05698198408981572
7.
Houpert
,
L. G.
, and
Hamrock
,
B. J.
,
1986
, “
Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads
,”
ASME J. Tribol.
,
108
(
3
), pp.
411
419
. 10.1115/1.3261220
8.
Lubrecht
,
A. A.
,
Ten Napel
,
W. E.
, and
Bosma
,
R.
,
1986
, “
Multigrid, an Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts
,”
ASME J. Tribol.
,
108
(
4
), pp.
551
556
. 10.1115/1.3261260
9.
Bissett
,
E. J.
, and
Glander
,
D. W.
,
1987
, “
A Highly Accurate Approach That Resolves the Pressure Spike of Elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
110
(
2
), pp.
241
246
. 10.1115/1.3261592
10.
Chang
,
L.
,
Conry
,
T. F.
, and
Cusano
,
C.
,
1989
, “
An Efficient, Robust, Multi-level Computational Algorithm for Elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
111
(
2
), pp.
193
199
. 10.1115/1.3261886
11.
Yang
,
P.
, and
Wen
,
S.
,
1990
, “
A Forward Iterative Numerical Method for Steady-State Elastohydrodynamically Lubricated Line Contacts
,”
Tribol. Int.
,
23
(
1
), pp.
17
22
. 10.1016/0301-679X(93)90034-X
12.
Venner
,
C. H.
,
1991
,
Multilevel Solution of the EHL Line and Point Contact Problems
,
University of Twente
,
The Netherlands
.
13.
Ai
,
X.
,
1993
,
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-system and Multigrid Methods
,
Northwestern University
,
Evanston, IL
.
14.
Kumar
,
P.
,
Jain
,
S. C.
, and
Ray
,
S.
,
2001
, “
Study of Surface Roughness Effects in Elastohydrodynamic Lubrication of Rolling Line Contacts Using a Deterministic Model
,”
Tribol. Int.
,
34
(
10
), pp.
713
722
. 10.1016/S0301-679X(01)00066-4
15.
Venner
,
C. H.
,
Berger
,
G.
, and
Lugt
,
P. M.
,
2004
, “
Waviness Deformation in Starved EHL Circular Contacts
,”
ASME J. Tribol.
,
126
(
2
), pp.
248
257
. 10.1115/1.1572514
16.
Wang
,
W.
,
Li
,
S.
,
Shen
,
D.
,
Zhang
,
S.
, and
Hu
,
Y. Z.
,
2012
, “
A Mixed Lubrication Model With Consideration of Starvation and Interasperity Cavitations
,”
Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
,
226
(
12
), pp.
1023
1038
. 10.1177/1350650112460830
17.
Wang
,
J.
,
Qu
,
S.
, and
Yang
,
P.
,
2001
, “
Simplified Multigrid Technique for the Numerical Solution to the Steady-State and Transient EHL Line Contacts and the Arbitrary Entrainment EHL Point Contacts
,”
Tribol. Int.
,
34
(
3
), pp.
191
202
. 10.1016/S0301-679X(01)00020-2
18.
Li
,
S.
, and
Kahraman
,
A.
,
2010
, “
A Transient Mixed Elastohydrodynamic Lubrication Model for Spur Gear Pairs
,”
ASME J. Tribol.
,
132
(
1
), p.
011501
. 10.1115/1.4000270
19.
Mongkolwongrojn
,
M.
,
Wongseedakaew
,
K.
, and
Kennedy
,
F. E.
,
2010
, “
Transient Elastohydrodynamic Lubrication in Artificial Knee Joint With Non-Newtonian Fluids
,”
Tribol. Int.
,
43
(
5–6
), pp.
1017
1026
. 10.1016/j.triboint.2009.12.041
20.
Yang
,
P.
,
Qu
,
S.
,
Chang
,
Q.
, and
Guo
,
F.
,
2001
, “
On the Theory of Thermal Elastohydrodynamic Lubrication at High Slide-Roll Ratios—Line Contact Solution
,”
ASME J. Tribol.
,
123
(
1
), pp.
36
41
. 10.1115/1.1330738
21.
Zhang
,
B.
,
Wang
,
J.
,
Omasta
,
M.
, and
Kaneta
,
M.
,
2015
, “
Effect of Fluid Rheology on the Thermal EHL Under ZEV in Line Contact
,”
Tribol. Int.
,
87
, pp.
40
49
. 10.1016/j.triboint.2015.01.024
22.
Pu
,
W.
,
Zhu
,
D.
, and
Wang
,
J.
,
2018
, “
A Starved Mixed Elastohydrodynamic Lubrication Model for the Prediction of Lubrication Performance, Friction and Flash Temperature With Arbitrary Entrainment Angle
,”
ASME J. Tribol.
,
140
(
3
), p.
031501
. 10.1115/1.4037844
23.
Li
,
S.
, and
Masse
,
D.
,
2019
, “
On the Flash Temperature Under the Starved Lubrication Condition of a Line Contact
,”
Tribol. Int.
,
136
(
March
), pp.
173
181
. 10.1016/j.triboint.2019.03.038
24.
Liu
,
Y.
,
Wang
,
Q. J.
,
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
25.
Elrod
,
H. G.
,
1981
, “
Cavitation Algorithm
,”
ASME J. Lubr. Technol
.,
103
(
3
), pp.
350
354
. 10.1115/1.3251669
26.
Braun
,
M. J.
, and
Hannon
,
W. M.
,
2010
, “
Cavitation Formation and Modelling for Fluid Film Bearings: A Review
,”
Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
,
224
(
9
), pp.
839
863
. 10.1243/13506501JET772
27.
Gropper
,
D.
,
Wang
,
L.
, and
Harvey
,
T. J.
,
2016
, “
Hydrodynamic Lubrication of Textured Surfaces: A Review of Modeling Techniques and Key Findings
,”
Tribol. Int.
,
94
, pp.
509
529
. 10.1016/j.triboint.2015.10.009
28.
Payvar
,
P.
, and
Salant
,
R. F.
,
1992
, “
A Computational Method for Cavitation in a Wavy Mechanical Seal
,”
ASME J. Tribol.
,
114
(
1
), pp.
199
204
. 10.1115/1.2920861
29.
Bayada
,
G.
,
Chambat
,
M.
, and
El Alaoui
,
M.
,
1990
, “
Variational Formulations and Finite Element Algorithms for Cavitation Problems
,”
ASME J. Tribol.
,
112
(
2
), pp.
398
403
. 10.1115/1.2920270
30.
Huang
,
P.
, and
Wen
,
S.
,
1992
, “
Study on Oil Film and Pressure Distribution of Micro-EHL
,”
ASME J. Tribol.
,
114
(
1
), pp.
42
46
. 10.1115/1.2920865
31.
Huang
,
P.
, and
Wen
,
S.
,
1993
, “
Sectional Micro-elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
115
(
1
), pp.
148
151
. 10.1115/1.2920968
32.
Kamamoto
,
S.
,
Sakuragi
,
M.
,
Fujimoto
,
K.
, and
Yamamoto
,
T.
,
1997
, “
Effect of Micro-cavitation on Oil Film Thickness and Pressure Distributions in Micro-EHL Line Contact
,”
Tribol. Ser.
,
32
(
1
), pp.
113
124
. 10.1016/S0167-8922(08)70441-3
33.
Chevalier
,
F.
,
Lubrecht
,
A. A.
,
Cann
,
P. M. E.
,
Colin
,
F.
, and
Dalmaz
,
G.
,
1996
, “
Starvation Phenomena in E.H.L. Point Contacts: Influence of Inlet Flow Distribution
,”
Tribol. Ser.
,
31
, pp.
213
223
. 10.1016/S0167-8922(08)70785-5
34.
Wijnant
,
Y. H.
,
1998
,
Contact Dynamics in the Field of Elastohydrodynamic Lubrication
,
University of Twente
,
Enschede, The Netherlands
.
35.
Rumbarger
,
J. H.
,
Filetti
,
E. G.
, and
Gubernick
,
D.
,
1973
, “
Gas Turbine Engine Mainshaft Roller Bearing-System Analysis
,”
ASME J. Tribol.
,
95
(
4
), pp.
401
416
. 10.1115/1.3451843
36.
Gao
,
L.
,
Boer
,
G. D.
, and
Hewson
,
R.
,
2015
, “
The Role of Micro-cavitation on EHL: A Study Using a Multiscale Mass Conserving Approach
,”
Tribol. Int.
,
90
, pp.
324
331
. 10.1016/j.triboint.2015.04.005
37.
Masjedi
,
M.
, and
Khonsari
,
M. M.
,
2015
, “
A Study on the Effect of Starvation in Mixed Elastohydrodynamic Lubrication
,”
Tribol. Int.
,
85
, pp.
26
36
. 10.1016/j.triboint.2014.12.014
38.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
39.
Roelands
,
C. J. A.
,
Vlugter
,
J. C.
, and
Waterman
,
H. I.
,
1963
, “
The Viscosity-Temperature-Pressure Relationship of Lubricating Oils and Its Correlation With Chemical Constitution
,”
ASME J. Fluids Eng.
,
85
(
4
), pp.
601
607
. 10.1115/1.3656919
40.
Barus
,
C.
,
1893
, “
Isothermals, Isopiestics and Isometrics Relative to Viscosity
,”
Am. J. Sci.
,
45
(
3
), pp.
87
96
. 10.2475/ajs.s3-45.266.87
41.
Dowson
,
D.
, and
Higginson
,
G. R.
,
1966
,
Elasto-hydrodynamic Lubrication: The Fundamentals of Roller and Gear Lubrication
,
Pergamon Press
,
London
.
42.
Liu
,
S.
,
2012
, “
On Boundary Conditions in Lubrication With One Dimensional Analytical Solutions
,”
Tribol. Int.
,
48
, pp.
182
190
. 10.1016/j.triboint.2011.11.021
43.
Ai
,
X.
, and
Yu
,
H.
,
1988
, “
A Full Numerical Solution for General Transient Elastohydrodynamic Line Contacts and Its Application
,”
Wear
,
121
(
2
), pp.
143
159
. 10.1016/0043-1648(88)90039-7
44.
Tae-Jo
,
P.
, and
Kyung-Woong
,
K.
,
1990
, “
A Numerical Analysis of the Elastohydrodynamic Lubrication of Elliptical Contacts
,”
Wear
,
136
(
2
), pp.
299
312
. 10.1016/0043-1648(90)90153-2
45.
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
46.
Dowson
,
D.
, and
Toyoda
,
S.
,
1979
, “
A Central Film Thickness Formula for Elastohydrodynamic Line Contacts
,”
Proceedings of the 5th Leeds-Lyon Symposium on Tribology
,
Leeds, UK
,
Sept., 1978
, pp.
60
65
.
47.
Wu
,
S. R.
,
1986
, “
A Penalty Formulation and Numerical Approximation of the Reynolds-Hertz Problem of Elastohydrodynamic Lubrication
,”
Int. J. Eng. Sci.
,
24
(
6
), pp.
1001
1013
. 10.1016/0020-7225(86)90032-7
48.
Venner
,
C. H.
, and
Lubrecht
,
A. A.
,
2000
,
Multi-Level Methods in Lubrication
,
Elsevier
,
New York
.
You do not currently have access to this content.