By coupling the equations of the modified Reynolds equation with the anisotropic slip effect, the piezoviscosity and piezodensity relations, the elasticity deformation equation, and the load equilibrium equation are solved simultaneously using the finite element method (FEM) for the elastohydrodynamic lubrication (EHL) of circular contact problems under constant load conditions. Results show that the film thickness is more sensitive to the slip length in a sliding direction (x-direction) than to the slip length in a transverse direction (y-direction). A slip in the y-direction concentrates the pressure toward the center region, and the film collects toward the central region and possesses a deeper dimple. The central pressure and coefficient of friction (COF) increase as the slip length in the y-direction increases. On the contrary, the central pressure and COF decrease as the slip length in the x-direction increases. Detailed results and animations for film thicknesses and pressure distributions are available under the “Supplemental Data” tab for this paper on the ASME Digital Collection.

References

1.
Voronov
,
R. S.
, and
Papavassiliou
,
D. V.
,
2008
, “
Review of Fluid Slip Over Superhydrophobic Surfaces and Its Dependence on the Contact Angle
,”
Ind. Eng. Chem. Res.
,
47
(
8
), pp.
2455
2477
.
2.
Watanabe
,
K.
,
Udagawa
,
Y.
, and
Udagawa
,
H.
,
1999
, “
Drag Reduction of Newtonian Fluid in a Circular Pipe With a Highly Eater-Repellent Wall
,”
J. Fluid Mech.
,
381
, pp.
225
238
.
3.
Neto
,
C.
,
Evans
,
D.
,
Bonaccurso
,
E.
,
Butt
,
H.
, and
Craig
,
V. S. J.
,
2005
, “
Boundary Slip in Newtonian Liquids: A Review of Experimental Studies
,”
Rep. Prog. Phys.
,
68
(
12
), pp.
2859
2897
.
4.
Fu
,
Z.
,
Guo
,
F.
, and
Wong
,
P. L.
,
2007
, “
Non-Classical Elastohydrodynamic Lubricating Film Shape Under Large Slide-Roll Ratios
,”
Tribol. Lett.
,
27
(
2
), pp.
211
219
.
5.
Kaneta
,
M.
,
Nishikawa
,
H.
, and
Kameishi
,
K.
,
1990
, “
Observation of Wall Slip in Elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
112
(
3
), pp.
447
452
.
6.
Craig
,
V. S. J.
,
Neto
,
C.
, and
Williams
,
D. R. M.
,
2001
, “
Shear-Dependent Boundary Slip in an Aqueous Newtonian Fluid
,”
Phys. Rev. Lett.
,
87
(
5
), p.
054504
.
7.
Zhu
,
Y.
, and
Granick
,
S.
,
2001
, “
Rate-Dependent Slip of Newtonian Liquids at Smooth Surfaces
,”
Phys. Rev. Lett.
,
87
(
9
), p.
96105
.
8.
Vinogradova
,
O. I.
,
1999
, “
Slippage of Water Over Hydrophobic Surfaces
,”
Int. J. Miner. Process.
,
56
(1), pp.
31
60
.
9.
Granick
,
S.
,
Zhu
,
Y.
, and
Lee
,
H.
,
2003
, “
Slippery Questions About Complex Fluids Flowing Past Solids
,”
Nat. Mater.
,
2
(
4
), pp.
221
227
.
10.
Cottin-Bizonne
,
C.
,
Jurine
,
S.
,
Baudry
,
J.
,
Crassous
,
J.
,
Restagno
,
F.
, and
Charlaix
,
E.
,
2002
, “
Nanorheology: An Investigation of the Boundary Condition at Hydrophobic and Hydrophilic Interfaces
,”
Eur. Phys. J. E
,
9
(1), pp.
47
53
.
11.
Guo
,
F.
,
Li
,
X. M.
, and
Wong
,
P. L.
,
2011
, “
A Novel Approach to Measure Slip-Length of Thin Lubricant Films Under High Pressures
,”
Tribol. Int.
,
46
(1), pp.
22
29
.
12.
Spikes
,
H. A.
,
2003
, “
The Half-Wetted Bearing, Part 1: Modified Reynolds Equation
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
1
), pp.
1
14
.
13.
Spikes
,
H. A.
,
2003
, “
The Half-Wetted Bearing, Part 2: Potential Application in Low Load Contacts
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
1
), pp.
15
26
.
14.
Spikes
,
H.
, and
Granick
,
S.
,
2003
, “
Equation for Slip of Simple Liquids at Smooth Solid Surfaces
,”
Langmuir
,
19
(
12
), pp.
5065
5071
.
15.
Chen
,
C. Y.
,
Chung
,
C. J.
,
Wu
,
B. H.
,
Li
,
W. L.
,
Chien
,
C. W.
, and
Wu
,
P. H.
,
2012
, “
Microstructure and Lubricating Property of Ultrafast Laser Pulse Textured Silicon Carbide Seals
,”
Appl. Phys. A: Mater. Sci. Process.
,
107
(
2
), pp.
345
350
.
16.
Jacobson
,
B. O.
, and
Hamrock
,
B. J.
,
1984
, “
Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts
,”
ASME J. Tribol.
,
106
(
2
), pp.
275
284
.
17.
Zhang
,
Y. B.
, and
Wen
,
S.
,
2002
, “
An Analysis of Elastohydrodynamic Lubrication With Limiting Shear Stress: Part I—Theory and Solutions
,”
STLE Tribol. Trans.
,
45
(
2
), pp.
135
144
.
18.
Stahl
,
J.
, and
Jacobson
,
B. O.
,
2003
, “
A Lubricant Model Considering Wall-Slip in EHL Line Contacts
,”
ASME J. Tribol.
,
125
(
3
), pp.
523
532
.
19.
Ehret
,
P.
,
Dowson
,
D.
, and
Taylor
,
C. M.
,
1998
, “
On Lubricant Transport Conditions in Elastohydrodynamic Conjunctions
,”
Proc. R. Soc. A
,
454
(
1971
), pp.
763
787
.
20.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
,
2004
, “
Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
381
411
.
21.
Bazant
,
M. Z.
, and
Vinogradova
,
O. I.
,
2008
, “
Tensorial Hydrodynamic Slip
,”
J. Fluid Mech.
,
613
, pp.
125
134
.
22.
Chen
,
C. Y.
,
Chen
,
Q. D.
, and
Li
,
W. L.
,
2013
, “
Characteristics of Journal Bearings With Anisotropic Slip
,”
Tribol. Int.
,
61
, pp.
144
155
.
23.
Li
,
W. L.
,
Chu
,
H. M.
, and
Chen
,
M. D.
,
2006
, “
The Partially Wetted Bearing—Modified Reynolds Equation
,”
Tribol. Int.
,
39
(
11
), pp.
1428
1435
.
24.
Jao
,
H. C.
,
Chang
,
K. M.
,
Chu
,
L. M.
, and
Li
,
W. L.
, “
A Modified Average Reynolds Equation for Rough Bearings With Anisotropic Slip
,”
ASME J. Tribol.,
138
(1), p. 011702.
25.
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
.
26.
Hamrock
,
B. J.
,
Schmid
,
S. R.
, and
Jacobson
,
B. O.
,
2004
,
Fundamentals of Fluid Film Lubrication
, 2nd ed.,
Marcel Dekker, Inc.
,
New York City
, Chap. 10, Sec. 3.
27.
Dowson
,
D.
, and
Higginson
,
G. R.
,
1996
,
Elastohydrodynamic Lubrication
,
Pergamon Press
,
Oxford, UK
.
28.
Roelands
,
C. J. A.
,
1966
, “
Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils
,” Ph.D. thesis, Delft University of Technology, The Netherlands.
29.
Chu
,
L. M.
,
Chen
,
C. Y.
,
Tee
,
C. K.
,
Chen
,
Q. D.
, and
Li
,
W. L.
,
2014
, “
Elastohydrodynamic Lubrication Analysis for Transversely Isotropic Coating Layer
,”
ASME J. Tribol.
,
136
(
3
), p.
031502
.
30.
Chu
,
L. M.
,
Lin
,
J. R.
,
Li
,
W. L.
, and
Lu
,
J. M.
,
2012
, “
A Model for Line-Contact EHL Problems—Consideration of Effects of Navier-Slip and Lubricant Rheology
,”
ASME J. Tribol.
,
134
(
3
), p.
031502
.
You do not currently have access to this content.