A novel model is constructed for solving elastohydrodynamic lubrication (EHL) of multilayered materials. Because the film thickness equation needs the term of the deformation caused by pressure, the key problem for the EHL of elastic multilayered materials is to develop a method for calculating their surface deformations, or displacements, caused by pressure. The elastic displacements and stresses can be calculated by employing the discrete-convolution and fast Fourier transform (DC-FFT) method with influence coefficients. For the contact of layered materials, the frequency response functions (FRFs), relating pressure to surface displacements and stress components, derived from the Papkovich–Neuber potentials are applied. The influence coefficients can be obtained by employing FRFs. The EHL of functionally graded material (FGM) can also be well solved using a multilayer material system. The effects of material layers and property gradient on EHL film thickness and pressure are further investigated.

References

1.
Gupta
,
P. K.
,
Walowit
,
J. A.
, and
Finkin
,
E. F.
,
1973
, “
Stress Distributions in Plane Strain Layered Elastic Solids Subjected to Arbitrary Boundary Loading
,”
ASME J. Lubr. Technol.
,
95
(
4
), pp.
427
432
.10.1115/1.3451848
2.
Gupta
,
P. K.
, and
Walowit
,
J. A.
,
1974
, “
Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid
,”
ASME J. Lubr. Technol.
,
96
(
2
), pp.
250
257
.10.1115/1.3451940
3.
King
,
R. B.
, and
O'Sullivan
,
T. C.
,
1987
, “
Sliding Contact Stresses in a Two-Dimensional Layered Elastic Half-Space
,”
Int. J. Solids Struct.
,
23
(
5
), pp.
581
597
.10.1016/0020-7683(87)90019-9
4.
Bentall
,
R. H.
, and
Johnson
,
K. L.
,
1968
, “
An Elastic Strip in Plane Rolling Contact
,”
Int. J. Mech. Sci.
,
10
(
8
), pp.
637
663
.10.1016/0020-7403(68)90070-2
5.
Nowell
,
D.
, and
Hills
,
D. A.
,
1988
, “
Contact Problems Incorporating Elastic Layers
,”
Int. J. Solids Struct.
,
24
(
1
), pp.
105
–1.10.1016/0020-7683(88)90102-3
6.
Guler
,
M. A.
, and
Erdogan
,
F.
,
2004
, “
Contact Mechanics of Graded Coatings
,”
Int. J. Solids Struct
.,
41
(
14
), pp.
3865
3889
.10.1016/j.ijsolstr.2004.02.025
7.
Chidlow
,
S. J.
,
Chong
,
W. W. F.
, and
Teodorescu
,
M.
,
2013
, “
On the Two-Dimensional Solution of Both Adhesive and Non-Adhesive Contact Problems Involving Functionally Graded Materials
,”
Eur. J. Mech., A/Solids
,
39
, pp.
86
103
.10.1016/j.euromechsol.2012.10.008
8.
Burmister
,
D. M.
,
1945
, “
The General Theory of Stresses and Displacement in Layered Systems. I
,”
J. Appl. Phys.
,
16
(
2
), pp.
89
94
.10.1063/1.1707558
9.
Chen
,
W. T.
,
1971
, “
Computation of Stresses and Displacements in a Layered Elastic Medium
,”
Int. J. Eng. Sci.
,
9
(
9
), pp.
775
800
.10.1016/0020-7225(71)90072-3
10.
Chen
,
W. T.
, and
Engel
,
P.
,
1972
, “
Impact and Contact Stress Analysis in Multilayer Media
,”
Int. J. Solids Struct.
,
8
(
11
), pp.
1257
1281
.10.1016/0020-7683(72)90079-0
11.
Kuo
,
C. H.
, and
Keer
,
L. M.
,
1992
, “
Contact Stress Analysis of a Layered Transversely Isotropic Half-Space
,”
ASME J. Tribol.
,
114
(
2
), pp.
253
262
.10.1115/1.2920881
12.
O’Sullivan
,
T. C.
, and
King
,
R. B.
,
1988
, “
Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space
,”
ASME J. Tribol.
,
110
(
2
), pp.
235
240
.10.1115/1.3261591
13.
Nogi
,
T.
, and
Kato
,
T.
,
1997
, “
Influence of a Hard Surface Layer on the Limit of Elastic Contact, Part I: Analysis Using a Real Surface Model
,”
ASME J. Tribol
.,
119
(
3
), pp.
493
500
.10.1115/1.2833525
14.
Liu
,
S. B.
, and
Wang
,
Q.
,
2002
, “
Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm
,”
ASME J. Tribol.
,
124
(
1
), pp.
36
45
.10.1115/1.1401017
15.
Bhushan
,
B.
, and
Peng
,
W.
,
2002
, “
Contact Mechanics of Multilayered Rough Surface
,”
ASME Appl. Mech. Rev.
,
55
(
5
), pp.
435
480
.10.1115/1.1488931
16.
Wang
,
Z. J.
,
Wang
,
W. Z.
,
Wang
,
H.
,
Zhu
,
D.
, and
Hu
,
Y. Z.
,
2010
, “
Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half Space
,”
ASME J. Tribol.
,
132
(
2
), p.
021403
.10.1115/1.4001011
17.
Wang
,
Z. J.
,
Wang
,
W. Z.
,
Meng
,
F. M.
, and
Wang
,
J. X.
,
2011
, “
Fretting Contact Analysis on Three-Dimensional Elastic Layered Half Space
,”
ASME J. Tribol.
,
133
(
3
), p.
031401
.10.1115/1.4004104
18.
Cai
,
S.
, and
Bhushan
,
B.
,
2005
, “
A Numerical Three-Dimensional Contact Model for Rough, Multilayered Elastic/Plastic Solid Surfaces
,”
Wear
,
259
(
7–12
), pp.
1408
1423
.10.1016/j.wear.2005.02.014
19.
Yu
,
C. J.
,
Wang
,
Z. J.
,
Sun
,
F.
,
Lu
,
S. N.
,
Keer
,
L. M.
, and
Wang
,
Q. J.
,
2013
, “
A Deterministic Semi-Analytical Model for the Contact of a Wafer and a Rough Bi-Layer Pad in CMP
,”
ECS J. Solid State Sci. Technol.
,
2
(
9
), pp.
P368
P374
.10.1149/2.017309jss
20.
Yu
,
C. J.
,
Wang
,
Z. J.
, and
Wang
,
Q. J.
,
2014
, “
Analytical Frequency Response Functions for Contact of Multilayered Materials
,”
Mech. Mater.
,
76
, pp.
102
120
.10.1016/j.mechmat.2014.06.006
21.
Bennett
,
A.
, and
Higginson
,
G. R.
,
1970
, “
Hydrodynamic Lubrication of Soft Solids
,”
J. Mech. Eng. Sci.
,
12
(
3
), pp.
218
222
.10.1243/JMES_JOUR_1970_012_037_02
22.
Elsharkawy
,
A. A.
, and
Hamrock
,
B. J.
,
1994
, “
EHL of Coated Surfaces, Part I—Newtonian Results
,”
ASME J. Tribol.
,
116
(
1
), pp.
29
36
.10.1115/1.2927041
23.
Elsharkawy
,
A. A.
, and
Hamrock
,
B. J.
,
1994
, “
EHL of Coated Surfaces, Part II—Non-Newtonian Results
,”
ASME J. Tribol.
,
116
(
4
), pp.
786
793
.10.1115/1.2927333
24.
Elsharkawy
,
A. A.
,
Holmes
,
M. J. A.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
2006
, “
Microelastohydrodynamic Lubrication of Coated Cylinders Using Coupled Differential Deflection Method
,”
Proc. Inst. Mech. Eng., Part J
,
220
(
1
), pp.
29
41
.10.1243/13506501J10005
25.
Xue
,
Y. K.
,
Gethin
,
D. T.
, and
Lim
,
C. H.
,
1996
, “
Elastohydrodynamic Lubrication Analysis of Layered Line Contact by the Boundary Element Method
,”
Int. J. Numer. Methods Eng.
,
39
(
15
), pp.
2531
2554
.10.1002/(SICI)1097-0207(19960815)39:15<2531::AID-NME965>3.0.CO;2-N
26.
Goryacheva
,
I.
,
Sadeghi
,
F.
, and
Xu
,
G.
,
1996
, “
Viscoelastic Effects in Lubricated Contacts
,”
Wear
,
198
(
1–2
), pp.
307
312
.10.1016/0043-1648(96)07206-7
27.
Jin
,
Z. M.
,
2000
, “
Elastohydrodynamic Lubrication of a Circular Point Contact for a Compliant Layered Surface Bonded to a Rigid Substrate, Part 1: Theoretical Formulation and Numerical Method
,”
Proc. Inst. Mech. Eng., Part J
,
214
(
3
), pp.
267
279
.10.1243/1350650001543160
28.
Jin
,
Z. M.
,
2000
, “
Elastohydrodynamic Lubrication of a Circular Point Contact for a Compliant Layered Surface Bonded to a Rigid Substrate, Part 2: Numerical Results
,”
Proc. Inst. Mech. Eng., Part J
,
214
(
3
), pp.
281
289
.10.1243/1350650001543179
29.
Fujinoa
,
T.
,
Iwamotob
,
K.
,
Tanakab
,
K.
, and
Shima
,
M.
,
2007
, “
Stress Distribution of Coated Film With a Range of Coated Film Thickness and Elastic Properties Under a Single EHL Operating Condition
,”
Tribol. Int.
,
40
(
10–12
), pp.
1638
1648
.10.1016/j.triboint.2007.02.012
30.
Habchi
,
W.
,
2014
, “
A Numerical Model for the Solution of Thermal Elastohydrodynamic Lubrication in Coated Circular Contacts
,”
Tribol. Int.
,
73
, pp.
57
68
.10.1016/j.triboint.2014.01.002
31.
Chu
,
L. M.
,
Chen
,
C. Y.
,
Tee
,
C. K.
,
Chen
,
Q. D.
, and
Li
,
W. L.
,
2014
, “
Elastohydrodynamic Lubrication Analysis for Transversely Isotropic Coating
,”
ASME J. Tribol.
,
136
(
3
), p.
031502
.10.1115/1.4027210
32.
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
33.
Liu
,
Y. C.
,
Chen
,
W. W.
,
Liu
,
S. B.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2007
, “
An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts
,”
ASME J. Tribol.
,
129
(
3
), pp.
509
516
.10.1115/1.2736433
34.
Liu
,
Y. C.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2008
, “
Effect of Stiff Coatings on EHL Film Thickness in Point Contacts
,”
ASME J. Tribol.
,
130
(
3
), p.
031501
.10.1115/1.2908908
35.
Wang
,
Z. J.
,
Wang
,
W. Z.
,
Wang
,
H.
, and
Hu
,
Y. Z.
,
2009
, “
Stress Analysis on Layered Materials in Point Elastohydrodynamic-Lubricated Contacts
,”
Tribol. Lett.
,
35
(
3
), pp.
229
244
.10.1007/s11249-009-9452-4
36.
Wang
,
Z. J.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2014
, “
Elastohydrodynamic Lubrication of Inhomogeneous Materials Using the Equivalent Inclusion Method
,”
ASME J. Tribol.
,
136
(
2
), p.
021501
.10.1115/1.4025939
37.
Bair
,
S.
,
2007
,
High Pressure Rheology for Quantitative Elastohydrodynamics
,
Elsevier, Amsterdam
,
The Netherlands
.
38.
Dowson
,
D.
, and
Higginson
,
G. R.
,
1966
,
Elastohydrodynamic Lubrication: the Fundamentals of Roller and Gear Lubrication
,
Pergamon
,
New York
.
39.
Ai
,
X.
,
1993
, “
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods
,” Ph.D. thesis, Northwestern University, Evanston, IL.
40.
Liu
,
Y. C.
,
Wang
,
Q. J.
,
Wang
,
W. Z.
,
Hu
,
Y. Z.
, 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
41.
Thomas
,
L. H.
,
1949
,
Elliptic Problems in Linear Difference Equations Over a Network
,
Watson Scientific Computing Laboratory Report, Columbia University
,
New York
.
42.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vellerling
,
W. T.
, and
Flannery
,
B. P.
,
1992
,
Numerical Recipes in Fortran 77: The Art of Scientific Computing
, 2nd ed.,
Cambridge University
,
Cambridge, UK
.
43.
Hamrock
,
B. J.
, and
Dowson
,
D.
,
1977
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results
,”
ASME J. Lubr. Technol.
,
99
(
2
), pp.
264
276
.10.1115/1.3453074
You do not currently have access to this content.