Abstract

Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

References

1.
Qi
,
K.
,
Zhou
,
Q.
, and
Yang
,
W.
,
2022
, “
Impact Contact Mechanical Performance Evaluation of Coated Medium by Semi-Analytical Method
,”
Surf. Coat. Technol.
,
444
, p.
128689
.
2.
Yang
,
W.
,
Bai
,
P.
,
Fang
,
J.
,
Qi
,
K.
, and
Zhou
,
Q.
,
2022
, “
Impact Contact Behaviors of Elastic Coated Medium With Imperfect Interfaces
,”
Int. J. Mech. Sci.
,
236
, p.
107743
.
3.
Ni
,
D.
,
Cheng
,
Y.
,
Zhang
,
J.
,
Liu
,
J.-X.
,
Zou
,
J.
,
Chen
,
B.
,
Wu
,
H.
, et al
,
2022
, “
Advances in Ultra-High Temperature Ceramics, Composites, and Coatings
,”
J. Adv. Ceram.
,
11
(
1
), pp.
1
56
.
4.
Beake
,
B. D.
,
2022
, “
The Influence of the H/E Ratio on Wear Resistance of Coating Systems–Insights From Small-Scale Testing
,”
Surf. Coat. Technol.
,
442
, p.
128272
.
5.
Fotovvati
,
B.
,
Namdari
,
N.
, and
Dehghanghadikolaei
,
A.
,
2019
, “
On Coating Techniques for Surface Protection: A Review
,”
J. Manuf. Mater. Process.
,
3
(
1
), p.
28
.
6.
Kumar
,
S. S.
,
Tripathi
,
V.
,
Sharma
,
R.
,
Puthilibai
,
G.
,
Sudhakar
,
M.
, and
Negash
,
K.
,
2022
, “
Study on Developments in Protection Coating Techniques for Steel
,”
Adv. Mater. Sci. Eng.
,
2022
, p.
2843043
.
7.
Sun
,
X.
,
Zhang
,
J.
,
Pan
,
W.
,
Wang
,
W.
, and
Tang
,
C.
,
2022
, “
Research Progress in Surface Strengthening Technology of Carbide-Based Coating
,”
J. Alloys Compd.
,
905
, p.
164062
.
8.
Wang
,
Z.
,
Yu
,
C.
, and
Wang
,
Q.
,
2015
, “
Model for Elastohydrodynamic Lubrication of Multilayered Materials
,”
ASME J. Tribol.
,
137
(
1
), p.
011501
.
9.
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.
Shi
,
Z.
, and
Ramalingam
,
S.
,
2001
, “
Thermal and Mechanical Stresses in Transversely Isotropic Coatings
,”
Surf. Coat. Technol.
,
138
(
2–3
), pp.
173
184
.
11.
Liu
,
Y.
,
Wayne Chen
,
W.
,
Zhu
,
D.
,
Liu
,
S.
, and
Wang
,
Q. J.
,
2007
, “
An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts
,”
ASME J. Tribol.
,
129
(
3
), pp.
509
516
.
12.
Bennett
,
A.
, and
Higginson
,
G. R.
,
1970
, “
Hydrodynamic Lubrication of Soft Solids
,”
J. Mech. Eng. Sci.
,
12
(
3
), pp.
218
222
.
13.
Liu
,
H.
,
Zhu
,
C.
,
Zhang
,
Y.
,
Wang
,
Z.
, and
Song
,
C.
,
2016
, “
Tribological Evaluation of a Coated Spur Gear Pair
,”
Tribol. Int.
,
99
, pp.
117
126
.
14.
Gupta
,
P. K.
,
1976
, “
On the Heavily Loaded Elastohydrodynamic Contacts of Layered Solids
,”
J. Lubr. Tech.
,
98
(
3
), pp.
367
372
.
15.
He
,
T.
,
Wang
,
Z.
, and
Wu
,
J.
,
2020
, “
Effect of Imperfect Coating on the Elastohydrodynamic Lubrication: Dislocation-Like and Force-Like Coating-Substrate Interfaces
,”
Tribol. Int.
,
143
, p.
106098
.
16.
Zhang
,
C.
,
Sun
,
Q.
,
Sun
,
W.
,
Shi
,
Z.
, and
Mu
,
X.
,
2023
, “
Performance-oriented Digital Twin Assembly of High-end Equipment: A Review
,”
Int. J. Adv. Manuf. Technol.
,
126
, pp.
4723
4748
.
17.
Ding
,
H.-J.
,
Chen
,
W.-Q.
, and
Xu
,
R.-Q.
,
2001
, “
On the Bending, Vibration and Stability of Laminated Rectangular Plates With Transversely Isotropic Layers
,”
Appl. Math. Mech.
,
22
(
1
), pp.
17
24
.
18.
Ding
,
H.-J.
,
Guo
,
F.-L.
,
Hou
,
P.-F.
, and
Zou
,
D.-Q.
,
2000
, “
On the Equilibrium of Piezoelectric Bodies of Revolution
,”
Int. J. Solids Struct.
,
37
(
9
), pp.
1293
1326
.
19.
Hao-jiang
,
D.
, and
Bo-hou
,
X.
,
1988
, “
General Solutions of Axisymmetric Problems in Transversely Isotropic Body
,”
Appl. Math. Mech.
,
9
(
2
), pp.
143
151
.
20.
Hanson
,
M. T.
,
1992
, “
The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy
,”
ASME J. Tribol.
,
114
(
3
), pp.
606
611
.
21.
Wang
,
W.
, and
Shi
,
M.
,
1998
, “
On the General Solutions of Transversely Isotropic Elasticity
,”
Int. J. Solids Struct.
,
35
(
25
), pp.
3283
3297
.
22.
Ding
,
H.
,
Chen
,
W.
, and
Zhang
,
L.
,
2006
,
Elasticity of Transversely Isotropic Materials
,
Springer Science & Business Media
,
Dordrecht, Netherlands
.
23.
Argatov
,
I. I.
,
Borodich
,
F. M.
, and
Popov
,
V. L.
,
2015
, “
JKR Adhesive Contact for a Transversely Isotropic Layer of Finite Thickness
,”
J. Phys. D: Appl. Phys.
,
49
(
4
), p.
045307
.
24.
Hou
,
P.-F.
,
Zhang
,
W.-H.
, and
Chen
,
J.-Y.
,
2019
, “
Three-Dimensional Exact Solutions of Transversely Isotropic Coated Structures Under Tilted Circular Flat Punch Contact
,”
Int. J. Mech. Sci.
,
151
, pp.
471
497
.
25.
Hou
,
P. F.
,
Zhang
,
W. H.
, and
Chen
,
J.-Y.
,
2019
, “
Three-Dimensional Exact Solutions of Homogeneous Transversely Isotropic Coated Structures Under Spherical Contact
,”
Int. J. Solids Struct.
,
161
, pp.
136
173
.
26.
Hou
,
P.-F.
,
Zhang
,
W.-H.
,
Tang
,
J.-P.
, and
Chen
,
J.-Y.
,
2019
, “
Three-Dimensional Exact Solutions of Elastic Transversely Isotropic Coated Structures Under Conical Contact
,”
Surf. Coat. Technol.
,
369
, pp.
280
310
.
27.
Vasiliev
,
A.
,
Volkov
,
S.
, and
Aizikovich
,
S.
,
2016
, “
Indentation of an Axisymmetric Punch Into an Elastic Transversely-Isotropic Half-Space With Functionally Graded Transversely-Isotropic Coating
,”
Mater. Phys. Mech.
,
28
, pp.
11
15
.
28.
Chen
,
C.-Y.
,
Tseng
,
Y.-F.
,
Chu
,
L.-M.
, and
Li
,
W.-L.
,
2013
, “
Soft EHL for Transversely Isotropic Materials
,”
Tribol. Int.
,
67
, pp.
240
253
.
29.
Wang
,
Z.
, and
Zhang
,
Y.
,
2019
, “
An Efficient Numerical Model of Elastohydrodynamic Lubrication for Transversely Isotropic Materials
,”
ASME J. Tribol.
,
141
(
9
), p.
091501
.
30.
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
.
31.
Pei
,
X.
,
Pu
,
W.
,
Yang
,
J.
, and
Zhang
,
Y.
,
2021
, “
Wear Law in Mixed Lubrication Based on Stress-Promoted Thermal Activation
,”
Friction
,
9
(
4
), pp.
710
722
.
32.
Pei
,
X.
,
Pu
,
W.
, and
Yang
,
J.
,
2021
, “
Numerical Simulation of Defective Gear Transmission Under Mixed EHL Conditions
,”
Eng. Fail. Anal.
,
127
, p.
105525
.
33.
Ai
,
X.
,
1993
,
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods. (Volumes I and II)
,
Northwestern University
,
Chicago, IL
.
34.
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
.
35.
Barus
,
C.
,
1893
, “
ART. X.–Isothermals, Isopiestics and Isometrics Relative to Viscosity
,”
Am. J. Sci.
,
s3-45
(
266
), pp.
87
96
.
36.
Chen
,
W. Q.
,
Zhu
,
J.
, and
Li
,
X. Y.
,
2019
, “
General Solutions for Elasticity of Transversely Isotropic Materials With Thermal and Other Effects: A Review
,”
J. Therm. Stresses
,
42
(
1
), pp.
90
106
.
37.
Yang
,
W.
,
Bai
,
P.
,
Cao
,
H.
,
Zhang
,
C.
,
Zhang
,
S.
, and
Tian
,
Y.
,
2023
, “
Thermoelastic Contact Responses of Transversely Isotropic Coating Considering Heat Partition
,”
Appl. Therm. Eng.
,
227
, p.
120399
.
38.
He
,
T.
,
Zhu
,
D.
,
Yu
,
C.
, and
Wang
,
Q. J.
,
2019
, “
Mixed Elastohydrodynamic Lubrication Model for Finite Roller-Coated Half Space Interfaces
,”
Tribol. Int.
,
134
, pp.
178
189
.
39.
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
.
40.
Lin
,
W.
,
Kuo
,
C. H.
, and
Keer
,
L. M.
,
1991
, “
Analysis of a Transversely Isotropic Half Space Under Normal and Tangential Loadings
,”
ASME J. Tribol.
,
113
(
2
), pp.
335
338
.
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