Elastohydrodynamic lubrication (EHL) analysis in finite line contacts is usually modeled by a finite-length roller contacting with a half-space, which ignores effect of the two free boundaries existing in many applications such as gears or roller bearings. This paper presents a semi-analytical method, involving the overlapping method and matrix formation, for EHL analysis in the finite line contact problem to consider the effect of two free end surfaces. Three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces, and three matrices can be obtained and reused for the same finite-length space. The isothermal Reynolds equation is solved to obtain the pressure distribution and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress related calculation. Different line contact situations, including straight rollers, tapered rollers, and Lundberg profile rollers, are discussed to explore the effect of free end surfaces.

References

References
1.
Wymer
,
D. G.
, and
Cameron
,
A.
,
1974
, “
Elastohydrodynamic Lubrication of a Line Contact
,”
Proc. Inst. Mech. Eng.
,
188
(
1974
), pp.
221
238
.
2.
Bahadoran
,
H.
, and
Gohar
,
R.
,
1974
, “
End Closure in Elastohydrodynamic Line Contact
,”
J. Mech. Eng. Sci.
,
16
(
4
), pp.
276
278
.
3.
Mostofi
,
A.
, and
Gohar
,
R.
,
1983
, “
Elastohydrodynamic Lubrication of Finite Line Contacts
,”
ASME J. Lubr. Technol.
,
105
(
4
), pp.
598
604
.
4.
Park
,
T.-J.
, and
Kim
,
K.-W.
,
1998
, “
Elastohydrodynamic Lubrication of Finite Line Contacts
,”
Wear
,
223
, pp.
102
109
.
5.
Park
,
T.-J.
,
2013
, “
Elastohydrodynamic Lubrication Analysis of a Lundberg Profile-Type Cylindrical Roller
,”
J. Korean Soc. Tribol. Lubr. Eng.
,
29
(
6
), pp.
353
359
.
6.
Liu
,
X.
, and
Yang
,
P.
,
2002
, “
Analysis of the Thermal Elastohydrodynamic Lubrication of a Finite Line Contact
,”
Tribol. Int.
,
35
(
3
), pp. 137–144.
7.
Zhu
,
D.
,
Wang
,
J.
,
Ren
,
N.
, and
Wang
,
Q. J.
,
2012
, “
Mixed Elastohydrodynamic Lubrication in Finite Roller Contacts Involving Realistic Geometry and Surface Roughness
,”
ASME J. Tribol.
,
134
(
1
), p.
011504
.
8.
He
,
T.
,
Wang
,
J.
,
Wang
,
Z.
, and
Zhu
,
D.
,
2015
, “
Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length
,”
ASME J. Tribol.
,
137
(
4
), p.
041505
.
9.
Hetenyi
,
M.
,
1970
, “
A General Solution for the Elastic Quarter Space
,”
ASME J. Appl. Mech.
,
37
(
1
), pp.
70
76
.
10.
Keer
,
L. M.
,
Lee
,
J. C.
, and
Mura
,
T.
,
1983
, “
Hetenyis Elastic Quarter Space Problem Revisited
,”
Int. J. Solids Struct.
,
19
(
6
), pp.
497
508
.
11.
Keer
,
L. M.
,
Lee
,
J. C.
, and
Mura
,
T.
,
1984
, “
A Contact Problem for the Elastic Quarter Space
,”
Int. J. Solids Struct.
,
20
(
5
), pp.
513
524
.
12.
Hanson
,
M. T.
, and
Keer
,
L. M.
,
1990
, “
A Simplified Analysis for an Elastic Quarter-Space
,”
Q. J. Mech. Appl. Math.
,
43
(
4
), pp.
561
587
.
13.
Yu
,
C. C.
,
Keer
,
L. M.
, and
Moran
,
B.
,
1996
, “
Elastic-Plastic Rolling-Sliding Contact on a Quarter Space
,”
Wear
,
191
(
1–2
), pp.
219
225
.
14.
Guilbault
,
R.
,
2011
, “
A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems
,”
ASME J. Tribol.
,
133
(
3
), p.
031402
.
15.
Najjari
,
M.
, and
Guilbault
,
R.
,
2014
, “
Modeling the Edge Contact Effect of Finite Contact Lines on Subsurface Stresses
,”
Tribol. Int.
,
77
, pp.
78
85
.
16.
Najjari
,
M.
, and
Guilbault
,
R.
,
2014
, “
Edge Contact Effect on Thermal Elastohydrodynamic Lubrication of Finite Contact Lines
,”
Tribol. Int.
,
71
, pp.
50
61
.
17.
Zhang
,
Z. M.
,
Wang
,
W.
, and
Wong
,
P. L.
,
2013
, “
An Explicit Solution for the Elastic Quarter-Space Problem in Matrix Formulation
,”
Int. J. Solids Struct.
,
50
(
6
), pp.
976
980
.
18.
Zhang
,
H.
,
Wang
,
W.
,
Zhang
,
S.
, and
Zhao
,
Z.
,
2015
, “
Modeling of Finite-Length Line Contact Problem With Consideration of Two Free-End Surfaces
,”
ASME J. Tribol.
,
138
(
2
), p.
021402
.
19.
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
.
20.
Love
,
A. E. H.
,
1929
, “
The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary
,”
Philos. Trans. R. Soc. London
,
228
(
1929
), pp.
377
420
.
21.
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
.
22.
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
,
217
(
2
), pp.
145
154
.
23.
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
.
24.
Zhu
,
D.
,
2007
, “
On Some Aspects of Numerical Solutions of Thin-Film and Mixed Elastohydrodynamic Lubrication
,”
Proc. Inst. Mech. Eng. Part J.
,
221
(
5
), pp.
561
579
.
25.
Lundberg
,
v. G.
,
1939
, “
Elastische Beruhrung Zweierhalbraume
,”
Forchung Auf Dem Gebiete Des IngenieurWesen
,
10
(
5
), pp.
201
211
.
26.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
London
.
27.
Johns
,
P. M.
, and
Gohar
,
R.
,
1981
, “
Roller Bearings Under Radial and Eccentric Loads
,”
Tribol. Int.
,
14
(
3
), pp.
131
136
.
28.
Fujiwara
,
H.
, and
Kawase
,
T.
,
2006
, “
Logarithmic Profile of Rollers in Roller Bearing and Optimization of the Profile
,”
Trans. Jpn. Soc. Mech. Eng. C
,
72
(
721
), pp.
3022
3029
.
29.
Sun
,
H. Y.
,
Chen
,
X. Y.
,
Liu
,
C. H.
, and
Yang
,
P. R.
,
2008
, “
Study on Thermal EHL Performance of Lundberg Profile Rollers and the Modification of Its Crowning Value
,”
Tribology
,
28
(
1
), pp.
68
72
.http://en.cnki.com.cn/Article_en/CJFDTOTAL-MCXX200801012.htm
30.
Fujiwara
,
H.
,
Kobayashi
,
T.
,
Kawase
,
T.
, and
Yamauchi
,
K.
,
2010
, “
Optimized Logarithmic Roller Crowning Design of Cylindrical Roller Bearings and Its Experimental Demonstration
,”
Tribol. Trans.
,
53
(
6
), pp.
909
916
.
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