Soft elastohydrodynamic lubrication (EHL) problems widely exist in hydraulic reciprocating rod seals and pose great challenges because of high nonlinearity and strong coupling effects, especially when the EHL problems are of high dimensions. In this paper, a strongly coupled fluid structure interaction (FSI) model is proposed to solve the transient soft EHL problems in U-cup hydraulic reciprocating rod seals. The Navier–Stokes equations, rather than the Reynolds equation, are employed to govern the whole fluid field in the soft EHL problems, with the nonlinearity of the solid taken into consideration. The governing equations of the fluid and solid fields are combined into one equation system and solved monolithically. To determine the displacements of nodes of the fluid field, a new moving mesh method based on the combination of the Laplace equation and the leader–follower methods is put forward. At last, the proposed FSI model runs successfully with the moving mesh method, and the boundaries of the hydrodynamic lubrication zones and the hydrostatic zones are formed automatically and change dynamically during the coupling process. The results are as follows: The soft EHL problems show typical characteristics, like the constriction effects of the lubricating films, and the law of dynamic development of the lubricating films and the fluid pressures is revealed. The minimum stroke lengths needed to generate complete lubricating films vary with the rod speeds and movement directions, so the design of the rod seals should be paid close attention to, in particular the rod seals of short stroke lengths. Furthermore, along with the dynamic development processes of the fluid pressures during the instroke of U-cup seals, the lubricating film humps expand and locate between the fluid pressure abrupt points and the outlet zones. After the U-cup seals reach the steady-states, the fluid abrupt points disappear and no changes of the film humps are observed. Theoretically, the proposed method can be popularized to solve similar soft EHL problems.

References

References
1.
Nikas
,
G.
,
2010
, “
Eighty Years of Research on Hydraulic Reciprocating Seals: Review of Tribological Studies and Related Topics Since the 1930s
,”
Proc. Inst. Mech. Eng., Part J
,
224
(
1
), pp.
1
23
.10.1243/13506501JET607
2.
Nau
,
B.
,
1987
, “
The State of the Art of Rubber-Seal Technology
,”
Rubber Chem. Technol.
,
60
(
3
), pp.
381
416
.10.5254/1.3536136
3.
Nau
,
B.
,
1999
, “
An Historical Review of Studies of Polymeric Seals in Reciprocating Hydraulic Systems
,”
Proc. Inst. Mech. Eng., Part J
,
213
(
3
), pp.
215
226
.10.1243/1350650991542956
4.
Kanters
,
A.
,
Verest
,
J.
, and
Visscher
,
M.
,
1990
, “
On Reciprocating Elastomeric Seals: Calculation of Film Thicknesses Using the Inverse Hydrodynamic Lubrication Theory
,”
Tribol. Trans.
,
33
(
3
), pp.
301
306
.10.1080/10402009008981959
5.
Dowson
,
D.
, and
Higginson
,
G.
,
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
6.
Stephenson
,
R. R.
, and
Osterle
,
J. F.
,
1962
, “
A Direct Solution of the Elasto-Hydrodynamic Lubrication Problem
,”
ASLE Trans.
,
5
(
2
), pp.
365
374
.10.1080/05698196208972480
7.
Thatte
,
A.
, and
Salant
,
R. F.
,
2009
, “
Elastohydrodynamic Analysis of an Elastomeric Hydraulic Rod Seal During Fully Transient Operation
,”
ASME J. Tribol.
,
131
(
3
), pp.
603
610
.10.1115/1.3139057
8.
Yang
,
B.
, and
Salant
,
R. F.
,
2008
, “
Numerical Model of a Tandem Reciprocating Hydraulic Rod Seal
,”
ASME J. Tribol.
,
130
(
3
), p.
032201
.10.1115/1.2908924
9.
Salant
,
R.
,
Yang
,
B.
, and
Thatte
,
A.
,
2010
, “
Simulation of Hydraulic Seals
,”
Proc. Inst. Mech. Eng., Part J
,
224
(
9
), pp.
865
876
.10.1243/13506501JET709
10.
Schmidt
,
T.
,
André
,
M.
, and
Poll
,
G.
,
2010
, “
A Transient 2D-Finite-Element Approach for the Simulation of Mixed Lubrication Effects of Reciprocating Hydraulic Rod Seals
,”
Tribol. Int.
,
43
(
10
), pp.
1775
1785
.10.1016/j.triboint.2009.11.012
11.
Stupkiewicz
,
S.
,
2009
, “
Finite Element Treatment of Soft Elastohydrodynamic Lubrication Problems in the Finite Deformation Regime
,”
Comput. Mech.
,
44
(
5
), pp.
605
619
.10.1007/s00466-009-0394-3
12.
Stupkiewicz
,
S.
, and
Marciniszyn
,
A.
,
2009
, “
Elastohydrodynamic Lubrication and Finite Configuration Changes in Reciprocating Elastomeric Seals
,”
Tribol. Int.
,
42
(
5
), pp.
615
627
.10.1016/j.triboint.2008.08.008
13.
Fatu
,
A.
, and
Hajjam
,
M.
,
2011
, “
Numerical Modelling of Hydraulic Seals by Inverse Lubrication Theory
,”
Proc. Inst. Mech. Eng., Part J
,
225
(
12
), pp.
1159
1173
.10.1177/1350650111417046
14.
Ongün
,
Y.
,
André
,
M.
,
Bartel
,
D.
, and
Deters
,
L.
,
2008
, “
An Axisymmetric Hydrodynamic Interface Element for Finite-Element Computations of Mixed Lubrication in Rubber Seals
,”
Proc. Inst. Mech. Eng., Part J
,
222
(
3
), pp.
471
481
.10.1243/13506501JET393
15.
Nikas
,
G. K.
, and
Sayles
,
R. S.
,
2004
, “
Nonlinear Elasticity of Rectangular Elastomeric Seals and Its Effect on Elastohydrodynamic Numerical Analysis
,”
Tribol. Int.
,
37
(
8
), pp.
651
660
.10.1016/j.triboint.2004.02.002
16.
Thatte
,
A.
, and
Salant
,
R. F.
,
2009
, “
Transient EHL Analysis of an Elastomeric Hydraulic Seal
,”
Tribol. Int.
,
42
(
10
), pp.
1424
1432
.10.1016/j.triboint.2009.05.026
17.
Habchi
,
W.
,
Eyheramendy
,
D.
,
Vergne
,
P.
, and
Morales-Espejel
,
G.
,
2008
, “
A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem
,”
ASME J. Tribol.
,
130
(
2
), p.
021501
.10.1115/1.2842246
18.
Bruyere
,
V.
,
Fillot
,
N.
,
Morales-Espejel
,
G. E.
, and
Vergne
,
P.
,
2012
, “
Computational Fluid Dynamics and Full Elasticity Model for Sliding Line Thermal Elastohydrodynamic Contacts
,”
Tribol. Int.
,
46
(
1
), pp.
3
13
.10.1016/j.triboint.2011.04.013
19.
Liu
,
H.
,
Xu
,
H.
,
Ellison
,
P. J.
, and
Jin
,
Z.
,
2010
, “
Application of Computational Fluid Dynamics and Fluid–Structure Interaction Method to the Lubrication Study of a Rotor–Bearing System
,”
Tribol. Lett.
,
38
(
3
), pp.
325
336
.10.1007/s11249-010-9612-6
20.
Hong
,
Y. P.
,
Chen
,
D. R.
,
Kong
,
X. M.
, and
Wang
,
J. D.
,
2002
, “
Model of Fluid–Structure Interaction and Its Application to Elastohydrodynamic Lubrication
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
37–38
), pp.
4231
4240
.10.1016/S0045-7825(02)00376-6
21.
Hartinger
,
M.
,
Dumont
,
M.-L.
,
Ioannides
,
S.
,
Gosman
,
D.
, and
Spikes
,
H.
,
2008
, “
CFD Modeling of a Thermal and Shear-Thinning Elastohydrodynamic Line Contact
,”
ASME J. Tribol.
,
130
(
4
), p.
041503
.10.1115/1.2958077
22.
Liao
,
C.
,
Huang
,
W.
,
Wang
,
Y.
,
Suo
,
S.
, and
Liu
,
Y.
,
2013
, “
Fluid–Solid Interaction Model for Hydraulic Reciprocating O-Ring Seals
,”
Chin. J. Mech. Eng.
,
26
(
1
), pp.
85
94
.10.3901/CJME.2013.01.085
23.
Thompson
,
J. F.
,
Soni
,
B. K.
, and
Weatherill
,
N. P.
,
2010
,
Handbook of Grid Generation
,
CRC Press
, Boca Raton.
24.
Plewa
,
T.
,
Linde
,
T.
, and
Weirs
,
V. G.
,
2005
,
Adaptive Mesh Refinement: Theory and Applications
,
Springer
, New York.
25.
Huang
,
W.
, and
Russell
,
R. D.
,
2010
,
Adaptive Moving Mesh Methods
,
Springer
, London.
26.
Bazilevs
,
Y.
,
Takizawa
,
K.
, and
Tezduyar
,
T. E.
,
2012
,
Computational Fluid–Structure Interaction: Methods and Applications
,
Wiley
, West Sussex, UK.
27.
Belytschko
,
T.
,
Liu
,
W. K.
,
Moran
,
B.
, and
Elkhodary
,
K.
,
2013
,
Nonlinear Finite Elements for Continua and Structures
,
Wiley
, West Sussex, UK.
28.
Sussman
,
T.
, and
Bathe
,
K. J.
,
1987
, “
A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis
,”
Comput. Struct.
,
26
(
1
), pp.
357
409
.10.1016/0045-7949(87)90265-3
29.
Shinkarenko
,
A.
,
Kligerman
,
Y.
, and
Etsion
,
I.
,
2009
, “
The Validity of Linear Elasticity in Analyzing Surface Texturing Effect for Elastohydrodynamic Lubrication
,”
ASME J. Tribol.
,
131
(
2
), p.
021503
.10.1115/1.3071973
30.
Eterovic
,
A.
, and
Bathe
,
K.
,
1991
, “
On the Treatment of Inequality Constraints Arising From Contact Conditions in Finite Element Analysis
,”
Comput. Struct.
,
40
(
2
), pp.
203
209
.10.1016/0045-7949(91)90347-O
31.
Bathe
,
K.-J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Englewood Cliffs, NJ
.
32.
Pantuso
,
D.
,
Bathe
,
K. J.
, and
Bouzinov
,
P. A.
,
2000
, “
A Finite Element Procedure for the Analysis of Thermo-Mechanical Solids in Contact
,”
Comput. Struct.
,
75
(
6
), pp.
551
573
.10.1016/S0045-7949(99)00212-6
33.
Zhang
,
H.
, and
Bathe
,
K. J.
,
2001
, “
Direct and Iterative Computing of Fluid Flows Fully Coupled With Structures
,”
Computational Fluid and Solid Mechanics
, Proceedings First M.I.T. Conference on Computational Fluid and Solid Mechanics, Amsterdam, pp.
1440
1443
.
34.
Adina R&D, Inc.
,
2011
, “
Theory and Modeling Guid Volum III: Adina CFD&FSI
,”
Report No. ARD 11-10
.
35.
Bathe
,
K. J.
, and
Zhang
,
H.
,
2002
, “
A Flow-Condition-Based Interpolation Finite Element Procedure for Incompressible Fluid Flows
,”
Comput. Struct.
,
80
(
14
), pp.
1267
1277
.10.1016/S0045-7949(02)00077-9
36.
Bathe
,
K. J.
, and
Pontaza
,
J. P.
,
2002
, “
A Flow-Condition-Based Interpolation Mixed Finite Element Procedure for Higher Reynolds Number Fluid Flows
,”
Math. Models Methods Appl. Sci.
,
12
(
4
), pp.
525
539
.10.1142/S0218202502001775
37.
Bathe
,
K. J.
,
Zhang
,
H.
, and
Zhang
,
X.
,
1997
, “
Some Advances in the Analysis of Fluid Flows
,”
Comput. Struct.
,
64
(
5–6
), pp.
909
930
.10.1016/S0045-7949(97)00040-0
38.
Rugonyi
,
S.
, and
Bathe
,
K.
,
2001
, “
On Finite Element Analysis of Fluid Flows Fully Coupled With Structural Interactions
,”
Comput. Model. Eng. Sci.
,
2
(
2
), pp.
195
212
. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.163.1964&rep=rep1&type=pdf
39.
Yang
,
B.
, and
Salant
,
R.
,
2011
, “
Elastohydrodynamic Lubrication Simulation of O-Ring and U-Cup Hydraulic Seals
,”
Proc. Inst. Mech. Eng., Part J
,
225
(
7
), pp.
603
610
.10.1177/1350650110397236
40.
Salant
,
R. F.
,
Maser
,
N.
, and
Yang
,
B.
,
2007
, “
Numerical Model of a Reciprocating Hydraulic Rod Seal
,”
ASME J. Tribol.
,
129
(
1
), pp.
91
97
.10.1115/1.2401222
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