International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2015)

Finite Element Analysis on Rubber Sealing Ring of

the Rotary Liner Hanger Bearing
Weiqing Li*, Yu Wang and Detian Miao
School of Engineering and Technology
China University of Geosciences (Beijing)
Beijing, China
*Corresponding author

AbstractRotary liner hanger bearing will be wear sharply and

decreased its service life if the sealing structure is not able to
prevent the drilling fluid to enter into the bearing. A twodimensional finite element model of the self-designed nonstandard rubber sealing ring was carried out on the software of
ABAQUS. The rules of deformation and stress for the sealing
ring with different value of initial interference, working pressure
and the deep-well temperature were studied. The result shows
that the maximum contact stress increases with the increase of
value of initial interference and the maximum contact stress is
always bigger than the value of work pressure. The effect of deepwell high temperature on sealing performance is not obvious
compared with normal temperature. The result of this study is
able to be the basis of modifying the structure and improving the
performance of sealing ring.

II.

A. Rotary liner Hanger Bearing and Its Sealing Ring

Structure
In order to meet the requirements of the axial load
60tons bearing capacity and service life20 hours of
the bearing in the working process, a full loaded thrust tapered
roller bearing is designed. Its main structures include upper just
ring, outer sealing ring, retaining ring, lower just ring, outer
sealing ring, inner sealing ring, seat ring, roller, axial ring, and
inner sealing ring. The overall structural model of the bearing is
shown in Figure I.
Part 5 and part10 are respectively inside and outside sealing
ring. The main structure and size of the sealing ring is shown in
Figure II.

Keywords-rubber sealing ring; non-linear finite element

analysis; contact stress; sealing performance;thermo-mechanical
coupling

I.

ANALYSIS MODEL OF RUBBER SEAL RING

INTRODUCTION

Rotary liner hanger bearing working in a high temperature,

high pressure and mud environment has special requirements
on sealing ring. Bearing system will wear sharply and decrease
the quality and service life of the rotary liner hanger once the
sealing structure cannot prevent the mud into the bearing [1].
Aliterature reported that about 15,000 oil and gas wells are not
able to work well because of the quality of rotary liner hanger
each year in China. So the performance of sealing ring is very
important [2].

1-Upper just ring 2-Outer sealing ring 1 3-Retaining ring 4-Lower just
ring 5-Outer sealing ring 6- Inner sealing ring 1
7-Seat ring
8-Roller
9-Axial ring
10-Inner sealing ring 2
FIGURE I

STRUCTURE OF BEARING FOR HUNGER

In this paper, the rotary liner hanger bearing is designed to

be lip rubber sealing ring. The lip sealing ring which has
complex geometry and nonlinear material property must meet
the requirements on deep-well temperature. Not only
theoretical data or application experience but also the relevant
literature and the cost of expensive experiments are the primary
difficulties. With the aid of the software of the non-linear finite
element ABAQUS, this paper simulated and obtained the result
of the performance of sealing ring used in rotary liner hanger
bearing by analyzing the maximum contact stress and
deformation variation with different initial interference,
working pressure and the deep-well temperature. The analysis
results could provide the related reference on the bearing and
seal design.
FIGURE II

2015. The authors - Published by Atlantis Press

229

STRUCTURE OF THE SEAL RING

This paper set the mesh density by the method of scattering

seeds. The rigid parts adopt the technology of free mesh
division. Lip sealing ring use hybrid element mesh CAX4H.

B. Finite Element Model

The nonlinearities of rubber sealing ring include three
aspects of material, contact and geometry, which increase the
difficulty of analysis. In order to make the calculations feasible
and satisfactory with actual working conditions, the hypotheses
are as follows:

III.

SIMULATION ANALYSIS

Two steps of loading calculations are carried out in the

simulation analysis in order to simulate the actual working
conditions.

a) The lip sealing ring model belongs to the axial

symmetry stress analysis due to the symmetry of the bearing
seal structure and its loading.

In the first step, an initial displacement of the retaining ring

to the left is given to make the rubber sealing ring reach the
pre- tightening state. In the second step, working pressure is
added to the lip position of the rubber sealing ring to simulate
fluid pressure of drilling fluid during the process of the rotary
liner hanger entering a well. According to the deep-well
pressure, the load in this paper ranges from 0 to 11Mpa[4].

b) Simplifying the sealing ring 3D model as the twodimensional model on the basis of the rubber sealing ring
geometry, loading ways and the boundary condition.
c) The sealing groove and retaining ring are the rigid
boundary because their stiffness is tens of thousands of times
higher than the rubber. The rubber sealing ring material is
incompressible one.

Boundary conditions and loading method: The axial

displacement of the retaining ring is defined as 0. The initial
interference is expressed by applying a certain amount of
retaining ring displacement along horizontal direction. The
displacements of sealing groove which is composed of shaft
ring and washer are defined as 0in the vertical and horizontal
direction of the sealing groove.

As is showed in the Figure I, the outer sealing structure is

the same as inner one, so they have the same sealing
performance. This paper only took the out sealing structure for
example to simulate the sealing performance of rotary liner
hanger bearing.
The structure of rotary liner hanger bearing is mainly
composed of shaft washer, seat ring, retaining ring and rubber
sealing ring in the sealing groove. This paper focuses on
carrying on the static analysis of the sealing ring. In order to
save computer resources, this paper only make an analysis on
the rubber sealing ring and its surrounding rigid parts but omit
other bearing rigid structures, which is able to keep the function
integrity of the bearing sealing structure and simplify the
analysis model. The simplified model is shown in Figure III.

The set of contact: Because the material of the ring is steel

and the material of the sealing ring is a rubber, their contact
property is defined as rigid-flexible contact. Two contact pairs
are built between retaining ring and rubber sealing ring. Three
contact pairs are built between rubber sealing ring and sealing
groove and their contact property is defined as rigid-flexible
contact. The rigid body belongs to the main surface, and rubber
sealing ring belongs to the subordinate surface.

The material parameters are shown in Table I. The material

of sealing ring is fluorine rubber. Its C10is 2. 2and C01 is
0.57[3].

By using ABAQUS, this paper focuses on the changing rule

of sealing ring in deformation, Von Mises stress and contact
stress under different initial interference, working pressure and
temperature conditions.

IV.

CALCULATION RESULTS AND ANALYSIS

The maximum contact stress is the reflection of the sealing

performance of the sealing ring. The necessary sealing
condition is that the maximum contact stress is bigger than or
equal to the working medium pressure[5,6].

FIGURE III
TABLE I

Von Mises stress is a reflection of the stress concentration

situation. Generally speaking, the stress relaxation of the super
elastic body material and the region of the crack are often the
site where Von Mises stress value is much bigger[7]. The
greater the Von Mises stress of sealing ring increases, the easier
the sealing ring is more prone to stress relaxation or cracks[8].

SIMPLIFIED MODEL
MATERIAL PARAMETERS

Parts

Materials

Young modulus
GPa

Poisson ratio

Sealing ring

Fluorine rubber

0.49

Shaft ring

Military armour steel

206

0.3

Seat ring

Military armour steel

206

0.3

Washer

45 steel

206

0.3

20CrMnTi

206

0.3

Retaining
ring

General expression for Von Mises stress is(1)

=

1
[(1 2 )2 + (2 3 )2 + (3 1 )2 ]
2

(1)

Where, 1 , 2 and 3 are respectively the first principal

stress, the second principal stress and the third principal stress.
A. Simulation of Differentinitial Interference
The initial interference is an important parameter in the
sealing performance. TOO small interference is easy to cause

230

TABLE II
THE CHANGES OF CONTACT STRESS, VON
MISES STRESS AND DEFORMATION WITH INITIAL
INTERFERENCE (F=0)

leakage, which will reduce the sealing performance. But too

large initial interference will cause excessive friction, which
will increase the wear and tear, and reduce the service life of
the sealing ring. Therefore, it is very important to choose the
appropriate amount of interference in the sealing performance
of the sealing ring. In order to study the effect of the initial
interference on the sealing performance, the stress and strain of
the working pressure at zero is firstly studied. Figure IV and
Figure V are the analysis results of the sealing ring contact
stress and Von Mises stress when working pressure is zero.

Magnitude

of

interference

mm

0.1

0.3

0.5

0.7

Maximum

contact

stress

(Mpa)

3.070

Maximum

deformation(mm)

0.114

0.368

0.632

With the increase of the initial interference, the maximum

contact stress of the sealing ring increase. The growth trend is
obvious at the beginning, and it reached the peak value when
the interference is 0.5mm. Then, the maximum contact stress of
the sealing ring slowly decreased and the variation amplitude
decreases as the interference continues to increase. The reason
is, with the increase of the initial interference, the contact width
of lip and retaining ring is increasing. When the width reaches
a certain value, contact width variation is smaller.

The peak area of Von Mises stress in the sealing ring is

approximately the same. Figure IV show that the maximum
Von Mises stress is mainly concentrated at the mouth of the
sealing ring. This indicates that the crack is the most likely to
appear
in
the
mouth
under
different
working
pressures[9].Figure V shows that the maximum contact stress
occurs in the place of the contact area between the sealing ring
and the retaining ring, which is required by the seal because the
contact stress is conducive to improve the sealing performance.
When the working pressure is zero and 0.1mm, 0.3mm,
0.5mm, and 0.7mm are taken as the initial value of interference,
Table II is the results of the maximum contact between the
retaining ring and the sealing ring, maximum Von Mises stress
and maximum deformation with different of the initial
interference.
Table II show that Von Mises stress increases with the
increase of the initial interference. So the initial interference
should not be too large.

Table II also shows that, with the increase of the initial

interference, the deformation of the seal ring lip increase
obviously at the beginning, and the contact width also
increased. Continue to increase the interference, the
deformation of the sealing ring is no longer significant. This is
determined by the geometry of the sealing ring and its ability to
resist deformation.
According to the above analysis, the structure of the sealing
ring can resist excessive deformation, which indicates that its
structure is basically reasonable. If the contact stress and Von
Mises stress varying are taken into account, this paper argues
that 0.3mm is an appropriate initial interference.
B. Simulation of Different Working Pressure
According to the above, analysis of this part is based on
the initial interference of 0.3mm and working pressure in the
range of 1-11Mpa.
Figure VI shows the change of maximum contact stress
and maximum Von Mises stress with different working
pressure. It shows that the maximum contact stress and the
maximum Von Mises stress increase with the increase of
working pressure.

FIGURE IV

Figure VI also shows that the maximum contact pressure is

always bigger than the working pressure in the range of 111Mpa, which shows that the sealing ring has a good sealing
performance that can meet the needs of deep well drilling.

DISTRIBUTION OF SEAL RING VON MISES

STRESS F=0, e=0.3mm

C. Simulation of Thermo-mechanical Coupling

The rotary liner hanger bearing is operated in high
temperature and high pressure environment. Besides the
medium pressure, the bearing also needs to withstand the test
of high temperature. Study on coupling of high temperature and
high pressure is able to provide a theoretical basis for the
design and optimization of sealing components of down hole
drilling tools[10].
This paper applied the sequential coupling method. Firstly,
the thermal stress was analyzed. Then, the working load was
loaded on the result of analysis of thermal stress.
FIGURE V

Table III show the maximum deformation, maximum

contact stress and maximum Von Mises stress when the
temperature load is respectively 25, 120, 130, 140

DISTRIBUTION OF SEALING RING CONTACT

STRESSF=0, e=0.3mm

231

Thhe structure annd the materiaal of the sealiing ring in thiis paper
is able to meet the
t conditionss of high temp
perature.

annd 150 .Thhe results arre on conditiion that the initial

intterference is 0.3mm
0
and thee working presssure is 7MPa..

ACKNOWLEDGMENT
This projectt was supportted by the Fu
undamental Research
R
Fuunds for the Central
C
Univeersities (265201304). This project
alsso thanks Luooyang Bearingg Science & Technology
T
C Ltd
Co.,
whho provide uss with test datta so that we have
h
the referrence of
thhe simulation research.
r
REFFERENCES
[1]]

Weiqing Li, Jianchong Wang, Analysis of Thermo-Meechanical

n of Rotary Lineer Hanger
Coupling Chaaracteristics and Structural Design
Bearing in Ultra-Deep
U
Well Drilling, Proceeedings of IMETI 2014,
pp.33-39, Julyy 15-18, 2014[Orrlando Florida, US
SA].
[2]] Tao Wei. Evaaluation of oil annd gas well cemeenting quality loggging[M].
Beijing: Petrooleum industry prress. 2010.
[3]] Zhiyu Wang,Anwen Wang. Determination of
o mechanics connstants of
Mooney-Rivliin model by usinng multilinear reggression method, College
of Science,Naaval Univ.of Engiineering, vol.23, No.2,
N
pp.18 -21, 2011.
[4]] Xiaomei Sonng, Dongzhe Z
Zhang, Yu Wanng and XiaoJunn Wang.
Improvemennt of the drilling rrotary blowout preventer
p
cooling system,
Drilling & Prooduction Technollogy, vol.37, No.3, pp.113-114, 20
014.
[5]] Zhi Chen,Yu Gao,Rong Dongg,Bo Wu and Jian
nMing Li. Finitee Element
Analysis of Sealing Characcteristics of the Rubber O-Rinng for a
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Journal off Sichuan Univerrsity(Engineeringg Science
Mechanical Seal,
Edition), vol.443, No.5, pp.234--239, 2011.
[6]] Wenjin Guann,Qungui Du,Piquun Liu. Finite Element Analyssis of the
Sealing Perforrmance of Rubbeer O-ring, Lubriccation Engineerinng, vol.37,
No.6, pp.60-664, 2012.
[7]] Min Chen,Xiiaomin Jiang,Zuxxin Zhao and Xiiaobo Huang. T
The Nonlinear Contacct Finite Elemennt Analysis of th
he Mouth Shapedd Rubber
Sealing Ring, Lubrication Enngineering, vol.34
4, No.11, pp.76-799, 2009.
[8]] Min Chen, X..M. Jiang, Zu Xinn Zhao, and X.B. Huang. The Noon-Linear
Contact Finitte Element Anaalysis of Seal Structure
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Cutting Tube Machine,Appliied Mechanics an
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[9]] Xiang Yu Dinng, Qiang Yu. T
The Influence off Performance off W-Type
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w
with
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D
vol. 83, ppp. 10-21, June 2014.

FIGURE VI
FVARIETION
NS OF MAXIMU
UM CONTACT STRESS
S
UM VON MISE STRESS WITH WORKING PRE
ESSURE
AND MAXIMU
THE CHAN
TABLE III
NGE OF DEFOR
RMATION, CONT
TACT
STRE
ESS AND VON M
MISES STRESS AT
A DIFFERENT
TEMPERATU
URE (F=7MPA, E=0.3
= MM)
Temperatur Defformatio Maximum contact
T
stresss (Mpa)
e()
n mm

Maximum
M
Von Mises
M
stressMpa

25

0
0.427

114.33

23.14

120

0
0.390

114.27

23.21

130

0.395

114.38

23.22

140

0
0.400

114.48

23.28

150

0
0.403

114.59

23.23

The increasse of maximuum Von Misses stress of rubber

seaaling ring and
a
maximum
m contact stress
s
of deeep-well
tem
mperature waas not obvious compareed with the value
of2
f25.It is conccluded that thee increase of temperature
t
haas little
efffect on the seaaling performance of the beearing. The sttructure
annd the materiall of the sealinng ring can meeet the condittions of
higgh temperaturre.
V.

CONCLUSION

With the aidd of the softw

ware of ABAQ
QUS, nonlineaar FEM
Coontact Model of self-desiggned lip sealiing ring is reealized.
Thhese simulatedd results providde the basis foor rotary liner hanger
bearing sealing ring design and
a optimizattion. The sim
mulation
ficiency.
meethod could cuut test cost, inccrease test effi
a) The maximum
m
conntact stress increases wiith the
inccrease of inittial interferennce. The contact stress is always
biggger than worrking pressuree with the action of differennt work
preessures, whichh ensure the sealing perform
mance of rubbber seal
rinng.
b) The maximum
m
Vonn Mises stress and deforrmation
graadually enlarrged with thee increases off working prressure,
whhich shows th
hat the probabbility of the relaxation
r
andd crack
wiill increase wiith the increases of workingg pressure.
c) The strress distributioons are obtainned by the sim
mulating
wiith FEM. The failure zone can
c be estimatted efficiently
d) The efffect of deep-w
well high tem
mperature on sealing
performance is not
n obvious coompared withh normal temperature.

232