Original article
Analysis of sealing performance of a kind
of profiled rubber gasket used in the
radial contact seal structure
Xinyi Song , Song Huang , Hu Hui
Proc IMechE Part E:
J Process Mechanical Engineering
0(0) 1–6
! IMechE 2020
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DOI: 10.1177/0954408920971995
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and Xindan Hu
Abstract
Sealing performance of standard rubber gaskets in the radial contact seal structure are observed through the experiment. A kind of profiled rubber gasket is proposed to replace the standard gasket. Leakage experiment and numerical
simulation are carried out to study the sealing performance and failure mode of the profiled gasket. Several equations
are presented to help analyze the failure reason. Results show that sealing performance of the profiled rubber gasket is
more reliable than that of the standard rubber gasket. The failure reason of the profiled rubber gasket is that the friction
force between the gasket external face and tube wall cannot balance the tube internal pressure. Dimension precision of
the metal compressive ring has a great effect on the failure pressure.
Keywords
Failure mode, profiled rubber gaskets, sealing performance, contact pressure, hydroforming
Date received: 13 March 2020; accepted: 30 September 2020
Introduction
Hydroforming technology is widely used in
manufacturing industry to produce tube fittings with
complex shape. Two kinds of seal methods are
applied to prevent leakage in the tube-forming process. One is axial contact seal,1–3 which ensures sealing performance by the axial close contact between
metal plugs and two ends of tube. However, it is
not suitable for thin-walled tube hydroforming,
because the thin-walled tube is easy to buckle or wrinkle under the axial force. The other is radial
contact seal,4–6 and the seal principle is as follows:
Axial pre-compression pressure is exerted on the
one end face of the non-metal seal element to make
it close contact to the inner face of the tube. Then, in
the hydroforming process, the forming pressure is
exerted on the other end face the seal element, and
the contact pressure between the sealing element and
the tube inner face increases with the increment of the
forming pressure. Compared with axial contact seal,
the radial contact seal has advantages of low requirement for shape accuracy of tubes and no axial load,
thus it is more suitable in thin-walled tube
hydroforming.
Common rubber sealing element is O-sealing
ring and column rubber gasket. Because of the
uneven distribution of contact pressure and short
contact length,7–9 the radial contact seal with
O-sealing rings is line contact seal, where the maximum contact pressure should not be less than the
medium pressure. In order to keep the good sealing
performance, O-sealing ring requires high dimension
accuracy and surface finish of the tube.10 The radial
seal structure with column rubber gaskets is face contact seal, which requires less dimension accuracy and
surface finish of tubes than the line contact seal.
Researchers have confirmed that the performance of
face contact seal depends on the contact dimension
and contact pressure distribution along the leakage
path.11,12 Sawa13 evaluates the sealing performance
of gaskets with different dimension in the bolted
flange connection according to the contact stress distribution on the contact faces. Bouzid14 investigates
the validity of the effective gasket width concept.
Feng15 investigates the gas leakage behavior of
bolted flanged connection with metal gaskets and
obtained the relationship between the leakage rate
School of Mechanical and Power Engineering, East China University of
Science and Technology, Shanghai, China
Corresponding author:
Hu Hui, School of Mechanical and Power Engineering, East China
University of Science and Technology,130 Meilong Street, Shanghai
200237, China.
Email: huihu@ecust.edu.cn
2
Proc IMechE Part E: J Process Mechanical Engineering 0(0)
Figure 1. The column rubber gasket under pre-compression
load.
and contact pressure distribution. In the radial contact seal structure.
Friction could reduce the level of contact pressure
distribution. Hao16 investigated the contact pressure
distribution of standard rubber gaskets along the tube
axial direction under compression load, as it shown in
Figure 1. Equation is presented as follows
ln
PRt
2f
¼
z
Pz0
Rt Ri
PRt ¼ PRi
(1)
Figure 2. Illustration of the seal joint with the standard
rubber gasket without load.
Sealing performance experiment for the
standard rubber gaskets
(2)
Introduction about test apparatus
where f is the friction coefficient between rubber
column surface and other component surface, H0 is
the original height of the gasket, Hp is the precompressive height, Ri is the inner radius of the
gasket, R0 is both the outer surface of the rubber
gasket and the inner radius of tube, PRt and PRi are
the contact pressure, Pz0 is the pre-compression load.
It shows that contact pressure decreases along the
axial direction, because of the influence of friction.
Therefore, even if the gasket thickness is raised, the
sealing capacity improvement is limited. Lubricants
can be used to reduce the coefficient of friction, but
it can also pollute the tube inner face and be difficult
to clean.16 Besides, some lubricants can be resolved by
the hydroforming medium. Thus, it is not suitable to
reduce friction of the seal structure used in
hydroforming.
In this paper, a kind of profiled rubber gasket is
put forward to reduce the effect of friction to replace
the standard gasket in the seal structure. The column
rubber gaskets and improved rubber are respectively
applied as the sealing element of the radial contact
seal structure, and experiment and numerical simulation are carried out to comparatively analyze the sealing performance of the two kinds of rubber gaskets.
Besides, the failure mode of the profiled rubber gasket
in the sealing structure is researched.
Neoprene is chosen as the gasket material because of
its good oil and abrasion resistance. The rubber density is 1:23 103 kg=m3 . Experiment apparatus is
shown in Supplementary Figure 1, which is composed
of a pressurization unit, a seal joint and a data acquisition unit. The rubber gasket in the lower end is precompressed. Liquid medium is delivered into the tube
until it flows over from the upper end in order to
eliminate air. Then the two gaskets are compressed
and the amount is controlled by the nut and dial.
Center shaft is connected with a pump. Data acquisition is composed of a pressure sensor and a computer.
Pressure is recorded 2.5 times per second to measure
internal pressure change. Structure of the seal joint
and dimensions of every component are respectively
shown in Figure 2 and Tables 1 and 2.
Before pressurizing, the two rubber gaskets are
pre-compressed by metal compression rings. Then
the rubber will be further compressed with the increment of internal liquid pressure.
Experiment result
Supplementary Figure 2 shows the speed of medium
pressure variation with standard rubber gaskets. It
indicates that the sealing structure does not keep
Song et al.
3
Table 1. Dimensions of each metal component (mm).
Ri
Rc
Rm1
Rm2
Rt
Rb
5.00
11.82
5.50
11.81
12.17
12.00
Table 2. Dimensions of the column rubber gasket (mm).
Standard gasket
Ri
Rb
H0
1
2
3
5.00
5.00
5.00
12.00
12.00
12.00
6.00
8.00
10.00
reliable performance when the medium pressure
increases up to more than 30MPa.
Figure 3. Structure and dimension illustration of the profiled
rubber gasket.
Profiled rubber gaskets
Table 3. Dimension of the profiled gasket (mm).
Structure introduction
Profiled gasket
Ri
Rim
Rib
a
b
H0
In order to improve the sealing performance of the
radial contact seal structure, the profiled rubber
gasket shown in Figure 3 is put forward, where Ri ,
Rim , and Rib are respectively the inner radius, minimum outer radius and maximum outer radius of the
profiled rubber gaskets, both a and b are the dimensions of the chamfering. The shape is designed to be
curved to reduce the influence of friction and make
the deformation under compression load more uniform. Chamfering can prevent the part at the edge
of the gasket to be squeezed into the gap between
the metal compressive ring and the tube inner wall.
Furthermore, the outside profile can avoid abraded
by the tube ends during installation.
1
2
3
5.00
5.00
5.00
11.00
11.00
11.00
12.00
12.00
12.00
2.00
2.00
2.00
1.50
1.50
1.50
6.00
8.00
10.00
Result of sealing performance test
Tightness experiment introduced in section 2 is used
to test sealing performance of the profiled rubber
gasket. Gasket dimensions are shown in Table 3.
Internal pressure variation with profiled rubber
gaskets is shown in Supplementary Figure 3. It
shows that the decline speed of the sealing performance with the profiled gasket is slow. Besides,
there is no abrasion or damage after removing the
load. Thus, the profiled rubber gasket can be used
repeatedly.
Numerical simulation. Simulation model
Numerical simulation is applied to obtain the contact
pressure distribution between the tube wall and the
outer surface of the gasket in order to analyze the
sealing performance of the gasket. Since it’s difficult
to convergence for the static analysis because of the
extremely mesh distortion in the FEA process, quasistatic analysis method is used in ABAQUS/Explicit
module. Three-dimensional axial symmetry model
(one quarter) shown in Supplementary Figure 4 is
established. Since the failure of the improved gasket
is instantaneous and the plastic deformation of the
rubber gasket before failure is negligible, rubber
material can be set as hyper-elastic body. Thus,
Mooney-Revlin constitutive model is used to describe
mechanical property of the rubber. The function is
expressed as
W ¼ C1 ðI1 3Þ þ C2 ðI2 3Þ; C1 ¼ 0:096;
C2 ¼ 1:873
where C1 and C2 are coefficients, I1 and I2 are tensor
invariants. The rubber gasket cell type is C3D8R.
Metal compression ring, center shaft and tube wall
are set as discrete rigid body, since their deformation
is much smaller than the rubber gasket. Besides, mesh
independence has been verified. Contact type is set as
hard general contact. Penalty method is used as contact algorithms. Coulomb friction (the friction factor
is 0.21) is applied between the contact faces, in order
to obtain the convergence calculation and enhance
the speed of convergence. Each symmetry border of
the rubber gasket is restricted by the displacement
along the normal direction and the rotation around
the other two directions. The six freedom degrees of
center shaft and tube wall are fully constrained. Axial
displacement is applied to the metal compression ring
to compress the rubber gasket. Two load steps are set
up: Firstly, axial displacement is applied to the metal
4
compression ring to compress the rubber gasket to
form the initial sealing condition. Secondly, the
medium pressure is applied to the section of gaskets
surface contacting with the liquid medium to simulate
the self-seal process. Besides, in order to eliminate the
effect of damping load and acceleration, the quality of
the rigid body must be much greater than rubber
gasket, and all the load speed should be set as a
small constant.
Proc IMechE Part E: J Process Mechanical Engineering 0(0)
Table 4. Pre-compressive load comparison of gaskets/KN.
Standard gasket
Improved gasket
1
Pre-compressive 5.61
load
2
3
1
2
3
6.07
6.24
3.82
2.63
2.65
Simulation result and discussion
Since the standard gasket is not suitable for the condition where the medium pressure is more than
30MPa, the contact pressure distribution when the
medium pressure is at 32.5MPa is shown in
Supplementary Figure 5. It shows that the level
of the contact pressure distribution of the profiled
gasket is higher than that of the standard
rubber gasket. For the profiled gasket, since the distribution level of PRi is higher than that of PRt ,
the medium mainly leakage along the outer surface
of the gasket.
The contact pressure distribution of the standard
gasket under different medium pressure(Pin ) is shown
in Supplementary Figure 6. The increment of the contact pressure is limited as the medium pressure
increases. Thus the seal structure with the standard
rubber gasket cannot keep reliable sealing performance when the medium pressure is at more
than 30MPa.
The contact pressure distribution of the profiled
gasket under different medium pressure(Pin ) is
shown in Supplementary Figure 7. The whole level
of the contact pressure still increases when the
medium pressure is at more than 30MPa. Therefore,
the seal structure with the profiled rubber gasket can
keep a good sealing performance.
The pre-compressive load of the profiled gasket is
lower than that of the standard gasket, which is calculated from the simulation result, as it is shown in
Table 4.
In conclusion, the radial contact sealing
structure with the profile rubber gasket can keep a
better performance in the hydroforming of thinwalled tube.
Failure analysis of the profiled gasket. Failure mode
analysis
When the pressure increases up to a certain value, the
profiled gasket is damaged and the medium flows out
of the seal structure. The damaged profiled rubber
gasket is shown in Supplementary Figure 8. In
order to keep the safety of the sealing structure, the
failure reason should be studied.
Force condition of the rubber gasket is shown in
Figure 4 with ideal installation where the axis of both
metal compression ring and center shaft coincides.
Figure 4. The force condition of the deformed profiled
rubber gasket with ideal installation.
Figure 5. The force condition of the profiled rubber gasket
with the maximum installing deviation.
Ff is the friction force between the rubber gasket
and the tube wall. Pin is the internal pressure. Both
of the two force are exerted on the segment of the
gasket between the metal compression ring and the
tube wall. Thus, equation (3) is expressed as
Pin p R2t R2m2 ¼ Ff
(3)
Song et al.
5
Table 5. Failure pressure with different dimension component size.
Type
Profiled
gasket
Hp /
mm
Rm2 /
mm
Rm1 /
mm
DRm /
mm
Pmax /
MPa
Pmin /
MPa
Pl /
MPa
1
2
3
4
5
6
7
8
1
1
1
1
2
2
2
2
2.50
2.50
2.00
1.25
3.00
3.00
2.00
1.50
11.81
11.81
11.81
11.81
11.81
11.81
11.81
11.81
5.50
5.20
5.20
5.20
5.50
5.50
5.50
5.50
0.72
0.56
0.56
0.56
0.72
0.72
0.72
0.72
54.76
61.66
47.83
46.25
89.36
90.04
81.08
72.32
27.38
39.64
30.75
28.13
44.68
45.02
40.54
36.16
33.25
43.19
33.54
31.86
50.62
49.74
42.61
38.70
Ff is expressed as
Experiment and calculation results
Z
Ff 2fpRt
PRt dl
(4)
where l and f are the contact pressure, contact length
and friction coefficient between tube wall and the
rubber gasket, respectively. Based on the equations
(3) and (4) equation (5) is expressed as
Pin Pmax ¼
R
f PRt dl
Rt Rm2
(5)
However, there is always an installation deviation
in the experiment. Therefore, it is very difficult to
achieve the ideal installation shown in Figure 5.
The “worst” condition is shown in Figure 13. Thus,
equation (6) is written as
Pmin
R
f PRt dl
¼
DRm
DRm ¼ Rt Rm2 þ Ri Rm1
(6)
(7)
where DRm is the largest value of the maximum gap
between the tube wall and the metal compression
ring. When the internal pressure (Pin ) increases up
to more than the failure internal pressure (Pl ), the
friction force (Ff ) cannot balance the internal pressure. Therefore, the segment of the gasket where DR
is maximum is cut from the whole by metal compression ring because of the shear force. Failure internal
pressure ðPl Þ is expressed as
R
f PRt dl
Pl ¼
DR
(8)
Rt Rm2 DR DRm
(9)
The experiment introduced in section 2 is operated
to obtain the failure pressure ðPl Þ with different precompressive height, gasket dimension, and metal
compressive rings dimension. The corresponding
contact pressure distribution under the failure pressure is shown in Supplementary Figure 9. It indicates that the failure mode analysis of the profiled
gasket is validity, because all the values of Pl in the
Table 5 meet the equation (10). Thus, the metal
compression ring should have enough accuracy
in dimension.
Conclusions
A kind of profiled rubber gasket is proposed.
Experiments and numerical simulation are carried
out to analyze its sealing performance and failure
mode in the radial contact seal structure. Several
equations are presented to help analyze the failure
reason. Conclusions are as follows:
1. The profiled rubber gasket is more suitable than
the standard rubber gasket as the sealing element
of radial contact seal structure which is used in the
hydroforming of thin-walled tubes.
2. Failure reason of the profiled rubber gasket is that
the friction force between the gasket external face
and tube wall cannot balance the tube internal
pressure in the axial direction. Thus, metal compressive ring dimension should have enough
precision.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of
this article.
Funding
where DR is the maximum gap between the tube wall
and the metal compression ring in one experiment.
Thus, equation (10) is shown as
Pmin Pl Pmax
(10)
The author(s) disclosed receipt of the following financial
support for the research, authorship, and/or publication
of this article: This project is supported by National
Natural Science Foundation of China (Grant No.
51775187).
6
ORCID iDs
Xinyi Song
https://orcid.org/0000-0002-5163-1262
Song Huang
https://orcid.org/0000-0001-6389-3131
Hu Hui
https://orcid.org/0000-0002-9342-4069
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