Finite Element Analysis of the O-ring Behavior Under Uniform

Squeeze Levels and Internal Pressure

E.EL BAHLOUL1, H. AISSAOUI1, M. DIANY 2, E. BOUDAIA 2, S. TOUAIRI2

1Automation and Energy Conversion Team, Faculty of Science and Technology, Sultan Moulay Sliman University, Beni

Mellal, MOROCCO

2Industrial Engineering Laboratory, Faculty of Science and Technology, Sultan Moulay Sliman University, Beni Mellal,

MOROCCO

Abstract: - The variety of applications, in all industrial fields, whether for routine use or a specific application, requires

the design of increasingly efficient sealing systems. O-rings are fundamental elements in many industrial devices and

machines, thanks to advantages such as low cost, small size, cleanliness, and ease of assembly. Moreover, the O-ring is

available in thousands of dimensions.

In this work, the analysis of the mechanical and leakage behavior of the O-ring seal, when installed either in a groove or

between two plates, is presented.

The behavior of the assemblies in both scenarios when the clamping force and fluid pressure are applied is investigated

using two numerical models generated with Ansys software.

The numerical model findings are compared to the analytical approach based on Hertz contact theory and other

researchers' experimental results. This study shows that the use of a groove to ensure the mounting of elastomeric O-rings

is important in pressurized installations. Furthermore, for different pressure conditions, the reliability of the O-ring

strongly depends on three parameters: compression ratio of the seal, the hardness of the seal, and the friction coefficient.

Keywords: - O-ring, groove, analytical model, finite element model, contact pressure, fluid pressure

Received: December 23, 2021. Revised: November 6, 2022. Accepted: December 4, 2022. Published: December 31, 2022.

1. Introduction

The modern industry nowadays handles a lot of polluting,

toxic, radiative, and flammable products which require

more precise knowledge of the sealing function to avoid any

possible leakage of these dangerous products. In practice,

commercial O-rings are designed to increase contact

pressure as the fluid pressure increases. They also require a

secure seal, as well as economical manufacturing and easy

assembly. Due to its symmetrical shape and inexpensive

production cost, the O-ring may appear to be an easy-to-use

and effective seal at first glance.

When consulting patent databases, it is only in the 1930s

that the term "O-ring" appears. The O-ring was invented by

Niels Christensen to seal a piston/cylinder application [1].

Lindley [2] points out the lack of scientific results that

would allow a better understanding of the functioning of O-

rings. And indeed, research on O-rings did not begin until a

few years after these. The equations developed until today

to analytically determine the distribution of the contact

pressure against the joint-structure contact surfaces are

deduced from the classical Hertzian contact theory [3]. Less

attention was paid to O-rings inserted in grooves until 1988

when Dragoni et al. [4] studied the mechanical behavior of

a non-pressurized O-ring installed in a rectangular groove.

The seal in this study is modeled by a flat disk and is

subjected to an axial deformation due to the clamping force.

This concept was subjected to numerical, experimental, and

analytical analysis. Karaszkiewicz [5] has just completed

and enriched these previous models, with an analytical

model allowing determining the geometrical distortion, the

width, and the contact pressure of an O-ring subjected to

radial compression and installed in a rectangular groove.

This model enables for the fluid pressure exerted to the

joint to be taken into account. The numerical results of

George [6] have supported the findings of this study.

However, the equations proposed in this model have an

error of up to 30% which explains the difficulty of modeling

the mechanical behavior of O-rings in pressurized

installations. Eshel [7] uses an experimental setup to predict

the fluid pressures that cause O-ring extrusion to determine

the parameters of his analytical model. Also, as a function

of service pressures and the hardness of the rubber utilized,

establish the limitations of mechanical extrusion clearance.

In 1998, Yokoyama et al. [8] experimentally determined the

change in contact pressure as a function of change in fluid

pressure for an O-ring installed in an axial assembly. The

seals used were Polyacrylate (ACM), Fluorocarbon (FKM)

propylene (EPDM) with different hardnesses. The results

obtained show that the lower the hardness of the seal, the

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E-ISSN: 2224-3429

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higher the rate of change of the contact pressure at the seal-

structure contact surfaces as a function of the fluid pressure.

Other experimental works [9], [10], [11] have obtained a

satisfactory agreement with the theoretical results. They

proposed a photoelasticity-inspired test method. They

devised the method to investigate the contact pressure

distribution and internal stresses of an O-ring in a

rectangular groove. Other researchers [12], [13] will focus

on the effect of the friction coefficient on O-ring sealing

performance.

In assemblies with O-rings, finite element analysis is present

in the majority of published works. This approach has been

used on a variety of seals in the literature, including

rectangular seals [14], [15], U-shaped seals [16], [17], and

O-rings [18], [19]. Using the same method Diany et al. [20]

[21] developed a finite element model to study the short-

term relaxation of a non-pressurized O-ring. This study

showed the effect of the groove in reducing the initial crush

required to create the contact pressure that can ensure

sealing. El Bahloul et al. [22] have shown that one of the

main parameters in the evaluation of O-rings installed in a

groove is undoubtedly the contact pressure distribution

between the seal and the contact surfaces and that the

proper functioning of the O-ring depends on the best choice

of the values of the extrusion clearance and the coefficient

of friction in pressurized installations. In other works [23],

[24], the same authors studied the effect of the groove shape

and the effect of introducing a metal core inside the

elastomer O-ring. The results of the first study showed that

the use of a concave groove, or rectangular groove link,

produces more contact pressure and thus further limits the

risk of leakage. The second study showed that the

introduction of a metal core inside the elastomeric O-ring

can improve not only the strength of the seal but also the

maximum value of the contact pressure.

O-rings are fundamental elements in many industrial

devices and machines, thanks to advantages such as low

cost, small size, cleanliness, and ease of assembly. In

addition, the O-ring is available in thousands of sizes.

However, seal failure due to incorrect mounting conditions,

wrong choice of O-ring material, or O-ring geometry leads

to lower system performance. Conversely, a better

knowledge of the characteristics of the O-ring and its

support will improve the performance and efficiency of the

systems being sealed. It will prolong the seal's life, allowing

it to be employed in a variety of industrial applications. In

this work, finite element models, using Ansys software [25],

are proposed to evaluate the behavior of the O-ring

assembly subjected to combined loads: clamping force and

fluid pressure.

2. Modeling of the Studied Assemblies

Large elastic deformations and quasi-incompressible

behavior are required when modeling the mechanical

behavior of elastomers. Thus, mechanical behavior laws

must be formulated in the context of large deformation

modeling [26],[27],[28]. The behavior laws most commonly

used by commercial calculation software are Mooney

Rivlin, Ogden, and Neo Hook. The so-called hyperelastic

model of Mooney Rivlin [29] is the most commonly

encountered model for describing the mechanical behavior

of elastomers. This one allows describing correctly the

behavior of an elastomer up to a strain level of 200 % [30].

Knowing all the geometrical parameters as well as the

behavior law of the seal material, the positioning of the O-

ring can be simulated. The elements of the assembly are

simulated in their operating position taking into account the

geometrical conditions of the ISO 3601 standard [31].

Figure 1 shows the studied assemblies. Table I lists the

mechanical and geometrical features of the assemblies. The

joint is modeled by a disk with 2D planar elements with

four nodes (PLANE182). Contact elements, CONTA171

and TARGE169, are used to simulate the reaction between

the elements that are in contact. Figure 2 shows an example

of the O-ring mesh.

Figure 1 - O-ring assembly between two plates (Assembly

1), O-ring assembly in a groove (Assembly 2)

Table I - Mechanical and geometrical characteristics of the

assemblies

Symbol

Designation

Contact

Top surface

O-ring -

groove

Lateral surface

Lower surface

Top surface

O-ring-

plates

Lower surface

Values

O-ring inner

diameter

16.35 mm

O-ring cross-section

diameter

2.65 mm

Young's modulus of

the O-ring

13.8 MPa

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Figure 2 - O-ring meshes

The simulation of the joint assemblies was performed in two

steps. In the first step, the joint is compressed between a

plate and a groove (Figure 3 (b)) or between two plates

(Figure 4 (b)) under the assumption of large deformations

and large displacements. The plates and grooves were

defined as rigid analytical elements. The displacements of

the inner plate in assembly 1 and the groove in assembly 2

were canceled in all directions. The top plate in both

assemblies, whose displacements are canceled in the radial

direction, is axially loaded by a uniformly distributed

clamping force. In the second step, fluid pressure is applied

to the active side of the joint (Figure 3 (c) and Figure 4 (c))

for all surface elements that are not in contact with the

groove and plates.

Figure 3 - (a) Mounting the O-ring in a groove. (b)

Compression of the O-ring. (c) Application of fluid pressure

Figure 4 - (a) Mounting the O-ring between two plates. (b)

Compression of the O-ring. (c) Application of fluid pressure

3. Conventional Analytical Theory

This part summarizes the set of equations that give the

distribution of the contact pressure, the maximum value of

this contact pressure, and the length of the contact that

characterizes the joint-plate contact area. The joint-plate

contact has been treated by Lindley [2] by adapting the

classical theory of Hertz. This researcher developed a

simple equation that expresses the compressive load, F, as a

function of the compression ratio of the joint, C, according

to the equation.

02 (1.25 50 )F d d E C C





(1)

The compression ratio of the joint, C, is determined as a

function of the crushing values, e, and the diameter of the

joint cross-section

. It is expressed as follows:

C e d

The contact width,

, the maximum value of contact

pressure,

are given by equations (2) and (3).

2PR





(2)

pdl





(3)

With

the relative radius of curvature and

the

equivalent modulus of elasticity.

The relative radius of curvature,

, is determined

according to the type of contact. Thus in the case of the

plane-cylinder contact adopted by Lindley we have

R

(4)

The equivalent modulus of elasticity is given by equation

(5).





(5)

The distribution of the contact pressure as a function of the

radial position on the joint is given by equation (6).

( ) 1 x

p x p l









(6)

4. Results and Discussions

To verify the finite element models developed in this

chapter, we have made comparisons with the theoretical

results presented by Lindley [2] and the experimental results

of Kim et al. [32]. A first simulation is performed

Geometry of PLANE182

2D elements with four

nodes (I, J, K, L)

O-ring

Meshing of the O-

ring cross section

with PLANE182 2D

elements

Groove

Top plate

O-ring

Fluid pressure

Contact surfaces

(a)

(b)

(c)

Top plate

Lower plate

O-ring

Contact surfaces

Fluid pressure

(a)

(b)

(c)

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considering a zero fluid pressure and a zero friction

coefficient. results were obtained with the FE model

presented in Figure 4 and compared to the results of the

values of equation (1) developed by Lindley [2] and those

published by Kim et al. [32]. We note a very good

agreement between the results obtained by the analytical

model and the results of the FE model. However, there is a

significant discrepancy between the two models and the

experimental test of Kim et al. for compression ratios

greater than 15%. This difference may be due to the

geometrical and physical data considered by the authors

when establishing their model.

Both the analytical and numerical models are used to

determine the contact width values and contact pressure

distribution profiles when a clamping load is applied. Figure

6 shows a comparison between the contact width values

given by equation (2) and the FE model results shown in

Figure 4. The FE model results are the average value of the

last nodes in contact and the first nodes not in contact. The

difference between the numerical and analytical curves is at

most 5% at a clamping force of 350 N, which corresponds

to a compression ratio of 27% in this case. It is important to

recall that Lindley [2] describes the relationship of contact-

displacement force, contact width, and contact pressure as a

function of O-ring radial position for a maximum O-ring

compression ratio of 25%.

Figure 7 shows the contact pressure distributions on the

surface A1 defined in Figure 1 for four values of clamping

force. This figure also shows a comparison between the

analytical and numerical models. The contact pressure

profiles have a parabolic shape that confirms the Hertzian

shape. The comparison between the values of the analytical

model and the results of the FE analysis indicates that the

maximum contact pressure increases as the clamping force

increases and the difference between the two models do not

exceed 4%. From these remarks, we can confirm that there

is a good agreement between the two approaches, analytical

and FE, when the only load applied is the clamping force.

The effect of friction was considered from the finite element

simulation of assemblies 1 and 2 shown in Figures 3 and 4.

The axial and radial deformations of the O-ring as a

function of clamping force and fluid pressure are obtained

for

values of 0, 0.1, and 0.2 (Figure 8). This figure

shows the importance of the location of this type of seal in

a groove. For a clamping force of 700 N and a fluid

pressure of 0.75 MPa, the increase in the friction

coefficient considerably reduces the axial and radial

deformation of the seal. Indeed, for friction coefficients

0, 0.1 and 0.2. The elongation decreases respectively

from 66.5, 19.5 to 2.7%. Regarding the compression ratio,

it decreases respectively from 48.9, 37.3 to 30.9. In

conclusion, the deformation of the joint as a function of

the clamping load and the pressure of the fluid depends

strongly on the value of the friction coefficient.

Figure 9 shows the variation of the maximum

contact pressure, at the surfaces B1, B2 and B3 defined in

Figure 3, for two values of friction coefficients 0.05

and 0.2,

according to the pressure of the confined fluid. It can be

seen that the influence of the friction coefficient on the

contact pressure is negligible. Furthermore, by studying

Figure 10, the increase of the friction coefficient can

decrease the maximum value of the von Mises stress inside

the O-ring installed in a groove for high fluid pressures and

the opposite for low fluid pressures.

Given the particularity of the material characteristics of the

O-ring, a parametric study to understand the influence of

Young's modulus E becomes necessary. Several simulations

were performed, for the same geometry of the FE model

presented in Figure 3, for Young's modulus ranging

from 6.96 MPa to 17.3 MPa. The numerical calculations

were carried out with a coefficient of friction of 0.2.

Figure 11 shows the evolution of the compression ratio

C, obtained for three values of Young's modulus E,

weighting the two phases of deformation of the seal:

clamping phase F, and pressurization phase P. The results

delivered by this figure serve as a basis for determining the

influence of these three parameters on the compression

ratio of the seal in the throat. It is obvious that the

compression ratio increases with increased clamping force

and decreases with increasing fluid pressure. As can be

seen in the same figure, the compression ratio is

proportional to Young's modulus. It can be observed in

the clamping phase that, the stiffer the seal material, the

lower the compression ratio will be. On the other hand,

when the fluid pressure is applied and increases

further, the value of the compression ratio decreases.

It is also observed that the curves corresponding to the

three values of Young's modulus are inverted when the

fluid pressure exceeds 4.75 MPa.

Figure 12 shows the contact pressure distribution curves at

the contact surfaces B1, B2 and B3 defined in Figure 1, for

a compression ratio of 20% and a fluid pressure of 5 MPa.

The simulations are performed for several values of E. The

curves in this figure confirm that the stresses are

proportional to the moduli of elasticity for the same

deformation. Thus, when the joint stiffness is greater, the

contact pressure is greater. Figure 13 shows the variation of

the maximum value of Von Mises stress inside the seal for

three values of E as a function of fluid pressure for a

compression ratio of 20%. Regardless of the value of E, the

maximum Von Mises stress increases with increasing rates

as the fluid pressure increases. We note that the difference

between the three seal hardnesses shows a high value for

pressures below 5.5 MPa and remains relatively low for

fluid pressures above this value. This result does not

surprise us. Indeed, whatever the value of E, when the fluid

pressure is applied and its value increases, the zone where

the stress is maximum moves towards the outside of the

joint to the side of the extrusion gap. Lastly, it is worth

mentioning that the compression ratio as a function of

clamping force - Numerical/ analytical/ experimental

comparison is presented in Figure 5.

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Figure 5 - Compression ratio as a function of clamping

force - Numerical/ analytical/ experimental comparison

Figure 6 - Contact width versus clamping force -

numerical/analytical comparison

Figure 7 - Distribution of contact pressure as a function of

clamping force - numerical/analytical comparison

Figure 8 - The influence of the friction coefficient on the

deformation of the O-ring

Figure 9 - The influence of the friction coefficient on the

maximum contact pressure

0.05f

0.2f

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Figure 10 - The influence of the friction coefficient on the

maximum value of the Von Mises stress

Figure 11 - Variation of compression ratio with the

variation of clamping force and fluid pressure

Figure 12 - Influence of Young's modulus on the contact

pressure distribution for a compression ratio of 20% and a

fluid pressure of 5 MPa

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Figure 13 - influence of Young's modulus on the maximum

value of the Von Mises stress for a compression ratio of

20%

5. Conclusions

This work is devoted to the study of the mechanical and

leakage behavior of pressurized assemblies equipped with

an O-ring which is placed in a groove and between two

plates. The material behavior of the O-ring has been

described by the Mooney Rivlin behavior law. The finite

element model of the gasket was carried out with

axisymmetric elements under the assumption of large

displacements and large deformations using the commercial

software (ANSYS).

The combined effect of clamping load and fluid pressure

has been analyzed for both assemblies. The numerical

results obtained are compared with the experimental results

published by Kim et al. [20] and theoretically based on the

classical Hertz theory. The comparison is made only on the

clamping force, contact width, and contact pressure. They

show agreement and confirm the classical form of the

contact pressure distribution.

This study shows that the use of a groove to ensure the

assembly of elastomer O-rings is important in pressurized

installations. On the other hand, under the same loading

conditions, the reliability of the O-ring is strongly

dependent on three parameters: compression ratio of the O-

ring, its hardness, and the friction coefficient.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author(s) contributed in the present research,

at all stages from the formulation of the problem

to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author(s) declare no potential conflicts of

interest concerning the research, authorship, or

publication of this article.

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