Effect of Valves Stiffness on the Performance of a Twin-Tube Hydraulic
Damper
AMINA BEN ABDELWAHED, JAMEL CHAKHARI, CHARFEDDINE MRAD
Laboratory of Applied Mechanics and Engineering,
National Engineering School of Tunis, University of Tunis El Manar,
Tunis 1002,
TUNISIA
Abstract: - In this paper, the dynamic behavior of a twin-tube automotive hydraulic damper is studied. A front
axle car damper is subjected to experiments in both phases compression and rebound. Accurate CFD
simulations are developed to improve the understanding of the performance of the damper by exploring its
hydraulic behaviors in transient response. Dynamic meshing is applied to simulate the fluid flow in terms of
velocity and pressure distribution in damper chambers. The deflections of base and piston valve membranes
respectively in compression and rebound are determined through an iterative method considering the fluid-
structure coupling. Numerical results are in good correlation with those issued from experiments. The presented
CFD model is a numerical tool if applied can minimize the number of experiments in the step of design and
testing of twin-tube dampers.
Key-Words: - Twin-tube hydraulic damper, Compression and rebound, Force-velocity curves, Valve
configurations, Membranes deflection, Testing of prototype, CFD simulation, Transient flow.
Received: April 16, 2024. Revised: October 22, 2024. Accepted: November 9, 2024. Published: December 21, 2024.
1 Introduction
The suspension on a vehicle is the term given to the
system composed of springs, dampers, and
mechanical links that connect the vehicle chassis to
the axles. Because of irregularities of some roads, a
running car can be subjected to different
displacements which greatly reduce the comfort of
passengers. Shock absorbers limit the oscillatory
movements, slow the bouncing of the wheels on
obstacles, and keep them in contact with the ground.
In order to lower the amplitude of vibration, all sorts
of shock absorbers are used. The hydraulic damper
is the main component of such systems.
Several studies have been carried out on
hydraulic dampers ; experimental characterization,
[1], [2], [3], [4], [5] and especially modeling [6],
[7], [8]. For characterization, car manufacturers use
a simple force-velocity curve as a computer model
of the damper. An experimental or numerical curve
should be found between two standard limit curves
for quality control and damper acceptance.
Hydraulic dampers that are used in recent
vehicles have characteristics that are generally
unsymmetrical and nonlinear. The damper is one of
the most difficult components to model because of
its highly nonlinear characteristics, [9]. In many
papers, researchers studied the twin-tube damper
type. A physical and mathematical nonlinear model
was created for a twin-tube hydraulic damper. To
analyze the theoretical model, methods of numerical
integration were incorporated, [10]. The
characteristics of the damping force depend mainly
on the geometrical and physical properties of the top
and bottom valves of the damper. This conclusion is
deduced also in research references [11] and [12],
where force displacement and force-time plots are
considered for damper characteristics analysis.
In paper [13], a numerical model was used to
show the advantage of a base valve to make a twin-
tube damper more performant than a mono-tube
one. In numerous published papers, the effect of
design parameters on hydraulic damper behavior is
shown. The the effect of number of orifices on the
damping force at different velocities for a two-
wheeler automobile mono-tube damper is
investigated, [14]. It is concluded that as the number
of orifices increases the damping force and the
damping coefficient decrease. The simulation of
failure characteristics of a twin-tube shock absorber
is done to show limit curves, [15]. The dynamic
stiffness and damping coefficients are computed
under multiple conditions. A nonlinear model is
established in order to analyze the effects of shim
stack and orifice parameters on damper
performance, [16]. The model helps in developing
controllable valving based on shim stacks in
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dampers. Results of the CFD orifice flow model of
hydraulic oil presented in reference [17], show that
orifices are employed to damp pressure pulsation to
improve the system control accuracy. In some
conditions the flow regime transition from laminar
to turbulence can be obtained, which affects the
valve membrane's deflection and therefore the
damper response.
In this context, this work consists of studying
experimentally and by CFD simulation the dynamic
behavior of a twin-tube hydraulic damper for front
axle of vehicles. Characteristic curves will be
plotted for several excitation velocities and for
different configurations of valves, in compression
and rebound. We interested mainly in transient
phase of damping. A dynamic meshing will be used
to study the fluid transient flow.
In addition to orifices, the piston and base
valves in a twin-tube damper consists of a stack of
thin membranes. The best configuration of
membranes, numbers, and thickness, will be chosen.
The deflection of these membranes under fluid
pressure passing through valves orifices will be
determined. It consists of showing how the
geometry of the dual-tube automotive damper
affects its hydraulic behavior and its performance.
In comparison with the corresponding studies of
other researchers, cited previously, the novelty in
this paper is the iterative method applied for
determining the shim stack deflection by coupling
with the CFD model of fluid domain. That
deflection controls all the hydraulic damper
response.
2 Design and Operating Phases of a
Twin-Tube Damper
The damper under study is a subassembly of a twin-
tube shock absorber for the automotive front axle. It
consists mainly of two coaxial tubes or cylinders as
shown in Figure 1.
Fig. 1 : Damper components
The chamber in which the piston and rod move
is the working chamber. The compensation chamber
is located between the inner tube and the body tube.
It is filled 2/3 with oil and 1/3 with air or gas.
Compared to single-tube construction, twin-tube
dampers offer the advantage of being shorter. In
twin-tube dampers, base valve and piston valve
consist of a system of small spring washers or thin
elastic membranes. The piston or base valves have
throttle holes for the passage of oil. The rod, guide,
and seal are extremely precise components.
The damper consists of three chambers. An
external compensation chamber and two internal
working chambers. Inside the working cylinder, the
piston is attached to the rod, and it separates the two
internal chambers. The piston rod is equipped with a
guide that limits its movement in the longitudinal
direction, Figure 2. The characteristic curves of the
damping force are specially determined for each
type of vehicle, taking into account the weight of the
vehicle, the construction of the axles, and the
chassis springs stiffness.
Fig. 2 : Operating phases of shock absorbers
During the rebound phase, the fluid in the
expansion chamber is forced to flow to the
compression one. During the compression phase, the
fluid in the compression chamber is forced to flow
to the expansion and compensation chambers,
Figure 3.
Fig. 3 : Fluid flow during operations
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3 Experimental Tests
The hydraulic test rig is used to show how the
damping force changes with the excitation velocity.
The damper is fixed at one end on the test bench and
is driven in translation attached to the other end,
Figure 4. A load cell is installed on the fixed end of
the damper. A data acquisition system records the
damping force measurements and the corresponding
displacements.
Three tests are carried out for different
configurations of base and piston valves. For each
test, the number and thicknesses of used metallic
membranes are precise. Membranes play the role of
valve spring in flow control. The number of valving
orifices is fixed; 8 orifices for piston and 6 for base.
The membrane configuration for each test is
mentioned in Table 1 (Appendix), where e signifies
the single membrane thickness.
The characteristics of test 1 are taken as initial
values and conditions. For test 2, the modification
concerned the piston valve, its stiffness is slightly
reduced. For Test 3, the modification is made to the
base valve, its stiffness is moderately reduced.
Fig. 4 : Test bench
The results of the calibration tests for three
excitation velocities: 0.1, 0.3, and 0.5 m/s; and
during the compression and rebound phases, are
presented in the form of force-displacement curves,
Figure 5, Figure 6 and Figure 7 in Appendix.
The upper part of the curves has positive
velocities, corresponding to rebound, while the
lower part of the curves has negative velocities,
corresponding to compression. Either in rebound or
in compression, the magnitude of damping force
increases when the excitation velocity increases.
The force increases and then decreases with
displacement in nonlinear response for a given
velocity. The measured values of the damping force
in the three tests are shown in Table 2.
By modifying the configuration of the piston
valve (Test 2), a slight variation is observed in the
damping force of the two operating phases. The
damping force increases by 2% in compression and
rebound at the velocity of 0.1m/s. It increases by 1%
in a rebound at the velocities 0.3 and 0.5 m/s, and it
decreases by 4% and 3% in compression at the
velocities 0.3 and 0.5m/s respectively.
By changing the base valve configuration (Test
3), a significant variation in the compression phase
damping force is observed. The damping force
increases by 13% in compression at a velocity
0.1m/s, and increases by 8% in compression at
velocities 0.3 and 0.5 m/s. It decreases by 0.02%,
0.8% and 1.2% in rebound respectively at velocities
0.1 ,0.3, and 0.5m/s.
Table 2. Experimental values of damping force for
three tests in compression and rebound
Compression
Rubound
Piston velocity
(m/s)
Piston velocity
(m/s)
0,1
0,3
0,5
0,1
0,3
0,5
51,3
93,4
117,5
28,4
50
71,3
52,5
94,1
118,5
29
48
69,8
58,4
101,1
127,7
28,1
49,6
70,5
The results of these three tests prove that the
damping force increasing can be obtained in case of
good choice of number and stiffness of membranes
controlling piston and base valves outlets.
4 CFD Simulation
As a consequence of an experimental previous
study, CFD simulation could be used to develop a
numerical model helping in more understanding
of the problem of valving. It also aims to enhance
the design of the twin-tube hydraulic damper. The
optimal solutions for design parameters can be
found through an iterative process. The fluid
velocities, pressure distribution, and resulting force
on the rod of the damper depend strongly on the
membranes stiffness and deformation. It’s a
coupling fluid-structure problem.
4.1 Mathematical Background
When the piston acts, in compression or rebound
direction, the fluid moves respectively through
geometrical volume shown in Appendix in Figure 8
and Figure 9. Laminar and turbulent flows can
happen. Fluid layers flow without mixing when
the flow is laminar. When there is turbulence, the
layers mix, and there are significant velocities in
directions other than the axial direction of flow in
the damper. Streamlines are smooth and continuous
when the flow is laminar but break up and mix when
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the flow is turbulent. Turbulence main causes are
obstruction or sharp corners and high speeds of
fluid, [18], [19], and [20]. The excitation piston
speed is generally low, so for the studied problem,
the concentration should be more on laminar flow.
Poiseuille’s law applies to the laminar flow of
an incompressible fluid of viscosity η through a tube
of length l and radius r. The direction of flow is
from greater to lower pressure. Flow rate Q is
directly proportional to the pressure difference
(P2−P1), and inversely proportional to the length l of
the tube and viscosity η of the fluid, Eqs 1 to 3.
Flow is proportional to pressure difference and
inversely proportional to resistance:

(1)
For laminar flow in a tube, Poiseuille’s law for
resistance states that:

 (2)
Poiseuille’s law for flow in a tube is:
󰇛󰇜
 (3)
Poiseuille’s law (Eq.3), shows that the flow rate
Q through the damper valve holes depends stongly
on the length l and radius r of holes. Therefore, the
damping force applied on the rod of the damper is
also influenced by the design parameters of
the valves.
Ansys Fluent is used for CFD simulation. It
provides comprehensive modeling capabilities for a
wide range of incompressible and compressible,
laminar, and turbulent fluid flow problems. Steady-
state or transient analyses can be performed. A
broad range of mathematical models is combined
with the ability to model complex geometries. The
mathematical model corresponding to laminar flow
is chosen for the simulation of the studied hydraulic
damper dynamics.
4.2 Simplified Geometrical Model and
Meshing
Figure 8 (Appendix) presents the geometrical model
filled by the fluid in the compression phase. The
holes and the membrane zones of the base valve are
considered. Based on that geometry a finite
elements model is built using the software Ansys.
The meshing is refined in confined zones.
The same work is done for the case of
the rebound phase, Figure 9 (Appendix). The holes
and membrane zones of the piston valve are
considered in the model.
4.3 Dynamic Meshing
Hexahedral 3D-finite elements are more adequate
for CFD problems. They generate for the model
fewer elements and more nodes which provide more
precision in results and make computation converge
more rapidly than in the case of tetrahedral meshing.
When the force is applied to the damper, the piston
moves, and the fluid geometry changes in some
zones. In stationary response, modification of
meshing is not necessary. But in the case of
transient response, a dynamic meshing should be
considered. Three types of dynamic meshing can be
applied in Ansys Fluent: Smoothing, layering, and
remeshing. The two first methods are applicable to
this problem, and they give similar results.
In the stationary case, the inlet velocity is
applied to the piston face. But in transient response,
the velocity of the subassembly piston-rod is applied
at its mass center. This rigid body moves in the
damper axis direction, its mass is mrod-piston = 1.15 kg
for the experimental case study. At the outlet, the air
or gas pressure is Ps = 1bar. The transient response
duration is td = 0.1 s and the computation time step
is Δt = 0.001 s.
4.4 Deflection of Membranes
In Appendix, Figure 10 presents the solution used
for valve control. It consists of thin elastic
membranes stuck with different thicknesses. For
numerical simulation of membrane deformation, the
points of application of pressure forces are situated
on a circular contour passing through the centers of
orifices outlets.
The determination of the membrane deflection on its
boundary is conducted in steps described in Figure
11 (Appendix):
a) The CFD simulation starts with an initial value of
deflection h=0.01 mm for a given velocity of the
piston.
b) Evaluate force at the outlet of holes.
c) Apply the found force for a separate membrane
structural model. For each hole corresponds a
force.
d) The computation of that membrane structural
model returns a new value of deflection
e) Restart the CFD simulation with the last value of
deflection for the given velocity of the piston.
The method rule is to apply these steps till the
deflection and hole outlet force remain constant. So,
the method needs many iterations. For example, for
the case of damper in compression for configuration
C1 and for a piston velocity of 0.3 m/s the results of
iterations are shown in Figure 12 (Appendix). The
base valve membrane deflection is found h=0.34
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mm. The same iterative method is also applied to
determine the deflection of the piston membranes in
the rebound phase for configuration D1. The piston
valve membrane deflection is found h=0.28 mm.
4.5 Computation of Damping Force
Fluid in the damper is distributed in three chambers
A, B, and C with average absolute pressures
respectively P1, P2, and P3. Damping forces in
compression and rebound are determined by
equilibrium equations respectively in Figure 13 and
Figure 14. Friction forces and those due to
atmospheric pressure on piston rod are neglected in
comparison to main forces. Ap is the piston section
side chamber B, and At is the piston-rod section.
The extremity of the rod side piston is conical which
induces a supplementary force Fcon on the piston-
rod. In the compression phase the damping force is
given by equation (Eq.4) and in rebound it is given
by equation (Eq.5).
FCompression = P2Ap – P1 (Ap –At) +Fcon (4)
FRebound = P1 (Ap –At) – P2Ap +Fcon (5)
Fig. 13: Piston equilibrium-compression phase
Fig. 14: Piston equilibrium-rebound phase
4.6 Numerical Results
For each numerical solution, the convergence is
tested by verification of the residual curves.
Velocity and continuity residuals should stay
constant after enough iterations. As shown in Figure
15 the residuals’ values are less than 0.001 and
remain constants after 50 iterations, which confirms
the convergence and acceptance of numerical
solutions given by the software.
Numerical results presented in Appendix in
Figure 16, Figure 17, Figure 18 and Figure 19, are
all computed for piston velocity v=0.3 m/s. Figure
16 (Appendix) presents the disribution in
compression in the case of configuration C1.
Pressure can reach 7.32 bar in the compression
chamber. Figure 17 (Appendix) shows the fluid flow
velocity distribution in compression in the case of
configuration C1. The high velocity of 12.95 m/s is
found through the base valve orifices.
Figure 18 (Appendix) presents the distribution
in a rebound in the case of configuration D1.
Pressure can reach 8.44 bar in the rebound chamber.
Figure 19 (Appendix) shows the fluid flow velocity
distribution in a rebound in the case of configuration
D1. The high velocity of 18.09 m/s is found through
the piston valve orifices.
Fig. 15: Residuals curves to test convergence of
numerical solution in case of configuration C1 and
for v=0.3 m/s
5 Results comparison and Discussion
Figure 20 (Appendix) presents both numerical and
experimental results on the same graph. The
damping force is plotted function of the velocity of
the damper piston. Curves are shown for both
phases compression and rebound. For each phase
are plotted two limit curves Dmax and Dmin for
rebound and Cmax and Cmin for compression. They
determine the acceptance zone for the tested
damper. Results are plotted for configurations D1
and C1. The maximum damping force is obtained in
the rebound phase. The results of the CFD
simulation agree well with the measured data. That
validates the numerical model of the twin-tube
hydraulic damper.
The CFD model will be now applied to simulate
more valve configurations. The choice of membrane
stack for the base and piston is precised in Table 3
(Appendix). Numerical results are computed for
piston velocity v=0.1 m/s. For both cases
compression and rebound the upper limit, the lower
limit, and the target value of damping force are
defined and determined by the standards respecting
to which vehicle the damper will be mounted, Table
3 (Appendix).
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Figure 21 (Appendix) shows the damping force
results in compression for different base valve
membranes stack. For cases BMS2 and BMS4,
values are out of limits. Cases BMS3 and BMS5
give acceptable values of damping force but
are very close to limits. The stack BMS1 gives the
nearest force to the target. It can be considered
the best choice for the design of the damper base.
Figure 22 (Appendix) shows the damping force
results in rebound for different piston valve
membrane stacks. For cases, PMS2 to PMS5, force
values exceed the upper limit. The stack PMS1
gives the nearest force to the target. It’s the best
choice for a damper piston.
The previous results show that the application of
the numerical model, through an iterative
computation of the membranes stack deflection, can
give precisely the value of the damping force for a
given piston velocity.
For different membrane stack configurations,
without experimental testing, and without numerical
simulations it is difficult to predict which one will
give the nearest value to the target value of damping
force. Considering the cost criterion, the numerical
tool is the best and most rapid way to select the
optimal valve configuration.
6 Conclusion
Testing a prototype of a hydraulic twin-tube dumper
was useful to verify its performance in compression
and rebound, under several excitation velocities, and
with different configurations of the piston and base
valves. The increasing of damping capacity or
damping force is dependent on different parameters.
The shim or membranes stack in pistons or base
valves play the role of mechanical spring that
controls fluid flow. The stiffness of such spring is an
influencing parameter on the damper behavior. A
numerical model was built and validated
experimentally. The model was then applied to
check the damping force value for different cases of
shim stack of base and piston valves. The presented
numerical model for a given twin-tube damper type
can be applied for other automotive damper types by
following the same calculation procedure and
preparing the appropriate geometrical model. The
presented method can contribute to the design of
performant automotive dampers in terms of
damping force.
Acknowledgement:
The authors thank the company « Leading
Technology in Mechanics-LTM, Z.I Agba-Denden,
Tunis, Tunisia » for the provision of experimental
facilities.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to the present
research, at all stages from the presentation of the
problem, experimental testing, to the numerical
solution and final findings.
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 authors have no conflicts of interest to declare.
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WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2024.19.16
Amina Ben Abdelwahed,
Jamel Chakhari, Charfeddine Mrad
E-ISSN: 2224-3429
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APPENDIX
Fig. 5: Result of test 1, Force-displacement curves
Fig. 6 : Result of test 2, Force-displacement curves
Fig. 7 : Result of test 3, Force-displacement curves
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DOI: 10.37394/232011.2024.19.16
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Fig. 8 : Geometrical model and meshing for compression phase
Fig. 9 : Geometrical model and meshing for rebound phase
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2024.19.16
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Fig. 10: Design of membranes for valve control and points of application of forces due to pressure of outlet
flow through orifices
Fig. 11: Iterative method for computation of membrane deflection for given piston velocity
(a)
(b)
Fig. 12: Results of iterative method : (a) membrane deflection (b) force at hole outlet
(a)
(b)
(c)
(d)
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DOI: 10.37394/232011.2024.19.16
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(a)
(b)
Fig. 16: Pressure distribution in compression in case of configuration C1 and for v=0.3 m/s : (a) outside view
(b) section view through two base valve holes
(a)
(b)
Fig. 17 : Fluid flow velocity distribution in compression in case of configuration C1 and for v=0.3 m/s : (a) 3D
view (b) flow through base valve holes
(a)
(b)
Fig. 18 : Pressure distribution in rebound in case of configuration D1 and for v=0.3 m/s : (a) outside view (b)
section view through two piston valve holes
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(a)
(b)
Fig. 19 : Fluid flow velocity distribution in rebound in case of configuration D1 and for v=0.3 m/s : (a) 3D view
(b) flow through piston valve holes
Fig. 20: CFD simulation and experimental results comparison
Fig. 21: Model results- Damping force for different stacks of base membranes
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
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Fig. 22: Model results- Damping force for different stacks of piston membranes
Table 1. Configuration of membranes in three tests
Base valve
Piston valve
Test 1
C1:
5 membranes with e=0.1 mm
D1:
1 membrane with e=0.1 mm and 2 notch flow
3 membranes with e=0.1 mm
1 membrane with e=0.2 mm
Test 2
C2:
5 membranes with e=0.1 mm
D2:
1 membrane with e=0.1 mm and 2 notch flow
2 membranes with e=0.2 mm
Test 3
C3:
1 membrane with e=0.1 mm
1 membrane with e=0.2 mm
D3:
1 membrane with e=0.1 mm and 2 notch flow
3 membranes with e=0.1 mm
1 membrane with e=0.2 mm
Table 3. Configurations of valve membranes stack
Base membranes stack (BMS) – Compression
Upper limit=366 N ; Lower limit=192 N
Target=280 N
Piston membranes stack (PMS) – Rebound
Upper limit=630 N ; Lower limit=370 N
Target=500 N
BMS1
5 membranes with e=0.1 mm
PMS1
5 membranes with e=0.1 mm
BMS2
1 membranes with e=0.1 mm
2 membranes with e=0.2 mm
PMS2
1 membranes with e=0.1 mm
2 membranes with e=0.2 mm
BMS3
2 membranes with e=0.1 mm
1 membranes with e=0.3 mm
PMS3
2 membranes with e=0.1 mm
1 membranes with e=0.3 mm
BMS4
1 membranes with e=0.2 mm
1 membranes with e=0.3 mm
PMS4
1 membranes with e=0.2 mm
1 membranes with e=0.3 mm
BMS5
3 membranes with e=0.1 mm
1 membranes with e=0.2 mm
PMS5
3 membranes with e=0.1 mm
1 membranes with e=0.2 mm
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2024.19.16
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