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The dynamic performance of air spring air damping
systems by means of small excitations
W. A. Fongue1,2
, P. F. Pelz2, J. Kieserling
1
1 Chassis Component & Innovation, Group Research of Advanced Engineering, Daimler AG
059/X578, 71059 Sindelfingen, Germany
e-mail: [email protected]
2 Chair of Fluid Systems Technology, Technische Universität Darmstadt
Magdalenenstrasse 4, 64289 Darmstadt, Germany
Abstract Air spring systems gain more and more popularity in the automotive industry and with the ever growing
demand for comfort nowadays they are almost inevitable. Some significant advantages over conventional
steel springs are appealing for commercial vehicles as well as for the modern passenger vehicles in the
luxurious class. Current series air spring systems exist in combination with hydraulic shock absorbers
(integrated or resolved). An alternative is to use the medium air not only as a spring but also as a damper:
a so-called air spring air damping system.
Air spring air damping systems (LFD) are force elements which could be a great step for the chassis
technology due to their functionality. Their major drawback is less damping at small excitations. This is
caused by invisible short waves on the road at speeds below 120 km/h, which lead to resonance vibrations
of the unsprung mass couple by the tire spring (micro juddering). Component specific countermeasures
would be a reduction of the friction in the rubber bellows and enough damping capacity at small
excitations.
This paper is about the dynamic performance of air spring air damping systems in case of small
excitations. First of all it presents the principle and the characteristics of the LFD, summarizes the state of
the art of simulation models for air spring air damping systems and gives some insight into the physics of
such systems and their sensitivity to some parameters. Then the existing model is calibrated based on an
existing air spring air damping hardware. The LFD model is expanded with a coulomb friction element
and validated with measurements. At the end a strategy to solve the micro juddering will be elaborated.
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1 Introduction
In recent years there has been an increased demand for ride comfort. These increased ride comfort
requests cannot always be fulfilled by a classic chassis setup with steel springs and hydraulic dampers.
These high requirements for ride comfort are achieved by conventional suspension and damping systems
only at the cost of ride safety. A solution to this conflict lies in the use of active suspension systems (see
figure.1).
To these active suspension systems belong air springs with active integrated hydraulic shock absorber, see
Figure 2a.The use of air as a spring medium enables a load independent adjustment of the body floor
height of the vehicle at a desired level (load leveling). The air suspension allows through its air supply and
pneumatic control equipment a variable stiffness and a decoupling of the body vibration behaviour and the
vehicle load: This is called load independent vibration behaviour. In conventional suspensions, the spring
must be stiff enough to avoid the body from sinking too much, even at full load. This is disadvantageous
in normal operation. The air suspension can be design softer than conventional suspension and provides
therefore a better ride comfort. However, the friction coming from the piston seal of their integrated shock
absorber causes rough handling. A solution is the use of air spring air damping systems, whose design
avoid dynamic seals (see Figure 2b)
L Limousine with a passive chassisS Sports car with a passive chassisA Vehicle with an active chassis
com
fort
acce
ptab
leun
acce
ptab
le
driving safetyacceptable unacceptablerelatively effective wheel load fluctuations
Perc
epti
on a
ccor
ding
to
VD
I 205
7
Limit for passiveadjustable damping
Limit for conventional
chassis
Figure 1: conflict between ride comfort and ride safety [2]
Through the use of rubber bellows, there is no more mechanical connection between the body and the
axle. This contributes to reduce the subjectively perceived rough handling. Experience has shown that the
rubber bellows hardening contributes to a force response, which is called harshness. It depends on design
and material specific parameters of the rubber bellows. That is the reason why it should be reduced, to
allow the best ride comfort by large scale production of the air spring air damping system.
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Figure 2: a) Air spring with integrated hydraulic shock absorber of the current Mercedes S class, b) Air
spring air damping prototype of the same class und c) Hysteresis curve of the both: blue for a) und red for
b) by an excitation frequency of 1 Hz
2 Suspension and damping by air: Principle and characteristic
The air spring air damping system is a force element that consists in its simplest version of two chambers
filled with air at a desired pressure p0 and separated by a piston. The chambers are connected to each other
through a valve, see Figure 3a). The LFD works with pure air as spring and damper medium. The
suspension is carried out by the change of the total air volume V and the damping by the throttle flow
from one chamber to another through the valve. According to [5] the desired dissipated energy is not
caused by the air internal friction in the valve but only down to the valve. Here splits the air jet into
turbulent swirl in which the kinetic energy of gas particles is dissipated into heat. The LFD requires, like
every air spring systems, an air supply and a pneumatic control equipment, hence its need for more
available space in comparison to the conventional suspension systems.
Figure 4 shows in the column to the left ( a)-c) ) the behaviour of LFD in different frequency ranges. In
the column to the right ( d)-f) ) there is a linear model of the LFD and its associated dynamic stiffness and
dissipated energy in comparison to a hydraulic shock absorber.
2.1 Frequency range f < < f0 (blue)
For frequencies less than f0 which is the tuning frequency, the pressure is the same any time in both
chambers. The piston has no effect and the LFD works in this case as a soft air spring with the total
volume V and the adiabatic stiffness c0, see figure 3a). For small excitation amplitudes about the initial
position stiffness c0 is given by
|
( )
|
(1)
0 0.05 -0.1 -0.15 -0.2 -0.05 0.1 -15
-10
-5
0
10
5
15
0.15
FO
RC
E i
n N
DISPLACEMENT in mm
AMPLITUDE 0.1 mm
c) a) b)
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with the bearing area
( ) ∑
(2)
the displacement area
∑
∑ ( ⁄ )
(3)
and the total volume
∑ (4)
Where is the adiabatic exponent, F0 the resulting force and p0 the initial pressure, both at the
initial position.
①
②
Figure 3: Physical parameters to describe a LFD. a) Principle Scheme and valve description and b)
Scheme of a 2-chamber LFD
2.2 Frequency range f > > f0 (yellow)
For frequencies f higher than the tuning frequency f0.There is no time for the air to achieve pressure
compensation in both chambers (stiff air spring). The valve has no effect and the two volumes of the LFD
act as two parallel connected air springs. In this case the highest level of stiffness c∞ is reached, see figure
4 c). For small excitation amplitude around the initial position the stiffness c∞ is given by
Pressure in the chamber i….…….......
Coefficient of discharge……………..
Volume of air in the chamber i…...…
Ambient pressure…….…..……...…
Temperature in the chamber ....……..
Ambient temperature……………….
Displacement area of chamber i….…
Density in the chamber i……….……
Bearing area of the chamber i……...
Valve area……….…………………
Wall area of the chamber i……..….
Overall heat transfer coefficient…..…
(i=1…n)
P1 ,V
1 , A
1 ,AT1 T
1
P2 ,V
2 , A
2 ,AT2 ,T
2
Ab
αAb
F ,z
F ,z
a) b)
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(
) ( )
|
. (5)
2.3 Frequency range f ≈ f0 (red)
At this range a transition takes place between the adiabatic stiffness and the upper stiffness c∞ with
increasing frequency. Energy is dissipated only in this range (damper).This characteristic, which allows a
damper to be adjustable and in terms of the desired frequency, is known in the literature as frequency
selectivity. For small perturbation around the equilibrium the behaviour of the LFD can be approximate by
a linear model, see figure 4d). For a harmonic excitation with frequency f and a small amplitude of
excitation the maximum energy dissipation can calculated as follows
∫
|
( ). (6)
Figure 4: a)-c) LFD behaviour in different frequency domain and d)-f) a linear LFD model and a
qualitative dynamic Behaviour of a LFD and a hydraulic damper
Compared to other conventional suspension systems, the LFD, which shows promising characteristics,
presents some disadvantages:
The Energy dissipation leads to an increase in temperature. The lower heat capacity of air
compared to oil leads to stronger warming. This must be accounted for in the design process.
All parameters must be set properly already in the design phase. Otherwise, new construction
requires subsequent changes.
A hardening of the roll bellows used as seal occurs at small excitation amplitude.
Linear model
Damper
Sti
ffn
ess
Stiff air spring
Soft air spring
Dis
sip
ated
En
erg
y
a)
b)
c)
d)
e)
f)
c∞-c0
d1
c0
c0
c∞
f0
f0 f
f
LFD
Hydraulic Damper
VEHICLE NOISE AND VIBRATION (NVH) 3895
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The coupling of the suspension and damping characteristic makes a vehicle tuning difficult.
3 Modelling and sensitivity analysis
This section presents the state of the art of the thermo-fluid-dynamic LFD model as well as presented
some insight into physics of such systems [4]. The model is based on physical fundamentals and plausible
assumptions. It allows not only a pure module description, but also dimensioning and tuning options.
Therefore it can be used simulations in all popular multi body simulation programs in the time and
frequency domains for ride comfort, handling and NVH simulation.
3.1 The thermo-fluid dynamic model of LFD
The following equations correspond to a two chamber LFD as illustrated in Figure 3b).For the explanation
of the quantities used please also refers to the figure 3. For convenience the partial differential is
denoted here by a dot. The model consists of:
3.1.1 Mass conservation equation
Considering an excitation ( ), the integral form of the conservation of mass in the both chamber
becomes:
( ) (7)
( ) (8)
The first term on left side in (7), (8) describes the local change of mass, the second term describes the
mass flow rate of the moving walls and the third term the mass flow rate as result of a valve flow.
3.1.2 Energy conservation equation
With the same consideration as in equations before, the integral form of the conservation of energy in the
both chamber becomes:
( )
( ) (9)
( )
( ) (10)
The first term on the left side in (9), (10) describe the local change of internal energy. The second term
describes the enthalpy flow of the moving walls and the third term the energy flow rate as a result of a
valve flow. Where Tt is defined as
[ ( ) ( )], (11)
to account of the direction of loading of the LFD. The fourth term is the heat flux over the wall of the LFD
neglecting the thermal inertia of the metal.
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3.1.3 Ideal Gas equation
The following equations give the thermal state of the gas in each chamber:
(12)
(13)
3.1.4 Valve conservation equation
The flow behaviour across the valve is given in (14). The mass flow rate is the only one responsible for
the dissipation, as it is shown in [5]. The mass flow rate can be described by the Mach number , the
speed of sound and the density of the air jet at the cross-section .
( ) { √ √
[( )
⁄ ( )
⁄ ]
√
(14)
With pt and pverh defined as
[ ( ) ( )], (15)
( )
( ), (16)
to account of the direction of loading of the LFD.
In the model is assumed that there is no internal fluid friction and no heat exchange through the wall of the
valve. Hence the acceleration of the air upstream until to the cross-section is isentropic, and the state
of the gas is determined by stationary compressible Bernoulli equation for ideal gases.
If the pressure ratio is equal to or less than 0.528 as it is shown in [6], that means critical or over
critical, the air in the chamber upstream is accelerated to the speed of sound. Because the information
downstream can be transported in the opposite of flow direction with a maximum of sound speed, the
mass and energy flow rate through the valve is independent of the thermodynamic state of the gas
downstream.
For under critical pressure ratio greater than 0.528, the air jet speed at the cross section is less
than the speed of sound. The pressure of the subsonic flow is determined by the surrounding it. Here the
mass and energy flow rate through the valve depends on the thermodynamic state of the gas downstream.
3.1.5 Resultant force
The following equation gives the resultant force at piston:
( ). (17)
The first and the second term on the right hand side describe the force response of the chambers pressure
on the piston and the third term the force response of the ambient pressure on the bearing area.
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3.2 Sensitivity analysis
The resulting force of the LFD defined in (17), is the force response to a harmonic excitation
( ). The application of the force and the displacement of the spring over time have a phase shift ,
which is known in the literature as loss angle. Plotting the force over the displacement of the spring, a
hysteresis curve is formed, see Figure 5.
To determine the transfer behaviour to harmonic excitation for the simulation and also for the
experiments, the following quantities can be defined: the dynamic stiffness and the dissipate energy. The
dynamic stiffness is defined as follows
, (18)
where and are the maximum and minimum forces and the excitation amplitude. The
dissipate energy corresponds to the dissipation energy per oscillation cycle. It can be calculated by a
numerical integration of the force-displacement-hysteresis curve of a vibration cycle ∮ .
With the help of the physical LFD model describe on the previous chapter, a prediction of amplitude- and
frequency-dependant behaviour of LFD can be derived.
Figure 5: on the left side the force response and displacement over time of the LFD and on the right side
the force-displacement hysteresis curve
An increase in the amplitude of the excitation causes an increase in the damping potential of the LFD, see
Figure 6a).By mean of dimension analysis it is show in [1] under the following condition:
, (19)
that the maximum energy dissipation , which occurs at the tuning frequency f0, is proportional to
the square of the displacement volume , the initial pressure p0 and the reciprocal function of the total
volume V
(
)
, (20)
with the displacement volume
0 0.2 0.4 0.6 0.8 1-4
-3
-2
-1
0
1
2
3
4
DIS
PL
AC
EM
EN
T
FO
RC
E
𝛿
TIME
Wd
FO
RC
E
DISPLACEMENT �� ��
𝐹𝑚𝑎𝑥
𝐹𝑚𝑖𝑛
0
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∑ , (21)
where is the excitation amplitude and the is displacement area of Chamber i.
If the valve in the LFD is a continuously variable valve the transition between the adiabatic stiffness
and the upper stiffness and the corresponding maximum energy dissipation can be shifted in the
relevant frequency range, see Figure 6 (b). It is shown in [1] using dimension analysis methods and under
condition (19), that the tuning frequency f0 is proportional to the valve area and the speed of sound :
(
)
. (22)
By equation (22) it is possible to adapt the tuning frequency f0 on the excitation frequency by adjusting the
valve area Ab, see figure 6b). Hence, it is possible to adapt the stiffness between the lower and upper
level which will be used for vehicle dynamics [7].
Instead the valve in the LFD runs as a pressure limiting valve, it is shown in [1], and under condition (19)
that the tuning frequency f0 is proportional to the area resilience , the pressure p0 and the speed of sound
(
)
, (23)
the maximum energy dissipation remains unchanged.
Figure 6: simulated dynamic stiffness and energy dissipation as a function of the excitation of two
chamber LFD, a) three amplitudes and one constant orifice area and b) three different orifice areas and
one constant amplitude
10-2
10-1
100
101
0
200
400
600
10-2
10-1
100
101
0
10
20
c dy
n in
N/m
m
1mm 2mm
3mm
a)
0
200
400
600
10-2
10-1
100
101
102
0
200
400
600
10-2
10-1
100
101
102
0
10
20
15% Abmax
10% Abmax
5% Abmax
b)
10-2
10-1
100
101
0
200
400
600
10-2
10-1
100
101
0
10
20
FREQUENCY in Hz
Wd i
n J
10-2
10-1
100
101
0
10
20 10
-210
-110
010
110
20
200
400
600
10-2
10-1
100
101
102
0
10
20
FREQUENCY in Hz 10
-2
10-1
100
101
102
0
10
20
Wd i
n J
c d
yn in
N/m
m
600
400
200
0
FREQUENCY in Hz FREQUENCY in Hz
10-2
10-1
100
101
100
10-2
10-1
100
101
VEHICLE NOISE AND VIBRATION (NVH) 3899
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0
100
200
300
400
500
4 Friction modelling
As explained above the forces caused by the rubber bellows contribute to a force response, which may be
identified harshness. Air spring rubber bellows consist off an elastomer matrix complemented by inline
reinforcement yarns. By the deformation of yarn in the cross-layered air spring bellows shears in the
elastomer occur and lead to a complex stress and deformation condition. This leads to inner material
friction in the air spring rubber bellows. Simplified described, the friction can be seen as a function of
comfort, see equation (23) [3].
Comfort
harshness
∑Coulomb friction. (23)
An improvement of comfort is possible through the reduction of friction forces. Their Knowledge and
their modelling allow them to be taken in consideration during the dimensioning of the vehicle.
Figure 7: nonlinear LFD-Model in addition to a single friction element (Coulomb friction)
Figure 7 takes the contribution of rubber bellows effects in the LFD into account. This contribution is
model here as a Coulomb friction element. The validation of the simulation with the measurement shows a
good alignment for frequencies greater than 0,8Hz. Instead of these alignments the dynamic stiffness
doubled for quasi-static stimulations, see figure 8. The effect can be explained with the fact that the inner
material friction cannot be considered as pure Coulomb friction. It is necessary to consider the rubber
bellows in its entire complexity to improve the model.
Figure 8: Simulation and measurement results with excitation amplitude of 3mm in a) und 2mm in b)
0.1 1 100
100
200
300
400
500
FREQUENCY in Hz FREQUENCY in Hz 10
0
10-1
101
10-1
100
101
100
200
300
400
500
c dy
n i
n N
/mm
Measurements Simulation
0.1, 45.4 0.1, 24.4
0.1, 51.5 0.1, 25.4
a) b)
F, z
LFD Rp
c dy
n i
n N
/mm
0 0
500
400
300
200
100
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5 Summary and Outlook
These previous chapters show the potential of the Air spring air damping systems as suspension elements.
But to allow them to be produce in series, some of its handicaps still have to be solve: e.g. its low
damping’s rate by small excitation and its poor heat exchange with environment.
To resorb the micro juddering, the effects of the rubber bellows have to be taken in consideration in the
LFD force response. Therefore a phenomenological model of the rubber bellows will be added parallel to
the existing LFD model. The idea is to model as simpler as possible and as complex as necessary. This
phenomenological model of the rubber bellows is a nonlinear model (see figure 9 a)), which can describe
the force-displacement behaviour of an elastomer by small excitations’ amplitude [8]. Its parameterisation
is done as follows:
The Maxwell series, which represent the viscoelasticity hysteresis effect of the rubber (elastomer),
is parameterised with a dynamic mechanic analysis (DMA) of the rubber. This Test yields the
information about the stiffness and the loss angle we need for the parameterisation of the Maxwell
Model.
The Masing model which represent the amplitude dependency hysteresis effect (inner material
friction) of the rubber bellows, are parameterised with a ‘double rolling pleat test’. This test has
advantage because of the symmetry of the mount bellows on the piston, to remove the Air spring
force and what is measured represented the rubber bellows effects.
The expanded model describe above will be validated with measurements, integrated into a complete
vehicle model to reproduce the micro juddering and will be optimized until the appropriate design is
found.
Figure 9: a) Nonlinear Elastomer model, b) Double rolling pleat test and c) Specific curve from a DMA
dm1
cm1 c0 cm3 cm2
dm3 dm2 R1 R3 R2
c1 c2 c3
Maxwell Model Masing Model
a) b)
c)
excitation
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References
[1] Ehrt, T: Simulation des dynamischen Verhaltens von Luft-Feder-Dämpfer, Diplomarbeit,
Technische Universität Darmstadt, 2001
[2] Heßing, B; Ersoy M: Grundlagen, Fahrdynamik, Komponente, Systeme, Mechatronik, Perspektiven
,ATZ/MTZ-Fachbuch, Vieweg & Sohn Verlag, Wiesbaden, 2007
[3] Meß, M; Pelz, P: Luftfederung und Luftdämpfung im Spannungsfeld Komfort, Dynamik und
Sicherheit, Automobiltechnische Zeitschrift, Ausgabe 03.2007, Wiesbaden, 2007
[4] Pelz, P: Theorie der Luft-Feder-Dämpfer, Freudenberg Forschung KG, interner Bericht, nicht
veröffentlich
[5] Pelz, P.: Beschreibung von pneumatischen Dämpfungssystemen mit dimensionsanalytischen
Methoden, VDI Bericht 2003, Wiesloch, 2007
[6] Pelz, P.: Fluidsystemtechnik, Skriptum zur Vorlesung, Institut Fluidsystemtechnik, Technische
Universität Darmstadt, 2008
[7] Puff, M: Entwicklung von Reglestrategien für Luftfederdämpfer zur Optimierung der Fahrdynamik
unter Beachtung von Sicherheit und Komfort, Dissertation, Technische Universität Darmstadt, 2011
[8] Wahle, M: Entwicklung eines Rechenmodells zur Beschreibung von Gummibauteilen bei statischer
und dynamischer Belastung. Schlussbericht zum Forschungsvorhaben, Aachen ,1999
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