the dynamic performance of air spring air damping systems...

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.

3891

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.

3892 PROCEEDINGS OF ISMA2012-USD2012

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)

VEHICLE NOISE AND VIBRATION (NVH) 3893

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)


(

) ( )

|

. (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


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.


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.


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


∑ , (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


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


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


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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