DYNAMIC MEASUREMENT OF THE FORCES IN THE FRICTION ...

F2006V218
DYNAMIC MEASUREMENT OF THE FORCES IN THE FRICTION
AREA OF A DISC BRAKE DURING A BRAKING PROCESS
Degenstein, Thomas * , Winner, Hermann
Institute of Automotive Engineering Department at Technische Universität Darmstadt,
Germany
KEYWORDS – disc brake, piezo brake pad prototype, clamping force, effective contact
point, braking process
ABSTRACT – In this paper a measuring device is described, which enables measuring the
clamping forces acting during a braking process in the friction area between pad and disc.
Thus the amount and the effective contact point of the clamping force are determined finger-
and piston-sided at the same time. State of research is the measurement of the distribution of
clamping forces by means of pressure indication films. However, these are destroyed by shear
stress or friction and in this way they can be only used with a stationary brake disc, that is,
under no circumstances during a braking process.
An analysis of the force lines in a caliper shows that the preferred position for the
measurement of the clamping and tangential forces can be found in the friction material of the
brake pads, since all forces which contribute to the braking process must be supported by the
brake pad. As soon as these forces are induced in the back plate of the brake pad, a correct
measurement becomes almost impossible because of the multitude of contact points with the
caliper.
For the measuring device four slim-line piezo quartz sensors are integrated in an original
brake pad. The slim design of the sensors enables the measurement with the same thickness of
the pad like the original ones.
The piezo quartz prototype was applied and tested in a standard brake on a brake test rig. The
measurements show the shifting of the point of application of load related to the back plate of
the brake pad during a braking process. The consideration of the point of application of load
of the clamping force by a stationary brake disc causes a radial shifting to the brake disc’s
outer edge (this is primarily adjudged to the expansion of the caliper). During a braking
process the acting tangential force causes a shifting in tangential direction. By reason of
movement of the caliper during a braking process a visual measurement method was
developed, which enables recording the movement of brake pads.
The chance of measuring the amount and the contact point of the piston- and finger-sided
clamping force opens a window for understanding the braking process more in detail, e.g. of
the emergence and development of the wear conditions of the pads and the brake disc.
Furthermore, measurements are carried out in order to analyze the influences on the clamping
force in a disc brake (e.g. of the hydraulic pressure and the pressure rate, of the wheel’s speed
and of the disc’s temperature).
- 1 -

TECHNICAL PAPER – INTRODUCTION, MOTIVATION AND STATE OF THE ART
In this paper a measuring device is introduced which for the first time enables measuring the
clamping forces acting during a braking process in the friction area between pad and disc.
Here the amount and the contact point are determined finger- and piston-sided at the same
time.
The motivation for measuring these quantities is that a lot of processes in the brake are
unknown. This is reflected in the large number of research and development papers as e.g.
papers about braking torque and variations of the friction coefficient, emergence caused by
expansion of DTV (e.g. 14), squeal (e.g. 8), brake judder (e.g. 22), emergence of Hot Spots
(16) and comfort and performance features as well. In many approaches one cautiously
approaches processes during a braking process by simulations of the wheel brake, e.g. (13),
who researches the emergence of Disc Thickness Variation (DTV) by means of a multi-body
model. The input of the simulation model is generally the brake’s clamping force as a causal
effective quantity. Thus, the information about the clamping force can serve to validate the
simulation model. However, as both the amount and the point of application of load of the
clamping force are not available, the piston force (the differences between piston and
clamping force will be discussed later in this paper) is generally used instead.
For future electromechanical vehicle brakes, according to (15), the measurement of the
clamping force in a force measuring pad, for example, would also be a missing “puzzle piece”
in the control circuit of electromechanical braking systems till now. It would not be necessary
any more to estimate the braking torque by complex models for reconstruction of the braking
force.
The main components of a disc brake are the brake pads, the brake disc and the caliper (Fig.
1).
Fig. 1: Components of a disc brake: brake pad, brake disc, caliper
The basic quantities of the forces in a brake are presented in Fig. 2.
y
z
p
AP
brake pad (19)
FC
x
brake pads
µ
brake disc
caliper
FC
brake disc
brake disc
Fig. 2: Forces acting on a disc brake (3, 20, 21)
- 2 -
FT
caliper (5)
ra
brake
pad
direction of rotation
x
z
y

From the hydraulic pressure p and the piston surface AP results the clamping force FC. The
latter causes the tangential force FT = F C ⋅ 2µ
on both friction areas. The tangential force
causes, together with the active friction radius ra, the braking torque M B = FT ⋅ ra.
After all,
the braking torque is the quantity which causes with the help of the dynamic tire radius in the
contact patch of the tire the desired braking force and thus the deceleration of the vehicle.
Detailed researches show that some simplifications are assumed in this model of forces. (4)
Fig. 3 observes the forces acting on a brake pad more exactly.
FP
FC,red
FT
FC,m
∆FC
Fig. 3: Forces acting on a brake pad during a
braking process (4)
A further phenomenon is presented in Fig.
4. The caliper can be assumed model-likely
as a u-profile which inevitably expands
itself under the high clamping forces.
Because of that, shifting of the points of
application of load and therefore a bigger
active friction radius can be expected.
Furthermore, the assumption that no
identical shiftings will appear finger- and
piston-sided seems reasonable, since the
finger side has more elastic qualities than
the piston side with regard to construction.
y
x
z
- 3 -
1 Brake disc
2 Brake pad
3 Back plate
4 Piston
5 Stator (the fixed part of the wheel
brake, connected to the wheel
suspension)
By the support of the tangential force
on the stator a force FC,red opposite to
the brake piston results. Thus, it
shows that the clamping force does
not correspond to the piston force
during a braking process.
Furthermore, this also shows that one
cannot start with a uniform surface
pressing (compare ∆FC) and that the
point of application of load shifts
while braking, correspondingly FC,m,
and does not lie on the same function
line as the piston force.
stator
brake pads
active
radius
brake disc
caliper
expansion
Fig. 4: Caliper expansion under brake pressure

In the analyses of the brake disc is also apparent that the distribution of the surface pressing
brake disc shielding will change by a blow or DTV.
Thermal effects as e.g. the shielding
of a brake disc (Fig. 5) let expect
changes of the surface pressing of the
clamping force as well.
initial
state
after 3
seconds
after 7
seconds
Figures 2 to 5 show that inconsistent/not uniform surface pressing can be expected in a disc
brake. According to (4) this would lead to a slanted wear of the brake pads. Furthermore, a
higher energy expenditure results on the positions with higher surface pressing which leads to
higher temperatures. On the other hand, according to (3), higher temperatures drop to lower
friction coefficients and this reduces the efficiency of the brake. According to (4), the comfort
of the brake is also reduced, since sloping worn pads increase the squealing sensibility.
In order to avoid or reduce the problems mentioned, different measures are used in serial
brakes. Nowadays piston offsets, cuttings in the metal sheet, shiftings of the centre of pressing
of the piston, drawn pads (push-pull principle), two-piston calipers with different piston
diameters and even further measures are used among other things to counteract these effects.
In order to determine the influence of these measures and the actual surface pressing various
methods were developed. State of the art are the tension-optical ball pressing process,
pressure indication films of the company Fuji and electrical pressure indication films of the
company Tekscan (18), for example.
In the tension-optical ball pressing process of the company Girling (4) one 1.5 to 2 mm thick
plastic plate with known tension-optical properties and a ball cage with balls with a diameter
of 3 mm between brake pad and brake disc are laid. By increase of the hydraulic pressure of
the brake system the balls are pressed into the plastic material. Tension curves, which help
one to make statements about the transmitting force, can be seen under polarized light.
Photographs taken by the authors with electrical
pressure indication films show an non-uniform
surface pressing of a brake pad by a hydraulic
pressure of 50bar and a stationary brake disc. The
contact pressure distribution of the clamping force
and the point of application of load calculated by the
red-white rhomb are to be derived.
Further researches with electrical pressure indication
films can be found in (1 and 9), for example.
- 4 -
Fig. 5: Shielding of a brake disc (3)
Fig. 6: A photograph of the fotostress-plastic
plate for the ball pressing process of the
company Girling under polarized light after
load. The number of the interference rings on
the particular ball indentation is a measure for
the pressing dominating there. (4)
⎡ g ⎤
⎢ 2
⎣ cm ⎥
⎦
Fig. 7: Surface pressing distribution
under a brake pad (stationary brake disc)

All these methods have, beside their limited accuracy (e.g. Tekscan fault indication >10%
(18)) the disadvantage that they can be only applied by a stationary brake disc. According to
Fig. 3, however, it appears that during the braking process other distributions lead to the
clamping force by the support of the tangential force. By these methods the effect of the
caliper expansion can be primarily examined, which, however, will not behave in the same
way during the braking process as one by a stationary disc. Measuring methods for
determination of the clamping force during a braking process do not exist until now.
The focus of this work lays on the determination of the point of application of the clamping
force of the finger and piston side during the braking process correspondingly to Fig. 8.
FC,piston
Fig. 8: Shifting of the point of application of the clamping force
DESIGN OF THE MEASURING SYSTEM
In order to measure the desired forces, an analysis of the force lines in a disc brake is
necessary. For this analysis and the following measurements a two-piston finger framework
caliper of the company Continental Teves (type 2 FNR-Al42, fig. 1) was chosen. This caliper
is currently used in many upper class vehicles.
In Fig.9 the force lines of the clamping and the tangential force are qualitatively presented.
force lines
p
FT,piston
brake disc
FT,finger
FC,finger
f
Fig. 9: Force Lines in a caliper
- 5 -
FC,piston
rC,p
rC,f
FC,finger
caliper

It can be derived that the clamping forces branch
as soon as they are induced into the back plate.
One part of the clamping force flows over the
finger respectively the pistons and another part
over the stator. To be able to register the whole
clamping force, it must be first measured in the
friction material (Fig. 10) before it is introduced
into the back plate. If the force would be
registered on the piston, for example, the portion
that flows over the stator could not be registered.
This corresponds to the model concept of Fig. 3
that the piston force is not equivalent to the
clamping force.
Important selection criteria for the sensor technology are the forces to be transmitted (up to
40kN), the building space requirement (integrable in a brake pad), use in a serial caliper,
quasi-statical and dynamical measurement, low temperature dependency…
After comparing a number of sensor principles (among others strain gauges, piezo ceramics,
capacitive sensors…) the use of the piezo-electrical (Fig. 11) effect was chosen. (12, page
184)
F
Fig. 11: Piezo-electrical effect without/under force effect / piezo quarz material (2)
Detail information about piezo quartz sensors can be found in (17). In the end piezo quartz
sensors of the company Kistler of type 9136B (Fig. 12) were chosen.
Fig. 12 Piezo quartz sensors principle and sensor (10)
F
Decisive were, besides the big measurement range, the low building height and the stiffness
that approximately corresponds to the pad's back plate of steel. The temperature range is
sufficient. In comparison, the adhesive with which the brake pad is fastened to the back plate
- 6 -
caliper
stator
sensor positions
brake disc
Fig. 10: Measuring position of the sensors
for registration of the clamping force
Excerpt from the data sheet (10)
• Measuring range 0 – 60 kN
• Stiffness 8 kN/µm
• Inside diameter 12,1 mm
• Outside diameter 30 mm
• Height 4 mm
• Temperature range: -20 to 120°C
• Weight 14 g

is resistant up to approx. 300°. These temperatures are reached only after various processes of
braking at high speeds. For the planned researches high temperatures are reached at the brake
disc only for a short time. The air cooling available at braking test benches is sufficient to
keep the sensors in the permissible temperature field of application.
STRUCTURE OF THE MEASURING BRAKE PAD:
For the measuring of the point of application of load
of the clamping force four piezo quartz sensors are
built between the back plate and a support plate (Fig.
13).
Fig. 13: CAD Model of the piezo prototype
Fig. 14: position of the piezo quarz sensors
Fig. 15 shows the original brake pad compared to the Piezo prototype of the 2. generation.
Fig. 15: Original brake pad and Piezo
prototype
CALIBRATION OF THE BRAKE PADS
The calibration of the Piezo prototype is carried
out on a calibrating station (Fig. 16) designed
especially for this application case. With its help
forces can be applied at the same time in two
directions.
With this construction forces can be applied to the
brake pad one by one or simultaneously, statically
or dynamically. For a defined force flow this
occurs with the help of balls (recognizable at the
arrowheads of the forces in Fig. 16).
- 7 -
4 sensors
back plate
friction
material
Fig. 14 shows the real sensors on the adapter
plate (the back plate was removed for this
photograph). To determine the acting clamping
force the aggregated signal of the four single
forces is formed. The point of application of
load is determined by a moment balance in the
sensor measuring level.
The main difference between the original and the
iPad is the steel plate and the reduction of the
friction material's thickness connected to it. The
expected low compression ability of the brake pad
could be counteracted by a suitable choice of the
friction material. This could be proved in a
compression tester for brake pads. The pad shown
had a deformation of 300 µm at a maximum
testing pressure of 160 bar (with the original piston
surface) - this value lies in the standard range of an
European brake pad (11 and 19).
FX
FY
Piezo
Prototype
Fig. 16: Calibration station of the
Piezo prototype

TEST SETUP AND TEST PARAMETERS
For the test execution the prepared brake pads
were fitted into the caliper above
correspondingly to Fig. 17. The following
researches were carried out at the centrifugal
force test bench of the industrial partner, the
TMD Friction Ltd. (19) Fig. 18 left, as well as
at the chair’s own roll test bench (Fig. 18
right). The same brake was used; the
advantage of the use of a centrifugal force test
bench is the better accessibility of the
components. The advantage of using a roll test
bench is the nearer illustration of the reality,
since parts of the original suspension are also
used along with the wheel and the caliper’s
motion is thus shown as well.
power
unit
8 sensors
supplies (piezos)
brake disc
thermo
elements
torque
measurement
- 8 -
Fig. 17: Brake pads with integrated piezo
quartz sensors assembled in the caliper
(without a stator)
original wheel
suspension
Fig. 18 left: Test execution on TMD brake test rig; right: test execution on FZD roll test rig
The wirings of the eight piezo quartz sensors are led through the gap between stator and frame
of the caliper to a charge amplifier. Further the temperature of the brake disc, the temperature
of the sensors, the brake pressure, the speed and the braking torque are recorded. The
reproduction of the vehicle parameters is carried out for the vehicle mass with the
corresponding centrifugal force of the test bench. The air amount for the cooling of the
components corresponds to the flow of a brake of an upper class vehicle.
The following test parameters were chosen:
• Brake pressure: Series in 10 bar – steps from 0 to 60 bar (> 60 bar blocks the wheel)
• Wheel speed 0 m/s (stationary wheel) and braking from 15 and 30 to 0 m/s
• Brake disc’s temperature at the beginning of a braking < 100°C (to protect the sensors)
MOVEMENT OF THE BRAKE PAD REGARDING THE CENTRE OF THE BRAKE DISC
The determination of the point of application of load of the clamping force is carried out with
sensors which are in the brake pads. The centre of the wheel or the brake disc is regarded as a
reference point of the radius. The design of a vehicle brake allows on the one hand
movements of the caliper, on the other movements of the brake pads during a braking process.

For this reason it was necessary to develop a measurement method which enables recording
the movement of a brake pad during a braking. Finally a visual measurement method was
used with a resolution of 10.2 million pixel. With regard to the following photographs, a pixel
corresponds to 0.124 mm - this therefore also corresponds to the maximum precision of this
method. Fig. 19 shows exemplarily the movement of the finger-sided brake pad during a
braking with a braking pressure of 40 bar.
RESULTS
Fig. 19: Movement of a brake pad
during a braking with 40 bar
As expected, the brake pad is drawn in the direction of rotation. Furthermore, it easily
screws out intake-sided correspondingly to the acting forces. Therefore, the sensors move
outtake-sided insignificantly in the direction of the wheel's centre. For the determination of
the point of application of load, which is near the middle of the pad's back plate, it means in
this case a deviation of approx. 0.66 mm, which has to be added to the measured value. By
using other caliper types this value can turn out considerably greater, since frame brakes are
construction-relatedly considerably stiffer than e.g. simple finger brakes.
The indications of the positions of the sensors in the
brake pad for the following results correspond to
Fig. 20.
The course of the four sensors of the piston-sided
pad is exemplarily presented in Fig. 21 at a braking
pressure of 40 bar and a stationary brake disc. In
Fig. 22 is the course during a braking process with
an initial speed of 15 m/s (425 rpm).
- 9 -
1 2
3 4
Fig. 20: Indication of the sensors
in the brake pad

FY [kN], p [10 bar]
5
4
3
2
1
0
-1
It can be derived that the outer sensors transfer the greater forces. This rises further at an
increasing braking pressure – this corresponds to the model concept of expanding the caliper
at increasing pressure.
In Fig. 23 the results of the measurements for the stationary brake disc and for the braking
with an initial speed of 30 m/s (850 rpm) at finger- and at piston-sided pad are summarized.
The representation corresponds to Fig. 21 from the view on the back plate.
radial [mm]
500
rpm
p p
1
2
rpm
0 0.5 1 1.5 2 2.5 3 -100
3
0 rpm 850 --> 0 rpm
10
8
finger side 0 rpm
6
4
2
0
piston side 0 rpm
finger side 850 --> 0 rpm
piston side 850 --> 0 rpm
60 bar 60 bar
-2
-4
-6
∆ = 10 bar
-8
-10
10 bar
10 bar
-12
-14
tolerance less than 1 mm
10 bar
hydraulic pressure
-10 -8 -6 -4 -2 0 2 4 6 8 10
trailing edge tangential [mm] leading edge
Fig. 23: Shifting of the point of application of load during a braking process
4
rel. tolerance less than 1,5%
Fig. 21: Course of the normal forces of
the single sensors of the piston-sided pad
(stationary brake disc)
400
300
200
100
0
It can be derived that the point of application of load moves by 7mm piston-sided to the
outside by a stationary brake disc when the braking pressure rises from 10 to 60 bar. This
effect is finger-sided by approx. 17mm clearly greater. This can be explained by the design of
a brake (compare Fig. 4), since the brake is connected to the suspension piston-sided and so it
is stiffer than the finger side, which has to be lead over the brake disc. During a braking
process the points of application of load shift into the direction of the leading edge. This
corresponds to the model concept according to (4), compare Fig. 3. If these results are
transferred to the change of the friction radius, a rise of the braking torque by approx. 7% for
- 10 -
FY [kN], p [10 bar]
5
4
3
2
1
0
-1
3
1
rpm
0 0.5 1 1.5 2 2.5 3 3.5
2
4
rel. tolerance less than 2%
Fig. 22: Course of the normal forces of
the single sensors of the piston-sided pad
(during braking process)
500
400
300
200
100
0
rpm
-100

this brake by braking pressure of 60 bar. If one compares this result with the error analysis of
the determination of the friction value of (6), who has determined a range of 10% for the
tolerance band of the friction value under the assumption of a constant friction radius, these
measurements confirm the assumption of (6) that the biggest error influence can be caused by
the neglect of the change of the friction radius.
CONCLUSION AND OUTLOOK
The measurement device presented here enables for the first time the measuring of the
amounts and points of application of the clamping forces during a braking process. The model
concepts according to (4) and the enlarging of the caliper under brake pressure (Fig. 4) could
be confirmed for this caliper.
The sensor integration in the brake pad makes it possible to apply this design principle in
almost every disc brake. Since smaller brakes have to transfer lower forces, smaller sensors
could be used. By a measuring range from 0 to 15 kN the sensors’ diameter decreases from 30
to 16 mm (10).
Among others, the benefit lays in the one-time determination of the change of the point of
application of load for a defined caliper. Subsequently, this information can be used as a
correction factor for test bench experiments and so some factors of the real friction coefficient
can be determined more exactly. The measurement device can now also be examined for a
uniform pressing of the brake pad on the brake disc during a braking process. Piezo quartz
sensors are very suitable for high frequency measurements. Thus, changes in the clamping
force can also be recorded in the range of squeal frequencies (up to approx. 20 kHz).
Further benefit can be found for investigation of brake disc geometrical failures (e.g. run-out,
disc thickness variation), which are reflected in changes of the point of application of load
dependent on the speed. In such researches a kind of a circular movement of the point of
application of load with a movement diameter of 1-2 mm was determined. This information
could be very helpful for investigations of e.g. judder and variation of brake torque.
According to the device shown shear sensors with identical measurements of the sensors used
for direct measurement of the tangential forces as well. These researches are currently
continued at the Automotive Engineering Department of Darmstadt FZD with the aim to
determine the active friction radius with the help of the known braking torque from the test
bench.
The stacking of these sensors is also possible and thus the simultaneous measurement of the
clamping and tangential component and therefore the direct determination of the brake pad on
all four sensor positions. However, it is thereby problematic that the original thickness of the
brake pads is exceeded and thus the brake in hand can be falsified in its features as e.g. the
support of the forces.
Nevertheless, in order to enable a measurement, the use of piezo ceramics is currently tested.
These are considerably thinner (from 0.5 mm) and can also be used as shear and normal force
sensors. Together with the less required space, the explicitly favorable lower costs should be
mentioned. Disadvantageous are the relatively heavy losses of charge during a static load
which possibly prevents a measurement of these quantities with piezo ceramics.
ACKNOWLEDGEMENTS
The authors would like to thank the TMD Friction Group for the outstanding cooperation and
financing this research project.
- 11 -

REFERENCES
(1) Abu Baker, A.R., Ouyang, H. and Siegel, J.E. “Brake pad surface topography Part I:
Contact Pressure Distribution“ SAE Technical Paper 2005-01-3941
(2) Bill, Bernhard ”Messen mit Kristallen – Grundlagen und Anwendungen der
piezoelektrischen Messtechnik“ Die Bibliothek der Technik, Band 227, Verlag
moderne Industrie, 2002
(3) Breuer, Bert; Bill, Karlheinz ”Bremsenhandbuch – Grundlagen, Komponenten,
Systeme, Fahrdynamik; 2. Auflage, ATZ-MTZ-Fachbuch, Vieweg Verlag, 2004
(4) Burckhardt, Manfred ”Fahrwerktechnik: Bremsdynamik und Pkw-Bremsanlagen“,
Prof. Dipl.-Ing. Jörnsen Reimpell (Editor), Vogel Fachbuch Kraftfahrzeugtechnik,
Vogel Buchverlag, Würzburg, 1991
(5) www.continentalteves.com, 2006
(6) Degenstein, T.; Dohle, A.; Elvenkemper, J.; Lange, J. * , ”The µ-value – Friction
Determination in Brake Systems“ 16./17. Juni 2006, Bad Neuenahr, VDI-Fortschritt-
Berichte Reihe 12 Nr. 620, Düsseldorf: VDI-Verlag; 2006
(7) Engel, Hans Georg ”Systemansatz zur Untersuchung von Wahrnehmung, Übertragung
und Anregung bremserregter Lenkunruhe in Pkw“ Dissertation, FZD, TUD, VDI-
Fortschritt-Berichte Reihe 12 Nr. 354, Düsseldorf: VDI-Verlag; 1989
(8) Eriksson, Mikael ”Friction and Contact Phenomena of Disc Brakes Related to
Squeal“, ACTA Universitatis Upsaliensis, Uppsala 2000
(9) Hammerström, L. et.al. ”Pressure Sensitive Film as a tool for investigation the
pressure distribution on brake pads“ Tribology; Nordtrip 2002
(10) Kistler Instrumente AG Slimline Sensoren (SLS) ”Messen von dynamischen und
quasistatischen Kräften Typ 9130B – Typ 9136B.“. Data sheet 000-110d-02.02
(DB06.020d-02.02), Kistler Instrumente AG, Winterthur, 2002
(11) Oehl, K.-H.; Paul, H.-G. ”Bremsbeläge für Straßenfahrzeuge – Entwicklung und
Erprobung“ Die Bibliothek der Technik, Band 49, Verlag moderne Industrie, 1990
(12) Schrüfer, Elmar ”Elektrische Messtechnik“ 8. edition, Technische Universität
München, Carl Hanser Verlag München Wien, München, 2004
(13) Schumann, Marcus ”Analysis method for assessing irregular brake disc wear on motor
vehicle disc brakes“ 16./17. Juni 2006, Bad Neuenahr, VDI-Fortschritt-Berichte Reihe
12 Nr. 620, Düsseldorf: VDI-Verlag; 2006
(14) Schumann, Marcus ”Vehicle brake disc wear progression model“ brems.tech,
München, 2004
(15) Schwarz, Ralf ”Rekonstruktion der Bremskraft bei Fahrzeugen mit elektromechanisch
betätigten Radbremsen“ Dissertation, Institut für Automatisierungstechnik (IAT),
TUD, Fortschritt-Berichte VDI, Reihe 12 Nr. 393, VDI-Verlag, 1999
(16) Suryatama, D. et. al. ”Contact Mechanics Simulation for Hot Spots Investigation“
Society of Automotive Engineers, Inc., 2001
(17) Tichy, J.; Gautschi G. ”Piezoelektrische Messtechnik – Physikalische Grundlagen,
Kraft-, Druck- und Beschleunigungsaufnehmer, Verstärker“ Springer Verlag, Berlin
Heidelberg New York, 1980
(18) Tekscan ”Industrial Sensor Catalog“ RevDD_072705, Tekscan, 2005
(19) www.tmdfriction.de, 2006
(20) Wallentowitz, H.: “Vertikal- / Querdynamik von Kraftfahrzeugen”,
Forschungsgesellschaft Kraftfahrwesen, Aachen mbH (fka), 1997
(21) Winner, Hermann ”Kraftfahrzeuge I – Folien zur Vorlesung“ Technische Universität
Darmstadt, Automotive Engineering Department (FZD), Darmstadt, 2004
(22) Vries, Alexander de ”The Brake Judder Phenomenon“ SAE 920554, 1992
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