methodology for determination of the effective radius by means of

EB2012-TM-14
METHODOLOGY FOR DETERMINATION OF THE EFFECTIVE
RADIUS BY MEANS OF THERMOGRAPH ANALYSIS ON THE DISK
SURFACE
1
Neis, Patric Daniel*, 1Duarte, Flavio Luçardo, 2Perez Delgado,Yeczain, 1Ferreira, Ney
Francisco, 2DeBaets, Patrick
1
Federal University of Rio Grande do Sul, Brazil, 2University of Ghent, Belgium
ABSTRACT - Effective radius is an important parameter for determination of the coefficient
of friction during brakings performed on laboratory-test machines. Some authors have
developed theories for the analytical calculation of the effective radius from simple
geometries of sample while others make it experimentally. The current paper aims to
determinate the effective radius by means of thermograph analysis on the surface of a disk
brake. For doing that, radial thermal profile on friction track is experimentally obtained and
the corrected value of emissivity is calculated based on the temperature measured via
thermocouple. A regression process is done in order to obtain the radial thermal profile on the
contact surface. Tests are performed on a laboratory-sccale tribometer able to operate in
different pressure, temperature and speed. It is assumed that during the braking process, the
energy that comes from the braking torque is totally absorbed by the disk in the form of heat.
This assumption allows determining the effective radius from the centroid of the thermal
curve. Results show a difference of 2.5% between the slipping radius, which is adjusted on
the tribometer, and the effective radius, which is experimentally obtained.
KEYWORDS – effective radius, friction, brake, thermography, braking.
INTRODUCTION
Nowadays, the development of brake systems more efficient has become an important
factor, since each year are produced faster and more powerful cars.In the 50’s, as described by
Rusnak et al., 1970, brake materials were evaluated directly on the cars, in tests called “on
road”. Currently, most tests of brake materials are performed on laboratory, due to more easy
instrumentation and better precision to control the conditions of the tests. Besides, laboratory
tests are faster and the costs involved are reduced [Rusnak et al., 1970].
The equipment most used to characterize friction materials from brakes is brake
dynamometer. However, this machine is expensive and its operation according to the
standards, such as the AK Master, 1998, or FMVSS 105, 1967, requires more than 24 hours to
be completed. The uncertainty of the coefficient of friction measured through a
brake dynamometer is around 10% of the nominal value [Dohle et al, 2006].
Grochowicz et al, 2011, provide a
survey
about
experimental
factors that exert significant influence on the variability of the friction obtained by means a
brake dynamometer. These factors are listed in descending order of importance: caliper
drag between the stops, environmental conditions and uncertainty related to the kinetic
energy (rotation speed). Although other factors are also evaluated in this study, their influence
on the friction results are not expressive.
According to Grochowicz et al, 2011, the caliper drag is the factor that most affects the
repeatability of the results from the braking tests. This is because the manufacturing process
of the caliper is less rigorous in terms of dimensional tolerances. In the laboratory-scale
tribometer used for performing the tests in the current paper, it is not observed the caliper
drag. It is because the retreat of the piston in the end of each stop. However, the tribometer is
able to control the drag condition during brakings, in case of necessity.
The second factor that induces significant effects on the coefficient of friction, the
environmental conditions of the tests, has relevant influence if the braking
process occurs below to 100°C or under cylinder pressure less than 2 MPa and speed below to
20 km/ h. Tests performed on the current paper are adjusted out of this range, since they
are conducted at temperatures above 100°C and under speed and pressure equivalent
to 100km/h and 3 MPa, respectively.
Finally, the last factor that induces variability, the uncertainty related to the kinetic level,
it is a variable precisely controlled in tribometer by means a closed loop circuit.
According to Grochowicz et al, 2011, the repeatability and reproducibility of the friction
results measured by means a brake dynamometer is, respectively, 0,02 and 0,03 of the
nominal friction value.
EXPERIMENTAL APPARATUS
The laboratory-scale used to perform the tests is a tribometer of scale braking (Figure 1),
especially developed to characterize friction materials used in brake pads.
Figure 1 – Tridimensional view of the laboratory-scale tribometer.
Regarding to the disk rotating system, the tribometer can operate in two modes:
1) Constant drag mode: rotation speed of the disk is kept constant over time during the tests.
2) Disk deceleration mode: the rotation speed of the disk decreases at a pre-set rate as the
braking proceeds, similar to a stop braking in cars or tests performed on brake dynamometers.
Regarding to the load/actuator system, the tribometer can operate in two different modes:
1) Constant force mode: the normal force on the disk, which is done by means a pneumatic
actuator, is kept constant over time during the tests, while the braking torque remains free to
vary according to the changes in the coefficient of friction.
2) Constant torque mode: the braking torque is kept constant independent of friction force.
This is done by a closed loop circuit that controls the applied force at each fraction of a
second. A feedback from the current torque is done by means of a torque transducer installed
on the tribometer shaft.
The laboratory-scale tribometer is also able to control the load or torque during the period
of cooling that occurs between two consecutives stops. Another important attribute of the
tribometer is that the piston moves the sample over linear guides, which ensures the
parallelism between the contact surfaces within a magnitude of 0,1mm.
The measures of the coefficient of friction are evaluated by an indirect way, described in
the equation 1:
μ
M
RFN
(1)
where M is the braking torque [Nm], R is the sliding radius [m] and FN is the normal force
exerted by the piston [N].
The normal force is measured through a load cell, the torque by means a torque
transducer and the sliding radius is automatically displayed by means a digital caliper
integrated to the radial displacement of the load system.
However, the sliding radius usually differs from the effective radius. This last parameter
corresponds to the infinitesimal point, in relation to the center of the disk, from which an
equivalent friction force can be multiplied in order to obtain the total braking torque [Dohle et
al, 2006]. The effective radius is not constant and it varies over time, since the contact
between the pad and disk is not uniform. Vieira et al, 2008, report errors in the magnitude of
3% on the friction results when the radius used to determine the coefficient of friction is
assumed to be equal to the distance between the center of the pad and disk. These authors
consider the effective radius equals to the centroid coordinate of the thermal profile on the
disk surface, assuming the emissivity as constant. The technique used in this paper considers
variations of emissivity along the radius of the disk surface in order to determine the effective
radius.
EXPERIMENTAL TESTS
The tests consist of 400 stops using a friction material commercially available in Brazil.
From the total of stops, it was registered thermographic images in the following stops: 2, 3, 4,
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 100, 150, 200, 250, 300, 350 and 400.
The operating conditions used in the tests are described in table 1.
Table 1 – Operating parameters set in the tribometer.
Initial
temperature [ºC]
100
Deceleration of
the disc [rpm/s]
250
Normal Load
[N]
1000
Initial velocity
[rpm]
2300
Braking time
[s]
9
The sample used has a cylinder shaped geometry, with a diameter of 24 mm. The sliding
radius was adjusted in 40 mm. The uncertainty associated to the coefficient of friction due to
the instruments used in the tribometer is about 3,2 % of the measured value. In order to avoid
transient effects, a bedding-in procedure is performed a prior to the experiments. The
bedding-in test is run with a constant rotating of 400rpm and a force of 1400N during a period
of 300s.
PRINCIPLE OF METHOD
Shigley et al, 2005, calculate the value of the effective radius for simple geometries,
while Dohle et al, 2006, determine it using thermography, the same technique used in the
current paper.
As noticed in the equation 1, the effective radius has an inverse relation with the
coefficient of friction. Thus, the more accurate is the effective radius the smaller is the error
of the coefficient of friction. The method currently applied is based on radiometric analysis of
the disk surface. An angular regression has been made in order to obtain the thermal profile of
the disk in the point of contact. Data o experimentally obtained by the thermographic camera
are post-processed in a computational tool based on sheets (Microsoft Excel).
Assuming that all energy produced by the braking process is absorbed by the disk in form
of heat, it is possible to determine the effective radius through the radial thermal profile of the
disk, which corresponds to the coordinate of the centroid of the curve radius vs. temperature.
In this paper, the temperature of the disk was also obtained by using a thermocouple
embedded 6 mm from the disk surface. The radial thermal profiles of the disk are taken from
an angular distance of 180 and 90 degrees from the point of contact (figure 2). This process is
repeated before, during (at time equal to 5s) and after the stops. From these experimental data,
radial thermal profile on the contact area is determined (angle of zero degrees).
Figure 2 – Location of the thermal profiles evaluated on the disk surface.
According to Morelli, 2002, during brakings, the temperature is higher on the surface
than inside the disk, especially in the initial instant. The temperature tends to be more
uniformly spread on the disk over time. Figure 3 shows the thermal profile of the disk over
time (t = 1s, t = 4s and t = 6.5 s) during a braking process.
Figure 3 - Distribution of the temperature in a radial section of the brake disc [Morelli, 2002].
It is assumed that the time among the stops (2 minutes) is enough to the temperature of
the disk becomes uniform.
The emissivity value was set equals to "1" in the measurements made by using the
infrared camera. So, from the relation between the temperature obtained via thermocouple and
thermography, the emissivity on the disk surface can be calculated:

Ttermocouple
4
Ttermografhy
4
(2)
T
where ε is the emissivity of the disk surface, termocouple is the temperature measured by
T
thermocouple in Kelvin, and termografhy is temperature measured by thermograph in Kelvin.
From the thermographic images obtained before and after the stops, it is determined the
emissivity to each pixel that belongs to the radial line that represents the thermal profiles at 90
and 180 degrees from the point of contact (Figure 4). In order to obtain the emissivity curve to
calculate the thermal profile during the braking process, the average between the emissivity
obtained before and after the stops is used.
.
Figure 4 – Thermograph images obtained on the disk at the period (a) before and (b) after a stop.
0,90
0,90
0,85
0,85
0,80
0,80
Emissivity (-)
Emissivity (-)
Two curves of the average of emissivity were generated, that are situated to 180 and 90
degrees from the contact (Figure 5).
0,75
0,70
0,75
0,70
0,65
0,65
0,60
0,60
28
30
32
34
36
38
40
42
44
46
48
50
28
52
30
32
34
36
38
40
42
44
46
48
50
52
Radius (mm)
Radius (mm)
Figure 5 – Curve of average of emissivity obtained between the period before and after the stops and situated at
(a) 90 degrees and (b) 180 degrees from the contact.
The curves of average of emissivity at 90 and 180 degrees are used to correct the radial
thermal profiles obtained by thermography through the equation (3)
TRe al  4
Ttermography
 average
4
(3)
where TRe al is the actual temperature of the corrected pixel [Kelvin], Ttermography is the
temperature measured by the infrared camera [kelvin] and  average is the average of emissivity
calculated before and after the stops in the angular position of 180 and 90 degrees [-].
In the current measurements, the thermographic images are obtained 5 seconds after the
braking process begins. In this moment, the speed of the disk is about 1250 rpm, which
represents a time interval of 0.01 s between 90 and 180 degrees. This interval is sufficiently
small to consider a linear decay to the temperature along the circumference of the disk
surface. By using the temperature corresponding to each pixel obtained at 90 and 180 degrees,
it is estimated the position of zero degree, which corresponds to the profile at the contact
point (equation 4).
T0  T90  (T90  T180 )
(4)
where T0 is the temperature in the point of contact of the sample on the disk[°C], T90 is the
temperature at an angular distance of 90 degrees from the point of contact [°C] and T180 is the
temperature at an angular distance of 180 degrees from the point of contact [°C].
A typical curve of temperature vs. radius measured in the contact area (zero degrees) is
shown in the Figure 6. The effective radius is located on the coordinate of the centroid of the
temperature curve, as shown in the vertical line on the graph. The resolution given by each
pixel represents a step of 0.40625 mm in radius.
160,00
Temperature ( C)
150,00
140,00
130,00
120,00
110,00
100,00
28
30
32
34
36
38
40
42
44
46
48
50
52
Radius (mm)
Figure 6 - Thermal profile of the disk evaluated at the contact, during stop number 55.
Results show an average of the effective radius equals to 38.986 mm for the evaluated
stop, which results in a variation of 2.5% compared to the radius of sliding adjusted in the
tribometer, whose value is 40 mm. In the worse case, during the stop number 150, the
difference between two radius is around 3%. Adding this value to the uncertainty associated
to the devices installed in the triobometer (3,2%), a total error of equivalent to 6,2% is found.
This value can still be considered low, since the error of a dynamometer is around 10%
[Dohle et al, 2006].
CONCLUSIONS
The methodology described in the current paper has shown effective and functional to
characterize the effective radius during braking and more accurate than the techniques used in
the past, which assume that the emissivity of the disk surface is constant.
.
The total error of the tribometer in terms of friction is around 6.2% in the range applied
in the current tests. From this total, 3,2% represents the variation due to the error associated to
the value of the effective radius.
REFERENCES
Dohle, A., Elvenkemper, A., Lange, J. "The μ Value” - Friction Level Determination in
Brake Systems", TMD Friction, Germany, 2006.
Rusnak R. M., Spurgeon W M., Aldrich F. W., "Friction Material Testing", Society of
Automotive Engineers, paper 700517, 1970.
Morelli, A.; “Progetto dell’ Autoveicolo”, Celidi, Torino – Italy, 2002.
Incropera F. P., Dewitt D. P. “Fundamentos de Transferência de Calor e de Massa”, LTC,
Brazil, 2003.
Shigley, J.E., Mishke, C.R., Budynas, R.G., “Projeto de Engenharia Mecânica”, Bookman, 7ª
edição, 2005.
Vieira, F. C., Ferreira, N. F., Neis, P. D., “Determination of the effective radius for disk brake
pads”, Federal University of Rio Grande do Sul, Brazil, 2008.
Grochowicz, J., Agudelo, C., Reich, A., Wollenweber, K., Abendroth, H., . “Brake
dynamometer Test Variability”, SAE International, 2011.