Measurement of the Thermal Diffusivity of a Tire Compound By Mean of Infrared Optical Technique

Abstract

A new technique for the determination of the thermal diffusivity of a tyre compound is proposed. The diffusivity is defined as the ratio between the thermal conductivity and the product of the specific heat and density. This technique is based on infrared measurement and successive analysis of the tyre cooling. Tyre samples were heated up by a laser at constant power rate and the heating and the next cooling of the tyres were registered versus time by mean of thermocouples and infrared cameras. Determination of the thermal diffusivity was thus estimated by mean of home-made model. The research activity was carried out in the laboratories of the department of Mechanics and Energetics of the University of Naples Federico II, in cooperation with the Combustion Institute of the CNR in Naples.

Full text

International Review of Mechanical Engineering (I.RE.M.E.), Vol. 6, N. 6
ISSN 1970 - 8734 September 2012
Manuscript received and revised August 2012, accepted September 2012 Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved
1104
Measurement of the Thermal Diffusivity of a Tire Compound
by Mean of Infrared Optical Technique
C. Allouis1, A. Amoresano2, D. Giordano2, M. Russo2, F. Timpone2
Abstract – A new technique for the determination of the thermal diffusivity of a tyre compound is
proposed. The diffusivity is defined as the ratio between the thermal conductivity and the product
of the specific heat and density. This technique is based on infrared measurement and successive
analysis of the tyre cooling. Tyre samples were heated up by a laser at constant power rate and
the heating and the next cooling of the tyres were registered versus time by mean of thermocouples
and infrared cameras. Determination of the thermal diffusivity was thus estimated by mean of
home-made model.
The research activity was carried out in the laboratories of the department of Mechanics and
Energetics of the University of Naples Federico II, in cooperation with the Combustion Institute of
the CNR in Naples. Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved.
Keywords: Diffusivity, Infrared Technique, Tyre Compound

Nomenclature
laser
P
 Laser power, W
T Temperature, °C
k Thermal conductivity, J/hm °C
ha Convectivecoefficient, J/hm2 °C
δ
Density, kg/m3
c Specific heat, J/kg °C
t Time, s
ρ Coordinate in the flow direction
I. Introduction
The working temperature of a tyre [1], especially for a
racing one, is an important parameter both for the car
performances [2], and abrasion phenomenon. The
temperature is closely connected to the interaction
between the tyre and the road [3]. The tyres undergo
strong temperatures changes during their work. A brief
theory of the tyre handling is existing but is not enough
exhaustive to model the tyre behavior and to find the
optimum working temperature. In the case of passenger
tyres this temperature ranges in a wide interval, while in
the case of the racing tyres the range is narrower.
Abrasion is also an important problem [4]. Also in this
case the temperature results as a key factor. It has to be
ranged in a narrow interval and has to be well controlled.
Both handling and wear are becoming more and more
important in modern tyres since compound compositions
are getting always more complex in order to both fit road
grip and abrasion resistance. It appears clear that tyre
working temperature forecast is primary to find out its
best performances.
A model [5] was previously developed in order to
forecast the tyretemperature. It is based on the thermal
diffusivity according to the Fourier equations [6]taking
into account the thermal fluxes due to friction between
road and tyre, to heat exchange between air and tyre [7].
Energy balances used in the model available in the
literature depend on parameters not always well defined
or enough accurate, in particular the tyre thermal
diffusivity. This parameter including conductivity,
density and specific heat comes out difficult to be
determined since a wide range of data is available due to
the huge number of tyre types [8].
For this reason, in order to determine a more realistic
value of the thermal diffusivity and to obtain a more
accurate temperature profile, experiments were
performed. A tyre sample was heated by means of a
continuous laser and the different temperature profiles
were measured by means of traditional thermocouples
and by infrared cameras. Both theoretical and
experimental approaches are discussed in this paper.
II. Experimental Set Up
In order to measure the thermal diffusivity an
experimental bench was set-up. Tyre samples (circle of
1.5 cm diameter) were cut and isolated in order to avoid
thermal losses as presented in Fig. 1. Two K type
thermocouples (diameter 1 mm) were also inserted as
reported in Figs. 2 at different distances, from the
surface.
One thermocouple is placed at e=1.5 mm and the other
one is placed at e=2.5 mm from the free surface.
The thermocouples were connected to a National
Instruments BNC 2120 acquisition system.

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
C. Allouis, A. Amoresano, D. Giordano, M. Russo, F. Timpone
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 6, N. 6
1106
energy
()
0
ρ
=:

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T
qk P
ρ
ρ
=
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=− =
∂
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P
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W
m
⎡⎤
⎢⎥
⎣⎦
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modulation:
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ρ
ρ
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∂ (5)

where a
h the natural heat exchanger coefficient.
Considering the acquired temperature profiles and the
laser power density, it was possible to simulate the blend
thermal diffusivity
Comparison between the theoretical and the
experimental results
The first experimental temperature profiles are
showed in the Fig. 6. The sample was heated by 10 s and
then naturally cooled down. During this test the laser
power was set at 2 W/cm2.
For IR measurement, the sample emissivity was
considered constant at 0.94. The Fig. 6 represents the
temperature profiles during the test.
Fig. 6. Temperature profiles versus time
Analyzing the experimental results it was possible to
calculate the thermal diffusivity of the sample.
Theoretical temperature profiles were then calculated.
The results are presented in Fig. 7. Fig. 7 represents
the theoretical temperature profiles computed at the same
experimental positions. Figs. 8-10 represent the
comparison between theoretical and experimental results
at the sample surface, 1.5 mm far from the surface and at
2.5 mm deep in the sample respectively.
During the second test the laser beam was modulated
by mean of a chopper at a frequency of 10 Hz (Fig. 11).
The laser power density was 4 W/cm2.
Fig. 7. Theoretical temperature profiles versus time
Fig. 8. Comparison of temperature profiles at the sample surface

Fig. 9. Comparison of temperature profiles at 1.5 mm
from sample surface

Fig. 10. Comparison of temperature profiles at 2.5 mm
from sample surface
Time, [s]
Temperature, [°C]
e=2. 5 mm
e=1.5 mm
surface
Time, [s]
Temperature, [°C]
e=2.5 mm
e=1.5 mm
surface
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve


C. Allouis, A. Amoresano, D. Giordano, M. Russo, F. Timpone
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 6, N. 6
1107
Fig. 11. Laser modulation wave
The temperature profiles measured in this case and the
respective theoretical temperatures profiles are presented
in Figs. 12 and 13 respectively.

Fig. 12. Experimental temperature profiles versus time
Fig. 13. Theoretical temperature profiles versus time
Figures 14-17 represents the comparison between
theoretical and experimental results at the sample
surface, 1.5 mm far from the surface and at 2.5 mm deep
in the sample respectively.
The results reported show in any case a good
agreement between the experimental tests carried out
with the technique described and those obtained from the
theoretical model based on the Fourier equation in which
it was introduced the value of the thermal diffusivity
measured.
Slight differences are highlighted with increasing test
time. Towards the end of the test in fact the values given
by the theoretical model overestimate the experimental
ones.
This is due to a greater amount of heat exchanged by
convection with the air compared to that provided by the
model, as confirmed for example the step of cooling
reported in Fig. 14.
Fig. 14. Comparison of temperature profiles
at the sample surface
Fig. 15. Magnification of the comparison between the theoretical
and experimental surface temperature distributions
Fig. 16. Comparison of temperature profiles at 1.5 mm
from sample surface
The measurement of the thermal diffusivity is
performed with a simple identification technique based
on the availability of experimental data derived from the
set up test and on the availability of the theoretical model
described. Knowledge of diffusivity identified and
validated by comparison between experimental data and
[
]
ts
0.1
[
]
PW

4
Time, [s]
Temperature, [°C]
e=2.5 mm
e=1.5 mm
Surface
Time, [s]
Temperature, [°C]
e=2.5 mm
e=1.5 mm
Surface
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve
Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve


C. Allouis, A. Amoresano, D. Giordano, M. Russo, F. Timpone
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 6, N. 6
1108
theoretical model, allows using models to predict the
thermal behavior of the tires.

Fig. 17. Comparison of temperature profiles at 2.5 mm
from sample surface
IV. Conclusion
An experimental approach to measure the thermal
diffusivity of tyre compounds was proposed. This
method is based on a well controlled heat source,
thermocouples and IR camera (non intrusive). This
combination gave interesting results with relative low
labor time in characterizing the thermal diffusivity. This
technique allowed to measure different unknown
compound of tyres. It allowed implementing an existing
theoretical model taking into account real intrinsic
parameters of the rubbers.
References
[1] A.N .Gent ,J.D. Walter: (2005) The pneumatic Tyre, NHTSA.
[2] H.B. Paceijka: (2011) Tyre mechanics and vehicle dynamics.
Butterworth, Oxford.
[3] S.K. Clark: (1981) Mechanics of Pneumatic. Ed. S.K. Clark,
Univ. of Michigan.
[4] O. Le Maitre, M. Sussner, C. Zarak: 1988 Evaluation of Tire
Wear Performance. SAE Technical Paper N. 2006-01-1477.
[5] De Rosa, F. Di Stazio, D. Giordano, M. Russo, M. Terzo: (2008)
Thermo Tyre: tyre temperature distribution during handling
maneuvers. Vehicle System Dynamics, 46(9)831–844.
[6] F Kreith, RM Manglik: (2010) Principles of heat transfer.MS
Bohn.
[7] B. Yavari, W. W. Tworzydlo, and J. M. Bass : (1993) A
Thermomechanical Model to Predict the Temperature Distribution
of Steady State Rolling Tires. Tire Science and Technology, July
1993, Vol. 21, No. 3, pp. 163-178.
[8] A. Bhattacharyya, T.L Smith, A.C Anderson: (1979) Low
temperature thermal conductivity andspecific heat of elastomers.
Journal of Non-CrystallineSolids, Vol 31 Issue 3.
Authors’ information
1Institute of Research onCombustion of the CNR – Naples, Italy
2Dep. of Mechanics and Energetics, University of Naples “Federico
II”- Naples, Italy
Amedeo Amoresano was born in Naples on
October 27, 1963. Hhe took his degree in
Mechanical engineering at University of Naples
Federico II in 1991 by discussing a thesis
concerning the analogic to digital conversion of
data of a 3D PDA. In 1994 he took his PhD in
Thermomechanical and Energetic Systems
discussing a thesis on the fluidodynamic of two
phase systems. In 1997 he became researcher of the University of
Naples “Federico II” at DiME (Mechanical and Energetic Department).
From 2001 he is Assistant Professor of Fluid Machinery and is an
adviser for the italian government of the Innovative Power Plant. In
2007 he was responsible of PRIN (National Research Program)
“Analysis and experimental characterization of fire suppression spray”.
From 2009 he is Aggregate Professor of “Innovative Power Plant”. His
principal research fields are:
- Spray and atomization systems
- Mild and diluted combustion and gasification systems
- Optical diagnostics and thermal images processing
- Aircraft Deicing System
During his career he tutored several graduated and PhD students and
gave lessons in the Italian Accademy Air Force where is responsible of
the experimental activity on the Wind Tunnelmework of the
combustion courses for chemical engineers at the University of Naples.
He is author of about sixty works among the ones published on
international journals, on the proceedings of international and national
meeting in reduced or extended form.
E-mail: amoresan@unina.it

Time, [s]
Temperature, [°C]
Theoretical curve
Experimental curve