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

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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.
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
AbstractA 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.
Copyright © 2
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2
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p
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k
δ
ρ
=
integrated
c
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mperature p
r
()
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ρ
=
heat Excha
n
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(
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=
:
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s
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at the samp
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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
=:
0
p
laser
T
qk P
ρ
ρ
=
=− =
(4)
where laser
P
is the laser power density 2
W
m
⎡⎤
⎢⎥
⎣⎦
.
- a convective heat flux due to the laser beam
modulation:
()
0
0
aaria
T
qk hT T,t
ρ
ρ
=
=− = ⋅ ⎡⎤
⎣⎦
(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
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One of the main reasons for major road accidents which often lead into loss of life's is the catastrophic tyre failure caused by vehicles running with improper tyre pressure. The phenomena where tyre loses pressure naturally and contracts over time is called air permeation, which is identified to be the main cause of tyre to deflate but rarely can be realised by naked eyes. Properly inflated tyres can safe tyre life up to 20% which is equivalent to nine months of its life span, save fuel from 4% to 10%, increase braking efficiency up to 20%, lightens steering system and ease self-steer. Therefore, this paper reveals the investigation findings by analysing the factors that affect the air permeation that eventually causes pressure loss in an automotive tyre. The experimentations were performed in both static and dynamic conditions where they were also tested with and without loaded situation to extract precise data of the pressure loss from tyre. The results show that no matter what type of tyre or condition it undergoes, it still experience pressure drop but at different rate subjected to air properties, temperature, tyre materials and mechanical fittings of the wheel.
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The thermomechanical behavior of pneumatic tires is a highly complex transient phenomenon that, in general, requires the solution of a dynamic nonlinear coupled thermoviscoelasticity problem with heat sources resulting from internal dissipation and contact and friction. This highly complex and nonlinear system requires in-depth knowledge of the geometry, material properties, friction coefficients, dissipation mechanisms, convective heat transfer coefficients, and many other aspects of tire design that are not fully understood at the present time. In this paper, a simplified approach to modeling this system that couples all of these phenomena in a straight forward manner is presented in order to predict temperature distributions in static and rolling tires. The model is based on a one-way coupling approach, wherein the solution of mechanical rolling contact problem (with friction and viscoelastic material properties) provides heat source terms for the solution of a thermal problem. The thermal solution is based on the thermodynamics of irreversible processes and is performed on the deformed tire configuration. Several numerical examples are provided to illustrate the performance of the method.
Article
A rbk od is presented to characterize wear in customer use. The procedure consists sampling 25 to 100 vehicles fitted with production tires for wear. The usage severity of each vehicle is determined. Then, development tires can be placed on a few of these vehicles chosen with the desired wear severity to represent the full range of customer usage correctly. Tread wear is measured in an annual cycle. The method takes into account road surface, weather, driving styles, routes, vehicles and other parameters that each can affect wear by factors of two to ten or more. Tire wear performance is presented as a statistical distribution. Mild, medium and severe usage tire life is highlighted. The wear performance of a tire is its ability to reach high mileaqes. One way of evaluating this wear performance i s u n s i d e r the duration of tire service life, which is the mileage after which a point on the tread has reached the legal limit of the wear indicator. The duration of a tire's Service life depends on the mass loss from the tread, which is usually expressed in g/100km, and by the tansversa1 worn profile which enables the wear shape of the tread to be qualified. The duration of a tire's service life depends on the conditions in which the tire is used, that is the type of driver and the geographical area. The wear performance of the tirelvehicle combination in a Specific market zone is described by a statistical diptribution of tire service durations. This is a lognormal distribution (see figure 1).
Book
PRINCIPLES OF HEAT TRANSFER was first published in 1959, and since then it has grown to be considered a classic within the field, setting the standards for coverage and organization within all other Heat Transfer texts. The book is designed for a one-semester course in heat transfer at the junior or senior level, however, flexibility in pedagogy has been provided. Following several recommendations of the ASME Committee on Heat Transfer Education, Kreith, Manglik, and Bohn present relevant and stimulating content in this fresh and comprehensive approach to heat transfer, acknowledging that in today's world classical mathematical solutions to heat transfer problems are often less influential than computational analysis. This acknowledgement is met with the emphasize that students must still learn to appreciate both the physics and the elegance of simple mathematics in addressing complex phenomena, aiming at presenting the principles of heat transfer both within the framework of classical mathematics and empirical correlations.
Article
The specific heat C and thermal conductivity κ of polybutadiene are characteristic of all non-crystalline materials at temperatures below ≈ K, reflecting the presence of localized excitations. The changes in C and κ with variation in crosslinking suggest that the relaxation times of the localized excitations may vary with crosslink density. Extension of an elastomer does not reveal a change in density of localized excitations as monitored by measuring κ, possibly because other phonon scattering mechanisms mask the effect. For T ≲ 10 K the phonon mean-free-path is independent of the microscopic anisotropy of the elastomer.
Article
Based on the Fourier heat equation, an analytical model to determine the tyre temperature distribution, during its employment, is described. The model, called ThermoTyre, analyses the tyre thermodynamic behaviour. The model is in one-dimensional form and is characterised by a low computational load. Therefore, it lends to be easily integrated with interaction models in order to execute handling analyses. The work takes advantage of the cooperation with the Bridgestone Technical Center Europe that produces expertise and experimental data. After an analytical model description, simplifying hypothesis and boundary conditions are illustrated. Finally, the comparison between experimental data and theoretical results are shown.
  • Le Maitre
  • M Sussner
  • C Zarak
O. Le Maitre, M. Sussner, C. Zarak: 1988 Evaluation of Tire Wear Performance. SAE Technical Paper N. 2006-01-1477.
Mechanics of Pneumatic
  • S K Clark
S.K. Clark: (1981) Mechanics of Pneumatic. Ed. S.K. Clark, Univ. of Michigan.
Tyre mechanics and vehicle dynamics
  • H B Paceijka
H.B. Paceijka: (2011) Tyre mechanics and vehicle dynamics. Butterworth, Oxford.