Measurement of the Thermal Diffusivity of a Tire ...

International Review of Mechanical Engineering (I.RE.M.E.), Vol. 6, N. 6 ISSN 1970 - 8734 September 2012

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 Plaser T k ha

δ c t ρ

Laser power, W Temperature, °C Thermal conductivity, J/hm °C Convectivecoefficient, J/hm2 °C Density, kg/m3 Specific heat, J/kg °C Time, s 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.

Manuscript received and revised August 2012, accepted September 2012

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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 © 2012 Praise Worthy Prize S.r.l. - All rights reserved

C. Allouis, A. Amoresano, D. Giordan no, M. Russo, F. Timpone

Fig. 1. 1 View of the isoolated tire samplee preparation Fig. 4. View V of the laserr illuminated samp ple

(a)

(b)

Figs. 2. (a) Fronnt view of the sam mple. (b) top vieew of the sample

The speciimen was heaated-up by a continuous c A Argon laser using different d outpput power botth in steady state and in modulated condditions. the laser beam was expanded annd collimated in order to obtain a connstant laser beam of 10 mm. The experiimental layouut is presented in the Fig. 3.

Fig. 5. infrared visualization oof the illuminated d sample

III. Results an nd Discussio on Termocamera per l’acquisizione della temperatura superficiale

Theoretical modeel The T model is based b on the Fourier’s law w according too the following equuation:

Scheda di acquisizione

kp

LASER

∂ 2T ∂ρ 2

= δ pcp

∂T ∂t

(1))

Eq. E (1) was integrated cconsidering th he followingg cond ditions:

Termocoppie annegate a diverse profondità

Fig. 3. Expperimental set-upp

c one dimensional flow, f In order too maintain a constant the sample was w insulatedd. Different laser l powervaalues were used ranged betw ween 2 and 4 W. Moreoover, experiments were perform med using a chhopper in ordder to modulate thee sample illum mination. Thee light modulaation stands as a tyyre rotation siimulation. Onn Figs. 4 and 5 are represented a visible andd an infrared visualization of a typical sampple respectiveely. The infraared camera is a Phoenix FLIIR with a sennsor sensitivityy ranged betw ween 1.5-5 micronn. Sensibility is i 5 mK. The frame acquissition rate was 3600 Hz full frame with a winddows size of 320 3 x 256 pixels. Acquired tem mperatures were w recorded and analyzed by a Matlab proggram.

Copyright © 20012 Praise Worthyy Prize S.r.l. - Alll rights reserved

the t sample teemperature prrofile is unifo orm at initiall conditions: c

T ( ρ ,0 ) = T0P -

a convective heat Exchannge is consiidered at thee sample s surfacce ( ρ = s ) : q = − kp

-

(2))

∂T ∂ρ

ρ =s

= ha ⋅ ⎡⎣T ( 0,t ) − Taaria ⎤⎦

(3))

a thermal fluxx at the samplle surface equ ual to the laserr

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C. Allouis, A. Amoresano, D. Giordano, M. Russo, F. Timpone

energy ( ρ = 0 ) :

q = − kp

∂ρ

= Plaser

(4)

ρ =0

⎡W⎤ where Plaser is the laser power density ⎢ 2 ⎥ . ⎣m ⎦ - a convective heat flux due to the laser beam modulation:

Temperature, [°C]

surface

∂T

e=1.5 mm

e=2.5 mm

Time, [s]

∂ρ

ρ =0

= ha ⋅ ⎡⎣Taria − T ( 0,t ) ⎤⎦

Fig. 7. Theoretical temperature profiles versus time

(5)

where ha 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.

Theoretical curve Experimental curve

Temperature, [°C]

q = −k

∂T

Time, [s]

Fig. 8. Comparison of temperature profiles at the sample surface

Temperature, [°C]


Temperature, [°C]

surface

e=1.5 mm

Time, [s]

e=2.5 mm

Fig. 9. Comparison of temperature profiles at 1.5 mm from sample surface

Time, [s]

Fig. 6. Temperature profiles versus time


Theoretical curve Experimental c urve

Temperature, [°C]

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.

Time, [s]


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P [W ]

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.

4


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.

Temperature, [°C]

t [s]

0.1

Temperature, [°C]

Surface

Time, [s]

Fig. 14. Comparison of temperature profiles at the sample surface


e=1.5 mm

Temperature, [°C]

e=2.5 mm

Time, [s]

Fig. 12. Experimental temperature profiles versus time

Surface

Temperature, [°C]

Time, [s]

Fig. 15. Magnification of the comparison between the theoretical and experimental surface temperature distributions e=1.5 mm


Temperature, [°C]

e=2.5 mm

Time, [s]

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.


Time, [s]


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 International Review of Mechanical Engineering, Vol. 6, N. 6

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theoretical model, allows using models to predict the thermal behavior of the tires.

Authors’ information 1

Institute of Research onCombustion of the CNR – Naples, Italy

2

Dep. of Mechanics and Energetics, University of Naples “Federico II”- Naples, Italy

Temperature, [°C]


Time, [s]


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.

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: [email protected]

References [1] [2] [3] [4] [5]

[6] [7]

[8]

A.N .Gent ,J.D. Walter: (2005) The pneumatic Tyre, NHTSA. H.B. Paceijka: (2011) Tyre mechanics and vehicle dynamics. Butterworth, Oxford. S.K. Clark: (1981) Mechanics of Pneumatic. Ed. S.K. Clark, Univ. of Michigan. O. Le Maitre, M. Sussner, C. Zarak: 1988 Evaluation of Tire Wear Performance. SAE Technical Paper N. 2006-01-1477. 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. F Kreith, RM Manglik: (2010) Principles of heat transfer.MS Bohn. 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. 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.


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