Thermophysical Properties of Automotive Brake

Disk MaterialsSok Won Kim

Department of Physics, University ofUlsan680 - 749 San 29, Mugeo 2-Dong, Nam-Ku, Ulsan Korea.

Abstract-The temperature distribution, the thermaldeformation, and the thermal stress of automotive brake diskshave quite close relations with car safety; therefore, muchresearch in this field has been performed. However, successful andsatisfactory results have not been obtained because thetemperature-dependent thermophysical properties of brake diskmaterials are not sufficiently known. In this study, the thermaldiffusivity and the specific heat capacity of three kinds of ironseries brake disk materials, FC250, FC170, and FCD50, and twokinds of aluminum series brake disk materials, Al MMC andA356, were measured in the temperature range from roomtemperature to 500 'C and the thermal conductivity wascalculated using the measured thermal diffusivity, specific heatcapacity, and density data. The result shows that thethermophysical properties of the aluminum series are larger thanthose of the iron series by 2-4 times. The obtained data areapplicable as basic input data in the study of the temperaturedistribution and in the thermal analysis of brake disks.

I. INTRODUCTION

Recently, the disk and pad of the automotive brake systembecame important parts of safety design because they absorbthe dynamic energy of the automobile therefore, the brakesystem directly related with the car safety. The development ofautomobile aims the high performance, high stability, lownoise, and low vibration [1]. The problems occurring in brakedisk as shown in Fig. 1 are surface temperature rising, cracksinduced by the heat, thermal deformation, abnormal vibration,over-abrasion, bending, noise etc. and these happen mainlyfrom the disk, pad, caliper, and their combinations. In order toanalyzer these phenomena, the study of temperature rising indisk system caused by the friction heat must be required [2,3 ].

The temperature over-rising caused by the long andcontinuous braking produces the irregular martensitecomponents on the disk surface and these are connected to theabnormal vibration of the brake system. Lots of researches inthe field of thermal deformation and thermal stress of brakesystem have been performed however, successful andsatisfactory results have not been obtained because thetemperature-dependent thermophysical properties of brake diskmaterials are not sufficiently known.

In this study, the thermal diffusivity and the specific heatcapacity of three kinds of iron series brake disk materials,FC250, FC170, and FCD50, and two kinds of aluminum seriesbrake disk materials, Al MMC and A356, were measured in thetemperature range from room temperature to 500 'C and the

thermal conductivity was calculated using the measuredthermal diffusivity, specific heat capacity, and density data.

aWing stal

Fig. 1. Traveling state and braking state of the brake disk system.

II. THEORETICAL BACKGROUND

A. Laser Flash MethodIn laser flash method as shown in Fig. 2 [4], when the

Fig. 2. Boundary condition of the disk-shaped thermal diffusivity sample.surface of disk-shaped sample with thickness L is irradiatedby delta-functional laser pulse, the temperature in depth xfrom the surface after time t is expressed as

1 2 - -n2z2at n L 0)1osT(x,t) =-J T((x,O)dx +-exp( ) fL T(x,c La dx (L L,=, L~~~ L L'

where a is the thermal diffusivity of the sample [5,6]. Whenthe flash energy Q is uniformly irradiated on the on thesample surface x = 0 and absorbed into the thickness of g,the temperature distribution becomes as follow;

T(x,O)-= QpC,g

0<x<g (2)

(3)T(x,O)=0 x>g

therefore, the temperature of the rear surface of the sample canbe expressed as

Q'Do

nx sin(nTg L)T(L,t) = 1 21nskz- )exp(-pCvL n=lL (nzTg/L)

-n2IT2at)L2

(4)

1-4244-0427-4/06/$20.00 ©2006 IEEE

ng .tbl.

- 163 - Oct. 18 -Oct. 20, 2006 FOST2006

where p is density and C. is specific heat capacity of sample at

constant pressure. The maximum temperature of the rearsurface is

T -L,max -pC L

and the ratio of this to T(L, t) becomes

V =1+ 25£ (-l)" exp(-nf - at)n=l

and TSm q = the heat flow between Tsm and TS~ and TrmIdtdq~ n dq I

Tr I Crm I Cr I Rr I Rr ' d and d have analogousmeanings for the reference side.

and has the value between 0 and 1. In this equation, the thermaldiffusivity can be obtained by the maximum temperature of therear surface as follow;

a=kx (7)tx

where k, is the constant for the increment of x -percent and

ti is the time.

B. Differential Scanning CalorimeterThe differential scanning calorimeter (DSC) is classified

into heat flux and power-compensation type. The former typeuses the method which utilizes the temperature differencebetween the sample and reference material for the same inputheat, and the latter type is the method which maintains thetemperature difference as zero by controlling the input heatduring the measurement [7].

Mraw suggested the new model which treats the twodifferent types of DSC's by the extension of classical model ofpower-compensation type DSC [8]. Fig. 3 is a sketch of an

idealized system which is applicable to almost any type ofdifferential thermal instrument. T]= the temperature of the

heat source, Tsm =the temperature at the point where

temperature is monitored on the sample side, Ts= the actual

temperature of the sample material(generally encapsulated in a

sample pan), Csm =the heat capacity of the sample-

temperature monitoring station, Cs heat capacity of the

sample material itself and its pan, Rs the thermal resistance

between the heater (at Ti ) and the sample-temperature

monitoring station (at Tsm ), Rsj = the thermal resistance

between the sample-temperature monitoring station (at Tsm,)

and the sample itself (at Ts), dq = the heat flow between TIdt

Fig. 3. Schematic diagram of the DSC modeling for the measurement ofspecific heat capacity.

III. EXPERIMENTS AND DISCUSSION

A. Thermal Diffusivity MeasurementThe schematic diagram of the laser flash thermal

diffusivity apparatus used in this experiment is shown in Fig. 4[9]. The pulsed Nd:glass laser beam (duration 0.8 ms) was usedas a heat source. In general, the spatial energy distribution ofthe pulsed laser beam is not uniform however, the analysis isperformed under the assumption of uniform energy distributionand several percents of errors can be produced. Therefore, inorder to obtain laser beam with uniform energy distribution,the 1 mm-diameter optical fiber was used with utilizing theinternal multi-reflection of optical. Also, to minimize thenonlinear effect and surface damage of the sample, the energy

of the pulse laser beam is kept less than 1 J.

o t atf

Fine > 1I iX r

FL wtr v J

ic~ ~~t0 |1 eo

Fig. 4. Schematic diagram of the laser flash thermal diffusivity apparatus.

The degree of vacuum chamber was maintained as 10-5 torrand the heater in the chamber is made by tantalum foil with0.05 mm thickness, and the temperature of the sample iscontrolled by R-type thermocouple.

The temperature evolution of the rear surface of the samplewas detected by HgCdTe infrared detector and transferred tothe PC, analyzed and displayed. The data acquisition system iscomposed with multi-meter, high-speed A/D converter, preamp,main amp, and energy meter.

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(5)

(6)

Five kinds of samples with 2 mm thickness and 10 mmdiameter were prepared and set up in the sample holder in thevacuum chamber. Table I summarizes the sample materials.The temperature evolution of the rear surface was obtainedwith the irradiation of uniform laser beam on the front surfacein the temperature range from room temperature to 500 'C. Theobtained temperature evolution was substituted into Eq. (7) andthe thermal diffusivity was calculated by Eq. (8).

TABLE ISAMPLE DESCRIPTIONS

Eleme T

nt C Si Mn~S P Cr Ti V Fe Cu Mg Al

1. 0.23.2 3 06 -0.05 -0.02 0015

FC250 5 0.15 0.42t04 BAL- -

352.

3000.2 -0.05 0.05 0.015FCD50 0.6 ~ BAL-4.0 3.

01,

3.4 6 07- 0.4 0.015FC17O 3810 Ott0.2{0.62 -- BAL

26.5 0.03 0.15 0.15 0.1 -BAA356 - - -0-037. .3 0.8 L58.5 0.45 B

Al1MMC - - - --0.2{ 0.2{ 0.2{ BAL9. 0.65

BAL=balanced

The obtained values of thermal diffusivity for five sampleswere shown in Fig. 5 and all the data points were the averageof five-time measurements. It shows that the thermaldiffusivities of all the samples decrease slowly for theincrement of sample temperature and the values of iron seriesmaterials are larger than those of the aluminum series materialsby 3-4 times therefore, clearly distinguished because the maincomponents of each series are iron and aluminum, respectively[10]. The uncertainty of the measurement values are with +5.5°O and Table II shows the thermal diffusivities.

TABLE II

TBE OBTAINED THERMAL DIFFUSIVITY VALUES(unit: 10-5 m2 s-' ).

Sample FC250 FCD50 FC170 A356 Al MMCT( )

20 11.98 7.63 16.60 64.21 66.71100 11.26 7.80 15.21 69.92 65.93200 10.89 7.96 13.31 69.04 61.69300 9.87 7.77 11.51 68.79 57.87400 8.79 7.32 9.97 69.29 56.15500 7.85 6.66 8.66 64.56 51.08

B. Specific heat capacity measurementIn general the type of DSC is classified into continuous

scanning type and step-wise heating type and the latter wasadopted in this experiment. The three-time measurements arerequired in DSC. As shown in Fig. 6, the blank pan, referencematerial, and sample were measured successively. Thereference material was SRM-720 of NIST. The process oftemperature control is as follows;

The time interval is determined in the isothermal range forthe enough stabilization of base line.The initial and final temperatures are determined.The increasing speed of temperature is determined.

. _

Fig. 6. An example of the obtained DSC signals from the sample,reference and blank pan.

The data of heat capacity obtained with the above processwere integrated in the all the temperature increasing ranges andthe average specific heat capacity was obtained in each ranges.The obtained average values of specific heat capacitys areshown in Fig. 7 and Table III. As the temperature rises, thevalues of specific heat capacity increase and the values of ironseries materials are larger twice than those of the aluminumseries materials. The uncertainty of the values was within+3.0Oo.

C Cakulation ofthermal conductivityThe thermal conductivity (k) was calculated by using the

obtained thermal diffusivity (a), specific heat capacity atFig. 5. Obtained thermal diffusivity values of the brake disk materials by laser

flash apparatus.

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+FC200 0 0 0 0

T+FCD50 rat re'

I-

70

60

50

40

30

2 0

1 0

E

E

constant pressure (C.), and the measured density (p ) of the

sample through Eq. (8) [ 1]. The measured densities of the

1.2

1.1

1. 0

0.9a)

tj 0.8

O' 0.7U)

0.6

0.5

,--FC250

+ FC1D05A F C 1 7 0

+56A356

0 100 200 300 400 500

Tem peratu re (°C)

Fig. 7. The obtained specific heat capacity values of the brake disk materialsby DSC apparatus.

TABLE IIITBE OBTAINED SPECIFIC TEAT CAPACITY VALUES(unit: J g-1 K-1 ).

Sample FC250 1 FCD50 J FC170 A356 Al MMC

T( )20 0.503 0.500 0.510 0.931 0.874100 0.530 0.522 0.537 0.952 0.912200 0.563 0.565 0.567 1.015 0.972300 0.611 0.615 0.629 1.019 1.011400 0.641 0.655 0.658 1.170 1.129500 0.701 0.721 0.712 1.228 1.197

samples are shown in Table IV and the densities of iron seriesare larger than those of aluminum by 2.5 times.

k =a C .pp (8)TABLE IV

THE MEASURED DENSITY OF THE SAMPLES(unit: 106 kg m-3).

Sample FC250 FCD50 FC170 A356 AlMMCDensity 7.22 7.04 7.08 2.14 2.73

Fig. 8 and Table V show the calculated thermalconductivities of the samples and the trends are similar tothermal diffusivities in Fig. 5.

210

y 180E9 150

120'6 1 2 0

° 90

- 60

30

0 100 200 300

Tem perature (°C)

400 500

Sample FC250 FCD50 FC170 A356 Al MMCT(

20 42.38 26.23 58.36 150.01 155.75100 43.06 28.64 57.84 169.13 164.06200 44.23 31.69 53.40 178.76 163.68300 43.55 33.60 51.23 177.37 159.71400 40.67 33.73 46.44 205.83 173.02500 39.72 33.80 43.70 201.39 166.85

IV. CONCLUSION

The thermal diffusivity and the specific heat capacity ofthree kinds of iron series brake disk materials, FC250, FC170,and FCD50, and two kinds of aluminum series brake diskmaterials, Al MMC and A356, were measured in thetemperature range from room temperature to 500 °C, by laserflash apparatus and DSC, respectively and the thermalconductivity was calculated. As the temperature increases, thethermal diffusivities decrease slowly and specific heatcapacitys increase, and the thermal conductivities of iron seriesdecrease or increase slowly and those of aluminum seriesincrease. The obtained data are applicable as basic input data inthe study of the temperature distribution and in the thermalanalysis of brake disks by using the finite element method.

ACKNOWLEDGMENT

This work was supported by Ministry of Commerce,Industry and Energy(MOCIE) of Republic of Korea, throughthe Research Center for Machine Parts and MaterialsProcessing (ReMM) at University of Ulsan.

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Acta 251, 199 (1995).[8] S. C. Mraw, Rev. Sci. Instrum. 53, 228 (1982).[9] S. W. Kim, S. H. Hahn, J. C. Kim, D. Chi and J. H. Kim,

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J. Thermophys. 24, 1355 (2003).

Fig. 8. The obtained thermal conductivity values by calculation using Eq. (8).

TABLE VTHE OBTAINED THERMAL CONDUCTIVITY VALUES BY USING EQUATION(8) (unit: Wi'r-K-

1)

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FC250FCCD50_FC1 70

AI MMC