International Communications in Heat and Mass Transfer xxx (2013) xxx–xxx

ICHMT-02878; No of Pages 6

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International Communications in Heat and Mass Transfer

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3D investigation of thermal stresses in a locomotive ventilated brake disc based on aconjugate thermo-fluid coupling boundary conditions☆

B. Ghadimi a,⁎, R. Sajedi b, F. Kowsary a

a School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iranb School of Mechanical Engineering, College of Engineering, University of Tabriz, Tabriz, Iran

☆ Communicated by W.J. Minkowycz.⁎ Corresponding author.

E-mail address: behnam.ghadimi@ut.ac.ir (B. Ghadimi

0735-1933/$ – see front matter © 2013 Elsevier Ltd. All rihttp://dx.doi.org/10.1016/j.icheatmasstransfer.2013.10.00

Please cite this article as: B. Ghadimi, et al., 3fluid coupling, Int. Commun. Heat Mass Trans

a b s t r a c t

a r t i c l e i n f o

Available online xxxx

Keywords:Brake discThermal stressLocomotive

The frictional heat generated during braking application can cause several negative effects on the brake systemsuch as brake fade, prematurewear, thermal cracks and disk thickness variation. It is then important to determinewith precision, the temperature field and thermal stresses of the brake disc. In this study, thermal stress analyseson a ventilated locomotive wheel-mounted brake disc R920Kwith a three-dimensional model for two cases (thefirst case considers braking to a standstill; the second case considers braking on a hill andmaintaining a constantspeed)were investigated. The rate of braking heat generation is calculated using the assumption of uniformpres-sure distribution at the contact area. Then, thermal stress analyses for each casewere performed. Finally, we havefound that the maximum thermal stresses occur in the case with an emergency braking in the beginning of thebraking process.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Brake discs are widely used for reducing velocity for their character-istics of braking stability, controllability and the ability to provide awide-ranging brake torque. As the speed restriction of trains continuesto expand, over-heating and thermal deformations on brake systemsare going to be critical for emergency braking. Hence, the increase oftrains speeds requires the improvement of the braking performances.The main problem of braking and stopping a heavy train system is theextraordinary input of heat flux into the disc in a very short time. Inthe braking process, thermal stresses are generated by the frictionalheat and thermal fatigue cracks appear due to the thermal stress on abraking surface. Due to high temperature difference, brake discs are ex-posed to large thermal stress during routine braking and remarkablethermal stresses during emergency braking. The result is a heat shock.Therefore, in order to secure the braking stability and to improve thefatigue life of a brake disc, it is necessary to research the thermal stresson a brake disc.

As the first works in this area, Limpert [1] investigated the thermalcharacteristics of solid cast iron rotors that led to surface rupture andcracking. The results of the thermal stress analysis revealed that surfacerupture occurred when the induced compressive stress exceeded theyield strength in compression in a single brake application. The axisym-metric and three-dimensional transient temperature field models ofbrake disc using the finite elements method have been proposed inarticles [2–9].

).

ghts reserved.9

D investigation of thermal stref. (2013), http://dx.doi.org/10

Belhocine and Bouchetara [2,3] analyzed the thermal behavior of thefull and ventilated brake discs of the vehicles. They studied the influenceof the braking mode on the thermal behavior of the brake discs. Theirsimulations showed that the radial ventilation plays a very significantrole in cooling of the disc in the braking process. Park et al. [8] have in-vestigated the heat transfer enhancement in the automobile ventilateddisc brake using helically fluted surface.

In this paper temperature and thermal stress distributions of the discbrake have been investigated. The disc brake is subjected to high axi-symmetric thermal load which may lead to non-uniform temperaturedistribution. Therefore three-dimensional analysis facilitates to exam-ine temperature alterations in the circumference and their influenceon the area inside the disc. Both convection and conduction have beenanalyzed. Particularly conductionwas considered to be themost impor-tant mode of heat transfer. In order to study the thermal stress of brakedisc, we are presented a numerical modeling in three dimensions toanalyze the thermal behavior of the ventilated disc brake. The thermalcalculation based on the finite element method will be carried outusing code ANSYS 12.1. Experimental data were used to verify themodeling results.

2. Modeling

In this paper, thermal analysis of the wheel-mounted brake discR920K for the ER24PC locomotive which is manufactured in MAPNALocomotive Engineering andManufacturing Company (MLC) in cooper-ationwith SIEMENSAG is investigated. The driving force of ER24PC Locois supplied using a diesel-electric engine with a maximum speed of160 km/h. This locomotive is used to pull the passenger wagons.

sses in a locomotive ventilated brake disc based on a conjugate thermo-.1016/j.icheatmasstransfer.2013.10.009

Table 1Brake disc R920K data.

Braking mass per brake disc (kg) 5456.5Wheel diameter origin (mm) 1100Brake disc outer diameter (mm) 920Brake disc inner diameter (mm) 640Width of ring (mm) 24Width of fins (mm) 30Density of brake disc material (kg/m3) 7246Specific heat of brake disc material (J/kg K) 500Thermal conductivity of brake disc material(W/m K) 58Density of brake pad (kg/m3) 2180Specific heat of brake pad (J/kg K) 1090Thermal conductivity of brake pad(W/m K) 1.67Average friction coefficient (μ) 0.32Ambient temperature(°C) 55Start temperature of brake disc(°C) 55Deceleration of vehicle (average) (m/s2) 1.177

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The ER24PC locomotive consists of two bogies. Each bogie hasfour wheels with one set of wheel-mounted brake discs which consistsof two brake discs arranged on both sides of a wheel and are boltedtogether through the wheel web (Fig. 1).

2.1. Thermal modeling

Regarding the uniform pressure or the constant wear boundaryconditions at the contact surface, two methods for calculating the rateof braking heat generation are available. The uniform pressure assump-tion in the contact region is often validwhen the pads are new. Howeverafter several braking, the assumption of uniformwear ismore pragmatic.In this study the pad was used several times and the uniform wear be-tween pad and brake disc is stabilized, so the heat flux is just a functionof time and it is independent of the space variable [10].

For a vehicle decelerating on a level surface from a higher velocity V1to a lower velocity V2 = 0 the braking energy Eb can be written as [7]

Eb ¼ 12m 1þ I

R2wm

� �V21 ¼ 1

2kcfmV2

1 ð1Þ

where I is the mass moment of inertia of rotating parts,m is locomotivemass, kcf is the correction factor for rotating masses and Rw is the wheelradius.

Braking power Pb is equal to braking energy divided by the time tduring which braking occurs; for a constant declaration one can writethat

Pb ¼ dEbdt

¼ kcfma V1‐atð Þ ð2Þ

where a is the deceleration of the locomotive. As an example, in the caseof an emergency braking at 154 km/h of the ER24PC Loco, the maxi-mum stopping distance is 778 m with an average deceleration of1.177 m/s2 corresponding to a dissipated energy of 5.14 MJ per brakingdisc.

The distribution of braking energy between pad and disc cannot bepredicted readily. Generally, the thermal conductivity of the brakepads material is smaller than that of the disc (kp b kd), so one can con-sider that the total amount of the braking heat will be completelyabsorbed by the brake disc. This assumption leads to higher tempera-ture estimation for brake disc. To avoid this issue, suppose that the brak-ing application time is short, so the pad and brake can be considered assemi-infinite solids and the heat generation ratio can be calculated asfollows [11]:

λ ¼ q0 0

d

q0 0p

¼ ρdCdkdρpCpkp

!1=2

ð3Þ

where λ is the heat generation ratio, q″d is the heat flux absorbed by thebrake disc,q″p is the heat flux absorbed by the pad, ρ represents density,C is the specific heat, k is the thermal conductivity and the subscript d

Fig. 1. Wheel-mounted brake disc of ER24PC locomotive.

Please cite this article as: B. Ghadimi, et al., 3D investigation of thermal strefluid coupling, Int. Commun. Heat Mass Transf. (2013), http://dx.doi.org/10

and p indicate disc and pad, respectively. Using Eqs. (2) and (3), theheat flux on the braking surface can be found as follows:

q0 0

d ¼ λA λþ 1ð Þ kcfma V1‐atð Þ ð4Þ

where A is the disc and pad contact area.

2.2. Modeling and boundary conditions

For FEM and CFD analysis, three-dimensional (3D) constructions ofbrake disc and cooling air domain were modeled. Mesh independencywas investigated and finally an unstructured mesh of 425,238 cellsfor brake disc and 369,765 cells for cooling air zone have been chosen.For solving the continuity, momentum and energy equations, FLUENTunsteady solver have been used with SIMPLE algorithm for pressureand velocity coupling.

For turbulentmodeling the RANS-based approachwas selectedwiththe realizable k–ε model. The realizable k–ε model is a variant of thestandard k–ε model that is tuned to perform better in situations withrotating flows. The continuity andmomentum equations can bewrittenas follows:

∂ρ∂t þ

∂∂xi

ρuið Þ ¼ 0 ð5Þ

Fig. 2. Experimental setup.

sses in a locomotive ventilated brake disc based on a conjugate thermo-.1016/j.icheatmasstransfer.2013.10.009

Fig. 3. Thermal simulation of the brake disc; one brakes from 154 km/h witha = 1.177 m/s2.

3B. Ghadimi et al. / International Communications in Heat and Mass Transfer xxx (2013) xxx–xxx

∂∂t ρuið Þ þ ∂

∂xjρuiuj

� �¼ ‐

∂p∂xi

þ ρ g!

þ ∂∂xj

μ∂ui

∂xjþ ∂uj

∂xi‐23δij

∂ul

∂xl

#þ ∂∂xj

‐ρu′iu

′j

� �"

ð6Þ

where the density is a function of temperature following ideal gas law.The realizable k–ε model consists of the following two transport

equations, one for turbulent kinetic energy (k) and the other for thedissipation rate (ε):

∂∂t ρkð Þ þ ∂

∂xjρkuj

� �¼ ∂

∂xjμ þ μt

σk

� � ∂k∂xj

" #þ Gk þ Gb‐ρε‐YM þ SK ð7Þ

∂∂t ρεð Þ þ ∂

∂xjρεuj

� �¼ ∂

∂xjμ þ μ t

σε

� � ∂ε∂xj

" #þ ρC1Sε‐ρC2

ε2

kþ ffiffiffiffiffiffiνε

p

þ C1εεkC3εGbþ Sε

ð8Þ

Additional details of the realizable k–ε model and the definition ofparameters using the earlier equations can be found in [12].

Fig. 4. Temperature distribution: (a) case 1 at t = 22

Please cite this article as: B. Ghadimi, et al., 3D investigation of thermal strefluid coupling, Int. Commun. Heat Mass Transf. (2013), http://dx.doi.org/10

One can obtain the temperature field solving the energy equation asfollows:

∂∂t ρCpT� �

þ ∂∂xi

ρuihð Þ ¼ ∂∂xj

λ∂T∂xj

" #ð9Þ

where λ is the thermal conductivity, which for the fluid region becomesλ + λt. The parameter λt is the turbulent thermal conductivity.

Temperature distribution of brake disc was obtained by solvingEqs. (5) to (9).

In the friction analysis, it is frequent to consider the pad to disc pres-sure loading contact and the thermo-mechanical loading due to thethermal gradients. In the railway application, the normal contact forceis low; so on the assumption of a uniform contact pressure, the contactpressure response is negligible in comparison with the thermal stresses[13]. Therefore, the model presented in this paper considers only theloading due to the thermal gradients. In the following, the procedureof thermal stresses calculation was described.

Thermal strain definition is required to calculate the thermal stresses.Thermal strain is an elastic strain that results from expansion withincreasing temperature, or contraction with decreasing temperature.The thermal strain at a given temperature T can be assumed to be pro-portional to the temperature change ΔT over a limited range of temper-atures and is described as

ε ¼ α T‐T0ð Þ ¼ α ΔTð Þ ð10Þ

where T0 is a reference temperature and α is the thermal expansioncoefficient.

The elastic deformation is satisfied by Hooke's law; hence thethermal stress σ is described as

σ ¼ Eα ΔTð Þ ¼ Eε ð11Þ

Physical properties of brake disc material and boundary conditionsfor analysis are given in Table 1. Heatflux in the braking surfacewas cal-culated using Eq. (4). At each time step, according to the locomotivespeed and distribution of temperature in the brake disc, the local heattransfer coefficient of fins was calculated by solving the RANS andenergy equations in the fluid zone, and used as a boundary conditionfor the brake disc thermal analysis. Then the energy equation wassolved in the brake disc and temperature distribution at the subsequenttime step was calculated. This procedure is continued until the locomo-tive comes to a stop.

.5 s, (b) case 2 at the end of braking (t = 75 s).

sses in a locomotive ventilated brake disc based on a conjugate thermo-.1016/j.icheatmasstransfer.2013.10.009

Fig. 5. Surface temperature and temperature gradients of braking between two nodes.

4 B. Ghadimi et al. / International Communications in Heat and Mass Transfer xxx (2013) xxx–xxx

2.3. Experimental setup

A railway brake disc system is tested on the ZF-Dynamometer(Fig. 2) in the Faiveley Transport Company and results were reportedto MLC [14]. The ZF-Dynamometer is able to run with specific missionprofiles in dry and wet conditions. The dynamometer has an electricmotor of 536 kWand up to four coupleableflywheelmasses to simulatevariousweights and loads of vehicles. Themeasurement of temperature

Fig. 6. Braking from v = 160 km/h with a deceleration rate o

Please cite this article as: B. Ghadimi, et al., 3D investigation of thermal strefluid coupling, Int. Commun. Heat Mass Transf. (2013), http://dx.doi.org/10

is a very important step in the test procedure. For this purpose, K TypeThermocouples having 1.5 mm diameter were used. For modeling thebraking process, the locomotive wheel was accelerated with a constantvalue of 0.8 m/s2, and after reaching the desired velocity, the brakingstarted and caused constant deceleration with a rate of 1.117 m/s2.During the brake period the temperatures of the braking surface andwalls of the fins were recorded and used for validating the numericalresults.

f 1.2 m/s2. (a) Thermal stress and (b) total deformation.

sses in a locomotive ventilated brake disc based on a conjugate thermo-.1016/j.icheatmasstransfer.2013.10.009

5B. Ghadimi et al. / International Communications in Heat and Mass Transfer xxx (2013) xxx–xxx

3. Results and discussions

In this paper thermal analysis of a locomotive ventilated brake dischas been investigated using a conjugate thermo-fluid coupling bound-ary conditions using code ANSYS 12.1.

Solution verification deals with the assessment of the numericalerrors which always exist when partial differential equations are solvednumerically. Therefore, to validate the proposed transient numericalmethod, temperature history of the brake disc in emergency brakingfrom velocity of 154 km/h with a constant deceleration rate of1.117 m/s2 was determined and was compared with experimentalresults. In Fig. 3 comparison between experimental and evaluated tem-perature is shown, which indicates that numerical results are in a goodagreement with the experimental data.

The lag in temperature evolution resulting from heat diffusion in thebrake disc can be observed in Fig. 3, for the fins' temperature.Maximumtemperature is observed to decrease with increasing node depth. Forexample, at the time 24 s, the maximum temperature for surfacenode was 512 K, whereas that of the 20 mm-deep node was 440 K.This indicates the presence of significant thermal gradients in the disc.

For further investigation, the thermal analysis has been performedfor two cases, first for the braking from 160 km/h with the decelerationrate of 1.2 m/s2 (case 1) and second for the braking in the downhill withthe slope of 5% at the constant speed of 160 km/h (case 2). Temperaturedistribution for these two cases is illustrated in Fig. 4.

According to Eq. (11), the thermal stress is proportional to thetemperature difference between two points. Thus, the temperaturegradients between two nodes, one in the braking surface and theother in the depth of 20 mm, are presented for both cases, in Fig. 5, to

Fig. 7. Braking in the downhill with the slope of 5% in the constant velocit

Please cite this article as: B. Ghadimi, et al., 3D investigation of thermal strefluid coupling, Int. Commun. Heat Mass Transf. (2013), http://dx.doi.org/10

find the time which implies maximum thermal stress. Since the brakingtimes are different for these cases, dimensionless time is defined as aratio of the actual time and themaximumbraking time. It can be inferredfrom this figure that the maximum thermal stress for case 1 occurred inthe beginning of the braking (t = 7.5 s) and does not happen when thesurface temperature reaches to its maximum temperature (t = 21 s).For case 2, due to the constant heat flux generation between padand disc, after a few seconds the temperature gradient between thenodes, reaches to a constant value, and thermal stress distributiontends to steady condition, hence temperature of the disc increasescontinuously.

So choosing the brake disc material has a crucial effect on the brakedisc engineering; if the brake material has low thermal conductivity,the temperature gradient across the brake disc width will be high. Asa result, the surface temperature rose faster than the brake disc body,resulting in different thermal expansions between the surface andbody of the brake disc. Due to the constraints associated with the coolerbrake disc body, compressive stresses are induced at the brakingsurfaces and tensile stresses occur over the brake rotor interior. Ifthese thermal induced stresses exceed beyond a certain magnitude orthey repeat many times, brake disc failure is not unexpected.

The thermal stress analysis has been performed for both cases andthe thermal stresses and the total deformation distribution for thesecases are illustrated in Figs. 6 and 7, respectively. Due to the non-uniform cooling of the brake disc, in both cases, the maximum thermalstresses are localized around the bolting hole.

Maximum temperature value, von-Mises stress and deformationfor braking in these two case studies are summarized in Table 2. Accord-ing to this table, the maximum temperature and the maximum total

y of 160 km/h for 75 s. (a) Thermal stress and (b) total deformation.

sses in a locomotive ventilated brake disc based on a conjugate thermo-.1016/j.icheatmasstransfer.2013.10.009

Table 2Comparison of the maximum temperature, thermal stress and deformation in two different cases.

Temperature (k) Thermal stress (MPa) Total deformation (mm)

Case 1 499.1 277.55 0.48079Case 2 591.36 211.76 1.3191

6 B. Ghadimi et al. / International Communications in Heat and Mass Transfer xxx (2013) xxx–xxx

deformation of case 2 are 18.4% and 174.4% bigger than case 1, respec-tively, but the maximum thermal stresses of case 1 are 23.7% biggerthan case 2.

Despite the 18.4% increases in the maximum temperature, the ther-mal stresses decrease 23.7%. This confirms the well design of the finsgeometry for this locomotive, and it dissipates the generated heat dur-ing the braking very well.

4. Conclusion

The thermal and stress analyses of the locomotive wheel-mountedbrake disc during the emergency and in the downhill braking atthe speed of 160 km/h considering airflow cooling were investigatedusing both finite element (FE) and computational fluid dynamics (CFD)methods.

Based on the numerical solution of the theoreticalmodel, the follow-ing points can be highlighted:

1. The experimental results are in good agreement with the simulationdata which prove the correctness of the numerical model.

2. For the emergency braking (case 1):(a) First, the temperature of the brake disc increases and then

decreases as the braking goes on.(b) The temperature gradient exists in the brake disc and has its

maximum value at the beginning of the braking (t = 7.5 s).3. For the downhill braking (case 2)

(a) The temperature of the brake disc increases steadily.(b) The temperature gradient exists in the brake disc and reaches to

a constant value as braking goes on.4. The highest values of the temperature after emergency and downhill

brakingwere found to be499.1 Kand591.36 K respectively,whichoc-curred at about 21 s and at the end of the braking(75 s), respectively.

Please cite this article as: B. Ghadimi, et al., 3D investigation of thermal strefluid coupling, Int. Commun. Heat Mass Transf. (2013), http://dx.doi.org/10

5. Themaximum stress could reach 277.55 MPa for emergency brakingand 211.76 MPa for downhill braking.

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