EXAMENSARBETE I ELEKTROTEKNIK 300 HP, AVANCERAD NIVÅ STOCKHOLM, SVERIGE 2015

An integrated brake disc and electric drive for vehicle propulsion

A FEASIBILITY STUDY

JOHAN LINDER

KTH KUNGLIGA TEKNISKA HÖGSKOLAN

SKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK An integrated brake disc and electric drive for vehicle propulsion -A feasibility study

JOHAN LINDER

Master of Science thesis in Electrical Machines and Drives at the School of Electrical Engineering KTH Royal Institute of Technology Stockholm, Sweden, February 2016.

Supervisor: Oskar Wallmark Examiner: Oskar Wallmark

TRITA-EE 2016:019 An integrated brake disc and electric drive for vehicle propulsion -A feasibility study JOHAN LINDER

c JOHAN LINDER, 2016.

School of Electrical Engineering Department of Electric Power and Energy Systems KTH Royal Institute of Technology SE–100 44 Stockholm Sweden Abstract

In this thesis, the feasibility to integrate an brake disc and electric machine is investigated. In wheel motors (IWMs) have several advantages, such as saving space in the vehicle, individual and direct control at the wheels and the absence of a mechanical transmission. However, today’s IWMs are heavy and, thus, negatively affect the driving performance of the vehicle due to the increase of the unsprung mass. By integrating an already existing part in the wheel, this increase of the unsprung mass can be minimized. The brake disc manages high temperatures, a significant wear in rough environ- ment, which puts high demands on the rotor. The second part of the machine, the stator, will be significantly affected by the high temperatures of the rotor. The temperatures of the stator are transferred by convection, conduction and radiation from the rotor or brake disc. Liquid cooling of the stator back is analyzed as a potential solution for handling the high temperatures. In order to analyze the feasibility of the concept, thermal, electric and mechanical modelling has been used. The evaluation whether it is possibleor not to integrate the brake disc has been with regard to the results of weight, cost, thermal tolerance and electric performance.

Key words: Axial flux, brake disc, core less rotor, in wheel motor, hub motor, quarter car model, segmented rotor, switch reluctance machine, single teeth winding.

iii iv Sammanfattning

I detta arbete unders¨oks m¨ojligheten att integrera en bromsskiva med elmaskin. Hjul- motorer har flera f¨ordelar, bland annat sparas utrymme i sj¨alva bilen, individuell kon- troll samt drivning av hjulen utan mekaniska transmissioner. Men hjulmotorer som kan anv¨andas idag v¨ager oftast s˚apass mycket att den od¨ampade massan ¨okar kritiskt och k¨oregenskaper av fordonet d˚ablir lidande. Genom att integrera en befintlig del i hjulet kan ¨okningen av od¨ampade massan minskas. Att anv¨anda bromsskivan som rotor, kr¨aver att denna t˚al temperaturer ¨over 500◦C samt p˚afrestningar och slitage som en vanlig mekanisk friktionsbroms m˚aste uth¨arda. Den andra delen av maskinen, statorn kommer ¨aven denna att p˚averkas av de h¨oga tem- peraturerna av bromsskivan som kommer ledas via konvektion, konduktion och str˚alning. M¨ojligheten att kyla statorn med v¨atska och om detta ¨ar tillr¨ackligt unders¨oks. F¨or att analyserna genomf¨orbarheten av projektet har termiska, elektriska och mek- aniska modeller anv¨ants. Resultaten har analyserats d¨ar maskinens vikt, kostnad, termisk t˚alighet och elektrisk prestanda har legat till grund f¨or bed¨omningen om l¨osningen; att integrera en broms-skiva med elmaskin ¨ar rimlig eller ej.

Nyckelord: Axialfl¨odes, bromsskiva, enkeltandad lindning, hjulmotor, hub motor kvartfordonsmodell, ryggl¨os rotor, segment rotor, variabel reluktansmaskin.

v vi Acknowledgements/Forfattarens¨ tack

F¨orst och fr¨amst vill jag tacka Doktor Oskar Wallmark som har handlett mig genom hela detta arbete genom alla dess niv˚aer och sv˚arigheter. Jag vill ocks˚atacka alla inblandade p˚aVolvo som varit mycket hj¨alpsamma och framf¨or allt S¨oren Eriksson som handlett och inspirerat mig samt Quintus Jalkler som hj¨alpt mig med kontakter och ¨ovriga fr˚agor under arbetet. Dessutom vill jag passa p˚aatt tacka alla mina goda v¨anner som gjort studietiden p˚a KTH minnesv¨ard. Ett speciellt tack till Anna Larsson som ¨agnade tid ˚at att granska min rapport. Samt Noj Kazemi, Sebastian H˚akansson, Erik Hallqvist och Alexander Sj¨oberg som jag ¨agnat ˚atskilliga timmar att studera med. Utan den kamratskapen och st¨odet hade min studietid blivit betydligt jobbigare och framf¨orallt tr˚akigare. Jag vill tacka alla d¨ar hemma, mor, far, syster och morfar, som st¨ottat och m¨ojlig- gjort mina studier under ˚aren. Mina v¨anner som under alla dessa ˚ar fortfarande h˚aller samman som det j¨arng¨ang vi alltid varit. Samt min mycket gode v¨an Viktor Andersson som delar mitt st¨orsta intresse och som introducerat mig till flertalet av fordonsv¨arldens alla h¨orn. Avslutningsvis vill jag tacka min K¨araste Lisa f¨or allt personligt st¨od hon har givit mig under detta examensarbete.

Johan Linder Stockholm, Sweden February 2016

vii viii Contents

Abstract iii

Sammanfattning v

Acknowledgements/Forfattarens¨ tack vii

Contents ix

1 Introduction 1 1.1 Background...... 1 1.2 Objectives...... 2 1.3 Thesisoutline...... 3

2 Previous work 5 2.1 Patents...... 5 2.2 VolvoReChargeConcept ...... 5 2.3 Hybridelectricvehicles...... 6 2.4 Inwheelmotors...... 7

3 Influence of unsprung mass 9 3.1 Suspension ...... 9 3.2 Quartercarmodel...... 10 3.3 Simulinkquartercarmodel ...... 11 3.3.1 Increasingtheunsprungmass ...... 15 3.4 Resonancefrequency ...... 19 3.5 Summaryofchapter...... 20

4 Brakes 23 4.1 Thefunction...... 23 4.2 Thedisc...... 24 4.3 Brakeregulation...... 24 4.4 Brakeforcedistribution...... 25

ix Contents

4.5 Heattransfer...... 25 4.5.1 Conduction ...... 25 4.5.2 Convection ...... 26 4.5.3 Radiation ...... 26 4.6 1Dthermalmodels ...... 27 4.6.1 Powerappliedonmass ...... 28 4.6.2 Powerappliedonsurface...... 28 4.7 3Dthermalmodels ...... 30 4.7.1 Forcedconvection ...... 31 4.7.2 Naturalconvection ...... 33 4.8 Summaryofchapter...... 35

5 Electrical machine 39 5.1 Designchallenges...... 39 5.2 Choiceofmachine ...... 40 5.3 Segmentalrotor ...... 41 5.4 Linearmodel ...... 42 5.5 Thewheelmotor ...... 44 5.6 Solidrotorinductionmachine ...... 46 5.7 Summaryofchapter...... 47

6 Implementation of brake disc 51 6.1 Heattransferbetweenthestatorandrotor ...... 51 6.2 3Dmodel ...... 52 6.3 Summaryofchapter...... 53

7 Conclusion and further work 59 7.1 Conclusion ...... 59 7.2 Furtherwork ...... 60

A Parameters of quarter car model 63

B Parameters of 1D thermal models 65

C Parameters of 3D thermal model 67

D Parameters and specification of the electrical machine 69

E Parmaters of implementation of machine thermal model 73

References 75

x Chapter 1

Introduction

In this part the background, the aim and goals of the project are presented.

1.1 Background

Hybrid electric vehicles (HEVs) and electric vehicles (EVs) are more than ever an impor- tant topic in the vehicle industry. Manufactures, such as Tesla, Volkswagen, Chevrolet and Toyota are only a few that offers EVs and/or HEVs to the market. However, the batteries used in the vehicle today has an upper limit of driving range. Even if there are supercharg- ers available that charge the batteries in 30 minutes and deliver a cruising range of around 270 km [10], the charging of the batteries is still considerable more slow than an ordinary refuel of a vehicle with internal combustion engines (ICEs). HEVs combining the ICE with an electric drive are one opportunity to overcome the limits of the pure EV. It offers the cruising range as ordinary cars thanks to the ICE and the fast refuels of fossil fuel. Compared to pure ICE propelled vehicles it (potentially) offers lower fuel consumption thanks to regeneration of brake energy to electric energy and the possibility to keep the ICE operating at points with high efficiency. Development of electric machinery and associated powertrain componets has opened up for a lot of opportunities. In wheel motors (IWMs) enable the possibility to direct and individual drive and control the wheels without expensive and difficult mechanical transmission and drive shafts. However, a drawback is the increasing of unsprung mass due to more weight in the wheel, effecting driving performance and comfort of the vehi- cle [46], [29]. By integrating the already existing brake disc as a rotor in an IWM, there is a possibility to reduce the total increase of unsprung mass. Today, Volvo XC90 and V60 are two HEV models using the Volvo Twin Engine which use an electric machine placed on the rear axle Fig. 1.1. The electric machine is using two drive shafts for driving each rear wheel. Recently Volvo introduced a new vehicle platform, the Scalable Product Platform (SPA). Presently the XC90 is the only manufactured model using SPA and therefore this thesis is focused on the XC90.

1 Chapter 1. Introduction

In this thesis, three main parts are investigated: effects on suspension by increased unsprung mass, thermal effects due to mechanical braking on the rotor and an electric model for analyse the torque production. The main softwares used in this study are Com- sol Multiphysics 1 and Matlab/Simulink2.

Fig. 1.1 V60 Twin Engine, with electric machine in blue at rear axle [13].

1.2 Objectives

The aim of the project is to investigate the possibilities of using a brake disc as rotor in an IWM. Without an external rotor there is a opportunity to reduce the increased mass compared to using an existing IWM. The mechanical brake system is, hence, still present, which challenges the design of the electric machine both due to high temperatures but also due to limited volume. The following goals were set for the investigation of the concept

• Suggest a design of an electric machine that can deliver 10 kW at each rear wheel.

• Propose changes on a current vehicle to make the design possible.

• Investigate the influence of the unsprung mass.

• Present other challenges of an implementation of this machine

• Estimate the cost associated with the machine.

1Comsol Multiphysics is registered trademark of COMSOL AB 2Matlab and Simulink are registered trademarks of The Mathworks Inc. Natick, Massachusetts, U.S

2 1.3. Thesis outline 1.3 Thesis outline

The thesis report is separated in five chapters as follows:

• Chapter 1:Introduction.

• Chapter 2: Briefly presentation of previous work, patents and in-wheel motors.

• Chapter 3: Influence of unsprung mass.

• Chapter 4: Brake disc and thermal analysis.

• Chapter 5: Design of the electric machine.

• Chapter 6: Thermal analysis of the stator.

• Chapter 7: Conclusion and further work.

3 Chapter 1. Introduction

4 Chapter 2

Previous work

In this chapter previous related work is presented e.g patents that can be intruded, ear- lier investigations at Volvo, machines that reminds of this concept and other important aspects.

2.1 Patents

Integration of a brake disc with an electric machine is not a new concept, however, the available literature is narrow. Brembo Sgl Carbon Ceramic Brakes S.P.A. developed a patent covering a brake disc as rotor in an electric machine. The patent defines the use of an external stator or implements such components in a calliper and how to implement ro- tor components such as inductors in a brake disc. The patent covers most of conceivable implementations of the brake disc and machine types: ”Preferably, the rotary electrical machine is an asynchronous axial machine or an asynchronous radial machine or a syn- chronous reluctance machine or an axial/radial hybrid machine.” [39]. The patent of Evans Electric comprises of an axial flux induction machine, where the stator only cover 180 degrees of the rotor Fig. 2.1. The rotor is suggested as a toroidal with ladder bars forming a squirrel cage. The stator of the machine is designed to replace the mechanical brake calliper. [25].

2.2 Volvo ReCharge Concept

In 2007, Volvo developed the Volvo ReCharge Concept car Fig. 2.2. The car was a Plug- In-Hybrid based on the C30 model. With pure electric drive, the reported driving range was around 100 km. [12]. IWMs from PML Flightlink (today named Protean Electric) were used in all four wheels. The car was installed with lightweight brake discs, but those were only used for parking assistance and not as service brakes.

5 Chapter 2. Previous work

Fig. 2.1 Evans Electric In-Wheel Motor [20].

2.3 Hybrid electric vehicles

The topology of a HEV can vary significantly, series hybrid, parallel hybrid, 4QT, plug- in, Micro hybrid, Mild hybrid and etc. The series hybrid use electric machines (EMs) for drivingthe vehicle meanwhile the ICE is coupled to a generator supplying the vehicle with electric power. The EM for drive and the ICE for charging are therefore not mechanical connected. In a parallel hybrid both the ICE and EM are connected mechanically to the drive shaft and enable the opportunity to use pure combustion drive mode [15]. The voltage level varies between the different types of vehicles. In conventional gasoline or diesel cars, the voltage level is usually 12V. Such a low voltage can be prob- lematic for EVs and HEVs due to the demand of higher electric power which would it necessary to use more copper in the cables due to the high voltage drop. Voltage lev- els for EVs and HEVs are therefore significantly higher [15]. For mild hybrids, voltage levels from 12-48V and up to 200V are considered and for full hybrids around 400V is common [26]. Hybrid vehicles can be divided in three main degrees; micro, mild and full hybrid. Full hybrid cars can be driven in pure electric mode, hybrid mode or with pure combus- tion mode. Mild hybrid vehicles are HEVs that not can be driven in pure electric mode. Micro hybrid are cars only use Stop-Start function, making the vehicle reduce the fuel consumption at stops and starts by turn off and re-start the ICE [8]. Today’s Volvo Twin Engine enables the possibility to drive in pure electric mode, hybrid mode or with pure combustion mode. Depending on model and ICE, the electric part delivers between 50 to 65 kW with a voltage level between 270V and 420V for the battery [14].

6 2.4. In wheel motors

Fig. 2.2 Volvo ReCharge Concept [12].

2.4 In wheel motors

There are several manufactures of IWMs and a few of them are presented below in brief. The machines differs in designs Fig 2.3, weight and performance (Table 2.1). Elaphe deliver liquid cooled machines such as L-type and M700. The L-type model is made to fit together with a conventional brake disc and caliper. The M700 model is a machine built to fit together with drum brakes. It is a synchronous permanent magnet (PM) machine with outer rotor and a high number of poles. This machine is lighter and delivers lower torque and power than the L-type. Elaphe LEV, is an air cooled machine that delivers considerable lower power and torque compared both to the L-type and M700 [1]. Mitsubishi in-wheel motor electric vehicle (MIEV) was a concept using four syn- chronous PM IWMs that is built around the brake disc with calliper. The motors were produced by Toyo Denki Seizo K.K. [11]. Printed motor works offer a series of IWMs. One of those is the XR32-11 model, a permanent magnet brushless motor with external rotor [2]. IWMs from Protean Electric were used in the Volvo Recharge Concept and have been demonstrated in other vehicles manufactured by Ford and Mercedes-Benz. The ma- chine is liquid cooled and the power electronics are integrated in the machine [3].

7 Chapter 2. Previous work

Table 2.1: In wheel motors from different manufacturers. Machine Weight[kg] Peak Power[kW] Peak Torque[Nm] L-type[1] 28 110 1000 M700[1] 23 75 700 LEV[1] 20 20 225 Mitsubishi[11] notspecified 50 518 XR32-11[2] 17 23.1 160 ProteanE[3] 34 75 1000

(a) (b)

(c) (d)

(e) (f)

Fig. 2.3 Different IWMs: a) M700 [1]; b) L-type [1]; c) LEV [1]; d) Mitsubishi [11]; e) XR32-11 [2]; f) Protean E. [3].

8 Chapter 3

Influence of unsprung mass

In this chapter the impact of increasing the unsprung mass is investigated. The quarter car model is introduced and implemented as a Simulink model and a transfer function.

3.1 Suspension

The mass of a vehicle can be divided into unsprung mass and sprung mass. The sprung mass is the mass of the vehicle body moving above the suspension and, thus, this mass is sprung. The unsprung mass is the mass moving below the suspension like wheels, axles, brakes and etcetera [38]. The wheel includes the tire and rim. The tire consists of some type of rubber that will have some impact on the unsprung mass due to elasticity. The suspension consists mainly of the spring and the shock-absorber [38]. The spring can be of different types and two common ones are the coil spring and leaf spring. Important functions of the suspension are to maintain good comfort for the passengers, good han- dling and good road holding [38]. In Fig 3.1 two different rear axles can be seen; one with leaf springs and one with coil springs.

(a) (b)

Fig. 3.1 Rear axles: a) Leaf spring [21]; b) Coil spring [21].

One issue to consider with IWMs is the impact of increasing the unsprung mass which will be one of the outcomes by placing more weight at the wheels. A common

9 Chapter 3. Influence of unsprung mass statement is that use of IWMs can have a significant impact on the vehicle performance with negative consequences including a decreased handling and comfort [29] [46]. Other statements indicates that this impact is less problematic than earlier believed [17] [47]. An investigation of the impact by increasing the unsprung mass is therefore investigated using the quarter-car model (QCM) present in the next section.

3.2 Quarter car model

By dividing the vehicle into four parts where each part comprises unsprung mass, sus- pension and sprung mass a simple model called the quarter-car model is introduced see Fig. 3.2. Each part represents a specific quarter of the car and those may differ between front and rear of the vehicle due to weight distribution, size of brakes, drive shafts and etc.

The QCM is parametrized using the coefficients for stiffness ks and damping cs to repre-

Fig. 3.2 Quarter-car model. sent the spring and shock-absorber see Fig. 3.3. In the same way, the characteristics of the 1 tire are represented by the tire stiffness kt and the tire damping ct tire . The sprung mass or body of the vehicle can differ between each quarter part of the car due to the weight distribution between front and rear axle. The unsprung mass can also differ by reasons such as different brakes between the front and the rear wheels, drive shafts at front, rear or four wheel drive (4WD). The sprung mass is designated as ms and the unsprung as mus. The height position the vertical z-direction for the wheel/unsprung mass is desig- nated with zus, the sprung mass/vehicle body with zs and the profile of the road with z0.

1In the thesis the coefficients of the QCM represents by constants, in reality those are non-linear [41].

10 3.3. Simulink quarter car model

Fig. 3.3 Spring and shock-absorber represent by spring factor and damp factor [41].

The forces acting on the sprung mass ms can be expressed as [47]

msz¨s = −ks(zs − zus) − cs(z ˙s − z˙us) − msg (3.1) while the forces acting on the unsprung mass mus can be expressed with [47]

musz¨us = ks(zs − zus)+ cs(z ˙s − z˙us) − kt(zus − z0) − ct(z ˙us − z˙0) − musg. (3.2)

This system is, however, not taken in an account when the wheel lift from the ground, called a wheel-hop. This occurs when the movement zus from the wheel’s original location compared to the movement z0 from the road’s original location is larger, namely zus −z0 ≥ 0. When this happens, the force from the road stops acting on the tire compared to (3.2) and for a wheel-hop this equation can be replaced with [47]

musz¨us = ks(zs − zus)+ cs(z ˙s − z˙us) − musg. (3.3)

Observe that the dynamic system is sometimes expressed with the influence of gravita- tional force [47] or without [38], varying between authors.

3.3 Simulink quarter car model

From (3.1)-(3.2)-(3.3) a Simulink model illustrated in Fig. 3.4 has been defined in the same way as in [47]. The model is used mainly for analysing the influence of the road z0 on the acceleration of the vehicle body z¨s that corresponds directly to the comfort. Road holding performance can be quantified by the tire deflection zus −z0 [38]. The values used for the parameters can be found in Appendix A. The profile of the road is represented as a sinusoidal signal which increases stepwise frequency with steps of 0.05 Hz from 0.5 Hz to 30 Hz with 10 periods for each frequency and the amplitude are decreasing with increased frequency Fig. 3.5. This test corresponds to one of the physical tests of the suspension at

11 Chapter 3. Influence of unsprung mass

Volvo. In order to simplify the graphics, the signals are plotted with frequency such as the displacements z0, zus and zs in Fig. 3.6. The unsprung mass zus follows a similar pattern as the road z0 except to a small gain at around 10Hz see Fig. 3.5. The sprung mass zs however has a distinct gain about 1.2Hz that thereafter follow with a damping effect. The acceleration z¨s can be seen in Fig. 3.7 and the tire deflection in Fig. 3.8

ms*g 1 1 1/ms zs ms*g s s Integrator2 Integrator3 1/ms 0 >= Wheel hop Relational zs_biss Operator Product ks 1 1 1/mus zus s s Gain2 kt Integrator Integrator1 cs mus*g 1/mus z0 Gain mus*g Input signal du/dt Gain3 ct Derivative Gain1

Fig. 3.4 Simulink model.

12 3.3. Simulink quarter car model

0.04

0.02

0 [m]

-0.02

-0.04 0 200 400 600 800 Time [s]

Fig. 3.5 Input signal z0, sinusoidal signal steping from 0.5 to 30 Hz.

0.04 z 0 z us 0.03 z s

] 0.02 m [

0.01

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.6 The displacements z0, zus and zs.

13 Chapter 3. Influence of unsprung mass

2.5

2

1.5 ] 2 m/s

[ 1

0.5

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.7 Acceleration z¨s.

×10 -3 4

3.5

3

2.5 ] m [ 2

1.5

1

0.5 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.8 Tire deflection.

14 3.3. Simulink quarter car model

3.3.1 Increasing the unsprung mass

In order to analyze the influence of increasing the unsprung mass, an ordinary two-wheel drive (2WD) XC90 is analyzed with no additional unsprung mass and then compared to the situation with an extra unsprung mass of 5, 10, 15, 20 and 25kg extra at each rear wheel. The increase of the unsprung mass has a relatively low impact on zus see Fig. 3.9 and almost no effect on zs Fig. 3.10. However, for the acceleration z¨s the increase of the unsprung mass has a more clear impact; especially of frequencies above 3Hz see Fig. 3.11. The impact from the unsprung mass of the tire deflection is obvious at the second reso- nance frequency with an increase from around 1.2mm for 0kg to almost 1.6mm for 25kg see Fig. 3.14. It is considered that an increase of only 5 to 10% of the vehicle body acceleration RMS value is enough to cause a distinct reduction of the comfort [48]. The RMS value for the whole frequency spectra of z¨s varying between shifting the unsprung masses and increase when the unsprung mass increases. In Table 3.1, the RMS values and the relative increase compared to the original vehicle (without additional unsprung mass) are summa- rized. For certain critical frequencies the results in Fig. 3.11 are compared to a increase by

5% of zs(0kg) Fig. 3.12. The results show that the most critical part of the acceleration z¨s occurs around 9Hz. The RMS value for a sinusoidal input signal of 9Hz and the relative increase are summarized in Table 3.2.

Table 3.1: Acceleration z¨2 at 0.5 to 30Hz. Increased unsprung mass RMS[m/s2] Increasing[%] 0kg 0.6227 0 5kg 0.6271 0.72 10kg 0.6311 1.35 15kg 0.6354 2.04 20kg 0.6393 2.68 25kg 0.6436 3.36

Table 3.2: Acceleration z¨s at 9Hz. Increased unsprung mass RMS[m/s2] Increasing[%] 0kg 0.5398 0 5kg 0.5626 4.22 10kg 0.5845 8.27 15kg 0.6046 12.0 20kg 0.6222 15.26 25kg 0.6364 17.88

15 Chapter 3. Influence of unsprung mass

0.035 25kg 0.03 20kg 15kg 0.025 10kg 5kg 0.02 0kg ] m [ 0.015

0.01

0.005

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.9 Displacement zus, 0 to 25kg increased unsprung mass.

0.04 25kg 20kg 0.03 15kg 10kg 5kg 0kg ] 0.02 m [

0.01

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.10 Displacement zs, 0 to 25kg increased unsprung mass.

16 3.3. Simulink quarter car model

2.5 25kg 20kg 2 15kg 10kg 1.5 5kg ]

2 0kg m/s

[ 1

0.5

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.11 Acceleration z¨s, 0 to 25kg increased unsprung mass.

2.5 25kg 20kg 2 15kg 10kg 1.5 5kg ]

2 0kg 5percent m/s

[ 1

0.5

0 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.12 Acceleration z¨s, 0 to 25kg increased unsprung mass with 5% increase limit.

17 Chapter 3. Influence of unsprung mass

0.95

0.9

0.85 ]

2 0.8

m/s 0.75 [ 0.7

0.65

0.6

6 7 8 9 10 11 12 13 Frequency [Hz]

Fig. 3.13 Zoom of Fig. 3.12.

×10 -3 4 25kg 3.5 20kg 15kg 3 10kg 5kg 2.5 0kg ] m [ 2

1.5

1

0.5 0 5 10 15 20 25 30 Frequency [Hz]

Fig. 3.14 Tire deflection, 0 to 25kg increased unsprung mass.

18 3.4. Resonance frequency 3.4 Resonance frequency

The resonance frequency for the unsprung mass should be below 1.5Hz in order to obtain good a comfort [24]. Therefore, it is of interest to analyze the transfer function of z¨s of the system from the QCM. From a bode plot of a transfer function the resonance frequency can easily be investigated see Fig.3.15. For the transfer function, the influence of wheel- hop from (3.3) is neglected which otherwise would introduce a non-linearity to the system [47]. In order to simplify the transfer function, the impact from gravity of the unsprung and sprung masses is neglected. Using the Laplace variable s and assuming all the initial conditions to be zero (3.1) can be rewritten as

2 mss Zs = −ksZs + ksZus − cssZs + cssZus (3.4) and in same way (3.2) can be expressed with

2 muss Zus = ksZs − ksZus + cssZs − cssZus − ktZus + ktZ0 − ctsZus + ctsZ0. (3.5)

The transfer function from the input signal z0 to the displacement zs can thereby be ex- pressed as

2 Zs as + bs + c H(s)= = 4 3 2 (3.6) Z0 ds + es + fs + gs + h where

a =(ctcs) (3.7)

b =(ctks + cskt)

c =(ktks)

d =(musms)

e =(csmus + ctms + csms)

f =(ctcs + ksmus + ktms + ksms)

g =(cskt + ctks)

h =(ktks).

The Bode plots for the different extra unsprung masses can be seen in Fig.3.15. For all the plots the resonance frequency occurs at 1.32Hz.

19 Chapter 3. Influence of unsprung mass 3.5 Summary of chapter

If an increase of the unsprung mass has a significant bad impact on the vehicle or not can be discussed. From Table 3.1 it can be seen that none of the increased unsprung masses result in a 5% rise of the RMS value for the frequency spectra. By increasing the unsprung mass, the comfort for some specific frequencies can actually be improved; this phenomena occurs especially for the higher frequencies above 10Hz. However, the simulations show that there is a compromise of the comfort from 4Hz if the increase of the unsprung mass is more than 5kg Fig 3.12. None of the unsprung masses between 0 to 25kg affected the resonance frequency around 1.32Hz in such negative manner that it exceeded 1.5Hz see Fig. 3.15. The measurements show that an increase of the unsprung mass does not affect the displacements zus and zs in such a manner that it considerable increases the displace- ments. The road holding is clearly effected by the increase of the unsprung mass already for only 5kg extra weight; a distinct difference can be seen in Fig. 3.14. What exactly the impact of the increased tire deflection exactly means for the road holding should be considered in coming investigations. It is important to have in mind that the test of z0 stepping from 0.5 to 30Hz only evaluates relative low amplitudes, a bump or pot hole on a real road can easily exceed 32mm. It can therefore be of interest to carry out additional simulations representing drive cycles, specific bumps etcetera. However, in order to definitely determine whether the total unsprung mass is acceptable or not is difficult to predict without physical tests. A given benchmark from Volvo, where to allow 5kg increase at each rear wheel or that the unsprung mass at the rear axle not were allowed to exceed the unsprung mass at the front axle. That gives a value between 10 to 15.5kg at each wheel depending on size of disc, rims and etcetera. With those benchmarks and the investigation previously mentioned, a weight of maximum 15.5kg increased unsprung mass is assumed as acceptable.

20 3.5. Summary of chapter

Fig. 3.15 Transfer function H(s), vehicle with 0 to 25kg unsprung mass.

21 Chapter 3. Influence of unsprung mass

22 Chapter 4

Brakes

In this chapter, the heat generation of the brake disc is studied. The aim is to design a thermal model that can be used in later chapters. At first the brake disc is analysed by simple 1D-models, the experiences is than used for a more complicated 3D-model. The investigated 3D-model is finally compared to a given data and is considered as a sufficient thermal-model of the brake disc.

4.1 The function

One of the most important parts of the vehicle is the brake system. The aim of the brakes is obviously to enable the possibility to rapidly decrease the speed of the vehicle. Two different brakes dominate, the drum brakes and the brake discs. At Volvo is however nowadays only brake discs used in the cars and therefore this is the system used in this thesis. Brake discs consist simply of a disc and a corresponding caliper where the caliper is pushing its pads against the disc Fig. 4.1. Due to the friction between the disc and the pads, the rotation of the disc is transferred to heat. Clarifying, the kinetic energy of the vehicle is by the brakes transferred into thermal energy and the outcome is a deceleration of the vehicle. The kinetic energy of a vehicle can be expressed as 1 E = m v2 (4.1) 2 car and the power

P = mcarva (4.2) there mcar, v and a are the mass of the vehicle, the speed of the vehicle and the accelera- tion or deceleration of the vehicle respectively.

23 Chapter 4. Brakes

Fig. 4.1 Brake disc [30].

4.2 Thedisc

The discs used at Volvo are made of cast iron but there has been smaller quantities made of aluminum. The latter type is not used today due to higher costs, mainly associated with the more elaborate casting process used in the manufacturing of the disc. However the aluminium disc has advantages including an improved wear resistance, a higher thermal conductivity and a reduced weight [16]. The disc can reach very high temperatures, up to at least 700◦C. It is easy to imagine that such high temperatures can have devastating effects. One way to increase the heat dissipation from the disc and thus prevent, or at least decrease, the high temperatures are the use of ventilation in the disc. Ventilations can differ for discs and one common solution is the use of vanes between the two brake surfaces. There are also more extreme ventilations such as discs with slits, drilled holes and discs including both Fig. 4.2. Discs can also have an even more extreme design; for motorcycles, the air or ventilations of the disc surface represents a large part of the area. It is important to have in mind that such extreme ventilations such as drilled holes and slits increase the possibilities for cracked discs, wear of the pads and disturbing noise such as growling and hissing [16].

4.3 Brake regulation

There are high demands on the brakes and there are several regulations such as the EEC 71/320 from Europe and FMVSS 105 from the U.S. EEC 71/320 [23]. The brakes also need to pass tests by the manufacturers and one real tough is the simAlp, a test corre- sponding to a ride downwards an alpine road. The test is performed during 45 minutes

24 4.4. Brake force distribution

Fig. 4.2 Brake disc with different ventilations [30]. beginning with braking prevent the speed not to exceed 10m/s during a ride of 25 min- utes. Thereafter the vehicle is leaved at standstill. This test is very demanding due to the long duration of braking that heat the surroundings. Therefore, simAlp is the test used for testing the possibility of integrating an electric machine that surrounds the disc later in this report.

4.4 Brake force distribution

Today, the brake force distribution is controllable which makes the vehicle able to main- tain the initial brake distribution. For the brake tests in this thesis, the distribution is as- sumed to be constant with 60% of the force distributed to the front wheels, a typical brake force distribution.

4.5 Heat transfer

As named earlier, the brake disc can obtain extremely high temperatures. This requires the possibility of the disc to be able to rapidly transfer the generated heat. Heat can be transferred in three ways; conduction, convection and radiation [19].

4.5.1 Conduction Conduction is when heat is transferred through a solid material and occurs at direct contact between materials. A material’s possibility to transfer heat is defined by its thermal con- ductivity κth. This properties differ between materials and a well-known phenomenon is

25 Chapter 4. Brakes that metals conduct heat well whereas, e.g., air, wood and epoxy conducts poor. Thermal conductivities for materials used in electric machinery (and air) are reported in Table 4.1. The heat transfer rate by conductivity can be expressed as

T2 − T1 Φ = κ A (4.3) th d there A, T2, T1 and d are the area of the material that is conducting, the higher temperature of the material there heat is transferred from, the lower temperature of the material there heat is transferred to and the thickness of the material, respectively [19].

Table 4.1: Thermal conductivities and heat capacities [49] Material κth[W/(m·K)] cth[J/(kg·K)] Air 0.026 1005 Aluminium 127 896 Castiron 32 502 Copper 166 376 Epoxy 0.68 1038

4.5.2 Convection Convection is when heat is trasnfered in a non-sold material such as gas and liquid. The heat is transferred through a flow of the gas or liquid that bring heat from a hot area to a cool area. Convection can occur both as natural or forced convection, where forced convection are such from fans, winds and etcetera. The heat transfer rate by convection can be expressed as

Φ = hthA(T1 − T2) (4.4) where hth,A, T1 and T2 is the heat transfer coefficient, the cross-sectional area of the body, the temperature at the surface or body and the temperature of the ambient gas or liquid respectively. In fact the heat transfer coefficient is often obtained experimental and can be hard to predict for the relevant body or area [19].

4.5.3 Radiation Radiation is often in literature of brake discs neglected since the impact at lower temper- atures are smaller than the heat transferred through convection and conduction. However, in the 3D-models used later in this thesis, the temperature reaches such high values that it has a considerable impact and should be included. The heat transfer rate by radiation can be expressed as

Φ = σǫAT 4 (4.5)

26 4.6. 1D thermal models where σ, ǫ, A, T is the Stefan-Boltzmann constant, the emissivity of the body, the area or surface of the body and the temperature of the body, respectively [19]. Obviously the impact of radiation increases rapidly with increased temperature due to the exponent of four. The emissivity is a value for the property of a material to reflect or absorb radiation and differ between materials. For a black body, the emissivity can reach almost ǫ = 1 meanwhile for blank metals the emissivity is below 0.3 [19].

4.6 1D thermal models

In this thesis, two simple 1D models have been used in order to investigate the impact of heat losses by convection and the heat distribution in the disc during short and longer braking times. The total power arising for the car while braking was given in (4.2). The input power for a rear brake disc in the models is therefore 20% of this power due to half of the 40% from the 60/40 brake power distribution. The deceleration is assumed to be a constant for a whole braking and the input power can therefore be expressed as

Pin =0.2 · mcar(v0 − at)a (4.6)

where mcar, v0, a and t are the mass of the vehicle, the initial speed of the vehicle, the acceleration or deceleration of the vehicle and the time for the duration of braking re- spectively. It is assumed that the heat is distributed evenly over the brake surface or cor- responding ring as the disc rapidly rotates and no energy is assumed to be spread out to such as hub or calliper through pads for simplify the models see Fig. 4.3.

Fig. 4.3 Disc with brake surface ring showing inner and outer radius rout, rout and disc thickness d. Disc is coloured grey and the pad dark grey.

27 Chapter 4. Brakes

4.6.1 Power applied on mass First, the power on the brakes was applied to the whole mass or volume that corresponds to the brake surface without any heat dissipation by convection. The output power used to obtain the temperature in the disc can be expressed as dT P = c m (4.7) out th disc dt where cth, mdisc and T is the heat capacity of the material of the disc, the mass of the brake surface of the disc and the temperature of the disc, respectively [6]. The mass of the disc can be expressed by

2 2 mdisc =(rout − rin)πdρdisc (4.8) there rout, rin, d and ρ is the outer radius of the brake surface, the inner radius of the brake surface, the thickness of the disc and the density of the material in the disc respectively.

By neglecting other dissipations, Pin = Pout and the temperature T can then be expressed as P T = in dt. (4.9) Z mdisccth This model is very simple but can be used to get a rough approximation of the average temperature in a brake disc. Therefore, this model where used to verify the more complex 1D-model.

4.6.2 Power applied on surface For the second model, the power is applied on the brake surface and the heat dissipation by convection is take into account. During braking, the heat appears due to the friction between the disc and pads. The heat is therefore applied in the model on the brake surface on the brake disc. The heat applied on the surface is then flown into the core of the disc and some heat is dissipated by convection at the surface to the ambient air. In this model, only the heat flow is analyzed for the x-axis parallel to the thickness d in Fig. 4.3. The heat flow for one direction can be expressed as 2 ∂T hth ∂ T = 2 . (4.10) ∂t ρcth ∂x where t, T , hth, ρ, cth and x represent the time, the temperature, the heat transfer coeffi- cient, the density, the heat capacity and the x-axis direction of the disc, respectively [19]. The equation can be complex to solve and therefore a numerical method from [42] is used d where the disc is divided in to a lot of layers or points such as 2 = n∆x in which the temperature can be expressed as T (x + ∆x, t)+ T (x − ∆x, t) T (x, t + ∆t)= (4.11) 2

28 4.6. 1D thermal models where ∆t and ∆x is a step to next point in time and x-axis. To clarify, a measured point at a specific time in the disc is equal to the mean value of the two adjacent points at the previously measured time. For the second point (counted from the disc surface) the temperature can then be expressed as

T1(t − ∆t)+ T3(t − ∆t) T2(t)= (4.12) 2

2 It is important that the the condition ∆x = hth is fulfilled so that (4.11) still holds. The ∆t ρcth temperature of the point at the surface can then be expressed as

∆x (Q(t)+ hth,airT0)+ kth,discT2(t) T1(t)= (4.13) kth,disc + ∆xhth,air where kth,disc, hth,th,disc, T0, T2 is the thermal conductivity of the disc, heat transfer coef- ficient of the disc,space temperature of the air and temperature of the next point at the Pin x-axis, respectively. Q(t) = 2A which is the input power for the braking in (4.6) divided 2 2 on the two sides of the disc. 2A = 2(rout − rout)π since the power is assumed to be shared equal between the two pads. The disc is assumed to be unventilated and therefore in the middle of the disc (at x=d/2), the temperature is equal to the point previously Tn =Tn−1. That is, the braking is assumed to be symmetric from the both pads and thus ∂T =0. (4.14) ∂x In order to verify the model, the average temperature of the disc is compared to the model presented in (4.9). The average temperature is calculated as

T1(t)+ T2(t)+ T3(t)+ ... + T (t) T (t)= n . (4.15) avg n Observe that heat dissipation through convection during the comparison is neglected i.e., hth,air =0 isassumed. The size of the stepin x-direction ∆x is chosen in such away thatthe solution converges to the model that distributes the power on the mass. The comparison can be seen in Fig.4.4 there red line represent the model that applies the power at the surface and the blue line represent the model that distributes the power on the mass. There are a small differences between the models in Fig. 4.4 but the model is assumed to be sufficiently correct for testing the impact of convection and heat distribution of the disc. The step ∆x is chosen to 50µm and the parameters for the brake disc can be found in Appendix B. Two cases of braking are tested, one shorter and one longer. The deceleration of -12m/s2 corresponds to the fast and short braking in Fig.4.5a and the deceleration of - 1m/s2 corresponds to the slow and long braking in Fig.4.5b. The heat distribution plotted is represented by seven points with a distributionof 1mm between each other. The average temperature Tavg(t) is represented as the black coloured line in the two plots.

29 Chapter 4. Brakes

250 Mass Surface 200

150

100 Temperature [C] 50

0 0 0.5 1 1.5 2 2.5 3 t [s]

Fig. 4.4 Verification of the model using power on surface.

In order to investigate the impact of convection, Tavg(t) is calculated for three values 2 of hth,air equal to 0, 50 and 100W/(m K). The impact of Tavg(t) are plotted for the fast braking in Fig.4.6 and slow in Fig.4.7. The heat is evenly distributed in the disc at slow and long braking compared to fast and short breaking where the temperature difference between the surface and centre is considerable. The impact of convection plays a larger roll on the temperature of the disc at slow and long braking compared to fast and short braking. Therefore, the 3D model needs to include convection since the simAlp is testing the brakes for a long time at slow braking. The power will be applied on the disc surface although the influence is not as large as at short and fast braking.

4.7 3D thermal models

The 3D model is built to represent a ventilated rear brake disc for an XC90 when subjected to the simAlp test. For the radiation, the emissivity of the disc ǫdisc were chosen to 0.51. To simplify the model, the pads were not included in the model (according to [6] only 5% of heat flows in to the pads). The conduction that will arise from the hub of the disc to the rim and rear axle is 2 represented by an equivalent heat transfer coefficient hth,hub assumed to 100W/(m K). At the middle of the disc (at d/2) the ventilated surface is applied with a heat trans- fer coefficient hth,V. However, if the disc is solid and there is no channels of ventilation this surface is chosen as a symmetry boundary in order to simplify the model.

30 4.7. 3D thermal models

300 250

250 200

T 200 surface 150 T 1[mm] 150 T 2[mm] T 100 3[mm] 100 T 4[mm] 50 T 50 5[mm]

Temperature [C] Temperature [C] T centre 0 0 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 35 t [s] t [s] (a) (b)

Fig. 4.5 Temperature distribution of the disc there each curve represent a measurement point with step in x-axis of 1mm compared to the Tavg(t) in black a) Fast braking; b) Slow braking

250 214

200 212

150 210

100 208

0 0 50 50 206 50 Temperature [C] 100 Temperature [C] 100 0 0 0.5 1 1.5 2 2.5 3 2.6 2.7 2.8 2.9 3 t [s] t [s] (a) (b)

Fig. 4.6 a) Impact on Tavg(t) with convection hth,air equal to 0, 50 and 100[W/(m2K)] ,fast braking time; b) Zoom of a).

All other heat transfer coefficients were obtained by calculations and the values can be found in Appendix C.

4.7.1 Forced convection

In the first part of the simulation the vehicle is driven constant in 10m/s, which means that there will be some airflow around the car, the wheels and the brake disc will rotate. The convection against the ambient will therefore be forced convection. Observe that the forced heat transfer coefficients were calculated specifically for this speed. The rims can differ a lot in dimension and design dependent on customers, car model etcetera. The airflow through the wheel can improve or deteriorate the convection inside the wheel house but can be hard to predict, especially at the rear wheels [22]. Hence

31 Chapter 4. Brakes

250 220

200 210

150 200

100 190

0 0 180 50 50 50 Temperature [C] Temperature [C] 100 100 170 0 0 5 10 15 20 25 30 35 24 26 28 30 32 34 36 t [s] t [s] (a) (b)

Fig. 4.7 a) Impact on Tavg(t) with convection hth,air equal to 0, 50 and 100[W/(m2K)] ,slow braking; b) Zoom of a). a computational fluid dynamics (CFD) analyze or measured data should be desirable. However,the low speed of the vehicle and the assuming a rim that can decrease the airflow the effect from the rims are assumed negligible except to some possible influence at hth,hub that then is included.

Rotating disc hth,DS The heat transfer coefficient for the brake surface was obtained by calculating the average heat transfer coefficient for a free rotating disc by

κ Nu h = th,air (4.16) rout where rout is the radius of the disc and Nu is the Nusselt number. For laminar flow the Nusselt number can be expressed as

2 2 1 Nu = (Re + Gr) 4 (4.17) 5 where Re and Gr is Reynolds number and Grashof number, respectively. The Reynolds number can be expressed as

2πnρ r2 Re = air out (4.18) µair where n, pair and µair is the rotational speed per seconds, density of air and dynamic viscosity of air, respectively. The Grashof number can be expressed as

3 3 2 βairgroutπ ∆T Gr = 2 (4.19) νair

32 4.7. 3D thermal models

where βair, g, ∆T , and νair is the thermal expansion coefficient of air, the gravitation con- stant, the temperature difference between the ambient air and disc, the kinematic viscosity of air, respectively. It is important while use the Nusselt number expressed in (4.17) the condition rc ≥ rout is fulfilled there 105ν r = 2.5 · air (4.20) c  2πn  otherwise the flow is not only laminar and may contain turbulent flow requiring the Nus- selt number need to be exchanged [27].

Rotating cylinder hth,HR and hth,edge Between the brake surface and where the rim is mounted, the geometry of the hub is cylin- drical. The same for the edge of the disc. These heat transfer coefficients are calculated assuming free rotating cylinder [27] there κ Nu h = th,air (4.21) Øout where Øout is the diameter of the cylinder. The Nusselt number can be expressed as 2 1 Nu =0.133Re 3 Pr 3 (4.22) where Pr is the Prandtl number given by c µ Pr = th,air air (4.23) κth,air and the Reynolds number for a rotating cylinder is expressed as 2πnØ2 Re = out . (4.24) νair

Ventilation

The disc model includes ventilation but the heat transfer coefficient can be hard to predict without a CFD analysis or corresponding experimental results. According to [34], test indicates that for low rotation (below around 400 rpm), the internal heat transfer coeffi- cient is comparable to the external heat transfer coefficient. For higher rotational speeds, the internal heat transfer coefficient exceeds the external. However, for a simAlp-test the rotational speed is low and for a 20” rim with 230/40 tire, the rotational speed is around

320rpm. The ventilation hth,V is therefore assumed to be identical to hth,DS.

4.7.2 Natural convection After the braking, the vehicle is left at standstill in the simAlp test. During this moment, it is assumed that there only will be natural or free convection of the disc. The heat transfer coefficient for the ventilated part will be assumed equal to hth,DS as above.

33 Chapter 4. Brakes

Vertical wall hth,DS

At the natural convection, the brake surface hth,DS will be calculated as a vertical wall. From [18], the heat transfer coefficient for a plane vertical wall can be expressed as κ Nu h = th,air (4.25) L where L is the characteristic length of the wall that will correspond to the diameter of the disc. The Nusselt number can be expressed as

Nu =0.59Gr0.25Pr0.25 (4.26) where the Grashof number is 3 βairgL ∆T Gr = 2 . (4.27) νair

Horizontal cylinder hth,HR and hth,edge

The heat transfer coefficient for the two cylinders, the hub hth,HR and the disc edge hth,edge can be expressed as the coefficient for a horizontal cylinder κ Nu h = th,air (4.28) Øout where the Nusselt number is

Nu =0.53Gr0.25Pr0.25 (4.29) where the Grashof number is 3 βairgØout∆T Gr = 2 . (4.30) νair where Øout is the outside diameter of a cylinder [18].

Simulation

The parameters used in the model can be found in Appendix C. The 3D model is imple- mented in Comsol and the resolution of mesh can be seen in Fig.4.8. The the location of the different heat transfer coefficients used can be seen in Fig. 4.10. The aim of the model is to represent a rear disc at a simAlp test such that the model thereafter could be used in a thermal model investigate the influence of a nearby stator or electric machine module. In Fig. 4.9, the comparison between the modelled data in blue and the simAlp data1 in red can be seen. The modulated data follow the simAlp

1The data is measured at the pads. According to Volvo and data of other models, the data were added 100◦C during the braking and at the stand still the disc is assumed to be about 25◦C cooler than the pad. The simAlp data can thereby differ to the actual disc temperature.

34 4.8. Summary of chapter

Fig. 4.8 3D model of the brake disc. data relatively well, but the temperature is a bit higher at some points. This is assumed to be acceptable due to testing the worst case for the electric machine later in the paper and a higher temperature is therefore better than a low. In Fig.4.11, the disc surface temperature of the disc can be seen at some periods during the brake test.

4.8 Summary of chapter

A 3D-model was built from assumptions, results from a 1D-model and parameters given by Volvo. The results from the 3D-model showed that the model corresponds quite well and will be used in the investigations in coming chapters. One important insight is the high temperatures of the disc that will challenge the design of the electric machine. Due to the fact that the simAlp data of the disc temperatures were obtained by manipulating the temperature of the pad, there can be an error that is important to have in mind. Especially if the implementation of the disc is on the border to success or fail in a thermal point of view.

35 Chapter 4. Brakes

600

500

400

300

200 Temperature [C]

100 3D-model simAlp 0 0 500 1000 1500 2000 t [s] Fig. 4.9 Comparison between the measured simAlp data and modulated data from the 3D-model.

36 4.8. Summary of chapter

(a) (b)

(c) (d)

(e) (f)

Fig. 4.10 Placement of heat transfer coefficients, placement represents by blue a)hth,DS; b)hth,V; c)hth,HR; d)hth,edge; e)hth,hub against rim; f)hth,hub against axle;.

37 Chapter 4. Brakes

(a) (b)

(c) (d)

(e) (f)

Fig. 4.11 Temperature of the disc at a) 100s; b)300s; c)500s; d)1000s; e)1500s ; f)1800s;.

38 Chapter 5

Electrical machine

In this chapter, the challenging design of an electrical machine that can act as an me- chanical brake and manage the high temperatures is addressed. A 2D-model is built from a previous tested machine and then dimensioned to fit the today brake system.

5.1 Design challenges

There are some fundamental challenges to overcome when choosing type of machine. The fact that the disc reaches very high temperatures and the lack of space to implement a machine especially in axial length between the disc and the wheel. The temperature of the disc reaches only for the simAlp 500◦C and therefore PM is excluded. Typical permanent magnets can manage temperatures between 130 to 240◦C but there are magnets that can manage rougher temperatures such high as 400◦C [9]. The windings in the stators usually don’t manage temperature over 180 due to the insulation, using the disc as a stator is also excluded [40]. The choice is therefore to investigate reluctance machines as a possible solution since no sensitive PMs and windings are used in the rotor. The rotor in reluctance machines is however consist of laminated electric-steel that does not manage more than about 180 to 270◦C [45] and the problematic of use unlam- inated steel is the skin effect that will provide the magnetic field to penetrate into the steel. To get round the skin effect without use laminated steel can be the use of Soft Mag- netic Composite(SMC). However, SMCs only manage temperatures around 200 ◦C [28]. No further investigation of SMC has not been done in the thesis. In order to investigate the size of a machine that can deliver 10kW the simulations has been performed with BH-curve of laminated steel. It is therefore important to have in mind that the machine in reality can’t be applied with the rotor as a brake disc if not the rotor parts manage temperatures up to 700◦C. The machine is chosen to be an axial flux machine, also called pancake machine. It uses less space in the axial direction compared to a radial flux. The torque of a radial

39 Chapter 5. Electrical machine

flux machine is proportional to the length of the rotor [49]. If the machine should be built as a radial flux machine using the disc as rotor and the size of the disc should be unchanged, then the rotor length should be the thickness of the disc. That is 20mm which is a very short axial length of a radial flux machine. Compared to an axial flux machine, the corresponding length instead could be somewhere between 60to 90mmforadiscwith the same size as today.

5.2 Choice of machine

There are mainly two common reluctance machines, the synchronous reluctance machine and the switch reluctance machine. The reluctance machine is not using expensive, sensi- tive PMs, instead the rotor consist of steel that is forced by reluctance. Synchronous reluctance machines usually require a complex design of the rotor that consist of laminated steel and is therefore excluded as a possible rotor for the machine Fig. 5.1.

Fig. 5.1 Synchronous reluctance machine [4].

A more simple construction of reluctance machines is switch reluctance machines. These machines have a simple design but require more complex control. However, today’s cheap control circuits opens the way for these machines. The stator often has more poles than the rotor, but there also exist investigations where the pole number in the rotor is higher than the stator. Switch reluctance machines require small air-gap lengths generally between 0.2 to 1mm [43]. Switch reluctance machines have simple designs of the rotor and is therefore of special interest due to the limitations of change the brake disc design. The choice of rotor design was done after opinions by Volvo, where the space re- quirements due to a mechanical brake are challenging. Claims such as that it is desirable that brake surface is equal for the two pads, to maintain a power distribution equal as possible. Slits can significantly increase the wear of the pads and the risk of a cracking disc.

40 5.3. Segmental rotor

Finally, the choice between a single-sided stator or double-sided stator machine. One opportunity is to place a stator at the surface behind the brake disc and replace the brake shield. However, due to the placement and design of the linkage, it is very chal- lenging to make place for a stator without changing the design of the rear axle and the linkage Fig. 5.2a. On the outside of the disc which faces the rim there is a better possibil- ity to cover a wider area of the disc, at least 270◦ Fig. 5.2b. A risk is that it is necessary to increase the axial space between the brake surface of the disc and the inside of the rim. It is however assumed to be less complicated to change a rim than redesign the rear axle. Thereby, due to the lack of space the machine is assumed to be a single-sided stator machine where the stator is placed between the disc and the rim.

(a) (b)

Fig. 5.2 a) Linkage of rear axle; b) Front of brake disc .

5.3 Segmental rotor

The proposed solution is the use of a disc with segments of iron placed into an aluminium disc as rotor. Then the brake surface can be kept as uniform as possible without slits. Segmental rotors use only segments of ferromagnetic materials and one advantage is the absence of a rotor back, especially beneficial due to the need of keeping the rotor as thin as possible. There are quite a few investigations about axial flux switch reluctance machines using segmental rotors. One physical model has been built in [50] see Fig. 5.3. The rotor consists of an aluminum alloy disc with embedded segments of laminated steel. The stator is of so-called single-teeth winding type which means that a tooth in the stator is wounded by only one phase. The width of the tooth therefore differ depending if the tooth is unwounded or wounded in order to avoid saturation. The prototype in [50] is much smaller both in dimension but also output toque than what is required here. The

41 Chapter 5. Electrical machine

Fig. 5.3 Axial flux switch reluctance machine with segmental rotor [7]. prototype rotor has a diameter of only 106mm, the rotor considered here is 340mm. The thin air gap in the prototype of 0.35mm can be problematic due to the rough environment of brake discs. Moreover the brake disc is allowed to be so worn such that the disc has a decrease of the thickness about 2.5mm, which is 1.25mm at each side of an even worn between the both sides. This worn will increase the air-gap and the possible influence this can have of the torque is of interest to investigate.

5.4 Linear model

The model used to investigate the machine was modelled as a simple linear model. The aim of the model was to analyze the torque the machine can produce at thus the power and the axial force. rout+rin The linear model is designed around the mean radius ravg = 2 of the effective machine. In an axial flux machine, the slot between the teeth in the stator has uniform width, independent of the radius. Instead the width of the teeth variate such that the width increase the further out of the radius. All the dimensions of the simplified linear model are selected at the mean radius. The length l in x-direction of the linear model is thus the circumference at ravg. The hight h in y-direction of the linear model corresponds to the length in the axial direction of the machine. The depth or length of the air-gap rout −rout is implemented as a condition or parameter of the length in z-direction for the 2D-model. The two models are depicted in in Fig. 5.4 and Fig. 5.5, respectively. The torque and forces are calculated at the mean radius of the machine. The torque can be obtained by

T = ravgF (5.1)

42 5.4. Linear model

Fig. 5.4 Common 2D of machine, showing stator.

Fig. 5.5 Linear model of 2D machine in Fig. 5.4 the showing stator above the rotor. where F is tangential force acting in direction of the rotation. The force is obtained by a built-in function in Comsol using Maxwell’s stress tensor. The power can thus be ex- pressed as

P = ωT. (5.2)

The claim of 10kW is chosen to calculated at a speed of 100km/h, which corresponds to ω ≈ 87.9 rad/s for a 20” rim with 275/45 tire. Due to the space of the caliper the stator can only cover about 270◦ of the brake disc. Therefore, the power that can be produced of the machine is assumed to be 70% of the simulated output torque. In order to reach 10kW at a speed of 100km/h the simulated model, needs to produce almost 14.3kW. That requires a torque of about 160Nm.

In axial flux machines, the large axial force Faxial that occurs can be problematic [27]. For a double-sided machine the axial force can be balanced due to the drag force acting from both sides. However, for a single-side machine the force is only acting on one side. The axial force is obtained in same way as F , obtained by Comsol’s built-in function using Maxwell’s stress tensor. The machine model was first built with similar dimensions as the prototype in the proceeding [50]. Some parameters were not presented and were chosen by own hand, such as the permeability of the electric steel which were chosen from [45]. The maximum

43 Chapter 5. Electrical machine applied current is 110A which corresponds to a current density of 17.4A/mm2 assuming an effective wire diameter of 2.836mm. The slot fill factor is 30% and the final applied current density in the slots is around 5.22A/mm2. The inner radius of the stator was not provided in [50] but was selected to 0.57735rout, according to [31] the ratio between inner and outer radius that maximize the average torque. The torque produced at one phase in the linear model compared with the prototype can be seen in Fig. 5.7. The linear model be seen in Fig. 5.6 with corresponding parts. In the model, the windings, opening to slots, the aluminium of the rotor and air-gap are modelled as air.

Fig. 5.6 The linear 2D-model there winding in orange, aluminium in dark grey, slots-opening in light grey, air-gap in blue, and electric-steel of rotor and stator in grey.

5 Linear model Data from [50]

0 Torque [Nm]

-5 0 5 10 15 20 25 30 35 Position [degree] Fig. 5.7 The comparison between the torque for a phase in the linear 2D-model and the corre- sponding data in [50].

5.5 The wheel motor

The model implemented is dimensioned with respect such that the outer diameter of the rotor segments is 330mm. Then some margin is assumed to be necessary for the outer rim of ambient aluminium Fig. 5.8. Other dimensions except the thickness of the air gap and

44 5.5. The wheel motor high of slot opening is kept with the same ratio to each other. The hight of slot opening is kept to 3mm and the air gap is increased to 1mm. The air gap were increased than 1mm is assumed as a more realistic thickness of the air gap. Due to lack of space between the ending of the windings and the hub of the brake disc, the inner radius of the stator was increased. The thickness of the disc was decreased from 24.4mm to 20mm to fit between the brake pads.

Fig. 5.8 Potential brake disc as segmented rotor. Aluminium in grey and segments of electric steel in dark grey.

The current density of 17.4A/mm2 is not realistic for longer operating times. Gener- 2 ally current density peak value Jˆs around 3.5 and 5.5A/mm are reasonable for machines cooled with forced convection [49]. With the possibility to cool the machine with water 2 or oil, the current density Js,rms is assumed to 10A/mm and the stator-winding fill factor Cs,fill is increased to 0.4.

45 Chapter 5. Electrical machine

The torque for one phase of the machine can be seen in Fig. 5.9, for this machine the axial length of the stator is 86mm. The peak torque is however so high that it can be sacrificed by decreasing the height of the slots but keeping the length of the stator back and, thus, decrease the axial length of the stator. To still reach a peak torque of 160Nm the axial length of the stator cannot be below 62mm Fig. 5.10.

400

200

0 Torque [Nm] -200

-400 5 10 15 20 25 30 Position [degree]

Fig. 5.9 Torque of one phase for varying rotor positions at an axial stator length of 86mm;

The cast iron disc must be allowed to be worn as mentioned earlier. The disc is assumed to be so worn that the thickness of the disc is decreased with 2.5mm to a disc of 17.5mm. The air gap is increased from 1 to 2.25mm, assumed that the disc is equally worn on the two sides. The peak torque due to the worn decreased from about 160Nm to 90Nm Fig. 5.11. The axial force of the machine can be seen in Fig. 5.12. The dimensions and parameters of the machine can be found in Appendix D.

5.6 Solid rotor induction machine

The high temperature is challenging the choice of material for the segments in the rotor. A way to get around is the use of a axial air gap solid rotor induction machine, there the rotor consist of solid aluminium and iron Fig.5.13 [36]. However, the induction machine require small air gap typical between 0.3 to 0.6mm [49]. As seen in next chapter a stator of typical size that can fit a brake disc with only an air gap of 1mm reach harmful temperatures. An air gap om 0.3mm will probably increase the harmful temperatures due to the increased heat transfer rate of conduction by smaller air gap.

46 5.7. Summary of chapter

200

100

0 Torque [Nm] -100

-200 5 10 15 20 25 30 Position [degree]

Fig. 5.10 Torque of one phase for varying rotor positions at an axial stator length of 62mm

5.7 Summary of chapter

It is according to the simulation possible to maintain a sufficient torque to produce the desired output power with a rotor that could fit the today brake system. However, the consequence is that the axial length of the stator requires changes to the rim. Moreover the total system with converter and motor in [50] only have an efficiency about 53%, however, such low efficiency should probably be able to improve. Research of a radial flux switch reluctance machine with segmental rotor resulted in efficiencies between 83.1% to 90.4% and in an investigation of converters for drive of such machines the efficiency for the system reached about 80% [51], [44]. There have been none additional analysis in order to improve the design of the machine, such as over saturation of the steel etcetera. A more accurate analysis could possibly enable a more effective machine with outcome increased output torque and decreased volume of the machine. A main consequence of using single-sided stator axial flux machine is a high axial force that is problematic, especially when the rotor acts as mechanic brake that adopts high temperatures with forces acting on the outer radius. If the brake disc will be worn it is necessary to take in account that the air-gap will increase as the thickness of the disc decrease. Then the air-gap is increased from 1mm to 2.25mm the peak-torque is decreased from about 160Nm to 90Nm. Thereby the air-gap should be needed to be adjusted by some mechanism or similar in axial direction that decrease the air-gap as the disc is more worn. Finally, the rotor segments consist of laminated steel that will be damage by the high temperatures that a brake disc reach. It is important if such rotor should be able to use, the

47 Chapter 5. Electrical machine

100

50

0 Torque [Nm] -50

-100 5 10 15 20 25 30 Position [degree]

Fig. 5.11 Torque of a worn disc. segments need to be a material with same electric properties as a electric laminated steel but can manage temperatures up to at least 700◦C.

48 5.7. Summary of chapter

10000

8000

6000

4000 Force [N]

2000

0 5 10 15 20 25 30 Position [degree]

Fig. 5.12 Axial force.

Fig. 5.13 Induction machines with solid rotor [36].

49 Chapter 5. Electrical machine

50 Chapter 6

Implementation of brake disc

The investigated electric machine is implemented with the brake disc as rotor. The temper- atures that occurs in the stator due to the high temperatures of the rotor during braking is analysed with a final thermal model.

6.1 Heat transfer between the stator and rotor

A brake disc used as rotor is assumed to be mainly built of aluminium without any ven- tilation. However, the disc should still have the same thickness as a ventilated disc. By placing the stator such that it covers the disc this will have impacts on the heat transfer to the ambient air. The heat transfer between the disc and the stator can occur as radiation, conduction or convection. The convection depends on the air flow between the two parts. If the flow is laminar, the heat transfer between the stator and rotor will be dominated by conduction and occur at low angular frequencies. But even at moderate speeds, the influ- ence of convection will increase [49]. At a speed of 10m/s for a vehicle with 20” rim and 230/40 tire the angular frequency is low about 33.5rad/s and the rotational speed is about 320rpm. According to [27], the flow rate Q for a typical axial flux PM machine is below 0.01m3/s at 400rpm and below 0.005m3/s at 200rpm. Assuming a flow rate of 0.0075m3/s at 300rpm and a there, the Nusselt can be expressed as

Q Nu =0.333 (6.1) πν(Øout/2) and the heat transfer coefficient between two discs is calculated as 2κ h = Nu (6.2) Øout which gives a heat transfer coefficient of h ≈ 45W/(m2K) between two disc with a diam- eter of 340mm.

51 Chapter 6. Implementation of brake disc

The heat transfer coefficient for the air-gap can be expressed as an equivalent ther- mal conductivity

kth,air gap = hth,air gapδ (6.3) where δ is the length of the air-gap [49]. From [49] and [27], the equivalent thermal conductivity during a rotation of 320rpm than can be assumed to be between 0.026 to 0.045W/(mK). During standstill, the equivalent thermal conductivity is assumed to be 0.026W/(mK) [49] and the Grashof number for interspace between to walls

3 βairgx ∆T Gr = 2 . (6.4) νair is below 2 · 103 with an air-gap x=δ =1mm there is no convection [18].

6.2 3Dmodel

The 3D model used to analyse the impact of the brake disc high temperature on the stator can be seen in Fig. 6.1, where the cross section can be seen in Fig.6.2 and the cut analysed is Fig.6.3. As seen in Fig 6.4, the stator reaches high temperatures1, especially the part that faces the brake disc. As seen, the stator and winding reach critical temperatures as the epoxy of the windings only manages temperatures up to 225◦C [35] and the laminated electric steel about 180 to 270◦C [45]. One way to handle high temperatures is usage of liquid-cooling, a technique that however can be expensive. A common technology is cool- ing of the stator back, where the stator is covered by a so-called mantle, jacket or housing of aluminium with channels there the liquid flow. In [37], a CFD-analysis of water cool- ing obtained a heat transfer coefficient as high as 1886.4W/(m2K). By implementing a heat transfer coefficient at the stator back in the model, the temperature decreases in the stator. The temperatures of the laminated steel is improved but although in the critical range. The winding is clearly still too hot especially in the end-windings against the hub Fig 6.5. The machine has been applied for an XC90, a heavy car. It could also be of in- terest to investigate the possibilities for a more light weight vehicle. All the parameters and dimensions are kept unchanged except to the weight which is changed to 2000kg. Then, the temperature of the electric steel is manageable, but the windings is still reach harmful temperatures Fig 6.6. It is important to have in mind that the equivalent thermal conductivity is only 0.026W/(mK). If the value should be increased to 0.045W/(mK), the temperatures of the stator probably should reach even more critical temperatures. More- over if the air gap should be decreased the heat transfer in the air gap probably increase,

1The temperatures are plotted such that red correspond to 300◦C and temperatures above. Thereby, it is easier to obtain the critical parts of the stator.

52 6.3. Summary of chapter

Fig. 6.1 3D model with implemented stator. thus the use of a induction machine with smaller air gap is even more problematic for a stator.

6.3 Summary of chapter

The thermal analysis of the machine shows that the high temperatures of the disc is clearly critical to the stator. The most damage will occur at the ending of the wires facing to the centre of the machine. Even if the machine should be applied with a cooling of the stator back, the machine will reach harmful temperatures. Then, lighter vehicles could be of interest for such implementation of machines, a simulation has been performed with less weight of the car. The harmful temperatures are decreased but still the stator reach temperatures that will damage the windings. The epoxy around the windings is black, and the emissivity is then high, ǫ≈0.9 and easily absorbs heat by radiation. If the end-windings could be shielded in order to prevent the radiation the high temperatures could probably be decreased. If it is possible to make

53 Chapter 6. Implementation of brake disc

Fig. 6.2 Cross sectional of 3D model. place for such shielding can, however, be discussed.

54 6.3. Summary of chapter

Fig. 6.3 2D model of cross section in Fig. 6.2, there orange is windings, blue is air, brake disc is grey and stator core is dark grey .

(a) (b)

(c) (d)

(e) (f)

Fig. 6.4 Temperature of the machine at a) 100s; b)500s; c)1000s; d)1500s; e)2000s ; f)2400s;.

55 Chapter 6. Implementation of brake disc

(a) (b)

(c) (d)

(e) (f)

Fig. 6.5 Temperature of the machine with cooling at a) 100s; b)500s; c)1000s; d)1500s; e)2000s ; f)2400s;.

56 6.3. Summary of chapter

(a) (b)

(c) (d)

(e) (f)

Fig. 6.6 Temperature of the machine with cooling at a) 100s; b)500s; c)1000s; d)1500s; e)2000s ; f)2400s;.

57 Chapter 6. Implementation of brake disc

58 Chapter 7

Conclusion and further work

Conclusion of the projects result and suggestion for further work.

7.1 Conclusion

It is possible to build a rotor that fits today’s brake system such that the machine delivers a power of 10kW. But the rims need to be changed by increase of the space in the axial length but the radial space can be unchanged1. A problem is that a brake disc will be worn, and the air gap will then increase and thus, the torque decrease. A solution could be some mechanism that can adjust the air gap. Another problem is the risk for saturation when the rotor gets thinner. Moreover such mechanism could be heavy and need space. An important drawback, is that the rotor consist of laminated steel and will therefore be damaged due to the high temperatures. It is therefore necessary to use a material with same electric properties as a laminated steel but can manage temperatures over 500◦C. A way to get around the use of laminated steel and other sensitive material, is the use of a solid rotor induction machine. However, the induction machine require smaller air gap, that will increase the critical temperatures of the stator. The stator will become too hot, especially the winding ends in the inner radius of the machine that are exposed against the brake disc. Even the laminated steel in the rotor will be damaged. There exist cooling of electric machines, but those can be expensive. However, one common and not to challenging way to cool electrical machines are using cooled jacket at the stator back. Even with implementation of this cooling, the stator will reach too high temperature both in the laminated steel and the windings. If the mass of the vehicle is decreased to 2000kg and the size of brake disc and machine is kept unchanged, then the laminated steel in the stator will reach acceptable temperatures with an assumed water cooling of stator back, but the windings will still be damaged. In a mechanical brake point of view, the rotor can be problematic. The high axial

1The machine require at least a 19” rims.

59 Chapter 7. Conclusion and further work force that arises in the peripheral of the disc can probably bend the disc, especially when the disc is very hot. For a segmented rotor the segments and the aluminium will probably not have same expansion coefficients that will make the disc surface uneven with peaks and valleys. This will give bad brake performance and assumed occurrence of noise [16]. In an economical point of view, the machine will have expensive parts such as need of cooling and the use of an aluminium brake disc. Moreover, the rotor shall have parts of iron that will be even more expensive and difficult to manufacture compared to the pure aluminium discs that already are more expensive than cast iron discs. Parts such as the mechanical transmission for the rear axle machine used today in the Volvo Twin Engine should be removed and save some cost. The rear axle machine is additionally liquid cooled and an assumptioncould be that the cost of a liquid cooling system therefore cancels out each other. The cost of the active material the copper and electric steel could approximately be around 500SEK with the today metal prices. Thereto the manufacturing cost that is assumed to be 40% of the total cost, that should give around 800SEK for the active material of the machine. Including, important parts such as epoxy, housing, linkage, the cost of the new brake discs etcetera, the total cost is very roughly assumed to about 4000SEK. In a unsprung mass point of view the machine will be too heavy, about 22kg only for the effective mass. One aim of implement an already existing part in a machine is to save the increase of mass. The rotor will be more or less of same weight as before. The increase of unsprung mass is than at least 7kg to high. For about the same weight without intrude on the mechanical brake there exist machines mentioned earlier in the thesis.

7.2 Further work

IWMs is usually relative heavy and the thought of implement an already existing part in the wheel can be a solution too minimize this increase of weight. The thesis showed that the space in the wheels is sufficient to install a machine that can reach at least 10kW peak power. In the thesis, it is found that it is challenging to design a rotor that can manage such high temperatures as an ordinary brake discs reaches and be able to use as a mechanical friction brake. Even if these problems are solved with a sufficient resistant material or a solid disc, used for induction machines. The thermal 3D-model showed that it is problem- atic to place a machine part such as a stator close to the brake disc. The simulations, even if it not was sufficient in these cases, showed that water cooling by jacket can significantly decrease harmful temperatures of a stator. The machine were built for a outer diameter of 330mm. In order to produce suffi- cient force and thus torque, it required a high applied current density of 10A/m2 and thus the size of the stator was relative massive. The stator was therefore heavy. The lack of space, limited the design to only a one sided stator and the axial force

60 7.2. Further work of an axial flux machine is harmful high. A suggested further work, is therefore to investigatethe possibility to implement the rim with an electric machine. The axial length of the inside of the rim is almost 200mm compared to the disc thickness of 20mm, it gives a better opportunity to use a radial flux machine. With a radial flux machine the problem with an axial force is avoided. The inside diameter of a 19” rim is about 480mm and require lower produced force to maintain the same torque, as for a machine with diameter of 330mm. Then the machine can produce a smaller force, thus the design can be neater and the weight then can be smaller. When placing a stator at the rim, the distance to the brake disc can be increased and the influence of its high temperature should probably be less problematic. Moreover, if the rim is an outer rotor, the stator back will be faced against the disc were a cooling jacket could be applied and protect the stator. In order to prevent sensitive and expensive magnets, which can be damaged by shocks etcetera, it is suggested to analyse the switch reluctance machine. In order to enable the use of today’s aluminium rims, it is suggested that the rotor shall be of segmented type and only use parts of laminated steel or SMC, placed on the inside of the rim band. At least two questions is of interest to early investigate in order to continue the work; how much the rims flex or deforms during driving, and how high temperatures the rim band reaches.

61 Chapter 7. Conclusion and further work

62 Appendix A

Parameters of quarter car model

Confidential

63 Appendix A. Parameters of quarter car model

64 Appendix B

Parameters of 1D thermal models

Table B.1: Specification of brake disc Specification Massofvehicle[5] kg 3000 Brake surface outer radius mm 170 Brake surface inner radius mm 117 Thickenessofbrakedisc mm 12 3 Density ρth,iron kg/dm Confidential Heat capacity cth,iron [49] W/(m·K) 502 Thermal conductivity κth,iron [49] J/(kg·K) 32

65 Appendix B. Parameters of 1D thermal models

66 Appendix C

Parameters of 3D thermal model

Table C.1: Specification of brake disc Specification Massofvehicle[5] kg 3000 Speedofvehicle0-1500s m/s 10 Speedofvehicle1500-2400s m/s 0 Decelerationofvehicle0-1500s m/s2 1 Deceleration of vehicle 1500-2400s m/s2 0 Brake disc outer diameter mm Confidential Brake disc inner diameter mm Confidential Thickenessofbrakedisc mm Confidential Thickenessofventilation mm Confidential Hubouterdiameter mm Confidential Disccenterdiameter mm Confidential Axiallengthofhub mm Confidential Thicknessofhub mm Confidential 3 Density ρth,iron kg/dm Confidential Emissivity ǫdisc Confidential Heat capacity cth,iron W/(m·K) 502 Thermal conductivity kth,iron J/(kg·K) Confidential 2 Heat tranfer coefficient hub hth,hub W/(m ·K) Confidential

67 Appendix C. Parameters of 3D thermal model

Table C.2: Heat transfer coefficients Forced convection 2 Disc surface hth,DS W/(m ·K) 16.8 2 Ventilation hth,V W/(m ·K) 16.8 2 Hub cylinder hth,HR W/(m ·K) 27.4 2 Disc surface edge hth,edge W/(m ·K) 35.6 Free convection 2 Disc surface hth,DS W/(m ·K) 9 2 Ventilation hth,V W/(m ·K) 9 2 Hub cylinder hth,HR W/(m ·K) 10 2 Disc surface edge hth,edge W/(m ·K) 10

68 Appendix D

Parameters and specification of the electrical machine

Table D.1: Machine data of modulated machine Specification Peaktorque Nm 160 CurrentdensityDC A/mm2 10 Air-gaplenght mm 1 Stator slot fill factor Cs,fill 0.4 Polenumberstator 12 Polenumberrotor 10 Statorcoreouterradius mm 330 Statorcoreinnerradius mm 234 Rotorsegmentouterradius mm 330 Rotorsegmentinnerradius mm 234 Statorslotwidth mm 39.4 Statorslotheight mm 42.4 Statorslotopeningheight mm 3 Activeaxiallengthstator mm 70 Activeaxiallengthrotor mm 20 Woundedtoothwidth,tip degree 30.25 Unwoundedtoothwidth,tip degree 18.5 Woundedtoothwidth,body degree 20 Unwoundedtoothwidth,body degree 8 Rotorsegmentswidth degree 30.25 Activeweightcopper kg 12.6 Activeweightepoxy kg 3.9 Activeweightlaminatedsteel kg 12.8 Totalactiveweightstator kg 29.3

69 Appendix D. Parameters and specification of the electrical machine

Table D.2: Machine data of 270◦ stator Specification Peaktorque Nm 112 Activeweightcopper kg 9.5 Activeweightepoxy kg 2.9 Activeweightlaminatedsteel kg 9.6 Totalactiveweightstator kg 22.0 Cost active copper SEK 407 Cost active laminated steel SEK 96 Total cost active stator SEK 839

Table D.3: BH-curve electric steel, SURA M330-35HP [45] B[Tesla] H[A/m] 0 0 0.1 30.2 0.2 39 0.3 44.9 0.4 50.2 0.5 55.5 0.6 61.2 0.7 67.8 0.8 76 0.9 86.5 1 101 1.1 123 1.2 160 1.3 238 1.4 466 1.5 1293 1.6 3344 1.7 6672 1.8 11361

70 Appendix D. Parameters and specification of the electrical machine

Table D.4: BH-curve cast iron, [32] B[Tesla] H[A/m] 0.000 0 0.004 3 0.008 6 0.014 11 0.023 17 0.035 25 0.050 35 0.068 47 0.090 59 0.114 73 0.140 86 0.168 100 0.196 112 0.250 136 0.300 157 0.392 199 0.437 222 0.562 301 0.695 419 0.813 564 0.850 619 0.929 768 1.000 955 1.025 1039 1.100 1408 1.149 1784 1.171 1995 1.222 2626 1.250 3106 1.325 5440 1.362 6885 1.403 9128 1.426 10539 1.490 15323 1.550 21719 1.588 27452 1.625 34628 1.662 43626 1.711 58218 1.744 73137 1.790 95813 1.801 101557 1.814 109710 1.819 112872 71 1.824 116398 1.832 123026 Appendix D. Parameters and specification of the electrical machine

Table D.5: Material properties from Comsol Property Air Electric steel Cast iron σ 0 0 0 ǫr 1 1 1 µr 1 - -

72 Appendix E

Parmaters of implementation of machine thermal model

Table E.1: Brake disc Specification of brake disc Massofvehicle[5] kg 3000 Speedofvehicle0-1500s m/s 10 Speedofvehicle1500-2400s m/s 0 Decelerationofvehicle0-1500s m/s2 1 Deceleration of vehicle 1500-2400s m/s2 0 Brake disc outer diameter mm Confidential Brake disc inner diameter mm Confidential Thickenessofbrakedisc mm Confidential Hubouterdiameter mm Confidential Disccenterdiameter mm Confidential Axiallengthofhub mm Confidential Thicknessofhub mm Confidential 3 Density ρth,alu [33] kg/dm 2.7 Emissivity ǫdisc Confidential Thermal conductivity kth,alu [49] W/(m·K) 127 Heat capacity cth,alu [49] J/(kg·K) 896 2 Heat tranfer coefficient hub hth,hub W/(m ·K) Confidential

The density of wire is calculated by

ρwire = τcopperρcopper + τexpoxyρepoxy (E.1) there τcopper =Cs,fill, τepoxy =1−τcopper, and the heat capacity can be expressed as

ρcopper ρcopper cth,wire = τcoppercth,copper + τexpoxycth,epoxy. (E.2) ρwire ρwire

73 Appendix E. Parmaters of implementation of machine thermal model

Table E.2: Heat transfer coefficients of brake disc Forced convection 2 Disc surface hth,DS W/(m ·K) κth,air gap 2 Ventilation hth,V W/(m ·K) Plane of symmetry 2 Hub cylinder hth,HR W/(m ·K) κth,air gap 2 Disc surface edge hth,edge W/(m ·K) 35.6 Free convection 2 Disc surface hth,DS W/(m ·K) κth,air gap 2 Ventilation hth,V W/(m ·K) Plane of symmetry 2 Hub cylinder hth,HR W/(m ·K) κth,air gap 2 Disc surface edge hth,edge W/(m ·K) 8

Table E.3: Machine data of stator Specification Air-gaplenght mm 1 Stator slot fill factor Cs,fill 0.4 Polenumberstator 12 Statorcoreouterradius mm 340 Statorcoreinnerradius mm 234 Statorslotwidth mm 27 Statorslotheight mm 44 Statorslotopeningheight mm 3 Axiallengthstator mm 70 3 Density ρth,core [45] kg/dm 7.65 3 Density ρth,copper [33] kg/dm 8.9 3 Density ρth,epoxy [35] kg/dm 1.83 3 Density ρth,wire kg/dm 4.68 Heat capacity cth,core [49] J/(kg·K) 486 Heat capacity cth,copper [49] J/(kg·K) 538 Heat capacity cth,epoxy [49] J/(kg·K) 1038 Heat capacity cth,wire J/(kg·K) 538.2 Emissivity ǫcore [19] 0.3 Emissivity ǫwire [19] 0.9 Thermal conductivity kth,core [49] W/(m·K) 28 Thermal conductivity kth,wire [49] W/(m·K) 0.07 2 Heat tranfer coefficient to ambient hth,hub W/(m ·K) 9

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