I , AVANCERAD NIVÅEXAMENSARBETE ELEKTROTEKNIK 300 HP

, STOCKHOLM SVERIGE 2015

An integrated brake disc andelectric drive for vehiclepropulsion

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 possible or 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 undersoks mojligheten att integrera en bromsskiva med elmaskin. Hjul-

motorer har flera fordelar, bland annat sparas utrymme i sjalva bilen, individuell kon-

troll samt drivning av hjulen utan mekaniska transmissioner. Men hjulmotorer som kan

anvandas idag vager oftast sa pass mycket att den odampade massan okar kritiskt och

koregenskaper av fordonet da blir lidande. Genom att integrera en befintlig del i hjulet

kan okningen av odampade massan minskas.

Att anvanda bromsskivan som rotor, kraver att denna tal temperaturer over 500◦C

samt pafrestningar och slitage som en vanlig mekanisk friktionsbroms maste utharda.

Den andra delen av maskinen, statorn kommer aven denna att paverkas av de hoga tem-

peraturerna av bromsskivan som kommer ledas via konvektion, konduktion och stralning.

Mojligheten att kyla statorn med vatska och om detta ar tillrackligt undersoks.

For att analyserna genomforbarheten av projektet har termiska, elektriska och mek-

aniska modeller anvants. Resultaten har analyserats dar maskinens vikt, kostnad, termisk

talighet och elektrisk prestanda har legat till grund for bedomningen om losningen; att

integrera en broms-skiva med elmaskin ar rimlig eller ej.

Nyckelord: Axialflodes, bromsskiva, enkeltandad lindning, hjulmotor, hub motor

kvartfordonsmodell, rygglos rotor, segment rotor, variabel reluktansmaskin.

v

vi

Acknowledgements/Forfattarens tack

Forst och framst vill jag tacka Doktor Oskar Wallmark som har handlett mig genom hela

detta arbete genom alla dess nivaer och svarigheter. Jag vill ocksa tacka alla inblandade

pa Volvo som varit mycket hjalpsamma och framfor allt Soren Eriksson som handlett och

inspirerat mig samt Quintus Jalkler som hjalpt mig med kontakter och ovriga fragor under

arbetet.

Dessutom vill jag passa pa att tacka alla mina goda vanner som gjort studietiden pa

KTH minnesvard. Ett speciellt tack till Anna Larsson som agnade tid at att granska min

rapport. Samt Noj Kazemi, Sebastian Hakansson, Erik Hallqvist och Alexander Sjoberg

som jag agnat atskilliga timmar att studera med. Utan den kamratskapen och stodet hade

min studietid blivit betydligt jobbigare och framforallt trakigare.

Jag vill tacka alla dar hemma, mor, far, syster och morfar, som stottat och mojlig-

gjort mina studier under aren. Mina vanner som under alla dessa ar fortfarande haller

samman som det jarngang vi alltid varit. Samt min mycket gode van Viktor Andersson

som delar mitt storsta intresse och som introducerat mig till flertalet av fordonsvarldens

alla horn.

Avslutningsvis vill jag tacka min Karaste Lisa for allt personligt stod 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 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Previous work 5

2.1 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Volvo ReCharge Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Hybrid electric vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 In wheel motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Influence of unsprung mass 9

3.1 Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Quarter car model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Simulink quarter car model . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3.1 Increasing the unsprung mass . . . . . . . . . . . . . . . . . . . 15

3.4 Resonance frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Brakes 23

4.1 The function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 The disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 Brake regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4 Brake force distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

ix

Contents

4.5 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.5.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.5.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.5.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.6 1D thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.6.1 Power applied on mass . . . . . . . . . . . . . . . . . . . . . . . 28

4.6.2 Power applied on surface . . . . . . . . . . . . . . . . . . . . . . 28

4.7 3D thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.7.1 Forced convection . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.7.2 Natural convection . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.8 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5 Electrical machine 39

5.1 Design challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Choice of machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.3 Segmental rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.5 The wheel motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.6 Solid rotor induction machine . . . . . . . . . . . . . . . . . . . . . . . 46

5.7 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 Implementation of brake disc 51

6.1 Heat transfer between the stator and rotor . . . . . . . . . . . . . . . . . 51

6.2 3D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.3 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7 Conclusion and further work 59

7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.2 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 AB2Matlab 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

driving the 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] not specified 50 518

XR32-11 [2] 17 23.1 160

Protean E [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

tire are represented by the tire stiffness kt and the tire damping ct tire1. 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]

mszs = −ks(zs − zus)− cs(zs − zus)−msg (3.1)

while the forces acting on the unsprung mass mus can be expressed with [47]

muszus = ks(zs − zus) + cs(zs − zus)− kt(zus − z0)− ct(zus − z0)−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]

muszus = ks(zs − zus) + cs(zs − zus)−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 z0on the acceleration of the vehicle body zs 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 zshowever has a distinct gain about 1.2Hz that thereafter follow with a damping effect. The

acceleration zs can be seen in Fig. 3.7 and the tire deflection in Fig. 3.8

kt

Gain

du/dt

Derivative

ct

Gain1

mus*g

mus*g

ks

Gain2

cs

Gain3

1/mus

1/mus

1

s

Integrator

1

s

Integrator1

1

s

Integrator2

1

s

Integrator3

1/ms

1/ms

ms*g

ms*g

0

Wheel hop

>=

Relational

Operator Product

zs

zus

zs_biss

z0

Input signal

Fig. 3.4 Simulink model.

12

3.3. Simulink quarter car model

0 200 400 600 800-0.04

-0.02

0

0.02

0.04

Time [s]

[m]

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

0 5 10 15 20 25 300

0.01

0.02

0.03

0.04

z0

zus

zs

Frequency [Hz]

[m]

Fig. 3.6 The displacements z0, zus and zs.

13

Chapter 3. Influence of unsprung mass

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

Frequency [Hz]

[m/s

2]

Fig. 3.7 Acceleration zs.

0 5 10 15 20 25 30

×10-3

0.5

1

1.5

2

2.5

3

3.5

4

Frequency [Hz]

[m]

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 zs 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 zs 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 zsoccurs 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 z2 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 zs 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 5 10 15 20 25 300

0.005

0.01

0.015

0.02

0.025

0.03

0.035

25kg

20kg

15kg

10kg

5kg

0kg

Frequency [Hz]

[m]

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

0 5 10 15 20 25 300

0.01

0.02

0.03

0.04

25kg

20kg

15kg

10kg

5kg

0kg

Frequency [Hz]

[m]

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

16

3.3. Simulink quarter car model

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

25kg

20kg

15kg

10kg

5kg

0kg

Frequency [Hz]

[m/s

2]

Fig. 3.11 Acceleration zs, 0 to 25kg increased unsprung mass.

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

25kg

20kg

15kg

10kg

5kg

0kg

5percent

Frequency [Hz]

[m/s

2]

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

17

Chapter 3. Influence of unsprung mass

6 7 8 9 10 11 12 13

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Frequency [Hz]

[m/s

2]

Fig. 3.13 Zoom of Fig. 3.12.

0 5 10 15 20 25 30

×10-3

0.5

1

1.5

2

2.5

3

3.5

4

25kg

20kg

15kg

10kg

5kg

0kg

Frequency [Hz]

[m]

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 zs 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

mss2Zs = −ksZs + ksZus − cssZs + cssZus (3.4)

and in same way (3.2) can be expressed with

muss2Zus = 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

H(s) =Zs

Z0

=as2 + bs+ c

ds4 + es3 + fs2 + gs+ h(3.6)

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

E =1

2mcarv

2 (4.1)

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 The disc

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

Φ = κthAT2 − T1

d(4.3)

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

Cast iron 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

Pout = cthmdisc

dT

dt(4.7)

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

mdisc = (r2out − r2in)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

T =

∫

Pin

mdisccth

dt. (4.9)

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

∂T

∂t=

hth

ρcth

∂2T

∂x2. (4.10)

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

where the disc is divided in to a lot of layers or points such as d2= n∆x in which the

temperature can be expressed as

T (x, t+∆t) =T (x+∆x, t) + T (x−∆x, t)

2(4.11)

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

T2(t) =T1(t−∆t) + T3(t−∆t)

2(4.12)

It is important that the the condition ∆x2

∆t= hth

ρcthis fulfilled so that (4.11) still holds. The

temperature of the point at the surface can then be expressed as

T1(t) =∆x (Q(t) + hth,airT0) + kth,discT2(t)

kth,disc +∆xhth,air

(4.13)

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

x-axis, respectively. Q(t) = Pin

2Awhich is the input power for the braking in (4.6) divided

on the two sides of the disc. 2A = 2(r2out − r2out)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

∂x= 0. (4.14)

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

Tavg(t) =T1(t) + T2(t) + T3(t) + ...+ Tn(t)

n. (4.15)

Observe that heat dissipation through convection during the comparison is neglected i.e.,

hth,air =0 is assumed. The size of the step in x-direction ∆x is chosen in such a way that the

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 distribution of 1mm between each other. The average

temperature Tavg(t) is represented as the black coloured line in the two plots.

29

Chapter 4. Brakes

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

Mass

Surface

t [s]

Tem

per

atu

re[C

]

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

of hth,air equal to 0, 50 and 100W/(m2K). 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

represented by an equivalent heat transfer coefficient hth,hub assumed to 100W/(m2K).

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

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

300

t [s]

Tem

per

atu

re[C

]

(a)

0 5 10 15 20 25 30 350

50

100

150

200

250

Tsurface

T1[mm]

T2[mm]

T3[mm]

T4[mm]

T5[mm]

Tcentre

t [s]

Tem

per

atu

re[C

]

(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

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

0

50

100

t [s]

Tem

per

atu

re[C

]

(a)

2.6 2.7 2.8 2.9 3

206

208

210

212

214

0

50

100

t [s]

Tem

per

atu

re[C

]

(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

0 5 10 15 20 25 30 350

50

100

150

200

250

0

50

100

t [s]

Tem

per

atu

re[C

]

(a)

24 26 28 30 32 34 36

170

180

190

200

210

220

0

50

100

t [s]

Tem

per

atu

re[C

]

(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

h =κth,airNu

rout

(4.16)

where rout is the radius of the disc and Nu is the Nusselt number. For laminar flow the

Nusselt number can be expressed as

Nu =2

5(Re2 +Gr)

1

4 (4.17)

where Re and Gr is Reynolds number and Grashof number, respectively. The Reynolds

number can be expressed as

Re =2πnρairr

2out

µair

(4.18)

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

Gr =βairgr

3outπ

3

2∆T

ν2air

(4.19)

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

rc =

(

2.5 ·105νair

2πn

)

(4.20)

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

h =κth,airNu

Øout

(4.21)

where Øout is the diameter of the cylinder. The Nusselt number can be expressed as

Nu = 0.133Re2

3Pr1

3 (4.22)

where Pr is the Prandtl number given by

Pr =cth,airµair

κth,air

(4.23)

and the Reynolds number for a rotating cylinder is expressed as

Re =2πnØ2

out

νair

. (4.24)

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

h =κth,airNu

L(4.25)

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

Gr =βairgL

3∆T

ν2air

. (4.27)

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

h =κth,airNu

Øout

(4.28)

where the Nusselt number is

Nu = 0.53Gr0.25Pr0.25 (4.29)

where the Grashof number is

Gr =βairgØ

3out∆T

ν2air

. (4.30)

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

0 500 1000 1500 20000

100

200

300

400

500

600

3D-model

simAlp

t [s]

Tem

per

atu

re[C

]

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 60 to 90mm for a disc with

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.

The linear model is designed around the mean radius ravg =rout+rin

2of 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.

0 5 10 15 20 25 30 35-5

0

5

Position [degree]

To

rqu

e[N

m]

Linear modelData from [50]

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-

ally current density peak value Js around 3.5 and 5.5A/mm2 are reasonable for machines

cooled with forced convection [49]. With the possibility to cool the machine with water

or oil, the current density Js,rms is assumed to 10A/mm2 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.

5 10 15 20 25 30-400

-200

0

200

400

Position [degree]

To

rqu

e[N

m]

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

5 10 15 20 25 30-200

-100

0

100

200

Position [degree]

To

rqu

e[N

m]

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

5 10 15 20 25 30-100

-50

0

50

100

Position [degree]

To

rqu

e[N

m]

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

5 10 15 20 25 300

2000

4000

6000

8000

10000

Position [degree]

Fo

rce

[N]

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

Nu = 0.333Q

πν(Øout/2)(6.1)

and the heat transfer coefficient between two discs is calculated as

h =2κ

Øout

Nu (6.2)

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

Gr =βairgx

3∆T

ν2air

. (6.4)

is below 2 · 103 with an air-gap x=δ=1mm there is no convection [18].

6.2 3D model

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 assumption could 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 investigate the 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

Mass of vehicle [5] kg 3000

Brake surface outer radius mm 170

Brake surface inner radius mm 117

Thickeness of brake disc mm 12

Density ρth,iron kg/dm3 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

Mass of vehicle [5] kg 3000

Speed of vehicle 0-1500s m/s 10

Speed of vehicle 1500-2400s m/s 0

Deceleration of vehicle 0-1500s m/s2 1

Deceleration of vehicle 1500-2400s m/s2 0

Brake disc outer diameter mm Confidential

Brake disc inner diameter mm Confidential

Thickeness of brake disc mm Confidential

Thickeness of ventilation mm Confidential

Hub outer diameter mm Confidential

Disc center diameter mm Confidential

Axial length of hub mm Confidential

Thickness of hub mm Confidential

Density ρth,iron kg/dm3 Confidential

Emissivity ǫdisc Confidential

Heat capacity cth,iron W/(m·K) 502

Thermal conductivity kth,iron J/(kg·K) Confidential

Heat tranfer coefficient hub hth,hub W/(m2·K) Confidential

67

Appendix C. Parameters of 3D thermal model

Table C.2: Heat transfer coefficientsForced convection

Disc surface hth,DS W/(m2·K) 16.8

Ventilation hth,V W/(m2·K) 16.8

Hub cylinder hth,HR W/(m2·K) 27.4

Disc surface edge hth,edge W/(m2·K) 35.6

Free convection

Disc surface hth,DS W/(m2·K) 9

Ventilation hth,V W/(m2·K) 9

Hub cylinder hth,HR W/(m2·K) 10

Disc surface edge hth,edge W/(m2·K) 10

68

Appendix D

Parameters and specification of the

electrical machine

Table D.1: Machine data of modulated machineSpecification

Peak torque Nm 160

Current density DC A/mm2 10

Air-gap lenght mm 1

Stator slot fill factor Cs,fill 0.4

Pole number stator 12

Pole number rotor 10

Stator core outer radius mm 330

Stator core inner radius mm 234

Rotor segment outer radius mm 330

Rotor segment inner radius mm 234

Stator slot width mm 39.4

Stator slot height mm 42.4

Stator slot opening height mm 3

Active axial length stator mm 70

Active axial length rotor mm 20

Wounded tooth width, tip degree 30.25

Unwounded tooth width, tip degree 18.5

Wounded tooth width, body degree 20

Unwounded tooth width, body degree 8

Rotor segments width degree 30.25

Active weight copper kg 12.6

Active weight epoxy kg 3.9

Active weight laminated steel kg 12.8

Total active weight stator kg 29.3

69

Appendix D. Parameters and specification of the electrical machine

Table D.2: Machine data of 270◦ statorSpecification

Peak torque Nm 112

Active weight copper kg 9.5

Active weight epoxy kg 2.9

Active weight laminated steel kg 9.6

Total active weight stator 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

1.824 116398

1.832 123026

71

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 discSpecification of brake disc

Mass of vehicle [5] kg 3000

Speed of vehicle 0-1500s m/s 10

Speed of vehicle 1500-2400s m/s 0

Deceleration of vehicle 0-1500s m/s2 1

Deceleration of vehicle 1500-2400s m/s2 0

Brake disc outer diameter mm Confidential

Brake disc inner diameter mm Confidential

Thickeness of brake disc mm Confidential

Hub outer diameter mm Confidential

Disc center diameter mm Confidential

Axial length of hub mm Confidential

Thickness of hub mm Confidential

Density ρth,alu [33] kg/dm3 2.7

Emissivity ǫdisc Confidential

Thermal conductivity kth,alu [49] W/(m·K) 127

Heat capacity cth,alu [49] J/(kg·K) 896

Heat tranfer coefficient hub hth,hub W/(m2·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

cth,wire =ρcopper

ρwire

τcoppercth,copper +ρcopper

ρwire

τexpoxycth,epoxy. (E.2)

73

Appendix E. Parmaters of implementation of machine thermal model

Table E.2: Heat transfer coefficients of brake discForced convection

Disc surface hth,DS W/(m2·K) κth,air gap

Ventilation hth,V W/(m2·K) Plane of symmetry

Hub cylinder hth,HR W/(m2·K) κth,air gap

Disc surface edge hth,edge W/(m2·K) 35.6

Free convection

Disc surface hth,DS W/(m2·K) κth,air gap

Ventilation hth,V W/(m2·K) Plane of symmetry

Hub cylinder hth,HR W/(m2·K) κth,air gap

Disc surface edge hth,edge W/(m2·K) 8

Table E.3: Machine data of statorSpecification

Air-gap lenght mm 1

Stator slot fill factor Cs,fill 0.4

Pole number stator 12

Stator core outer radius mm 340

Stator core inner radius mm 234

Stator slot width mm 27

Stator slot height mm 44

Stator slot opening height mm 3

Axial length stator mm 70

Density ρth,core [45] kg/dm3 7.65

Density ρth,copper [33] kg/dm3 8.9

Density ρth,epoxy [35] kg/dm3 1.83

Density ρth,wire kg/dm3 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

Heat tranfer coefficient to ambient hth,hub W/(m2·K) 9

74

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