Design of a high speed transmission for an electric vehicle

Design of a high-speed transmission
for an electric vehicle

Carlos Daniel Pires Rodrigues

Dissertation submitted to
Faculdade de Engenharia da Universidade do Porto
for the degree of:
Mestre em Engenharia Mecânica

Advisor:
Prof. Jorge Humberto Oliveira Seabra
Co-Advisor:
Prof. José António dos Santos Almacinha

Unidade de Tribologia, Vibrações e Manutenção Industrial
Departamento de Engenharia Mecânica
Faculdade de Engenharia da Universidade do Porto

Porto, Julho de 2018


The work presented in this dissertation was performed at the
Tribology, Vibrations and Industrial Management Unit
Department of Mechanical Engineering
Faculty of Engineering
University of Porto
Porto, Portugal.

Carlos Daniel Pires Rodrigues
E-mail: ,

Faculdade de Engenharia da Universidade do Porto
Departamento de Engenharia Mecânica
Unidade de Tribologia, Vibrações e Manutenção Industrial
Rua Dr. Roberto Frias s/n, Sala M206
4200-465 Porto
Portugal


Abstract

For decades, the hegemony of internal combustion vehicles has led to an improvement, by
the automotive industry, of transmissions, in order to increase the torque and reduce the
rotational speed from the engine.
These transmissions are quite complex, having up to 7 speeds, with the aim of retrieving
the highest possible efficiency from the considerably inefficient internal combustion engines.
Nowadays, environmental concerns and strong governmental regulations, as well as,
buying incentives, have presented electric vehicles as a viable solution to consumers while
being in line with the new global paradigm of sustainability.
Electric vehicles turn to electric motors to transform electric energy in mechanical
energy. Since these motors are widely used in other industrial applications, they are
already a mature technology. They have an ideal torque and power curves regarding
vehicle operation. Due to these favourable characteristics, the transmission of an electric
vehicle is simpler, presenting itself as a conventional reducer with respect to the overall
geometry, having usually only one speed ratio between the input and the output.
However, the high rotational speed associated with compact electric motors, makes it
necessary to take some factors into account when designing a transmission: gear design,
lubrication method selection, as well as rolling bearing selection are just some of the
concerns that will be further elaborated in this thesis, in order to reduce power losses,
ensuring a good efficiency and, at the same time, control the noise generated.

The mechanical differential, which is present in all internal combustion vehicles, is a
system that provides the vehicle with the capacity to change direction steadily, however it
cannot be continually controlled. Thus, the idea of using an electronic differential seems
interesting, since it would reduce the number of mechanical components and, through
the ever-increasing network of sensors and data acquired by the vehicles themselves, it is
possible to independently control the rotational speed of each front wheel continuously,
leading to greater safety and comfort when the vehicle is changing direction.

Keywords:
lubrication.

electric vehicles, transmission, gears, electronic differential, splash
i



Resumo

Durante largas décadas, a hegemonia dos veículos de combustão interna levou a um
aperfeiçoamento por parte da indústria automóvel das transmissões para aumentar o
binário e reduzir a velocidade provenientes do motor.
Estas transmissões são bastante complexas, podendo ter até 7 velocidades, de forma a
extrair o mais rendimento possível dos pouco eficientes motores de combustão interna.
Atualmente, preocupações ambienteais e fortes regulações governementais, bem como,
elevados incentivos de compra, tornaram os veículos elétricos como uma solução viável para
os consumidores e que vai de encontro ao novo paradigma mundial de sustentabilidade.
Os veículos elétricos recorrem a motores elétricos para transformar a energia elétrica
em energia mecânica. Uma vez que estes motores são amplamente utilizados em outras
aplicações industriais, já se apresentam como uma tecnologia madura. Eles possuem uma
curva de binário e de potència ideal para os automóveis. Devido a estas características

favoráveis, a transmissão de um veículo elétrico é mais simples, apresentando-se como
um redutor convencional em termos geométricos, tendo apenas uma razão de velocidades
entre a entrada e a saída. Porém, a elevada velocidade de rotação associada aos motores
elétricos compactos, leva a que sejam necessários cuidados na concepção da transmissão:
desenvolvimento das engrenagens, escolha do método de lubrificação ideal e escolha dos
rolamentos são apenas algumas das questões que serão aprofundadas nesta dissertação, de
forma a que as perdas de potência sejam reduzidas, garantindo uma boa efficiência e, ao
mesmo tempo, controlar o ruído gerado.
O diferencial mecânico, presente em todos os veículos de combustão interna, é um
sistema que proporciona a capacidade para um veículo curvar de forma correta, mas que
não é possível regular enquanto veículo está em movimento. Assim, surgiu a ideia de usar
um diferencial eletrónico, reduzindo o número de componentes mecânicos e, através da
cada vez mais elevada rede de sensores e informação adquirida pelos próprios veículos,
seja possível realizar um controlo independente e continuado das velocidades de rotação
das duas rodas da frente, levando a uma maior segurança e conforto quando o veículo está
a mudar de direção.

iii



‘Nós somos o que fazemos. O que não se faz não existe.’

Padre António Vieira

v



Acknowledgements

I would like to thank my thesis advisor Prof. Jorge Seabra and co-advisor Prof. José
Almacinha of the Faculty of Engineering at University of Porto. They consistently allowed
this thesis to be my own work and steered me in the right direction providing guidance
and support, as well as recommendations and several revisions throughout the semester.
I would also like to thank all my friends which provide a very pleasant environment to
evade, for short periods of time, the work atmosphere.
Finally, I give my warmest thanks to my family, in particular to my parents, for the
continuous encouragement and everything that they have provided me along the years,
and whose support after all is the most essential.

vii



Contents

Abstract

i

Resumo

ii

Acknowledgements

vii

1 Introduction

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Background Theory
2.1 Electric vehicles . . . .
2.2 Electrification . . . . .
2.3 Automotive industry .
2.4 Energy storage . . . .
2.4.1 Battery . . . .
2.4.2 Fuel cell . . . .
2.4.3 Ultra-capacitor
2.5 Powertrain . . . . . .
2.5.1 Electric motor
2.5.2 Transmission .
2.5.3 Differential . .
2.5.4 Projects . . . .

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3 Project characteristics
3.1 Vehicle specifications . . . . . . . . . . . . . . . .
3.2 Electric motor . . . . . . . . . . . . . . . . . . . .
3.3 Vehicle performance . . . . . . . . . . . . . . . .
3.3.1 Maximum speed and gradeability . . . . .
3.3.2 Acceleration performance . . . . . . . . .
3.3.3 Preliminary results . . . . . . . . . . . . .
3.4 Transmission . . . . . . . . . . . . . . . . . . . .
3.4.1 Number of stages and overall transmission
3.4.2 Geometry . . . . . . . . . . . . . . . . . .

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1
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2

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5
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8
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22

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27
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4 Gear design
37
4.1 Application factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Road profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Tooth root and flank safeties . . . . . . . . . . . . . . . . . . . . . . . . . . 38
ix


CONTENTS
4.4
4.5
4.6

4.7
4.8
4.9
4.10
4.11
4.12
4.13

Material . . . . . . . . . . . .
Manufacturing Quality . . . .
Tooth flank surface roughness
Module . . . . . . . . . . . .
Helix angle . . . . . . . . . .
Face width . . . . . . . . . .
Profile shift . . . . . . . . . .
Contact ratio . . . . . . . . .
Comparison . . . . . . . . . .
Final results . . . . . . . . . .

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39
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5 Shaft design and bearing selection
5.1 Shaft layout . . . . . . . . . . . . . . . . . . . . .
5.1.1 Material . . . . . . . . . . . . . . . . . . .
5.1.2 Relative position and direction of rotation
5.1.3 Shaft ends . . . . . . . . . . . . . . . . . .
5.1.4 Splines . . . . . . . . . . . . . . . . . . . .
5.1.5 Key connections . . . . . . . . . . . . . .
5.2 Rolling bearings . . . . . . . . . . . . . . . . . .
5.2.1 Rolling bearings selection criteria . . . . .
5.2.2 Arrangement . . . . . . . . . . . . . . . .
5.3 Rolling bearings selected . . . . . . . . . . . . . .
5.4 Shaft analysis . . . . . . . . . . . . . . . . . . . .
5.4.1 Final shafts . . . . . . . . . . . . . . . . .
5.4.2 Applied stresses (static and fatigue) . . .

5.4.3 Deflection . . . . . . . . . . . . . . . . . .
5.4.4 Critical speed . . . . . . . . . . . . . . . .

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49
49
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53
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55
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56
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60
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64
64
66

6 Gear modification sizing
67
6.1 Theoretical flank modifications . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Crowning to compensate tolerances . . . . . . . . . . . . . . . . . . . . . . . 68
6.3 Profile modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7 Lubrication and Sealing
7.1 Lubricant selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Lubrication method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Sealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75
76
77
80

8 Thermal analysis
83
8.1 Power losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.2 Heat dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9 Housing and Parts
9.1 Housing . . . . .
9.1.1 Material .
9.1.2 Design . .
9.2 Parts . . . . . . .
9.2.1 Flanges .
9.2.2 Screws . .
9.2.3 Set pins .

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93
93
93
94
96
96
96
98


CONTENTS
9.2.4
9.2.5
9.2.6
9.2.7

Shaft spacer sleeves . . .

Retaining rings (circlips) .
Plugs . . . . . . . . . . .
Parts list . . . . . . . . .

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10 Assembly

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99
99
99
100
101

11 Electronic differential
107
11.1 Critical cornering speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
11.2 Ackerman steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
12 Conclusions and future work
115
12.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
12.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References

118

Appendix A Steel 18CrNiMo7-6

127

Appendix B Lubricant - Castrol ATF Dex II Multivehicle

131

Appendix C Cylindrical gear pairs KISSsoft report

133

Appendix D Shaft calculation KISSsoft report

175

Appendix E Deep groove rolling bearings

301

Appendix F Radial shaft seals

307

xi



List of Figures

2.1
2.2
2.3
2.4
2.5
2.6

2.7
2.8
2.9

2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
3.1
3.2
3.3

Historical fleet CO2 emissions performance and current standards for
passenger cars (gCO2 /km normalized to NEDC) . . . . . . . . . . . . . . .
Evolution of the global electric car stock 2010 – 2016 . . . . . . . . . . . . .
Typical performance characteristics of gasoline engine (left) and electric
motor (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average footprint over average mass per vehicle segment in the EU 2010
Note: The error bars around the averages represent the standard deviation
Examples of sales prices in German market, e thousands (not including
external incentives) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plot of a few electrochemical energy storage devices used in the propulsion

application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Six types of EV configurations . . . . . . . . . . . . . . . . . . . . . . . . .
Typical torque speed curve of an electric traction motor . . . . . . . . . . .
Schematics of four types of motors: Brushed DC motor (a), Permanent
Magnet Synchronous Motors (b), Switched Reluctance Motor (c), Induction
Motor (d). Adapted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exemplary efficiency maps of different electric motors with constant power
Single speed transmission in a PEV powertrain. S1, S2 – shafts . . . . . . .
Two speed dual clutch transmission in PEV powertrain. S1, S2, S3 – shafts.
C1, C2 – clutches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Twinspeed transmission with two planetary gear sets . . . . . . . . . . . . .
Continuously variable transmission with servo-electromechanical actuation
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical front-wheel drive powertrain components: in an ICE vehicle (left)
and in a PEV vehicle (right) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rear-wheel drive powertrain components (left) and BMW rear differential
(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
GETRAG 1eDT330 electrical transmission with independent transmission
components and electric motors. . . . . . . . . . . . . . . . . . . . . . . . .
GKN electric axle - ’eTwinsterX’. . . . . . . . . . . . . . . . . . . . . . . . .
ESKAM axle module with integrated motors (left). Gearbox (right). . . . .
Schematic design of the drive train (left) and gear set (right). . . . . . . . .
Dual motor transmission from Visio.M project (left) and transmission
diagram (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6
6
8
8
10

12
14
15

16
19
19
20
20
21
22
22
23
23
24
24
25

Torque-power peak curve of the Zytek 25 kW electric motor . . . . . . . . . 28
Forces acting on a vehicle moving uphill . . . . . . . . . . . . . . . . . . . . 30
Road load as function of vehicle speed . . . . . . . . . . . . . . . . . . . . . 31
xiii


LIST OF FIGURES
3.4
3.5
3.6

Two-stage parallel transmission arrangement with the input and output at

opposites shaft ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Two independent transmission arrangements in the same housing . . . . . . 34
Direction of forces acting on a helical gear mesh . . . . . . . . . . . . . . . . 35

4.1

Axial pitch (px ) of helical gears . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1
5.2
5.3
5.4
5.5
5.6

DIN 509 - Type E undercut . . . . . . . . . . . . . . . . . . . . . . . . . .
Initial shaft relative position . . . . . . . . . . . . . . . . . . . . . . . . . .
Final shaft relative position . . . . . . . . . . . . . . . . . . . . . . . . . .
Direction of shaft rotation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Final shaft arrangement and respective shaft rotational directions . . . . .
Vehicle forward direction with associated tire rotation and transmission
architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Locating/non-locating bearing arrangement . . . . . . . . . . . . . . . . .
Shaft A final design layout. . . . . . . . . . . . . . . . . . . . . . . . . . .
Torque diagram of shaft A . . . . . . . . . . . . . . . . . . . . . . . . . . .
Force diagram of shaft A . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shaft B final design layout . . . . . . . . . . . . . . . . . . . . . . . . . . .
Torque diagram of shaft B . . . . . . . . . . . . . . . . . . . . . . . . . . .
Force diagram of shaft B . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shaft C final design layout . . . . . . . . . . . . . . . . . . . . . . . . . . .

Torque diagram of shaft C . . . . . . . . . . . . . . . . . . . . . . . . . . .
Force diagram of shaft C . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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50
51
51
52
52

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53
56
60

60
61
61
62
62
63
63
63

. 68
. 68

6.9

Crowning (left) and helix angle modification (right) . . . . . . . . . . . .
Load distribution over face width, before and after modifications . . . . .
Load distribution over face width considering manufacturing allowances
with previous modifications (left) and proposed (right) . . . . . . . . . . .
Load distribution over face width considering manufacturing allowances
with the final modifications . . . . . . . . . . . . . . . . . . . . . . . . . .
Arc-like profile modification . . . . . . . . . . . . . . . . . . . . . . . . . .
Peak-to-peak transmission error . . . . . . . . . . . . . . . . . . . . . . . .
Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Peak-to-peak transmission error, radar chart with 100 % load (red) and 80
% load (blue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Efficiency, radar chart with 100 % load (red) and 80 % load (blue) . . . .

7.1
7.2
7.3

7.4
7.5
7.6
7.7

Relation between coefficient of friction and sliding speed (Stribeck curve)
Typical friction zones on tooth flanks at high contact pressures . . . . . .
Flanges position relative to the gear . . . . . . . . . . . . . . . . . . . . .
Influence of axial and radial clearances on churning losses . . . . . . . . .
Housing layout with flange and deflectors . . . . . . . . . . . . . . . . . .
Transmission arrangement with the defined oil level . . . . . . . . . . . . .
Pumping effect by the SKF Wave seal . . . . . . . . . . . . . . . . . . . .

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75
76
78
78
79
79
80

8.1

8.2
8.3
8.4

Composition of transmission power loss . . .
Partially submerged gear in oil bath . . . . .
Splash lubrication method with two oil levels
Housing with thermal finning . . . . . . . . .

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83
84
88
89

5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
6.1

6.2
6.3
6.4
6.5
6.6
6.7
6.8

xiv

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. 69
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70
71
72
72

. 73
. 73


LIST OF FIGURES
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13

Types of housings . . . . . . . . . . . . . . . . . . . . .
Housing interior . . . . . . . . . . . . . . . . . . . . . .
Housing exterior . . . . . . . . . . . . . . . . . . . . .
Housing exterior, detailed view of connection structure
Housing interior (other view) . . . . . . . . . . . . . .
Cover interior . . . . . . . . . . . . . . . . . . . . . . .
Cover exterior . . . . . . . . . . . . . . . . . . . . . . .
Cover exterior, detailed view of fins . . . . . . . . . . .
Interior flange . . . . . . . . . . . . . . . . . . . . . . .
Exterior flange . . . . . . . . . . . . . . . . . . . . . .
Detail of flange sheet corrugation . . . . . . . . . . . .
Spring-Type Straight Pin . . . . . . . . . . . . . . . .
Conical thread plugs . . . . . . . . . . . . . . . . . . .

11.1
11.2
11.3
11.4
11.5

Free-body diagram of a vehicle turning left . . . .
Ackerman model of cornering trajectory . . . . . .
Rotational speed of wheel and motor over a vehicle
Rotational speed of wheel and motor over a vehicle
Influence of K gradient in steering . . . . . . . . .

xv

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speed range
speed range
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94
94

95
95
95
96
96
97
97
97
98
98
100

. . . . . 108
. . . . . 110
= 9 m) 112
= 30 m) 112
. . . . . 113



List of Tables

2.1
2.2
2.3
2.4

Specifications for two ICE vehicles and the EV counterpart
Properties of several energy storage types . . . . . . . . . .
Categories of EV powertrain structures . . . . . . . . . . . .

Evaluation of four electric machine types . . . . . . . . . . .

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. 9
. 12
. 14
. 18

3.1
3.2
3.3
3.4

Technical data for the Zytek Automotive 25 kW electric motor
Vehicle properties, coefficients and other factors . . . . . . . . .
Relevant calculations for three specified points (see figure 3.3) .
Relevant calculations for acceleration . . . . . . . . . . . . . . .

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28
29
32
32

Application factor (K a ) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Single motor input for an urban road profile . . . . . . . . . . . . . . . . .
Road profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gear surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cylindrical gear pair for the first stage (Designs A – F) . . . . . . . . . .
Cylindrical gear pair for the second stage (Designs G – I) . . . . . . . . .
General transmission results . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the first stage cylindrical gear pair specifications . . . . . . .
Summary of the first stage cylindrical gear pair specifications according to
maximum torque and maximum speed . . . . . . . . . . . . . . . . . . . .
4.10 Summary of the second stage cylindrical gear pair specifications. . . . . .
4.11 Summary of the second stage cylindrical gear pair specifications according
to maximum torque and maximum speed. . . . . . . . . . . . . . . . . . .

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37
38
38
40
43
44
45
46

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

5.1

5.4
5.5
5.6
5.7
5.8
5.9
6.1
6.2
6.3

Proposed tooth trace modifications . . . . . . . . . . . . . . . . . . . . . . . 67
Face load factor K Hβ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Crowning modification and resultant highest face load factor K Hβ . . . . . 70

5.3

xvii

parameters
. . . . . . .
parameters
. . . . . . .
parameters
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
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for
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for
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for
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. .

. 47

Summary of selected bearings for shaft A and
maximum torque . . . . . . . . . . . . . . . . .
Summary of selected bearings for shaft B and
maximum torque . . . . . . . . . . . . . . . . .
Summary of selected bearings for shaft C and
maximum torque . . . . . . . . . . . . . . . . .
Gear forces and moments . . . . . . . . . . . .
Summary of the static and fatigue analysis . .
Stressed zones in the shafts . . . . . . . . . . .
Deflection analysis for the transmission shafts .
Deflection analysis at meshing zones . . . . . .
Shaft critical speeds . . . . . . . . . . . . . . .

5.2

operating
. . . . . .
operating
. . . . . .
operating
. . . . . .
. . . . . .
. . . . . .

. . . . . .
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. . . . . .

. 46
. 47

. 57
. 58
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59
64
64
65
65
66
66


LIST OF TABLES
6.4
6.5

6.6

Initial proposed values for tip relief . . . . . . . . . . . . . . . . . . . . . . . 71
Tip relief minimum and maximum values for step analysis . . . . . . . . . . 71
Summary of concluding values for the considered solutions . . . . . . . . . . 73

7.1
7.2
7.3
7.4
7.5

Parameters necessary for the calculation of Γ
Calculations results for Γ parameter . . . . .
Operating temperature of seal materials . . .
Input shaft radial seal characteristics . . . . .
Output shaft radial seal characteristics . . . .

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79
80
81
82
82

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8

General calculation parameters . . . . . . . . . . . . . . .
Calculations parameters that change with load . . . . . .
Summary of calculation results for churning torque . . . .
Churning losses for the right wheel transmission . . . . . .
Transmission power losses for the right wheel transmission
Parameters to perform thermal calculations . . . . . . . .
Variables which depend on load . . . . . . . . . . . . . . .
Heat dissipation results . . . . . . . . . . . . . . . . . . .

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85
86
86
87
87
91
91
91

9.1

Transmission parts list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

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10.1 Transmission assembly steps . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
11.1 Calculation parameters and results . . . . . . . . . . . . . . . . .
11.2 Summary of the required parameters . . . . . . . . . . . . . . . .
11.3 Summary of the results for the critical cornering speed (R
v=v c = 29,8 km/h) . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4 Summary of the results for understeer and oversteer conditions .

xviii

. . .
. . .
= 9
. . .
. . .

. .
. .
m;
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. .

. 109
. 111

. 111
. 113


Acronyms

AC
BEV
BLDC
BMS
BRS
CVT
DC
EM
EREV
ESKAM
EV
FPM
FVA
GHG
HEV
iBAS
ICE
IM
LSD
NBR
NEDC
NVH
OEM
PEV

PHEV
PMSM
PPTE
SRM
TUM
WRSM

Alternating Current
Battery Electric Vehicle
Brushless DC
Battery Management System
Boost Recuperation System
Continuously Variable Transmission
Direct Current
Electric Motor
Extended Range Electric Vehicle
Electrically Scalable Axial-Module
Electric Vehicle
Fluorocarbon rubber
Forschungsvereinigung Antriebstechnik, the Research Association for
Drive Technology
Greenhouse Gas
Hybrid Electric Vehicle
Integrated Belt Alternator Starter
Internal Combustion Engine
Induction Motor
Limited Slip Differential
Acrylonitrile-butadiene rubber
New European Driving Cycle
Noise, Vibration and Harshness

Original Equipment Manufacturer
Pure Electric Vehicle
Plug-In Hybrid Electric Vehicle
Permanent Magnet Synchronous Motor
Peak-to-Peak Transmission Error
Switched Reluctance Motor
Technical University of Munich
Wound Rotor Synchronous Motor

xix



Nomenclature

Symbol

Description

Unit

a
Aair
ad
Aca
Afin
Aoil
Apro
Af
b

C ch
Cd
Cm
C rr
Cα
C αf
C αr
Cβ
C Hβ
d
da
dw
D hub
Dp
f ma
f Hβ
fs
Fa
Fg
Fr
F rr
Ft
Fx
Fz
FC
Fr
g
Gr

Center distance

Ventilated housing area
Reference center distance
External housing area
Total fin area
Internal housing area
Projected fin area
Frontal area
Face width
Churning losses
Aerodynamic drag coefficient
Churning losses parameter
Rolling resistance coefficient
Tip relief
Front tire cornering stiffness
Rear tire cornering stiffness
Crowning
Helix angle modification
Shaft diameter, distance between left and right wheel
Gear tip diameter
Gear operating pitch diameter
Hub diameter
Pitch diameter
Manufacturing allowance (axis misalignment)
Manufacturing allowance (gear lead variation)
Horizontal static friction
Aerodynamic drag, Axial force
Grading force
Radial force
Rolling resistance
Tractive force

Shearing force X
Shearing force Z
Centrifugal force
Froude number
Gravitational acceleration (= 9,81)
Grashoff number
xxi

mm
m2
mm
m2
m2
m2
m2
m2
mm
W
µm
µm
µm
µm
µm
mm
mm
mm
mm
mm
N
N

N
N
N
N
N
N
m2 s−1
-


Nomenclature
h
h ca
Hf
Ht
i1
i2
ig
Ja
k
K
Ka
K AF
K AH
K Hβ
l fin
lx
L
LCa
LCa*

m
mn
Mx
Mz
N, n
P
Pm
P¯ res
P VD
P VL
P VZP
P VZ0
PV
px
Q ca
rt
R
R1
R2
Rp
Ra
Rz
Re
Rm
SF
SH
Sm
S md
S mf
ta

Submerged height, height of vehicle center of mass
Overall transmission height
Flange height
Gear tooth height
First stage transmission ratio
Second stage transmission ratio
Overall transmission ratio
Axial distance between flange and gear
Heat transfer coefficient
Ackerman steering gradient
Application factor
Root strength application factor
Flank strength application factor
Face load factor
Depth of one fin
Flow length (path of flow filament along the housing wall)
Length between front and rear axle
Roll length of the tip relief
Length factor
Mass
Normal module
Bending moment X
Bending moment Z
Rotational speed
Distance between left and right front wheel kingpins
Electric motor power
Average resistance power
Seal power loss
Rolling bearing power loss

Gear power loss
Churning loss
Total power loss
Axial pitch
Housing heat dissipation
Tire radius
Turning radius
Turning radius of left-front wheel
Turning radius of right-front wheel
Gear pitch radius
Average roughness
Mean peak-to-valley roughness
Reynolds number
Tensile strength
Tooth root safety
Tooth flank safety
Gear submerged surface
Wet surface of the gear flank
Wet surface of the gear teeth
Acceleration time
xxii

mm
mm
mm
mm
mm
W m−2 K−1
mm
mm

m
µm
kg
mm
Nm
Nm
rpm
m
kW
kW
W
W
W
W
W
mm
W
m
m
m
m
mm
µm
µm
N mm−2
m2
m2
m2
s

T air
Tm
T oil
T wall
T∞
Ta
v
v arg
v ga
V0
xi
Wf
Wr
Z

Air temperature
Torque (electric motor)
Oil temperature
Housing wall temperature
Ambient temperature
Taylor number
Velocity, Circumferential speed, Cornering speed
Air Velocity
Sliding velocity at tip
Oil volume
Gear profile shift
Front vehicle load
Rear vehicle load
Gear number of teeth

Greek
symbol

Description

α
αca
αcon
αn
αoil
αrad
β
Γ
δ
δ fin
ε
εα
εβ
εγ
ζa
η
λfin
µs
ν
ν air
ρ
ω

Road grade

Air-side heat transfer coefficient
Convection heat transfer coefficient
Pressure angle
Oil-side heat transfer coefficient
Radiation heat transfer coefficient
Helix angle
Flange parameter
Rotating inertia factor, Ackerman angle
Fin thickness
Housing emission ratio
Transverse contact ratio
Overlap ratio
Total contact ratio
Specific sliding at the tip
Efficiency
Fin thermal conductivity
Static friction coefficient
Oil kinematic viscosity
Air kinematic viscosity
Density
Rotational velocity

K
Nm
K
K
K
−1
ms
m s−1

m s−1
m3
N
N
-

Unit

xxiii

rad
W m−2 K−1
W m−2 K−1
◦

W m−2 K−1

W m−2 K−1
◦

mm
W m−1 K−1
2
[mm /s]
[mm2 /s]
kg m−3
rad/s