Mechanical design and development of a drivetrain system

UNIVERSITY OF PATRAS

DEPARTMENT OF MECHANICAL ENGINEERING AND

AERONAUTICS

LABORATORY OF MANUFACTURING SYSTEMS AND

AUTOMATION

DIPLOMA THESIS

Mechanical design and development of a drivetrain system

for an electric FSAE racecar

Siangas Georgios

246631

Dr. Panagiotis Stavropoulos,

Associate Professor

This Diploma Thesis is submitted to the Department of Mechanical and Aeronautics

Engineering of the University of Patras.

PATRAS, [07/2020]

Mechanical design and development of a drivetrain system for an

electric FSAE racecar

Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector ii

University of Patras,

Department of Mechanical and Aeronautics Engineering,

Georgios Siangas

© [2020] – All rights reserved.



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector iii

UNIVERSITY OF PATRAS

DEPARTMENT OF MECHANICAL AND AERONAUTICS

ENGINEERING

MANUFACTURING SECTOR

LABORATORY OF MANUFACTURING SYSTEMS AND

AUTOMATION

This current diploma thesis was presented

by

Mr. Georgios Siangas

246631

at 30/07/2020.

The approval of this diploma thesis does not declare the acceptance of the writer‟s opinions.

During the writing of this diploma thesis the principles of academic ethic were respected.



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector iv

ABSTRACT

The current diploma thesis describes the design and the development of the drivetrain system

used by the UoP5e, an electric racecar which took place in Formula Student UK 2017 and FSG

2017 competitions, representing the University of Patras, and specifically the department of

Mechanical and Aeronautics Engineering. Formula Student competition is an international

design competition organized by the SAE International (former Society of Automotive

Engineers). The concept of the competition is the design of a single seat open wheeled racecar,

for a fiction manufacturing company, focused on the weekend racer. The student teams design

and manufacture their own prototypes, based on rules published by the competitions. The final

scoring divides into two categories, the static events which include the design presentation (150

points), the cost and manufacturing (100 points) and the business plan presentation (75 points),

and the dynamic events which include acceleration (75 points), skidpad (75 points), autocross

(100 points), endurance (325 points) and finally efficiency (100 points). Considering the current

developments in the field of the automotive industry, the competition has created an electric

racecar class, and UoP Racing has been developing electric racecars since 2012, when the

change from internal combustion power units to full electric power units was decided. This

diploma thesis will cover the decision making process, the mechanical design and development

and the manufacturing of the drivetrain system of an electric racing vehicle.

Mechanical design and development of a drivetrain system

for an electric FSAE racecar

Georgios Siangas



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector v

Key Words

Drivetrain, Gearbox, Electric Racecar, Electric Motor, Mechanical design



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector vi

LIST OF TABLES

Table 1: UoP4e Powertrain Characteristics (Baseline Design). ..................................................... 6

Table 2: Weight Table of UoP4e Powertrain. ................................................................................. 6

Table 3: Demographic powertrain setup comparison. .................................................................... 9

Table 4: Comparison between direct drive HTEM and HREM. .................................................. 10

Table 5: Entry data for HTEM and HREM [Optimum Lap]. ....................................................... 11

Table 6: Time lap comparison between HREM and HTEM. ....................................................... 14

Table 7: EMRAX 228 CC HV Technical Specifications. ............................................................ 18

Table 8: Dynamometer testing specifications. .............................................................................. 19

Table 9: Battery voltage selection. ................................................................................................ 23

Table 10: Endurance load case. .................................................................................................... 27

Table 11: Motor shaft material properties. ................................................................................... 29

Table 12: Cross section properties. ............................................................................................... 29

Table 13: Motor shaft – Section A‟A stress –strain calculation. .................................................. 30

Table 14: Motor shaft – Static analysis results. ............................................................................ 31

Table 15: Dynamic structural analysis loads. ............................................................................... 31

Table 16: Motor shaft- Dynamic stresses calculation. .................................................................. 31

Table 17: Motor shaft – Dynamic analysis results........................................................................ 32

Table 18: Motor shaft- Involute spline characteristics. ................................................................ 32

Table 19: Motor shaft - Spline stress analysis. ............................................................................. 33



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector vii

Table 20: Electric motor mount FEA model results. .................................................................... 36

Table 21: Electric motor mount - Factors of fatigue life. ............................................................. 36

Table 22: UoP4e characteristics - COF extrapolation. ................................................................. 40

Table 23: UoP5e characteristics. ................................................................................................... 42

Table 24: Coefficients of aerodynamic load. ................................................................................ 44

Table 25: Newton‟s second law expressed for the transmission shafts. ....................................... 46

Table 26: Angular acceleration of each shaft. .............................................................................. 47

Table 27: Service life of chain drive reduction estimation. .......................................................... 53

Table 28: Chain load factor K1. .................................................................................................... 54

Table 29: Chain lubrication factor K2. ......................................................................................... 54

Table 30: Chain service factor K3. ............................................................................................... 54

Table 31: Geometrical characteristics of DID 520VO chain. ....................................................... 55

Table 32: Chain mechanical properties. ........................................................................................ 56

Table 33: Sprockets pitch action diameters. ................................................................................. 56

Table 34: Chain drive concept calculations. ................................................................................. 57

Table 35: Spur and helical gears comparison. .............................................................................. 59

Table 36: Enclosed gearbox characteristics. ................................................................................. 61

Table 37: Desired material properties based on components. ...................................................... 64

Table 38: Available materials for gear manufacturing. ................................................................ 65

Table 39: Case carburized and tempered 15CrNi6 [DIN 1.5919] steel material properties. ........ 66

Table 40: Available materials for shaft manufacturing. ............................................................... 67

Table 41: Specific Young‟s Modulus comparison for different materials. .................................. 68



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector viii

Table 42: Specific Yield Strength comparison for different materials. ........................................ 69

Table 43: AL 7075-T6 Material properties at 100 0C. .................................................................. 73

Table 44: Gearbox internal components design constrictions. ..................................................... 75

Table 45: Geometry of gears......................................................................................................... 76

Table 46: Maximum loads applied per stage. ............................................................................... 76

Table 47: Dynamic loads applied per stage. ................................................................................. 76

Table 48: Results of gears structural analysis. .............................................................................. 77

Table 49: 1st shaft bearing reactions. ............................................................................................ 77

Table 50: 1st shaft results of structural analysis. ........................................................................... 78

Table 51: 2nd

shaft bearing reactions. ........................................................................................... 78

Table 52: 2nd

shaft results of structural analysis. .......................................................................... 78

Table 53: 3rd

Shaft bearing reactions. ........................................................................................... 79

Table 54: 3rd

shaft results of structural analysis............................................................................ 79

Table 55: Spline geometry according to DIN 5480. ..................................................................... 80

Table 56: Spline results of structural analysis. ............................................................................. 81

Table 57: Selected ball bearings. .................................................................................................. 81

Table 58: Selected ball bearing load capabilities. ......................................................................... 81

Table 59: Selected ball bearings static safety factor. .................................................................... 81

Table 60: Selected ball bearings rotational speed safety factor. ................................................... 81

Table 61: Selected ball bearings life cycles calculation. .............................................................. 83

Table 62: Gearbox casing parts list. .............................................................................................. 86

Table 63: Results of gearbox casing FEA stress-strain analysis................................................... 89



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector ix

Table 64: Aluminum alloy 7075-T6 material properties at 95 0C. ............................................... 90

Table 65: Factors of fatigue life of AL 7075-T6. ......................................................................... 91

Table 66: ISO interference fit of gearbox end caps bores. ........................................................... 93

Table 67: Thermal expansion of the gears. ................................................................................... 94

Table 68: Oil level angle compared to acceleration. ..................................................................... 99

Table 69: Differential coupling – Bolt pattern calculation. ........................................................ 111

Table 70: Differential coupling FEA model stress results. ......................................................... 111

Table 71: Factors of fatigue life differential coupling. ............................................................... 112

Table 72: Differential ramp angles and theoretical lockup. ........................................................ 114

Table 73: Torque bias ratio and applied torque depending ramp angle. ..................................... 115

Table 74: Stub shaft material properties. .................................................................................... 118

Table 75: Cross section properties. ............................................................................................. 119

Table 76: Stub shaft – Section A‟A stress –strain calculation. ................................................... 119

Table 77: Stub shaft – Static analysis results. ............................................................................. 120

Table 78: Stub shaft- Dynamic stresses calculation. .................................................................. 120

Table 79: Stub shaft – Dynamic analysis results. ....................................................................... 121

Table 80: Stub shaft- Involute spline characteristics. ................................................................. 122

Table 81: Stub shaft - Spline stress analysis. .............................................................................. 122

Table 82: FIAT 127 Sport Edition CV joint specifications. ....................................................... 123

Table 83: Tripod Housing – Bolt pattern calculation. ................................................................ 125

Table 84: Tripod Housing FEA model stress results. ................................................................. 126

Table 85: Factors of fatigue life tripod housing. ......................................................................... 127



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector x

Table 86: Driveshaft material properties. ................................................................................... 129

Table 87: Driveshaft stress –strain calculation. .......................................................................... 130

Table 88: Driveshaft – Static analysis results. ............................................................................ 130

Table 89: Driveshaft- Dynamic stress calculation. ..................................................................... 131

Table 90: Driveshaft – Dynamic analysis results. ...................................................................... 131

Table 91: Driveshaft resonance analysis. .................................................................................... 132



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xi

LIST OF FIGURES AND DIAGRAMS

Figure 1: Maximum Longitudinal Acceleration to Vehicle Speed UoP4e. .................................... 7

Figure 2: CAD Design of UoP4e Powertrain (Baseline Design). ................................................... 8

Figure 3: Power / Torque to Engine Speed diagram for the HREM concept. .............................. 12

Figure 4: Power / Torque to Engine Speed diagram for the HTEM concept. .............................. 12

Figure 5: Batch run simulation for the selection of initial FDR for the HREM concept. ............. 13

Figure 6: Speed to distance diagram HREM vs. HTEM. ............................................................. 14

Figure 7: Distance to time diagram HREM vs. HTEM. ............................................................... 14

Figure 8: EMRAX 228 CC HV Drawing. .................................................................................... 16

Figure 9: Eddy current brake dynamometer setup. ....................................................................... 19

Figure 10: Dynamometer load cell sensor mounting. ................................................................... 21

Figure 11: Eddy-current brake. ..................................................................................................... 21

Figure 12: Example of logged Torque/Power map from the dynamometer. ................................ 22

Figure 13: Battery DC Voltage selection. ..................................................................................... 23

Figure 14: Power map of EMRAX 228 HV LC at 504 Volt. ....................................................... 25

Figure 15: Torque map of EMRAX 228 HV LC at 504 Volt. ...................................................... 25

Figure 16: Logged endurance run from previous racecar. ............................................................ 26

Figure 17: Motor shaft design. ...................................................................................................... 28

Figure 18: Stress concentration factor Kt. .................................................................................... 29

Figure 19: Section A‟A motor shaft.............................................................................................. 30



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xii

Figure 20: Electric motor mount design. ...................................................................................... 34

Figure 21: Electric motor mount – FEA stress results. ................................................................. 35

Figure 22: Electric motor mount – FEA displacement results. ..................................................... 35

Figure 23: Electric motor protective casing design. ..................................................................... 38

Figure 24: Electric motor assembly design. .................................................................................. 38

Figure 25: Vehicle speed to engine speed diagram. ..................................................................... 43

Figure 26: Downforce to vehicle speed diagram. ......................................................................... 45

Figure 27: Drag force to vehicle speed diagram. .......................................................................... 45

Figure 28: Inertial losses. .............................................................................................................. 47

Figure 29: Propulsion- Traction Forces to vehicle speed [km/h]. ................................................ 48

Figure 30: DID Chain specifications for O-ring and X-ring chains. ............................................ 55

Figure 31: Chain drive concept. .................................................................................................... 58

Figure 32: Enclosed gearbox concept. .......................................................................................... 61

Figure 33: Comparison of Yield strength between AL 7075-T6 and AL 2024-T3. ..................... 71

Figure 34: Comparison of Young‟s Modulus between AL7075-T6 and AL2024-T3. ................. 71

Figure 35: AL 7075-T6 Material properties to temperature. ........................................................ 72

Figure 36: Gearbox internal components drawing. ....................................................................... 75

Figure 37: 1st shaft drawing. ......................................................................................................... 77

Figure 38: 2nd

shaft drawing. ........................................................................................................ 78

Figure 39: 3rd

shaft drawing. ......................................................................................................... 79

Figure 40: Shafts external spline dimensions according to DIN 5480. ........................................ 80

Figure 41: SKF W61906R ball bearing datasheet. ....................................................................... 83



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xiii

Figure 42: SKF 16006 ball bearing datasheet. .............................................................................. 84

Figure 43: Kaydon KC042CP0 thin section ball bearing datasheet. ............................................ 84

Figure 44: Gearbox casing drawing .............................................................................................. 86

Figure 45: Meshed gearbox casing model. ................................................................................... 88

Figure 46: Von Mises gearbox casing stress FEA results. ............................................................ 88

Figure 47: Displacement gearbox casing FEA results. ................................................................. 89

Figure 48: Notch sensitivity factor q. ........................................................................................... 90

Figure 49: Static stress concentration factor Kt for plate in axial loading. ................................... 91

Figure 50: Lubrication type selection chart. ................................................................................. 96

Figure 51: Gear oil SAE 75 W-140 specifications. ...................................................................... 97

Figure 52: Gear oil level drawing. ................................................................................................ 98

Figure 53: Gear oil level for splash lubrication. ........................................................................... 98

Figure 54: Gear oil CAD representation. ...................................................................................... 99

Figure 55: Gear oil flow bench test simulation. .......................................................................... 100

Figure 56: Gear oil temperature to time at an endurance event. ................................................. 101

Figure 57: Radial shaft seal......................................................................................................... 102

Figure 58: Sealing of 1st shaft assembly. .................................................................................... 104

Figure 59: Sealing of 1st shaft section. ........................................................................................ 104

Figure 60: Sealing of the 3rd

shaft assembly. .............................................................................. 105


shaft section. ................................................................................. 105

Figure 62: Assembly drawing of rear axle. ................................................................................. 107

Figure 63: Assembly drawing of rear axle 2. .............................................................................. 107



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xiv

Figure 64: Implementation of differential into crown gear drawing. ......................................... 108

Figure 65: Differential coupling drawing. .................................................................................. 109

Figure 66: Differential coupling FEA stress results. .................................................................. 111

Figure 67: Modified DREXLER LSD drawing. ......................................................................... 114

Figure 68: Stub shaft drawing. .................................................................................................... 117

Figure 69: Stress concentration factor Kt. .................................................................................. 118

Figure 70: Section A‟A stub shaft. ............................................................................................. 119

Figure 71: Tripod CV Joint FIAT 127 Automobile. ................................................................... 123

Figure 72: Driveshaft relative movement to differential. ........................................................... 123

Figure 73: Aluminum tripod housing joint drawing. .................................................................. 125

Figure 74: Aluminum tripod housing FEA stress analysis results. ............................................. 126

Figure 75: Driveshaft drawing. ................................................................................................... 128

Figure 76: E-drivetrain photographs. .......................................................................................... 137



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xv

LIST OF SYMBOLS

ax [m/sec2]: Longitudinal acceleration

F [N]: Force

m [kg]: Mass

ay [m/sec2]: Lateral acceleration

M [Nm] : Moment

U [m/sec]: Velocity

P [kW]: Power

V [V]: Voltage

I [Amp]: Current

n [rpm]: Rotational speed

T [Nm]: Torque

Kt: Stress concentration factor

Kf: Dynamic stress concentration factor

D [mm]: Major diameter

d [mm]: Minor diameter

Ε [GPa]: Modulus of elasticity

v: Poisson ratio

ρ [kg/m3]: Density



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xvi

a [10-6

/C]: Coefficient of thermal expansion

w [mm]: Width

up [m/sec]: Peripheral speed

r [mm]: Radius

J [mm4]: Polar moment of inertia

τ [MPa]: Torsional stress

θ [0]: Angle of twist

σ [MPa]: Tensile stress

Sf: Safety factor

G [GPa]: Modulus of rigidity

Sy [MPa] Yield tensile strength

Su [MPa] Ultimate tensile strength

Sn [MPa] Fatigue strength

Se [MPa] Modified fatigue strength

Z: Gear teeth

m: Module

a [0]: Pressure angle

N: Safety factor

wb [mm]: Wheelbase

hcog [mm]: Center of gravity height

X [N] : Longitudinal force



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xvii

μ : Coefficient of friction

ω [rad/sec]: Angular velocity

c : Aerodynamic factors

A [mm2]: Area

fdr: Final drive ratio

rt [m]: Tire radius

α [rad/sec2] : Angular acceleration

Ι [mm4]: Moment of inertia

i : Gear ratio

t [sec]: Time

x [m]: Distance

q : Notch sensitivity factor

C [μm]: Clearance

Q [N]: Shear load

h [mm]: height

TBR : Torque bias ratio

S [%]: Lockup torque percentage



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xviii

CONTENTS

ABSTRACT ................................................................................................................................. IV

LIST OF TABLES ...................................................................................................................... VI

LIST OF FIGURES AND DIAGRAMS ................................................................................... XI

LIST OF SYMBOLS ................................................................................................................. XV

CONTENTS........................................................................................................................... XVIII

PROLOGUE .................................................................................................................................. 1

1. INTRODUCTION: CONCEPT DESIGN AND DESIGN GOALS ................................. 2

1.1 DESIGN GOALS ................................................................................................. 2

1.2 BASELINE DESIGN ........................................................................................... 5

1.3 POWERTRAIN TYPE COMPARISON ........................................................... 8

1.4 POWERTRAIN LAYOUT SELECTION ......................................................... 9

2. CHAPTER 1: POWER UNIT SELECTION AND DYNAMOMETER TESTING ... 16

2.1 POWER UNIT ................................................................................................... 16

2.2 DYNAMOMETER TESTING ......................................................................... 18

2.3 LOAD CASES .................................................................................................... 26

2.4 MOTOR SHAFT ............................................................................................... 27

2.5 ELECTRIC MOTOR MOUNTING TO CHASSIS ....................................... 34

2.6 ELECTRIC MOTOR PROTECTIVE SHIELD AND ASSEMBLY ............ 37

3. CHAPTER 2: FINAL DRIVE RATIO SELECTION .................................................... 39



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xix

3.1 POINT MASS SIMULATION PROGRAM DEVELOPMENT ................... 39

3.2 VEHICLE VELOCITY..................................................................................... 42

3.3 AERODYNAMIC FORCE CALCULATION ................................................ 43

3.4 PROPULSION AND INERTIAL FORCES CALCULATION .................... 46

3.5 AVAILABLE TRACTION AND MOTION CALCULATIONS. ................. 48

4. RECHAPTER 3: REDUCTION UNIT TYPE SELECTION ........................................ 52

4.1 CHAIN DRIVE .................................................................................................. 52

4.2 ENCLOSED GEARBOX CONCEPT.............................................................. 58

4.3 REDUCTION DRIVE SELECTION CONCLUSION .................................. 61

5. CHAPTER 4: MATERIALS AND MANUFACTURING METHODS SELECTION 63

5.1 MATERIALS AND TREATMENTS. ............................................................. 63

5.2 GEARS MATERIAL SELECTION ................................................................ 64

5.2 SHAFTS MATERIAL SELECTION .............................................................. 66

5.3 GEARBOX AND DIFFERENTIAL CASING MATERIAL ......................... 68

5.4 MOUNTING AND GENERAL-PURPOSE MATERIAL SELECTION. .... 73

6. CHAPTER 5: GEARBOX MECHANICAL DESIGN ................................................... 74

6.1 GEARBOX INTERNAL COMPONENTS DESIGN ..................................... 74

6.2 GEARBOX CASING DESIGN ........................................................................ 85

7. CHAPTER 6: LUBRICATION AND SEALING METHODS ...................................... 95

7.1 LUBRICATION ................................................................................................. 95

7.2 SEALING ......................................................................................................... 101

8. CHAPTER 7: DIFFERENTIAL AND DRIVE AXLES MECHANICAL DESIGN .. 106



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector xx

8.1 DIFFERENTIAL COUPLING....................................................................... 107

8.2 DIFFERENTIAL ............................................................................................. 113

8.3 STUB SHAFT DESIGN .................................................................................. 116

8.4 TRIPOD HOUSING DESIGN........................................................................ 122

8.5 DRIVESHAFTS DESIGN............................................................................... 128

9. CONCLUSION ................................................................................................................. 133

REFERENCES .......................................................................................................................... 138



Georgios Siangas

Department of Mechanical and Aeronautics Engineering – Manufacturing Sector 1

PROLOGUE

The realization of the drivetrain system was a four-year project, including initial design,

analysis, manufacturing, testing, and optimization and would not have been possible without the

support of certain individuals. First of all, I would like to thank my family for their unwavering

support during this endeavor. Then I would like to thank the Laboratory of Manufacturing

Systems and Automation "LMS", which housed the entire effort, providing its facilities.

"Pagoulatos BROS" machine shop, especially Mr. Sotiris Pagoulatos, for the manufacturing of

the gears and the splines in the form of a sponsorship. The company "SKLERO SA" and

especially Mr. Euripidis Kechagias, for the sponsorship of the necessary case hardening steels,

and their heat treatment services, as well as for his advice on materials selection and heat

treatment. The company "CNC Solutions" and especially Mr. Panos Gounas, for the sponsorship

of the manufacturing of the gearbox end caps, as well as for the training provided to us, in the

form of seminars, on CNC machining programming and operation. Finally, I would like to thank

the UoP Racing team, the team leader, Mr. Harry Bikas, and all the members of the team who

trusted me to complete this project. I wish the best for the future of the team and I hope that this

diploma thesis will help the future members of UoP racing team and anyone who is interested in

the development of drivetrain systems for electrified vehicles.



Georgios Siangas


1. INTRODUCTION: CONCEPT DESIGN AND DESIGN GOALS

1.1 DESIGN GOALS

The beginning of any design process starts with a clear definition of targets or otherwise

stated “design goals”. During the design phase of the powertrain unit of UoP5e, these goals were

stated, in conjunction with the rest of the sub-teams of “UoP Racing”, at the conceptual design

period. These goals were divided into two distinct categories, firstly the design goals that could

be easily quantified as a marginal improvement over a baseline design, which was considered the

previously developed racecar of the team, and secondly some general goals that cannot be easily

quantified , but they set the design “philosophy” of each component designed and manufactured

for the powertrain unit, both the categories target towards a faster but also reliable racecar, which

is the essence of motorsport engineering. In the conclusion of the diploma thesis the goals are

reevaluated, and the success or failure of the whole process is revealed.

Quantifiable Targets in comparison with the baseline design:

Over 40% Overall weight reduction of the powertrain unit.

Over 20% Increase in the longitudinal acceleration of the racecar.

Over 20 % Reduction of the occupied space.

Non-Quantifiable Targets:



Georgios Siangas


Safety - Reliability

Cost - Effectiveness

Simplicity – Ease of Manufacturing

The next step is the reasoning of these arguments. Again, the explanation is more

intuitive for the quantifiable goals, but when it comes to the non-quantifiable goals the reasoning

becomes more fluent and is vastly depended on the team‟s and engineer‟s philosophy and

experience on mechanical design. The first two goals, overall weight of the powertrain unit

and longitudinal acceleration are co-depended and can be explained, in the conceptual design

phase, by an oversimplified approach, that of considering the racecar as a point mass with

infinite traction between the wheels and the track, which is Newton‟s Second Law of Motion

Dynamics.

Where is the weight of the racecar minus the weight of the powertrain unit. It is

apparent that a reduction in the weight of the powertrain unit will result in an increase in the

longitudinal acceleration, while the ΣF symbol represents the sum of all the forces that act on the

vehicle, the force that is produced by the powertrain unit is the force of propulsion, thus

intuitively increasing the propulsion force at any moment will result in an increase in the

longitudinal acceleration of the racecar. The next quantifiable target, the reduction of the

occupied space is targeting to the reduction of the polar moment of inertia and the center of

gravity‟s height of the racecar, by locating the powertrain‟s center of gravity lower and closer to

the racecar center of gravity or practically speaking the driver‟s seat. Again, this can be



Georgios Siangas


explained by utilizing the Newton‟s Second Law of Motion Dynamics expressed for a circular

motion.

Where represents the racecar‟s yaw acceleration, and represents the sum of all

the moments acting on the racecar‟s center of gravity as a result of turning forces experienced by

the tires. It is apparent that lowering the polar moment of inertia of the racecar will result in an

increase in the yaw acceleration of the racecar, thus resulting in a faster change of the heading of

the racecar, or in the motorsport terminology increases the responsiveness of the vehicle. When it

comes to the reduction of center of gravity height, it is counter-intuitive as it leads to fewer

weight transfer to the rear wheels , resulting to a lower traction force between the drive wheels

and the track, but through vehicle dynamics sensitivity analysis performed by the Vehicle

Dynamics sub team indicated that a reduction in the center of gravity would have better

influence on the cornering performance of the vehicle, that outweighs the benefit of increased

traction characteristics in an acceleration situation, the explanation is mainly based on the lateral

weight transfer and it‟s result on the lateral acceleration of the racecar and is not a part of this

diploma thesis, therefore for the purposes of this thesis it is taken for granted. Moving on to the

non-quantifiable targets safety and reliability are two similar notions with the difference that

safety is legally essential in any mechanical design and for this competition is expressed through

the annual published rulebook and is enforced through the technical scrutineering before each

competition by an independent party , whereas reliability depends on the design approach of the

engineering team and separates a dependable product with a questionable product, it is apparent



Georgios Siangas


that any unreliable product, even if it is theoretically better performance wise, will most likely

result in failure, during an overload situation, possibly harming the rest of the racecar or even

worse harming the driver and the crew that operates the vehicle, this is solved through rigorous

analysis of each component. Cost effectiveness is of paramount importance in any project, as all

projects have certain economic budget limits, the real world engineering dictates to invest on the

aspects that have the most influence of the racecar‟s performance rather than the aspects that

most likely won‟t have a measurable impact on it. Finally simplicity and ease of manufacturing

is the product of the above non quantifiable targets, as a simple mechanical product with purpose

the ease of manufacturing leads not only to a more economically feasible product, but also a

reliable one, as the methods of design, analysis and manufacturing of simple components are

proven through years of the mechanical engineering science rather than supporting your designs

with new and non-standardized analysis techniques, this is why in this diploma thesis, whenever

the geometry allows it, a hand mechanical calculation based on first principle mechanical

engineering criteria is preferred over Computer Aided Engineering software tools and complex

part geometries.

1.2 BASELINE DESIGN

As it is mentioned above, the design of the previously developed racecar UoP4e is

considered as the baseline design. UoP4e powertrain unit consists of a high – torque output 3-

phase axial flux permanent magnet electric motor YASA 750 controlled by a SEVCON



Georgios Siangas


inverter/controller, with a directly mounted limited slip differential that transfer the power to the

drive wheels through a system of drive shafts. The exact characteristics of this powertrain design

are presented in the table below.

UoP4e Powertrain Characteristics

Power Unit: Electric Motor

Power Unit Type: 3-phase Axial Flux Permanent Magnet

Power Unit Commercial Name: YASA 750

Controller/Inverter: SEVCON

Accumulator DC Voltage: 400 Volt

Differential: Drexler Clutchpack LSD

Transmission: Direct Drive

Driveshafts System: Tubular Steel Shafts/Aluminum CV

Housings

CV Joints: Tripod Joint

Maximum Power Output: 80 kW (Electronic Restriction)

Maximum Torque Output: 750 Nm

Maximum Motor Speed: 2000 RPM Table 1: UoP4e Powertrain Characteristics (Baseline Design).

Weight Table of UoP4e Powertrain

Electric Motor YASA 750: 25.3 kg

HV Cables and HV Connectors: 1.3 kg

SEVCON Inverter, Inverter Mounts: 9.628 kg

Drive shafts Assembly: 5.358 kg

Differential Assembly: 3.069 kg

Impact Safety Structure: 5.052 kg

Total Weight Estimation: 49.7 kg Table 2: Weight Table of UoP4e Powertrain.

A maximum longitudinal acceleration to vehicle speed was extrapolated through logged

data for the UoP4e Racecar.



Georgios Siangas


Figure 1: Maximum Longitudinal Acceleration to Vehicle Speed UoP4e.

The baseline design has been proven through various competitions, amongst an overall

winning one, as simple and very reliable solution. The problem with the baseline design is two

folded, firstly the motor speed range is not matched with the actual vehicle speed range, resulting

in a not optimal torque output range at the drive wheels leading to a reduced longitudinal

acceleration of the vehicle, and secondly it is heavier compared to the competition racecars.

0 20 40 60 80 100 120 140 160

0

2

4

6

8

10

12

Vehicle Speed [km/h]

Acc

eler

atio

n [

m/s

^2]

Maximum longitudinal acceleration to vehicle speed UoP4e



Georgios Siangas


Figure 2: CAD Design of UoP4e Powertrain (Baseline Design).

1.3 POWERTRAIN TYPE COMPARISON

The powertrain type of any car has a great impact on its performance characteristics,

since it is quite difficult to perform a sensitivity analysis on every possible combination of

powertrain type, mainly because of the lack of logged data, the main criterion to decide upon it,

was the average power output to average racecar weight ratio of the racecars competing on the

competition FSUK. The typical values are presented in the table below.



Georgios Siangas


Powertrain Type Weight [kg] Power [HP] Power/Weight

Ratio

Single Cylinder NA

Engine:

160 60 0.38

Single Cylinder TC

Engine:

165 70 0.42

V-Twin TC Engine: 175 75 0.43

Four Cylinder NA

Engine:

190 85 0.45

AWD Electric Motors: 180 80 0.44

RWD Electric Motor: 210 107 0.51 Table 3: Demographic powertrain setup comparison.

Through this demographic comparison, along with technical experience gained by

developing a fully electric racecar by the previous team, lead to the decision of proceeding with

the concept of a rear wheel drive, with an electric motor as a power unit, racecar.

1.4 POWERTRAIN LAYOUT SELECTION

There are two distinctive layout choices for a rear wheel drive electric racecar. A high

torque output electric motor directly driving the drive wheels (HTEM) or a high revving motor

with a reduction unit (HREM). The three main advantages of using a high-revving electric motor

in conjunction with a reduction unit are, firstly that the torque output range can be shifted to

match the autocross and acceleration track velocities, thus increasing the longitudinal

acceleration of the racecar, due to the increased propulsion force applied at the drive wheels,

while also increasing the maximum torque output figure to the drive wheels. Secondly the torque

output capacity of a motor is directly associated with its size, specifically its diameter, a high

torque output electric motor setup results in heavier powertrain unit, with increased rotational



Georgios Siangas


mass moment of inertia. Due to the mismatch of typical vehicle speeds and the engine speed

range of a direct drive electric motor, the motor is operating for a longer period of time, in areas

of the motor map that are less efficient, compared to an electric motor with a reduction drive

engineered to perform in a certain vehicle speed range. This leads to excessive heat losses of the

motor, leading to the design of a larger cooling system to dissipate the heat from the motor.

Having explained the advantages of a high – revving electric motor coupled with a reduction

drive, the development of a reduction drive adds complexity to the design and manufacturing

process. A table below summarizes the advantages and disadvantages of the two options.

Comparison between HTEM and HREM

Design target HTEM HREM Reason

Weight

Reduction:

Disadvantage Advantage Smaller EM,

Less Cooling

Requirements

Acceleration: Disadvantage Advantage Increased

Propulsion Force

Occupied Space: Disadvantage Advantage Smaller EM

Reliability: Advantage Disadvantage Fewer Components

Cost

Effectiveness:

Disadvantage Advantage Higher Cost HTEM

Simplicity: Advantage Disadvantage Less development Table 4: Comparison between direct drive HTEM and HREM.

The performance advantages of choosing a high revving electric motor as opposed to

using a high torque output electric motor were investigated, through a commercially available

open source point mass vehicle dynamic simulations program Optimum Lap. This software is

great for selecting between different concepts of design, with the need of basic data. The

disadvantage relies on accuracy of the calculation mainly because it doesn‟t take into account

several factors that actively affect the outcome of the simulation, such as dynamic load transfer



Georgios Siangas


or mass moment of inertia of the powertrain unit. In the design process, a self – developed

software tool is developed to predict accurately how certain aspects of the powertrain affect its

acceleration.

Entry Data for HTEM and HREM [Optimum Lap]

Entry Data HTEM HREM

Overall Weight [Incl.

Driver]:

300 kg 280 kg

Drag Coefficient: 0.7 0.7

Downforce Coefficient: 3.63 3.63

Frontal Area: 1.024 1.024

Air Density: 1.25 1.25

Traction: Unlimited Unlimited

Tire Radius: 0.2286 m 0.2286 m

Rolling Resistance: 0.015 0.015

Drive Efficiency: 70 % 80 %

Final Drive Ratio: 1 4 Table 5: Entry data for HTEM and HREM [Optimum Lap].

The entry data reflect the design targets of the team regarding the development of the

racecar. The only change between the entry data of the two concepts are the advantages

described previously regarding weight, efficiency and concept of propulsion.

Weight

Assuming the previous racecar powertrain as a baseline design, it weighs roughly 50 kg,

and the expected weight reduction target of the unit approaches 40%, hence the difference of 20

kg in the overall weight entry.

Drive Efficiency

The drive efficiency of the unit is expected to be higher in the HREM reduction drive

unit, and this is represented in a conservative 10% increase in the drive efficiency.



Georgios Siangas


Power – Engine Speed Diagrams

The power – engine speed diagram for its concept was entered through the typical

advertised engine maps for each electric motor.

Figure 3: Power / Torque to Engine Speed diagram for the HREM concept.

Figure 4: Power / Torque to Engine Speed diagram for the HTEM concept.

To calculate an initial final drive ratio, the build-in batch run simulation of the software

was used. The final drive ratio is set as a sweep parameter, in a simulated track of acceleration

from standstill to 75 m. The concept design FDR is in the 3.8-4.2 range, according to the



Georgios Siangas


software. The final FDR will be calculated, through a self-developed racecar acceleration model

based on experimental data later in this diploma thesis.

Figure 5: Batch run simulation for the selection of initial FDR for the HREM concept.

Finally, by simulating the two proposed concepts in an acceleration event, the results are

presented as motion curve plots.



Georgios Siangas


Figure 6: Speed to distance diagram HREM vs. HTEM.

Figure 7: Distance to time diagram HREM vs. HTEM.

Elapsed time for acceleration 0-75 m

Concept: HREM HTEM

Elapsed Time: 3.85 s 4.43 s Table 6: Time lap comparison between HREM and HTEM.



Georgios Siangas


The slope of each curve in the elapsed distance vs. elapsed time plot represents the

momentary speed of the vehicle.

Therefore, the steeper the slope of the curve means higher momentary velocities of the

vehicle, resulting in smaller lap times. This is reflected in the vehicle speed vs. elapsed distance

plot (Figure 5), where the HREM concept has higher momentary velocities until it reaches a top

speed, at an elapsed distance of 42.5 m, and it maintains this speed until the finish line. The

HTEM concept constantly increases its speed, until it reaches a higher top speed at the finish

line, but at a slower rate than the other concept. This clearly depicts the performance gains from

following the HREM concept. The HREM concept was chosen as powertrain unit of UoP5e, due

to the significant performance gains.



Georgios Siangas


2. CHAPTER 1: POWER UNIT SELECTION AND DYNAMOMETER

TESTING

2.1 POWER UNIT

The decision of using a high revving electric motor, lead to reviewing the commercially

available motors based on three main criteria power to weight ratio, available budget and lead

time for the order. EMRAX 228 CC HV was chosen, an engine used for amateur aviation

purposes, as a prime mover for propellers.

Figure 8: EMRAX 228 CC HV Drawing.



Georgios Siangas


EMRAX 228 CC HV Electric Motor Technical Specifications (According to manufacturer)

Cooling Method: CC: Combined Cooling

Ingress Protection: IP 21

Weight: 12.3 kg

Maximum DC Battery Voltage: 670 Vdc

Peak Power: 100 kW (Restricted to 80 kW)

Maximum Rotational Speed: 5500 RPM

Maximum Motor Current: 240 Arms

Torque per Motor Current: 1.1 Nm/Arms

Maximum Windings Temperature: 120 cC

Internal Phase Resistance: 18 mOhm

Input Phase Wire Cross Section: 10.2 mm2

Wire connection: Star

Motor signal: Sine wave / Resolver sensor type

Specific load speed: 8 – 9.8 RPM/Vdc

Temperature sensor: Thermistor (kty 81/210) Silicon type

Pole Pairs: 10

Rotor Inertia: 421 kg*cm2

Power to Weight Ratio: 6.5 kW/kg



Georgios Siangas


Table 7: EMRAX 228 CC HV Technical Specifications.

2.2 DYNAMOMETER TESTING

The development of a semi-automatic eddy-current brake dynamometer setup was

decided in the second year of the development of UoP5e racecar for the physical testing of the

powertrain unit outside of the racecar. The testing allowed quick changes and experimenting on

the power unit without the need of modifying the racecar‟s element each time, and actively

contributed in the optimization of the unit. The performance tests were mainly focused around

two elements.

Dynamometer testing elements

Accurate power/torque vs. engine speed plots.

Selection of optimal DC battery voltage input.



Georgios Siangas


Figure 9: Eddy current brake dynamometer setup.

Dynamometer Testing Specifications

Electric Motor: EMRAX 228 HV CC

Controller/Inverter: Unitek BAMOCAR D3

DC Battery Voltage: 400-600 Volt

Brake Type: Eddy current brake

Control Unit: Dynastar

Table 8: Dynamometer testing specifications.

The setup consisted of an eddy current brake, with a control unit developed by Dynastar,

and the powertrain unit to be tested. The components are mounted in a self-developed rigid steel

welded frame that was anchored to the ground through hinge joints. The eddy current brake is

mounted to the steel frame by using two industrial type ball bearing Plummer type units. The



Georgios Siangas


powertrain spins the rotor through a commercial driveshaft system to counterbalance the possible

misalignment between the eddy current brake and the powertrain unit. The engine speed is

logged through a four-tooth optical speed sensor mounted in the main shaft, while the stator is

restrained by a load cell unit as shown in the drawing below.



Georgios Siangas


Figure 10: Dynamometer load cell sensor mounting.

Figure 11: Eddy-current brake.

The working function of the semi-automatic dynamometer is the following. The

powertrain spins the rotor close its engine speed limitations, while the speed is monitored

through the four - tooth optical shaft speed sensor. As the operator starts to gently applying the

brake, the powertrain starts to lose engine speed, while increasing its applied torque on the main



Georgios Siangas


shaft. The rotation of the eddy current brake stator is only restrained through a load cell unit. The

increasing torque applied at the main shaft, is logged at the load cell unit as force units. Through

the static equilibrium at the eddy current brake a linear relation between the force applied at the

load cell and the torque applied at the main shaft is expressed.

Then by constantly logging torque [Nm] – engine speed [RPM], a torque to speed

diagram is created for a certain torque demand at the accelerator pedal, also as a derivative curve

the power to speed diagram is created, as power is the product of torque times rotational speed.

An example of a logged torque/power to engine speed map is presented below.

Figure 12: Example of logged Torque/Power map from the dynamometer.

The first main variable of the test is the battery dc voltage input. Various voltage setups

were tested in the range of 400 Volts to a maximum of 600 Volts as permitted by the FSAE

Rulebook.

The results of the testing are presented below.



Georgios Siangas


Battery Voltage Selection

Battery Voltage: 400 V 500 V 550 V 600 V

Average Efficiency: 76 % 81 % 82 % 82 %

Battery Cells Weight: 41.208 kg 40.32 kg 41.8 kg 42.3 kg

Maximum Power Output: 65.4 kW 90.5 kW 95.3 kW 99.4 kW

Battery Cells Space: 0.01763 m3

0.01737 m3

0.01833 m3

0.01877 m3

Table 9: Battery voltage selection.

Figure 13: Battery DC Voltage selection.

In the diagram above (Figure 12) the only strong correlation between an input variable

and an output value is between the battery DC voltage [Volts] and the maximum power output

[kW]. The maximum current drawn from the batteries is fixed at a safe value to prevent any

damage due to unsafe discharge of LiPo battery cells, so increasing the DC Voltage, by Joules

Law, results in increased power drawn from the battery pack.



Georgios Siangas


The power drawn from the battery pack is also restricted by the rules to 80 kW. The

lowest voltage that could produce maximum power output over 85 kW was chosen. The safety

implications of high voltage systems, and the battery cells arrangement dictates that the final

input DC Voltage is 504 Volt. The load depended maximum speed is calculated below.

( )

With dynamometer testing at the final battery DC Voltage the torque/power map at full

throttle is extrapolated. The values represented below are corresponding to the actual values of

mechanical power as all the efficiency power losses are incorporated in this diagram.



Georgios Siangas


Figure 14: Power map of EMRAX 228 HV LC at 504 Volt.

Figure 15: Torque map of EMRAX 228 HV LC at 504 Volt.

0

20000

40000

60000

80000

100000

0 1000 2000 3000 4000 5000 6000

Power (Watt)

Engine Speed (RPM)

Power map EMRAX 228 HV LC at 504 Volt

0

50

100

150

200

250

0 1000 2000 3000 4000 5000 6000

Torque(Nm)

Engine Speed (RPM)

Torque Map of EMRAX 228 HV LC at 504 Volt



Georgios Siangas


2.3 LOAD CASES

With the electric motor selected it is possible to estimate the load cases that all the

components of the drivetrain will be subjected to. Every component at the powertrain is

subjected to the maximum theoretical torque figure that the electric motor can produce.

As for the dynamic structural analysis a half endurance run from a previous racecar is

analyzed regarding average engine speed, average engine power and average speed of the vehicle

is extrapolated from the logged data, as shown below.

Figure 16: Logged endurance run from previous racecar.

The logged data represent half an endurance run.

Dynamic Load Case

Average motor speed navg: 2648 RPM

Average motor power Pavg: 24000 Watt

Average motor torque Tavg: avg ( avg) / navg = 86.5Nm



Georgios Siangas


Average vehicle speed: 63.6 km/h

Table 10: Endurance load case.

Every mechanical component of the drivetrain is subjected to fluctuating loads as shown

in the logged data, so it is critical to perform a dynamic structural analysis, a static analysis at the

maximum theoretical torque figure, and a critical speed calculation for every rotor in the system.

The gears are the only component sized according to DIN 3990 Part 41 Standard, specialized for

vehicle transmissions.

2.4 MOTOR SHAFT

The motor shaft is the component that connects the electric motor with the transmission.

The final design is a tubular steel shaft with a flanged end that connects to the motor and a

splined end that connects to the transmission.



Georgios Siangas


Figure 17: Motor shaft design.

Motor shaft material properties

Material: AISI 4340 (DIN 1.6582) (+QT) [Nitrided]

Young‟s Modulus E: 200 GPa

Poisson ratio v: 0.3

Tensile strength Su: 1200 MPa

0.2% Proof strength Sy: 1000 MPa

Fatigue strength Se: 290 MPa

Modulus of rigidity G: 80 GPa

Surface Hardness: 58-60 HRC

Core Hardness: 30-35 HRC



Georgios Siangas


Table 11: Motor shaft material properties.

Stress concentration factor Kt, for stepped shaft loaded in torsion.

Figure 18: Stress concentration factor Kt.

Cross section properties

Outer Diameter D: 24 mm

Inner Diameter d: 16 mm

Radius/Chamfer r: 5x450

D/d coefficient: 2.5

r/d coefficient: 0.18

Stress concentration factor Kt: 1.35

Table 12: Cross section properties.

The critical point of the shaft is located at connection of the main shaft with the motor

flange. The section A‟A below is showing the critical point of the shaft.



Georgios Siangas


Figure 19: Section A‟A motor shaft.

Section A‟A stress –strain calculation

Polar moment of inertia: ( ) 26138 mm4

Torsional stress: ( ) (

)

148.5 MPa

Angle of twist: ( ) ( ) 0.329 0

Table 13: Motor shaft – Section A‟A stress –strain calculation.

Static analysis results

Von Mises equivalent stress: =√ 256.9 MPa

Tresca equivalent stress: =√ 297 MPa

0.2% Proof strength: Material Property 1000 MPa



Georgios Siangas


Safety factor Von Mises:

3.9

Safety factor Tresca:

3.3

Table 14: Motor shaft – Static analysis results.

Dynamic structural analysis loads

Mean applied torque :

Applied torque range

Table 15: Dynamic structural analysis loads.

The motor shaft speed is 2648 RPM and the average vehicle speed is 63.6 km/h. The load

cycles are calculated to the 106

area and the motor shaft is not an expendable part, the motor

shaft is designed for infinite life.

Dynamic stress calculation

Torsional stress τm: ( ) (

)

53.6 MPa

Torsional stress τr: ( ) ( ) 53.6 MPa

Table 16: Motor shaft- Dynamic stresses calculation.

Soderberg equation for dynamic torsional loads:

=√ (

)

, where α = 3 for Von Mises theory, and α = 4 for Tresca theory.



Georgios Siangas


Dynamic analysis results

Von Mises equivalent dynamic stress: 413.2 MPa

Tresca equivalent dynamic stress: 477 MPa

0.2% Proof strength: 1000 MPa

Safety factor Von Mises: 2.2

Safety Factor Tresca: 2.1

Table 17: Motor shaft – Dynamic analysis results.

An involute spline is used to transmit the power from the electric motor to the transmission.

Involute spline characteristics, according to DIN 5480

Module m: 1.25

External diameter D: 24 mm

Teeth z: 18

Pressure Angle a: 30

Effective Length Le: 35 mm

Maximum Applied Torque: 240 Nm

Application Factor Ks: 2

Tooth Thickness t: 1.9625 mm

Pitch Diameter: 22.5 mm

Tooth Height h: 1.125 mm

Table 18: Motor shaft- Involute spline characteristics.



Georgios Siangas


Motor shaft spline analysis results

Maximum shear stress: ( )

Maximum compressive stress: ( )

Equivalent stress: = √ 150 MPa

0.2% Proof strength Sy: Material Property 1000 MPa

Safety Factor Tresca:

6.67

Table 19: Motor shaft - Spline stress analysis.



Georgios Siangas


2.5 ELECTRIC MOTOR MOUNTING TO CHASSIS

An aluminum 12 mm 7075-T6 milled plate is developed to mount the electric motor onto

the chassis.

Figure 20: Electric motor mount design.

The electric motor mount design incorporates flange for the motor mounting, cut-out hole

for the resolver sensor and its wiring, cut-out holes for the three phase cables input and milled

sockets for the coolant fluid input and output. A finite element model is constructed, to

investigate the structural integrity of the motor mount.



Georgios Siangas


Figure 21: Electric motor mount – FEA stress results.

Figure 22: Electric motor mount – FEA displacement results.



Georgios Siangas


Electric motor mount FEA model results.

Equivalent maximum Von Mises stress: 46.7 MPa

Equivalent mean Von Mises stress: 16.8 MPa

Maximum displacement: 0.142 mm

Table 20: Electric motor mount FEA model results.

The maximum displacement is in an acceptable range, as the motor will be also mounted

in the transmission through the motor shaft. The static safety factor under full load is calculated.

Factors of fatigue life

Factor: Reason: Value:

Yield Strength Sy: Aluminum 7075-T6 503 MPa

Laboratory fatigue strength Sn: Aluminum 7075-T6 156 MPa

Surface factor Cf : Machined aluminum surface 0.9

Reliability factor CR: 90% Reliability 0.897

Size factor CS: Plane-axial stress 1

Welding factor Cw: No welding 1

Dynamic stress concentration

factor Kf:

Estimate 2

Table 21: Electric motor mount - Factors of fatigue life.



Georgios Siangas


Modified Fatigue Strength Se:

Soderberg equivalent static stress:

√(

)

The dynamic safety factor is.

2.6 ELECTRIC MOTOR PROTECTIVE SHIELD AND ASSEMBLY

The electric motor is housed inside the chassis, so according to the rulebook, there is no

need to implement an impact safety structure. The FSAE rulebook states that a 1 mm thick

aluminum protective shield must be implemented in the design to protect the electric motor from

various environmental hazards. The design and implementation of the electric motor protective

shield is presented below.



Georgios Siangas


Figure 23: Electric motor protective casing design.

Having concluded with the electric motor choice and mounting configurations, an

assembly design is presented in order to visualize the final product.

Figure 24: Electric motor assembly design.



Georgios Siangas


3. CHAPTER 2: FINAL DRIVE RATIO SELECTION

3.1 POINT MASS SIMULATION PROGRAM DEVELOPMENT

The reduction unit‟s final drive ratio selection is based upon a self-developed

acceleration simulating model that considers the available tractive forces, the aerodynamic forces

and the inertial forces of the power unit. The simulation is coded in Matlab, to allow the

experimenting in the characteristics of the racecar, in a software environment, with the purpose

of predicting the performance gains or losses of a change in the system. The simplification of the

simulation is based on two assumptions. Firstly it is assumed that the coefficient of friction

between the tire and the tarmac is stable.

To estimate the minimum coefficient of friction for the simulation, data from the previous

racecar are used. UoP4e achieved a longitudinal acceleration of 0.95g, by using the same tires as

UoP5e. It is safe to get an estimate of the coefficient of friction between the tire and the tarmac,

as UoP4e was traction limited, meaning that the actual coefficient of friction is expected to be

higher than the simulated one. The values used to extrapolate the coefficient of friction from the

previous racecar are presented below.



Georgios Siangas


UoP4e characteristics for COF extrapolation

Maximum longitudinal acceleration ax: 0.95g

Weight m (including 68kg driver): 303 kg

Weight distribution rear WD: 55%

Wheelbase wb: 1600 mm

Center of gravity height hcog: 300 mm

Table 22: UoP4e characteristics - COF extrapolation.

The trust force needed to accelerate the vehicle at a rate of 0.95g is calculated.

The normal force acting upon the rear tires as the vehicle starts from a standstill is

calculated.

The ratio of the thrust force and the normal force is the coefficient of friction between the

tire and the tarmac.



Georgios Siangas


The second assumption made in the simulation is that the acceleration of the vehicle

remains stable between the step points of the calculation. The average value of the two calculated

acceleration values at the step points is used. This represents the type of the numerical method

used to calculate the integral of the vehicle speed to time [v(t)] function.

UoP5e Characteristics

Tire radius rt: 0.2286 m

Aerodynamic drag coefficient cd: 0.7

Aerodynamic downforce coefficient cl: 3.63

Aerodynamic force distribution rear AD: 40%

Frontal area of the racecar Af: 1.024 m2

Air density ρ: 1.225 kg/m3

Vehicle weight mc: 210 kg

Driver weight md: 70 kg

Rolling resistance μr: 0.02

Weight distribution rear WD: 60 %

Wheelbase wb: 1.6 m

Center of Gravity Height h: 0.25 m

Drivetrain efficiency: 100%

Motor Inertia: 0.0421 kgm2

Tire-Rim-Axle Shafts Inertia: 0.2 kgm2



Georgios Siangas


Table 23: UoP5e characteristics.

3.2 VEHICLE VELOCITY

To calculate the vehicle velocity to engine speed, the engine speed n [RPM] is converted

to engine rotational speed ω [rad/s].

Since the wheel is coupled to the engine through a reduction gear unit , the wheel „s

rotational speed is equal to the engine‟s rotational speed divided by the final drive ratio, to

simulate the direct drive option the final drive ratio is set to 1.

[

]

Assuming zero tire slip, the linear velocity of the tire contact patch is equal to the

velocity of the vehicle. The linear velocity of the tire contact patch is equal to the rotational

speed of the wheel times the tire radius.

*

+

Substituting these equations and multiplying by 3.6 to convert [m/s] to [km/h], the

resulting expression calculates the vehicle velocity for a given engine speed n [RPM] .

[

]



Georgios Siangas


Figure 25: Vehicle speed to engine speed diagram.

3.3 AERODYNAMIC FORCE CALCULATION

The aerodynamic force acting upon the racecar, as it accelerates, has two components.

The first component acts along the x-axis slowing down the vehicle and is referred to as the drag

force. The second component acts along the z -axis and is divided to two categories according to

its direction. If the direction is upwards, the second component of the aerodynamic force is

referred to as the lift force, else if the direction is downwards is referred to as the downforce. The

optimal design of a racecar is having a combination of low drag force and high downforce, as the

downforce increases the vertical load applied to the tires, thus increasing the traction provided by

the tire, without adding any extra inertial weight to the racecar. The aerodynamic load is

proportional to the vehicle speed squared and is characterized by two coefficients, the drag

coefficient and the downforce coefficient. These coefficients are provided from the



Georgios Siangas


aerodynamics sub-team of UoP Racing, after multiple iterations of Computational Fluid

Dynamics analysis of the racecar 3D model. The final coefficients are provided in the table

below.

Coefficients of aerodynamic load

Drag Coefficient cd: 0.7

Downforce Coefficient cl: 3.63

Table 24: Coefficients of aerodynamic load.

The aerodynamic load is equal to the air density ρ times the aerodynamic factor c times

the frontal area of the vehicle Af times the vehicle velocity squared divided by 2.

The aerodynamic factor c is substituted for the drag or the downforce coefficient.



Georgios Siangas


Figure 26: Downforce to vehicle speed diagram.

Figure 27: Drag force to vehicle speed diagram.



Georgios Siangas


3.4 PROPULSION AND INERTIAL FORCES CALCULATION

In the simplified point mass simulation, it is assumed that the motor torque is statically

applied throughout the driveline chain and it is reduced through the driveline efficiency factor nd.

Τhe propulsion force applied to the drive wheels of the simplified model is expressed below.

This approximation is fine for a conceptual design phase of the vehicle development, but

in order to simulate between different types of engines, transmissions and various driveline

components it is imperative to take into account the rotational mass inertia of the rotating

components and the aerodynamic drag force. To estimate the inertial losses in the driveline, the

Newton‟s second law is used in polar form is expressed for each shaft.

Newton‟s second law expressed for the transmission shafts

1st (Input) Shaft:

2nd

(Counter) Shaft: ( )

3rd

(Output) Shaft: ( )

Table 25: Newton‟s second law expressed for the transmission shafts.

Combining the equations of table 26, the expression of the output torque is the following.

The propulsion force is expressed, and the driveline efficiency factor is added.



Georgios Siangas


The angular acceleration of each shaft is expressed in terms of the vehicle‟s longitudinal

acceleration .

Angular acceleration of each shaft

1st (Input) Shaft:

2nd

(Counter) Shaft:

3rd

(Output) Shaft:

Table 26: Angular acceleration of each shaft.

The expression of the propulsion force, aerodynamic and inertial loads included.

( (

) (

) (

) )

Figure 28: Inertial losses.



Georgios Siangas


3.5 AVAILABLE TRACTION AND MOTION CALCULATIONS.

The available traction of the vehicle X is expressed through the following equation.

(

)

(

)

Figure 29: Propulsion- Traction Forces to vehicle speed [km/h].

The calculations on figure [28], were based on the torque map retrieved from the

dynamometer testing described in CHAPTER 1. In the calculation the lowest value (Fuseful)

between propulsion force and available traction is selected to proceed with the motion analysis.

The first calculation is the acceleration at the calculation points.

Then the calculation continues with the average acceleration calculation between the step

points.

The time elapsed between step points is calculated.



Georgios Siangas


The distance elapsed between step points is calculated

( )

The total time of the acceleration run is calculated.

(

)

Through experimenting with the acceleration model, it was decided that a final drive ratio

in the range of 3.6 to 3.8 for UoP5e, yielding a theoretical acceleration run at a lap time of 4.1 to

4.2 sec. The final lap time simulation code is presented in the next two pages.

%Acceleration Model%

clear; clc;

%Input Vehicle Variables%

fdr = 3.625; %Final Drive Ratio% N = 0.9; %Drivetrain Efficiency% rt = 0.2286; %Tire Radius [m]% cd = 0.7; %Aerodynamic Drag Coefficient% cl = 3.63; %Aerodynamic Downforce Coefficient% AD = 0.4; %Aerodynamic Load Distribution Rear% Af = 1.024; %Frontal Area [m2]% d = 1.225; %Air density [kg/m3]% mc = 210; %Vehicle Weight [kg]% md = 70; %Driver's Weight [kg]% RR = 0.02; %Rolling Resistance Coefficient% WD = 0.6; %Weight Distribution Rear% wb = 1.6; %Wheelbase [m]% hcog = 0.25; %Center of Gravity Height [m]% COF = 1.5; % Tire Coefficient of Friction% Accel = 75; %Acceleration Distance% Imotor = 0.0421; %Motor Inertia kg*m2%



Georgios Siangas


Idrive = 0.2; %Driveline Inertia kg*m2%

%Calculated Vehicle Variables% me_motor = Imotor*((fdr/rt)^2); %Equivalent inertia mass motor [kg]% me_drive = Idrive*((1/rt)^2); %Equivalent inertia mass driveline [kg]% mt = mc + md ; %Total weight [kg]% K1 = (WD - (RR * hcog / wb))/(1-(COF * hcog / wb)); %Weight Transfer

Coefficient K1% K2 = AD/(1 - COF * hcog / wb) ; %Weight Transfer Coefficient K2% FRR = mt * RR * 9.81 ; %Rolling Resistance Force%

%Engine Map%

max_rpm = 4800; %Engine Maximum RPM% rpm_steps = 100; %RPM Steps% steps = max_rpm / rpm_steps; %Steps of calculation%

c_m = zeros (steps,18);

Torque =

[220,217,214,211,208,205,202,199,196,193,190,189,188,187,186,185,184,183,182,

181,180,179,178,177,176,175,175,175,175,175,175,175,175,175,175,175,175,175,1

75,175,175,175,175,175,174,91,87,84,84];

for i = 1:steps+1 c_m(i,1) = (i-1)*rpm_steps; %Engine Speed Table [RPM]% c_m(i,2) = Torque(i); %Engine Torque Table [Nm]% c_m(i,3) = (c_m(i,1)/9.55)*c_m(i,2); %Engine Power Table [Watt]% c_m(i,4) = (c_m(i,1)/9.55)*rt/fdr ; %Vehicle Speed [m/s]% c_m(i,5) = 0.5*d*cd*Af*((c_m(i,4))^2); %Aerodynamic Drag Force [N]% c_m(i,6) = 0.5*d*cl*Af*((c_m(i,4))^2); %Aerodynamic Downforce Force [N]% c_m(i,7) = COF*9.81*mt*K1 +COF*c_m(i,6)*K2; %Available Traction [N]%

%Propulsion and Inertia Forces calculation% if i==1 c_m(i,8) = c_m(i,2)*fdr*N/rt - c_m(i,5);%Thrust [N]% c_m(i,18) = 0;%Inertia Forces% else c_m(i,8) = c_m(i,2)*fdr*N/rt - c_m(i,5) - (Imotor*((fdr/rt)^2) +

Idrive*((1/rt)^2))*c_m(i-1,10); %Thrust [N]% c_m(i,18) = (Imotor*((fdr/rt)^2) + Idrive*((1/rt)^2))*c_m(i-1,10);

%Inertia Forces% end

%Useful Thrust% if (c_m(i,8)>c_m(i,7)) c_m(i,9) = c_m(i,7); %Useful Thrust [N]% else c_m(i,9) = c_m(i,8); %Useful Thrust [N]% end



Georgios Siangas


c_m(i,10) = c_m(i,9) / mt; %Acceleration [m/sec2]% c_m(i,11) = c_m(i,9)*c_m(i,4); % Wheel Power [Watt]%

if(i==1) c_m(i,12) = c_m(i,10); %Average Acceleration% c_m(i,13) = 0; %Stepped Time [s]% c_m(i,14) = 0; %Stepped Time Difference [s]% c_m(i,15) = 0; %Stepped Distance[m]% else c_m(i,12) = (c_m(i,10)+c_m(i-1,10))/2; %Average Acceleration% c_m(i,13) = ((c_m(i,4)-c_m(i-1,4))/c_m(i,12)) + c_m(i-1,13); %Stepped

Time [s]% c_m(i,14) = c_m(i,13)- c_m(i-1,13); %Stepped Time Difference [s]% c_m(i,15) = c_m(i-1,4)*c_m(i,14) + 0.5*c_m(i,12)*c_m(i,14)*c_m(i,14)

+ c_m(i-1,15); %Stepped Distance[m]% end

end time = c_m(steps+1,13) + ((Accel-c_m(steps+1,15))/c_m(steps+1,4)); %Elapsed

Time Total[sec]% X= sprintf('Lap Time: %0.3f sec\n',time); disp(X);



Georgios Siangas


4. RECHAPTER 3: REDUCTION UNIT TYPE SELECTION

The main options for a reduction unit of an electric rear wheel drive formula style racecar are

gearbox and chain drive. The design goals set in the introduction of this diploma thesis can be

evaluated in this design decision. The design constraints performance wise are the weight,

occupied space, driveline efficiency and safety wise the behavior of the device under an

overloaded condition.

4.1 CHAIN DRIVE

A chain drive reduction unit is a straightforward design. The components needed for a

chain drive reduction unit can be purchased from the motorcycle spare parts industry. This

design simplicity is the biggest advantage of the chain drive, as the build time for a transmission

unit is significantly minimized. The disadvantages with the chain drive reduction unit are the

occupied space, the rotational mass inertia of the chain and the increased sensitivity to outside

factors, because it is a non-fully enclosed rotating component. A brief examination of the chain

drive reduction unit will be performed.



Georgios Siangas


The final drive ratio is set to i = 3.6, according to the simulation. For smooth operation at

moderate and high speeds it is considered a good practice to use a driving sprocket with at least

17 teeth. Where space limitations are severe, smaller tooth numbers may be used by sacrificing

the life expectancy of the chain.

Service life of chain drive reduction estimation

Average vehicle speed uavg:

Expected distance covered dc: 600 km

Service Life in hours: L=dc/uavg=10 hr

Table 27: Service life of chain drive reduction estimation.

The service life is very low compared to a nominal service life of a chain drive application

(L=15.000 hours). Since it is a racing application, the chain drive will be inspected thoroughly

and lubricated properly before every testing or racing session, the small sprocket is set to have 15

teeth Z1=15 T.

The teeth number of the large sprocket is calculated by multiplying the teeth of the small

sprocket [Z1] with the final drive ratio [i].

The workload correction factor [Ks] is calculated, by choosing the coefficients depending

on the nature of the machine.

Chain load factor K1

Smooth operation: 1 Medium shock loads: 1.25 High shock loads: 1.5



Georgios Siangas


Table 28: Chain load factor K1.

Since it‟s a chain drive for a motorsport vehicle application with sudden load changes, a

load coefficient for high shock loads is chosen K1=1.5.

Lubrication factor K2

Continuous lubrication: 0.8 Interrupted lubrication: 1 Periodical lubrication: 1.5

Table 29: Chain lubrication factor K2.

Since there is no lubrication system, and the lubrication is achieved by spray lubricant

before every testing or racing session, a lubrication coefficient for periodical lubrication is

chosen K2=1.5.

Service factor K3

Less than 8 hrs/day : 1 Less than 16 hrs/day: 1.25 Continuous operation: 1.5

Table 30: Chain service factor K3.

The maximum service hours per day are 2 hours, so a service factor of 8 hours per day or

less is chosen K3=1.

The workload correction factor can be calculated by multiplying the three coefficients.

The design power PD can be calculated by multiplying the peak power of the engine Pe =

80 kW with the workload correction factor Ks=2.25.

To select a roller chain drive for industrial application, the next step is to consult

DIN/ANSI chain selection diagrams and according design power and rpm, make a first selection



Georgios Siangas


of a roller chain. But since it is motorsport application, it is preferable to consult a motorsport

chain manufacturer chart.

Figure 30: DID Chain specifications for O-ring and X-ring chains.

For the first design iteration a 520VO chain is selected, for its O-ring design, which leads to

increased wear resistance, high load capacities, low weight, and readily available.

Geometrical characteristics of DID 520VO chain

Chain Type: Pitch: Roller Diameter: Pin Length: Width:

DID 520VO 15.875 mm 10.16 mm 20.20 mm 7.94 mm

Table 31: Geometrical characteristics of DID 520VO chain.



Georgios Siangas


Chain mechanical properties

Chain Type Weight/100 links m100 Tensile Strength F Seal Type

DID 520 VO 1.5 kg 35.6 kN O-ring

Table 32: Chain mechanical properties.

The pitch action diameter of a sprocket can be calculated using the following formula.

( )

Sprockets Pitch Action Diameters

Pinion sprocket action diameter D1 Pinion sprocket action diameter D2

76.32 mm 273.7 mm

Table 33: Sprockets pitch action diameters.

Chain drive calculations


Maximum engine torque Te: Fact 240 Nm

Peak engine power Pe: Fact 80 kW

Design Power Pd: Pd=Ks x Pe 180 kW

Design engine speed nd: nd = Pe / Te 3183 rpm

Peripheral speed ud: ud= (pi x D1 x n) / 60 12.71 m/s

Peripheral design load Fd: Fd = Pd / ud 14.162 kN

Tensile strength of chain F: Manufacturer 35.6 kN

Safety Factor: N=F / Fd 2.51



Georgios Siangas


Table 34: Chain drive concept calculations.

The center distance can be calculated from setting an arc of contact for the small

sprocket, since reliability is a serious factor, an arc of contact a=1500 is chosen:

The center distance can be calculated from the following equation:

(

)

Through an iterative procedure a center distance of c= 320mm with a=150.770, is chosen.

The number of chain links can be calculated through the following formula:

(

)

Rounding up to the next even number K=78 links. The chain length is equal to the link

number times the pitch.

The chain weight is equal to the specific weight per 100 links multiplied by K/100.

The final center distance can be calculated:

((

) +√ (

) (

) ) = 330.6 mm



Georgios Siangas


Figure 31: Chain drive concept.

4.2 ENCLOSED GEARBOX CONCEPT

There are two options of mounting an electric motor in a rear wheel drive single seat

racecar, perpendicular and across the longitudinal axis of the racecar. In the perpendicular

way of mounting the engine rotation is transferred to the rear wheels through a bevel or

hypoid gear transmission, while in the across way through a spur or helical gear transmission.

The perpendicular way of mounting was dismissed, because of the following reasons. Bevel

and hypoid gears are more difficult to precision manufacture, the rotation of the engine will

result in a roll moment in the chassis which can affect the handling of the racecar and the



Georgios Siangas


reaction forces in a bevel gear couple lead to a heavier casing, shaft and bearing selection.

The across way motor mounting (transaxle gearbox) is leading to the choice between spur

and helical gears.

Spur and helical gears comparison

Advantages Disadvantages

Spur Gears Helical Gears Spur Gears Helical Gears

No axial forces Slightly better load

bearing capabilities

Slightly worse load

bearing capabilities

Axial Forces

Ease of manufacturing Silent operation Noisy operation Difficult manufacturing

Table 35: Spur and helical gears comparison.

In vehicle transmission helical gears are preferred, due to their silent operation and better

load bearing capabilities. In the design of this gearbox spur gear design was chosen, due to the

absence of axial forces transmission from the gear couple. Axial forces in a gearbox lead to

bending loads in the gearbox casing and axial loads to the bearings. Bending loads in the casing

are compensated with the design of a heavier structure and axial loads in the bearings lead to the

choice of thrust bearings that add unnecessary complexity and weight to the design.

The conclusion of a transaxle gearbox of spur gears sets the next design decision, the

arrangement of the gears inside the gearbox. There three possible ways of arrangement the 1-

stage transmission, the 1.5-stage transmission and the n-stage transmission. The 1-stage

transmission is a single gear couple between the electric motor and the drive wheels. The 1.5-

stage transmission is the same arrangement, as the 1-stage, with a reversing gear between the



Georgios Siangas


gears. The n-stage transmission is the use of n gear couplings. The reduction ratio of the 1 and

1.5 –stage is the division of the gear wheel teeth with pinion wheel teeth.

The reduction ratio for an n-stage is the product of the gearing couplings reduction ratios.

The main criteria in the decision of the arrangement of the gears are the minimum

allowable center distance to avoid collision with the electric motor which is over 160 mm and

minimum gear teeth that could be manufactured without undercut (Z=16 T). Through multiple

iterations of preliminary structural analysis, considering weight, efficiency and rotational mass

inertia, the choice of a 2-stage design was made.

Enclosed gearbox characteristics

Gearbox type: Transaxle

Gears type: Spur gears

Arrangement of gears: 2-stage design

First gear couple teeth: 16-29

Second gear couple teeth: 23-46

Module: 3

Reduction Ratio: 3.625

Center Distance: 171 mm



Georgios Siangas


Table 36: Enclosed gearbox characteristics.

Figure 32: Enclosed gearbox concept.

4.3 REDUCTION DRIVE SELECTION CONCLUSION

The comparative analysis between a chain drive concept and an enclosed gearbox drive

concept lead to the following conclusions.



Georgios Siangas


An enclosed drive of rotating parts is always safer and more reliable than an open

drive of rotating parts.

The occupied space of a chain drive is significantly larger, due to the increased

center distance.

The weight of the components of the two concepts is similar, but the weight

added by the increased center distance of the chain drive (e.g. longer chassis, need

of differential mounts, chain tensioner, steel chain scatter shield etc.) is

significantly higher.

Therefore the enclosed gearbox casing was selected.



Georgios Siangas


5. CHAPTER 4: MATERIALS AND MANUFACTURING METHODS

SELECTION

5.1 MATERIALS AND TREATMENTS.

The main criterion in material selection is their immediate availability in the Greek market. The

materials are then selected based on the desired material properties for the optimal function of

each design component. For the drivetrain design the material selection is broken to four main

parts, material selection for the shafts, for the gears, for the gearbox and differential housing and

finally material for the mounting of the powertrain components.

Desired material properties based on components

Shaft Design: High Modulus of Elasticity, Yield strength

Gear Design: Wear resistance, Ductility, Fatigue strength

Gearbox /Diff Casing: Low density, High modulus of elasticity in increased temperatures.

Mounting: Low Density, High Yield strength



Georgios Siangas


Table 37: Desired material properties based on components.

5.2 GEARS MATERIAL SELECTION

A gear pair, during its operation, develops bending stresses at the root of the tooth, while

also develops surface pressure stresses at the flank of the tooth. The material selection for the

given load conditions, according to bibliography, is case hardened steel. Its hardened outer layer

bears the developed surface pressure stresses making the gear wear resistant and its soft core can

withstand shock loading without the development of internal cracks. Its retained ductility after

the heat treatment increases the fatigue strength of the gear. All possible combinations of

materials and heat treatments, that could be delivered by the steel provider of the team, were

evaluated according to the standard ISO 6336-5 over the two previously stated criteria, fatigue

strength and allowable surface pressure in order to select the best combination.

Material Type Material Name Heat-Treatment Fatigue Strength Surface Pressure

Carburizing

Steels

15CrNi6

[DIN 1.5919]

Case carburizing

and tempering

430 MPa 1500 MPa

Alloy Steels 34CrNiMo6

[DIN 1.6582]

Induction

hardening

370 MPa 1180 MPa

34CrNiMo6

[DIN 1.6582]

Nitriding 370 MPa 1000 MPa

34CrNiMo6 Quench and 290 MPa 700 MPa



Georgios Siangas


[DIN 1.6582] tempering

42CrMo4

[DIN 1.7225]

Induction

hardening

370 MPa 1220 MPa

42CrMo4

[DIN 1.7225]


42CrMo4

[DIN 1.7225]

Quench and

tempering

280 MPa 650 MPa

31 CrMoV9

[DIN 1.8519]


Carbon Steels Ck45 Quench and

tempering

210 MPa 540 MPa

Ck45 Induction

hardening

370 MPa 1220 MPa

Ck45 Nitriding 370 MPa 1000 MPa

Ck60 Quench and

tempering

215 MPa 560 MPa

Table 38: Available materials for gear manufacturing.

The comparison shows that the use of 15CrNi6 [DIN 1.5919], along with the case

carburizing and tempering process show the best performance results. The only downside of the

case carburizing particularly for small sized gears is the possible dimensional distortions that

could happen, due to the increased temperatures of the process. The gears that will be used will

be in the medium size region, so the solution of case carburizing and tempering is selected along



Georgios Siangas


with a lapping manufacturing technique that will enhance the surface roughness of the flank of

the gear and the meshing quality of the gears.

Case carburized and tempered 15CrNi6 steel [DIN 1.5919]

Case Hardness: 60 HRC

Core Hardness: 27 HRC

Tensile Strength: 1000 MPa

Yield Strength: 685 MPa

Young‟s Modulus: 206 GPa

Poisson Ratio: 0.3

Density: 7830 kg/m3

Coefficient of Thermal Expansion: 11.5 10-6

/0C

Fatigue Strength: 430 MPa

Allowable Surface Stress: 1500MPa

Table 39: Case carburized and tempered 15CrNi6 [DIN 1.5919] steel material properties.

5.2 SHAFTS MATERIAL SELECTION

The drivetrain shafts are mainly susceptible to combined bending and torsion loads such

as the gearbox‟s shafts or to pure torsion loading such as the drive-shafts. The material properties

that matter in these load conditions is the Young‟s Modulus in order to attain the least possible

displacements at the gearbox shafts, thus maintaining optimal meshing conditions for the gear



Georgios Siangas


teeth under load and the Yield Strength for the bearing of the load conditions. The increased

Young‟s modulus property leads to the use of steel, which overall has very little differences

regarding Young‟s Modulus, depending on its alloys and carbon percentage. The second

property Yield Strength leads to a comparison similar with the comparison of the gear materials,

except that the sweep parameter is the Yield Strength of the materials. It is worth mentioning that

the steel used for the shafts is not going to be heat treated, but it is rather going to be used in the

quench and tempered delivery condition (+QT) . The post – heat treatment processes such as the

grinding of the bearing seats, that are necessary to counterbalance the dimensional distortion due

to the heat treatment process complicates the manufacturing of the shafts. The machining of the

material in the +QT condition requires tungsten carbide tooling in the lathe processes and surface

coated hobbing tools in the spline manufacturing.

Material Type Material Name Yield Strength

Carburizing Steels 15CrNi6 [DIN 1.5919] 685 MPa

Alloy Steels 34CrNiMo6 [DIN 1.6582] 1000 MPa

42CrMo4 [DIN 1.7225] 900 MPa

31CrMoV9 [DIN 1.8519] 900 MPa

Carbon Steels Ck45 490 MPa

Ck60 580 MPa

Table 40: Available materials for shaft manufacturing.

Alloy steel 34CrNiMo6 [DIN 1.6582] was selected due to its high yield strength, and

alloy steel 42CrMo4 [DIN 1.7225], in case there is a shortage in the desired dimension, again

due to its high yield strength.



Georgios Siangas


5.3 GEARBOX AND DIFFERENTIAL CASING MATERIAL

The gearbox casing is susceptible to plane stress, as a reaction to bending forces

developed by the gear meshing and the design goal is the minimum displacement between the

bearing seats. Thus keeping the gear pairs center distances under load, whereas the differential

casing transmits torque from the crown gear to internal mechanism of the differential. The main

material property for the minimization of developed displacements is the Young‟s Modulus and

for attaining the most lightweight design the Yield Strength. As the whole design philosophy is

focused around lightweight design, these parameters are divided with the material density in

order to provide a detailed view over a lightweight design.

Material Young‟s Modulus Density Young‟s Modulus/

Density

Aluminum 70000 MPa 2780 kg/m3

25.2

Steel 210000 MPa 7850 kg/m3

25.47

Magnesium 45000 MPa 1700 kg/m3

26.47

Titanium 110000 MPa 4400 kg/m3

25

Table 41: Specific Young‟s Modulus comparison for different materials.

Material Yield Strength Density Yield Strength/

Density

Aluminum 7075-T6 570 MPa 2780 kg/m3 0.205

Steel 34CrNiMo6 1000 MPa 7850 kg/m3 0.127



Georgios Siangas


Magnesium AZ31C 200 MPa 1700 kg/m3 0.1176

Titanium Ti-6Al-4V 910 MPa 4400 kg/m3 0.207

Table 42: Specific Yield Strength comparison for different materials.

For the displacement – oriented design (i.e. the gearbox casing design) it is evident that

there is no observable performance gains between the available materials. The expensive

materials titanium and magnesium are ruled out. Aluminum alloys are chosen for the

displacement-oriented design for two reasons, firstly due to its lower density. Considering that

with the selection of steel, in order to attain the same displacement levels of an aluminum design

would lead to a thin sectioned profile that would be difficult to manufacture with the

conventional machining procedures (Milling processes). Also the increased rate of thermal

conductivity of the aluminum alloys makes the gearbox casing dissipate heat faster from the the

gear oil. Moving on to the stress -based design (i.e. the differential casing design), there is a clear

difference between the four materials involved. The yield strength to material density factor is

higher for the titanium and the aluminum alloy, given the higher cost and limited availability of

the Titanium Ti-6Al-4V alloy in the Greek market the choice of an aluminum alloy is made for

the gearbox casing and the differential coupling of the drivetrain. Special consideration was

given in the specific alloy selection, as the whole gearbox will operate in increased temperatures,

and a degradation of material properties at these temperatures is to be expected. The typical

range of maximum operating temperatures of a racing gearbox is 90-100 0C, a more detailed

thermal analysis and oil temperature tests will be explained further down in this thesis, but this

range is adequate for the initial material selection.



Georgios Siangas


Maximum Operating Gearbox Temperature: 100 0C

The material properties that were considered are Young‟s Modulus to Temperature and

Yield Strength to Temperature. The selection of aluminum alloy was made between the two

available aircraft grade aluminum alloys 7075-T6 and 2024-T3. These data were extrapolated

from NACA‟s Technical Note 3462 Tensile Properties of 7075-T6 and 2024-T3 Aluminum

Alloy Sheet Heated at Uniform Temperature.



Georgios Siangas


Figure 33: Comparison of Yield strength between AL 7075-T6 and AL 2024-T3.

Figure 34: Comparison of Young‟s Modulus between AL7075-T6 and AL2024-T3.



Georgios Siangas


The point of interest in these diagrams is the temperature of 100 0C, as it is apparent the

difference in the Young‟s Modulus is insignificant, but there is substantial difference of about

100 MPa in the yield strength characteristics between the two alloys. Given this difference

aluminum alloy 7075 -T6 is selected as a construction material for the gearbox casing and the

differential coupling.

Figure 35: AL 7075-T6 Material properties to temperature.

In the above diagram degradation in the Ultimate strength minus the Yield strength is

occurring with the increase of temperature. This means that at increased temperatures this alloy

is becoming brittle, so in case of a failure it is expected for the component to shatter instead of a

permanent deform. A break in these components, especially in the gearbox casing would be

catastrophic for the racecar and possibly harmful to the driver. Increased attention should be

given in the structural analysis and physical testing of this component.

Aluminum Alloy 7075-T6 Material Properties at 100 0C

Young‟s Modulus: 68 GPa



Georgios Siangas


Yield Strength: 450 MPa

Ultimate Strength: 475 MPa

Shear Strength: 280 MPa

Fatigue strength: 130 MPa

Coefficient of thermal expansion: 25.2 10-6

/0C

Density: 2780 kg/m3

Poisson‟s Ratio: 0.33

Table 43: AL 7075-T6 Material properties at 100 0C.

5.4 MOUNTING AND GENERAL-PURPOSE MATERIAL SELECTION.

The selection of a mounting and general-purpose material selection follows a similar

approach to the selection of the gearbox casing and the differential coupling. The main criterion

is the yield strength to density ratio and the availability to the Greek market, so following the

above considerations aluminum alloy 7075-T6 is chosen for this purpose.



Georgios Siangas


6. CHAPTER 5: GEARBOX MECHANICAL DESIGN

6.1 GEARBOX INTERNAL COMPONENTS DESIGN

The internal components of the gearbox are the gears transmitting the power from the

electric motor to the drive wheels, the shafts that they are mounted and the bearings that allow

the rotational movement of the shafts. The design goals and targets described in the previous

chapters pose topological and geometrical constrictions in the design, and are presented below.

Gearbox internal components design constrictions

Specification: Target:

Type of transmission: 2-stage single speed gearbox

Type of gearing: Spur gears, standard 200 pressure angle

Final drive ratio: 3.5-3.7

Input Connection: Splined shaft

Output Connection: Differential mounting in hollow crown gear

Diameter of crown gear bore: 105 mm

Maximum overall width: Under 60 mm

Target center distance (input-output): 160-180 mm



Georgios Siangas


Minimum clearance between rotating parts: 1 mm

Table 44: Gearbox internal components design constrictions.

After multiple design iterations the final geometry of the internal components of the

gearbox is presented.

Figure 36: Gearbox internal components drawing.

The gearbox internal components design and structural analysis is a subject that was

vastly analyzed in the student thesis „Design, development and manufacturing of an electric



Georgios Siangas


racecar gearbox‟, and it is out of the scope of this diploma thesis. The final results of the design

are the following.

Gears:

Geometry of gears

Gear Teeth

Z

Module

m

Pressure

Angle a

Base diameter

D0

Width

w

Pinion Ζ11 : 16 3 200

48 mm 15 mm

Gear Ζ12 : 29 3 200

87 mm 15 mm

Pinion Ζ21 : 23 3 200

69 mm 15 mm

Gear Ζ22 : 46 3 200

138 mm 15 mm

Table 45: Geometry of gears.

Maximum loads applied per stage

Stage: Torque: Tangential Force: Radial Force:

First: 240 Nm 10000 N 3640 N

Second: 435 Nm 12608 N 4589 N

Table 46: Maximum loads applied per stage.

Dynamic loads applied per stage

Stage: Torque: Tangential Force: Radial Force:

First: 70 Nm 2917 N 1062 N

Second: 127 Nm 3682 N 1340 N

Table 47: Dynamic loads applied per stage.



Georgios Siangas


Results of gears structural analysis

Gear Root Safety Flank Safety Width

Pinion : 1.413 1.009 15 mm

Gear : 1.664 1.162 15 mm

Pinion : 1.34 1.233 15 mm

Gear : 1.526 1.374 15 mm

Table 48: Results of gears structural analysis.

Shafts:

1st Shaft

Figure 37: 1st shaft drawing.

1st shaft bearing reactions

Rmax1 7204.5 Ν

Rmax2 3437.5 Ν

Rm1 2101.6 N

Rm2 1002.7 N Table 49: 1st

shaft bearing reactions.

1st shaft results of structural analysis

Static Safety Factor: 6.7

Dynamic Safety Factor: 1.2

Maximum Deflection: 3.3 μm

Critical speed according to Rayleigh Ritz: 11531.2 rpm



Georgios Siangas


Table 50: 1st shaft results of structural analysis.

2nd

shaft

Figure 38: 2nd shaft drawing.

2nd

shaft bearing reactions

Rmax1 -2870.5 N

Rmax2 5646.1 N

Rm1 -836 N

Rm2 1649.9 N Table 51: 2nd

shaft bearing reactions.

2nd

shaft results of structural analysis




Critical speed according to Rayleigh Ritz: 11438 rpm Table 52: 2nd

shaft results of structural analysis.



Georgios Siangas


3rd

Shaft

Figure 39: 3rd shaft drawing.

3rd

shaft bearing reactions

Rmax1 9137.1 Ν

Rmax2 4280.1 Ν

Rm1 2668.5 N

Rm2 1250 N Table 53: 3rd

Shaft bearing reactions.

3rd

shaft results of structural analysis




Critical speed according to Rayleigh Ritz: 63729 rpm Table 54: 3rd

shaft results of structural analysis.



Georgios Siangas


External Spline

Figure 40: Shafts external spline dimensions according to DIN 5480.

Spline geometry according to DIN 5480

Module m: 1.25

External Diameter De: 34 mm

Teeth Z: 26

Pressure angle a: 300

Operation coefficient KA: 1.25

Tooth width s: 1.9625 mm

Base Diameter Do: 32.5 mm


Effective length Le: 15 mm

Table 55: Spline geometry according to DIN 5480.

Spline results of structural analysis

Static Safety Factor Shaft: 11.8

Static Safety Factor Hub: 7.1

Dynamic Safety Factor Shaft: 0.124 μm

Dynamic Safety Factor Hub: 63729 rpm



Georgios Siangas


Table 56: Spline results of structural analysis.

Bearings:

Selected ball bearings

Location: Left: Right:

1st Shaft: SKF 16006 SKF W61906R

2nd

Shaft: SKF 16006 SKF 16006

3rd

Shaft: Kaydon KC042CP0 Kaydon KC042CP0 Table 57: Selected ball bearings.

Selected ball bearings load capabilities

Bearing Static Load Capacity: Dynamic Load

Capacity:

Rotational Speed

Limit:

SKF W61906R: 5000 Ν 6240Ν 19000 RPM

SKF 16006: 7350 N 11900N 17000 RPM

Kaydon KC042CP0: 9875 N 10542N 1600 RPM Table 58: Selected ball bearing load capabilities.

Selected ball bearings static safety factor

Location: Bearing: Maximum

load Applied:

Safety Factor:

1st Shaft Right: SKF W61906R 3437.5 Ν 1.45

1st Shaft Left: SKF 16006 7204.5 Ν 1.02

2nd

Shaft Right: SKF 16006 5646.1 Ν 1.3

2nd

Shaft Left: SKF 16006 2870.5 Ν 2.56

3rd

Shaft Right: KC042CP0 4280.1 Ν 2.3

3rd

Shaft Left: KC042CP0 9137.1 Ν 1.1 Table 59: Selected ball bearings static safety factor.

Selected ball bearings rotational speed safety factor

Location Bearing Maximum

rotational

speed:

Safety Factor:

1st Shaft Right: SKF W61906R 5000 RPM 3.8

1st Shaft Left: SKF 16006 5000 RPM 3.4

2nd

Shaft Right: SKF 16006 2760 RPM 6.15

2nd

Shaft Left: SKF 16006 2760 RPM 6.15

3rd

Shaft Right: KC042CP0 1380 RPM 1.16

3rd

Shaft Left: KC042CP0 1380 RPM 1.16 Table 60: Selected ball bearings rotational speed safety factor.



Georgios Siangas


Selected ball bearings life cycles calculation

Location Bearing Dynamic Load Life Cycles

1st Shaft Right: SKF W61906R 1002.7 N 241013141

1st Shaft Left: SKF 16006 2101.6 N 181547680

2nd

Shaft Right: SKF 16006 1649.9 N 375204481

2nd

Shaft Left: SKF 16006 836 N 2884177947

3rd

Shaft Right: KC042CP0 1250 N 599844935

3rd

Shaft Left: KC042CP0 2668.5 N 61654873



Georgios Siangas


Table 61: Selected ball bearings life cycles calculation.

Figure 41: SKF W61906R ball bearing datasheet.



Georgios Siangas


Figure 42: SKF 16006 ball bearing datasheet.

Figure 43: Kaydon KC042CP0 thin section ball bearing datasheet.



Georgios Siangas


6.2 GEARBOX CASING DESIGN

The design of the gearbox casing needs to incorporate the following considerations.

Accurate location of bearings, and minimum deflection between those distances,

to ensure the optimal meshing of the gearing.

Structural integrity under the dynamic loading of the gears.

Lightweight characteristics.

Complete sealing of the transmission oil and separation from the environment.

Incorporation of oil temperature sensor and vent hose for air depressurizing, as

the temperature of the gear oil is expected to reach 95 0C.

Design that can be manufactured with conventional machining processes.



Georgios Siangas


Figure 44: Gearbox casing drawing

Gearbox casing parts list

A: Radial oil seal housing

B: Gearbox end cap

C: Gearbox bell housing

E: Guide pin

F: Vent hose fitting

G: Vent hose fitting mount

H: Oil temperature sensor

Table 62: Gearbox casing parts list.

The lubrication, air depressurizing and sealing will be further discussed in the Chapter

lubrication and sealing. The first three targets require an iterative process of stress – strain



Georgios Siangas


analysis that is difficult to present in this diploma thesis. Instead the finite element analysis

model of the final design of the gearbox casing will be presented below. The simulation contains

the two gearbox end caps connected through a virtual connection with bolts to the bell housing.

The whole assembly is rigidly mounted to the points that will be fixed on the transmission

mounts. The maximum loads posed by bearing reactions to the gear forces are acting upon the

two end caps. To estimate the tightening force between the end caps and the bell housing a hand

calculation is needed.

The whole assembly is pressed together and tightened with sixteen M5x60 mm grade 8.8

bolts and metal lock nut configuration, to prevent the bolt-nut assembly to loosen under

increased temperatures and vibrations. Since there are no axial forces acting upon the end caps

and the bolts, the empirical method of loading the bolts to 50% of their yield strength is chosen

for the gearbox application. The yield strength of the M5x60mm grade 8.8 bolt is Sy = 640 MPa

and its tensile area A = 14.2 mm2. The tightening force and the tightening torque are calculated

below.

A tightening force of 5000 N is selected for the clamping of the end caps to the bell

housing, to calculate the tightening torque the following method is used, where coefficient

K=0.2 for dry steel bolt.

The total tightening force of the gearbox is 80 kN, and it is plugged in the simulation as

tightening force between the end caps and the bell housing holes.

Meshed gearbox model.



Georgios Siangas


Figure 45: Meshed gearbox casing model.

Von Mises gearbox stress FEA results.

Figure 46: Von Mises gearbox casing stress FEA results.



Georgios Siangas


Displacement gearbox FEA results.

Figure 47: Displacement gearbox casing FEA results.

Results of gearbox casing FEA stress – strain analysis

Maximum Stress σmax: 216 MPa

Mean stress σm: 62 MPa

Maximum displacement between shafts: 20 μm

Mean displacement between shafts: 7.2 μm

Table 63: Results of gearbox casing FEA stress-strain analysis.

To evaluate the structural integrity of the gearbox casing, it is imperative to estimate the

materials strengths at the operating temperature of the gearbox. The material, as stated above is

Aluminum 7075-T6 and the maximum operating temperature is estimated to reach 95 0C.

Aluminum Alloy 7075-T6 Material Properties at 95 0C




Georgios Siangas


Yield Strength Sy: 450 MPa

Ultimate Strength Su: 475 MPa

Fatigue strength Sn: 130 MPa

Coefficient of thermal expansion a: 25.2 10-6

/0C

Density ρ: 2780 kg/m3

Poisson‟s Ratio ν: 0.33

Table 64: Aluminum alloy 7075-T6 material properties at 95 0C.

Static structural analysis:

The static safety factor under full load is calculated.

Dynamic structural analysis:

Notch sensitivity factor q:

Figure 48: Notch sensitivity factor q.

The minimum radius of the gearbox casing is r = 4 mm, so the equivalent notch

sensitivity factor for an aluminum alloy is q = 0.85.

Static stress concentration factor Kt for plate in axial loading:



Georgios Siangas


Figure 49: Static stress concentration factor Kt for plate in axial loading.

The width w=9 mm, the lowest thickness d=3 mm and the radius is r=4 mm. From

extrapolating the plot in Figure 48, the static stress concentration factor is Kt=1.4.

Dynamic stress concentration factor:

( )

Factors of fatigue life of AL7075-T6





Welding factor Cw : No welding 1


factor Kf:

Calculation 1.34

Table 65: Factors of fatigue life of AL 7075-T6.





Georgios Siangas


√(

)


Dimensional Tolerances:

The final manufacturing drawing of the gearbox needs to incorporate tolerances on the

called dimensions. The critical dimensions of the end caps are the dimension tolerance of the

bearing fit and the tolerance between the three bearing bores.

The outer ring of a bearing deforms proportionately to the load applied. This deformation

can loosen the interference fit between the outer ring and the gearbox casing bore, causing the

bearing to spin freely inside the bore and inducing catastrophic damage to the aluminum gearbox

end cap. The required interference is estimated for the most loaded bearing of the assembly

(Radial Force Fr=7.2kN, diameter d=47mm, width B=9mm), according to the bearing

manufacturer.

√

The gearbox end caps are machined at a room temperature of 25 0C and reach and an

operation temperature of 95 0C. The aluminum alloy thermally expands by approximately twice



Georgios Siangas


the rate of steel. For this reason it is decided to double the interference of the aluminum bore to

the steel bearing at Δ=30μm. To achieve this interference an ISO bore tolerance P6 was called in

the manufacturing drawings for the 1st and 2

nd shaft bearings and an ISO bore tolerance N6 for

the 3rd

shaft.

ISO interference fit of gearbox end caps bores

Bore dimension Lower interference Higher interference

1st shaft d=47 mm P6: -21 μm -37 μm

2nd

shaft d=55mm P6: -26 μm -45 μm

3rd

shaft d=127mm N6: -20 μm -45 μm

Table 66: ISO interference fit of gearbox end caps bores.

To set the dimension tolerance between bearing seats, it is important to mention that the

gears are machined with 100 μm deeper hobbing cut, in order to compensate for the tolerance of

the bearing bores, the thermal expansion and possible run out of the gears. The maximum

permissible run out in the gears was called 20 μm. The thermal expansion of the gears is

simulated as the thermal expansion δ of a steel disk (a=11.5 10-6

/0C, ΔΤ=70

0C).

Thermal expansion of gears

Pinion : 38 μm [δ/2=19μm] Interference between pair:



Georgios Siangas


Gear : 70 μm [δ/2=35μm] 54 μm

Pinion : 55 μm [δ/2=27.5μm] Interference between pair:

83 μm Gear : 111 μm [δ/2=55.5μm]

Table 67: Thermal expansion of the gears.

The tolerance between the gearbox end caps bores is set to +-15 μm. In order for the

gears not to bind at operating temperatures, the operating clearance under load must be positive

at the worst case scenario.

The maximum deformation of the end cap, between the bearing bores is estimated at

approximately 20 μm, according to the FEA displacement model [Figure 46]. The operating

clearance under load is estimated.

Clearance of first stage:

Clearance of second stage:

The gearbox loses efficiency through this clearance as there is sliding induced in the

meshing of the gears, but the reliability of the gearbox is significantly increased.



Georgios Siangas


7. CHAPTER 6: LUBRICATION AND SEALING METHODS

7.1 LUBRICATION

The lubrication of a gearbox is described by three parameters.

The type of lubrication.

The lubricant.

The quantity of lubricant.

Type of lubrication:

There are three distinct methods of lubricating a gearbox, grease lubrication, oil splash

lubrication and forced circulation lubrication. The main criterion of selecting a lubrication

method is the pitch line velocity of the meshing gears.

According to bibliography, at pitch line velocity under 3 m/s grease lubrication is

preferred, at a pitch line velocity between 3 m/s and 12 m/s splash or oil bath lubrication is

preferred and at a pitch line velocity over 12 m/s forced circulation or oil mist lubrication is

preferred, as shown in Figure 49.



Georgios Siangas


Figure 50: Lubrication type selection chart.

The splash method lubrication is chosen for the gearbox application, with gear oil as

lubricant.

Lubricant selection:

The first step in the gear oil selection is an estimation of the kinematic viscosity needed.

√

Where V40 is the oil viscosity at 40 0C and V is the maximum pitch line velocity of the

fastest gear in fpm. Since our application is heavily loaded and our expected operating

temperature is 50 0C over ambient temperature slightly higher viscosity gear oil is selected. In

addition to the viscosity number the use of extreme pressure and anti-foam additives is preferred,

so synthetic oil SAE 75W-140 is selected.



Georgios Siangas


Figure 51: Gear oil SAE 75 W-140 specifications.

Gear oil SAE 75W-140 has a kinematic viscosity of V40=173 cSt. If the gearbox runs on

lower oil temperatures, in case of other events (acceleration, skidpad, autocross), it is safe to

operate at full load because of the higher viscosity levels, but viscous oil drag losses are to be

expected, so the efficiency of the power unit will be reduced.



Georgios Siangas


Quantity of lubricant:

Figure 52: Gear oil level drawing.

The gear oil level in a splash lubrication system is defined from the height submersion of

the gears in the oil bath.

Figure 53: Gear oil level for splash lubrication.

For spur gears and horizontal shaft transmission each gears must be submerged to the oil

bath from 1h to 3h, where h is the tooth height of the gears.



Georgios Siangas


A CAD representation of the gear oil is created, where the oil bath level is set to 3h, and

the gears and shafts volumes are removed.

Figure 54: Gear oil CAD representation.

The computed gear oil volume needed, according to the CAD representation is 182 ml.

The gear oil level also reaches the lower side of each shaft, to ensure adequate lubrication of the

ball bearings. The gear oil volume specification for the gearbox is set to 0.2 lt.

Since the gearbox is accelerated both longitudinally and laterally the oil bath level poses

an angle θ compared to the ground.

( )

Event Acceleration (m/s2) Angle (

0)

Acceleration 11 48.2

Braking 15 56.8

Cornering 19 62.7 Table 68: Oil level angle compared to acceleration.

The acceleration and the braking event are causing the oil level to move towards the

crown gear and the pinion gear, which through their rotation will feed the rest of the system with



Georgios Siangas


lubricating oil. In the case of lateral acceleration the width of the gearbox is so small, that at least

one gear in either direction will be submerged to the oil bath and feed the rest of the gears with

lubricating oil.

Gear oil bench test:

To visualize the oil flow inside the gearbox, a transparent gearbox end cap was

manufactured, the gearbox was mounted on the lathe in the same level that it is mounted on the

racecar and with the use of a high fps camera the following images were taken.

Figure 55: Gear oil flow bench test simulation.



Georgios Siangas


As it is apparent in the shots the crown gear, by having a small clearance of 1mm with

the bell housing acts as an oil pump, feeding the rest of the components with oil lubricant at a

high flow rate.

Figure 56: Gear oil temperature to time at an endurance event.

The gear oil heating rate can be extrapolated from [Figure 54], for potential future

analysis of the system. The gear oil heating rate is 0.12 0C/s.

7.2 SEALING

The complete sealing of the gearbox is important for the reliability and safety of the

drivetrain system. It is regulated in the FSAE Rules that any leakage of fluid during a dynamic

event will lead to the disqualification of the team. There are two distinct problems with oil

leakage the first is the potential hazard that can be caused by lubricant leakage, such as slippery

track or potential fire hazard if the oil comes in touch with a hot surface. The second one is the



Georgios Siangas


reliability of the unit as if the gearbox runs dry, the increased temperatures at gear contacts and at

the ball bearings will result in a possible seizing of the gearbox.

To achieve an oil tight transmission radial shaft seals are used in the rotating parts

openings and chemical gasket in the static flanges. Radial shaft seals are placed between the

shaft and the seal bore. A radial shaft seal depends on two components to seal. The first one is a

press fit that seals the housing bore. The second one is a sealing lip that ensures the dynamic and

static seal against the shaft. HMSA10 design radial shaft seals were used in the design of the

gearbox as they are specifically designed for oil retention, while also having an extra sealing lip

to protect the gearbox from contamination with dirt. These type of seals are rated up to 100 0C,

with a permissible short term temperature of 120 0C. The maximum operating pressure of the

seal in 0.03 MPa, but since the gearbox is depressurized through the oil ventilation system, the

working pressure difference is zero.

Figure 57: Radial shaft seal.



Georgios Siangas


The sealing of the input shaft is achieved through a HMSA10 30x47x6 mm radial shaft

seal, as shown in figures 56 and figure 57.



Georgios Siangas


Figure 58: Sealing of 1st shaft assembly.

Figure 59: Sealing of 1st shaft section.

The sealing of the output shaft is achieved through a HMSA10 110x130x12 mm radial

shaft seal, as shown in figures 58 and figure 59.



Georgios Siangas



shaft assembly.


shaft section.



Georgios Siangas


8. CHAPTER 7: DIFFERENTIAL AND DRIVE AXLES MECHANICAL

DESIGN

The implementation of the differential inside the crown gear of the gearbox led to a

design of a rear axle that is mounted on the 3rd

gearbox shaft‟s ball bearings. The final

assembly drawing of the rear axle is shown in figure 60, 61.



Georgios Siangas


Figure 62: Assembly drawing of rear axle.

Figure 63: Assembly drawing of rear axle 2.

8.1 DIFFERENTIAL COUPLING

The first component in the transmission of power is the differential coupling. It transmits

the power from the crown gear to the differential housing. The main design feature of the rear

axle is the implementation of the differential into the crown gear. This feature saves space and

weight by eliminating the need of extra differential mounts, bearings, and splined shafts, leading



Georgios Siangas


to an integrated differential - rear axle design. The implementation is achieved as shown in figure

62.

Figure 64: Implementation of differential into crown gear drawing.

The differential coupling besides the torque transfer point between the crown gear and

the differential housing, also serves as a radial shaft seal bearing surface. As stated at the radial

shaft seal manufacturers handbook the bearing surface must be machined at a standard ISO h8

shaft tolerance, provide a surface roughness under 1.5 Ra and a surface hardness over 45 HRC.

To cope with surface hardness of 45 HRC, the aluminum 7075-T6 differential coupling went



Georgios Siangas


through a hard anodizing process in order to achieve a rough 65 HRC aluminum oxide surface

layer.

The use of integrated milled alignment pins of the coupling ensures the concentricity of

the rear axle assembly is ensured without the need of extra steel guide pins that complicate the

assembly procedure.

Figure 65: Differential coupling drawing.

To calculate the stresses developed in the differential coupling a finite element analysis

model is made. The maximum torque applied to the differential coupling is calculated.

The torque is transferred through a bolt pattern of 12 x M6x100 mm grade 8.8 bolts,

capped with lock nuts, to prevent the bolt-nut assembly from loosening.



Georgios Siangas


Differential Coupling - Bolt Pattern Calculation

Bolts: Fact 12 x M6x100 mm 8.8 at r=49 mm

Tightening torque M: Design Input 10 Nm

Torque transfer T: Design Input 435 Nm

Bolt Area A:

28.3 mm2

Bolt shear load Q:

740 N

Bolt tensile load F:

8300 N

Bolt shear stress τ:

26.14 MPa

Bolt tensile stress σ:

293.3 MPa

Equivalent stress σv: =√ 298 MPa

Safety factor:

2.14



Georgios Siangas


Table 69: Differential coupling – Bolt pattern calculation.

Figure 66: Differential coupling FEA stress results.

Differential coupling - FEA model stress results.

Equivalent maximum Von Mises stress: 74.5 MPa

Equivalent mean Von Mises stress: 26.85 MPa

Table 70: Differential coupling FEA model stress results.




Georgios Siangas











factor Kf:

Estimate 2

Table 71: Factors of fatigue life differential coupling.



√(

)




Georgios Siangas


8.2 DIFFERENTIAL

A clutch-pack limited slip differential is chosen for the drivetrain design. In this type of

differentials, thrust is not limited by the lowest grip tire, such as in an open or a Torsen type

differential. It provides adjustability over torque bias ratio, through initial preload and ramp

angles adjustment. Essentially the more pressure exercised in the multi-disk clutch of the

differential, the higher the torque bias ratio of the differential.

The differential was purchased from DREXLER Motorsport and it was modified to fit to

the crown gear. The final drawing of the modified limited slip differential is presented.



Georgios Siangas


Figure 67: Modified DREXLER LSD drawing.

Ramp angle and theoretical lockup torque percentage S, according to manufacturer

Ramp angles Acceleration lockup Deceleration lockup

45°/60° 51% 29%

40°/50° 60% 42%

30°/45° 88% 51%

Table 72: Differential ramp angles and theoretical lockup.

The theoretical lockup torque percentage S describes the maximum applied torque

difference between rear wheels of the vehicles. The maximum torque that can be applied in a full

throttle situation in each wheel can be calculated.

High traction wheel maximum applied torque:



Georgios Siangas


( )

Low traction wheel maximum applied torque:

( )

The ratio of the two applied torques is referred to as the torque bias ratio. It describes

how much higher is the high traction wheel compared to the low traction wheel maximum

applied torque.

Torque bias ratio depending on ramp angle

Ramp angle S TBR Maximum Torque on High

Traction Wheel TH

Maximum Torque on Low

Traction Wheel TL

60° 29% 1.8 561.15 Nm 308.85

50° 42% 2.5 617.7 Nm 252 Nm

45° 51% 3 656.85 Nm 213.15 Nm

40° 60% 4 696 Nm 174 Nm

30° 88% 15.7 817.8 Nm 52.2 Nm

Table 73: Torque bias ratio and applied torque depending ramp angle.

The maximum torque that can be applied in a component in the drive shaft assembly can

happen during acceleration, with the 300 ramp angle installed. This value is calculated above at



Georgios Siangas


817.8 Nm. All the components of the drive shaft assembly will be designed to withstand that

torque value.

8.3 STUB SHAFT DESIGN

The stub shaft is the component that connects the differential with the aluminum tripod

housing. The final design is a tubular steel shaft with a flanged end that connects to the tripod

housing and a splined end that connects to the differential.



Georgios Siangas


Figure 68: Stub shaft drawing.

Stub shaft material properties











Georgios Siangas



Table 74: Stub shaft material properties.

Stress concentration factor Kt, for stepped shaft loaded in torsion.

Figure 69: Stress concentration factor Kt.

Cross section properties

Outer Diameter D: 28 mm

Inner Diameter d: 25 mm

Radius/Chamfer r: 3

D/d coefficient: 1.12

r/d coefficient: 0.12

Stress concentration factor Kt: 1.2



Georgios Siangas


Table 75: Cross section properties.

The critical point of the shaft is located at the spline relief cut. The section A‟A below is

showing the critical point of the shaft.

Figure 70: Section A‟A stub shaft.

Section A‟A stress –strain calculation


Torsional stress: ( ) (

)

367.5 MPa

Angle of twist: ( ) ( ) 1.228 0

Table 76: Stub shaft – Section A‟A stress –strain calculation.



Georgios Siangas



Von Mises equivalent stress: =√ 636.52 MPa

Tresca equivalent stress: =√ 735 MPa

0.2% Proof strength: Material Property 1000 MPa


1.57

Safety factor Tresca:

1.36

Table 77: Stub shaft – Static analysis results.

To perform a dynamic structural analysis, average engine power and average engine rpm

during an endurance race and a 50-50 torque split from the differential is assumed.


Torsional stress τm: ( ) (

)

55.5 MPa


Table 78: Stub shaft- Dynamic stresses calculation.


=√ (

)

, where α = 3 for Von Mises theory, and α = 4 for Tresca theory.



Georgios Siangas



Von Mises equivalent dynamic stress: 384 MPa

Tresca equivalent dynamic stress: 444 MPa



Safety Factor Tresca: 2.25

Table 79: Stub shaft – Dynamic analysis results.

The stub shaft critical speeds are not calculated because the distance between the needle

bearing and the spider gear is too short, and the only bending load is the axle‟s own weight,

meaning that axle‟s critical speeds are too high.

An involute spline is used to transmit the power from the spider gear to the stub shaft.

Involute spline characteristics, according to DIN 5480

Module m: 1.058

External diameter D: 28 mm

Teeth z: 25

Pressure Angle a:

Effective Length Le: 20 mm

Maximum Applied Torque: 817.8 Nm

Application Factor Ks: 2

Tooth Thickness t: 1.66 mm



Georgios Siangas


Pitch Diameter: 26.5 mm


Table 80: Stub shaft- Involute spline characteristics.

Stub shaft spline analysis results

Maximum shear stress: ( )

Maximum compressive stress: ( )

Equivalent stress: = √ 650 MPa

0.2% Proof strength Sy: Material Property 1000 MPa

Safety Factor Tresca:

1.54

Table 81: Stub shaft - Spline stress analysis.

8.4 TRIPOD HOUSING DESIGN

To proceed with the design of the tripod housing, the continuous velocity joint that will

allow the power transmission at different relative angles of differential - suspension must be

selected. CV Joints allow the drive - shafts to transmit power through a variable angle, produced

due to the relative movement of the suspension to the chassis. It is calculated that the maximum

angle of possible power transmission is 4.10, at the top end of the suspension travel. Due to the

low angle of power transmission a Fiat 127 production tripod joint was chosen, being the lightest

and most efficient design at these relatively small angles, and also available at most automotive

stores at a competitive price.



Georgios Siangas


Figure 71: Tripod CV Joint FIAT 127 Automobile.

FIAT 127 Sport Edition CV Joint specifications

Engine torque FIAT 127: 95 Nm

Maximum gear ratio FIAT 127: 3.91

Final drive ratio FIAT 127: 4.462

Differential type FIAT 127: Open Differential (Equal torque split)

Maximum torque applied to CV Joint FIAT 127: 830 Nm

Maximum torque applied to CV Joint UoP5e: 817.8 Nm

Table 82: FIAT 127 Sport Edition CV joint specifications.

Figure 72: Driveshaft relative movement to differential.



Georgios Siangas


The tripod housing design was made possible, through multiple iterations of CAD design

and physical testing. The final part is a cnc milled hard-anodized aluminum 7075-T6 component

that bolts onto the stub shaft through 3 x M8x60 mm grade 8.8 bolt pattern, capped with lock

nuts.

Tripod Housing - Bolt Pattern Calculation

Bolts: Fact 3 x M8x60 mm 8.8 at r=30 mm

Tightening torque M: Design Input 20 Nm

Torque transfer T: Design Input 820 Nm

Bolt Area A:

50.25 mm2

Bolt shear load Q:

9100 N

Bolt tensile load F:

12500 N

Bolt shear stress τ:

181.11MPa

Bolt tensile stress σ:

248.75 MPa

Equivalent stress σv: =√ 400.3 MPa

Safety factor:

1.6



Georgios Siangas


Table 83: Tripod Housing – Bolt pattern calculation.

Figure 73: Aluminum tripod housing joint drawing.

A stress analysis was performed in the finite element model of the aluminum tripod

housing.



Georgios Siangas


Figure 74: Aluminum tripod housing FEA stress analysis results.

Tripod Housing - FEA model stress results.

Equivalent maximum Von Mises stress: 119 MPa

Equivalent mean Von Mises stress: 43 MPa

Table 84: Tripod Housing FEA model stress results.









Georgios Siangas







factor Kf:

Estimate 2

Table 85: Factors of fatigue life tripod housing.



√(

)




Georgios Siangas


8.5 DRIVESHAFTS DESIGN

The final component in the rear axle design is the driveshaft. The driveshaft is the

component that connects the drivetrain assembly with the suspension. The design of the

driveshaft is a tubular steel shaft with splined ends. The CV Joints attach to the splined

ends of the driveshaft and enable the power transmission, between two not co-axial shafts.

The shape of the driveshaft makes it perform as torsional spring between the drivetrain and

the suspension, dampening any sudden shock loads in the system. The importance of its

torsional stiffness plays a major role in the performance of the system. It is worth

mentioning that a difference of torsional stiffness between the two driveshafts, may result

in “torque steer” under full throttle situations. The design of the drivetrain placed the

gearbox at the middle of the racecar, thus allowed the use of equal length driveshafts. Since

the driveshafts are equal in length there is no need of modifying their dimensions to

achieve equal torsional stiffness. They are a symmetrical design.

Figure 75: Driveshaft drawing.

The driveshafts are manufactured from a solid steel rod of 25mm diameter, and then they

are gun drilled to achieve an accurate positioning of the drilled hole.



Georgios Siangas


Driveshaft material properties










Table 86: Driveshaft material properties.

A slightly different approach will be exercised in the static analysis of the driveshaft.

Since the torsional stiffness of the driveshaft needs to be as low as possible, the component will

be designed with safety against shattering and not safety against yielding. This will be achieved

by changing the yield strength in static analysis with the ultimate strength of the material. The

goal of this design strategy is to fully exploit the elastic properties of the material, and develop

safely a shaft with lowest possible torsional stiffness. The material choice in this decision is very

important. Steel alloys have very low differences between them in the modulus of rigidity

material property, while having vast difference in the yield strength property. Choosing the steel

of the highest yield strength property, allows the designer to produce lighter structures that have

the minimum possible torsional rigidity, for a given dimension.



Georgios Siangas


Driveshaft stress –strain calculation


Torsional stress: ( ) ( ) 598 MPa

Angle of twist: ( ) ( ) 15 0

Table 87: Driveshaft stress –strain calculation.

To perform a static structural analysis, a non-traction limited situation is assumed. The

maximum torque transferred by the drive shaft is 817.8 Nm.


Von Mises equivalent stress: =√ 1034 MPa

Ultimate Strength Su: Material Property 1200 MPa


1.16

Table 88: Driveshaft – Static analysis results.

To perform a dynamic structural analysis, we take in account average engine power and

average engine rpm during an endurance race and a 50-50 torque split from the differential is

assumed. Mean torque applied and torque range is estimated.


Torsional stress τm: ( ) ( ) 90.42 MPa



Georgios Siangas



Table 89: Driveshaft- Dynamic stress calculation.


=√ (

)

, where α = 3 for Von Mises theory.


Von Mises equivalent dynamic stress: 568 MPa



Table 90: Driveshaft – Dynamic analysis results.

The final step of the design of the driveshaft is an estimation of its critical speed,

according to Rayleigh-Ritz method.

(

)

The b term in the calculation is the deflection of the shaft through its own weight bending

moment. A resonance analysis of the driveshaft is performed.

Driveshaft resonance analysis

Own weight estimation m: 0.578 kg

Second moment of Inertia Ixx: 6836.1 mm4

Deflection y: 4 μm

Driveshaft critical speed n: 11220 rpm



Georgios Siangas


Driveshaft maximum speed: 1380 rpm

Safety factor against resonance: 8.13

Table 91: Driveshaft resonance analysis.

.



Georgios Siangas


9. CONCLUSION

This diploma thesis was focused on the first custom developed e-drivetrain designed and

manufactured in Greece, under the supervision of Laboratory of Manufacturing Systems and

Automation of the University of Patras. The e-drivetrain system has competed in 6

international motorsport engineering FSAE competitions and made over 1000 km. It has

achieved all the design goals, on the arguments stated in the introduction of this thesis,

thanks to the meticulous analysis, the testing and continuous optimization of each component

of the system. This diploma thesis also fulfills a secondary target, as it represents a written

guide for the next team members of UoP Racing and other engineers, who wish to develop a

similar project on fully electric vehicles. My recommendations to UoP Racing on the

development of the e-drivetrain components in the future are the investigation of developing

a multiple-speed gearbox, on profile-shifted gear profiles, on a thermo-mechanical analysis

of the gearbox, on advanced manufacturing techniques such as EDM and additive

manufacturing and on advanced materials, heat treatments and chemical coatings. I

personally believe that the automotive sector is headed to the direction of fully electric

vehicles and that the development and optimization of e-drivetrain units will have a major

role in the efficiency and reliability of the future automotive industry.



Georgios Siangas


In the following pages, there are some photos from the actual e-drivetrain unit.



Georgios Siangas




Georgios Siangas




Georgios Siangas


Figure 76: E-drivetrain photographs.



Georgios Siangas


REFERENCES

[1] Chryssolouris G., Manufacturing Systems: Theory and Practice 2nd Edition. Springer-

Verlag, New York; 2006

[2] Chris A. Papadopoulos, Machine Elements, Tziolas Publications, University of Patras

[3] Th. Kermanidis, Strength of Materials, University of Patras Publications, University of Patras

[4] Thomas D. Gillespie, “Fundamentals of Vehicle Dynamics”, SAE Publications, Warrendale

[5] K. Salonitis, T. Chrondros, G. Chryssolouris, "Grinding wheel effect in the grind-hardening

process", International Journal of Advanced Manufacturing Technology, Volume 38, No. 1-

2, pp. 48-58 (2008)

[6] D. Miler, A. Lončar, D. Žeželj, Z. Domitran, "Influence of profile shift on the spur gear pair

optimization", Mechanism and Machine Theory, Volume 117,Pages 189-197 (2017)

[7] C. Xie, L. Hua, X. Han, J. Lan, X. Wan, X. Xiong, "Analytical formulas for gear body-

induced tooth deflections of spur gears considering structure coupling effect", International

Journal of Mechanical Sciences, Volume 148, Pages 174-190 (2018)

[8] M. Hu, H. Xie, C. Fu, “Study on EV transmission system parameter design based on vehicle

dynamic performance”, International Journal of Electric and Hybrid Vehicles, Vol. 6, pp.

133-151(2014)

[9] Budynas, Richard G., J. Keith Nisbett, and Joseph Edward Shigley. “Shigley's Mechanical

Engineering Design”. New York: McGraw-Hill, 2011.

[10] Heimerl George J, Inge John E, “Tensile Properties of 7075-T6 and 2024-T3 Aluminum-

a. alloy Sheet Heated at Uniform Temperature Rates Under Constant Load”, NASA Technical

b. Reports Server

[11] KHK Gears Technical Documents, retrieved from, https://khkgears.net/new/

https://khkgears.net/new/



Georgios Siangas


[12] DIN 5480-1, Splined connection with involute splines based on reference diameters

[13] SKF Rolling Bearings online catalogue, retrieved from,

http://www.skf.com/gr/products/bearings-units-housings/product-tables/index.html

[14] Kaydon bearings online catalogue, retrieved from,

https://www.kaydonbearings.com/RealiSlim_open_bearings.htm

[15] KISSsoft manual, retrieved from, http://www.kisssoft.ch/Manual/en/

http://www.skf.com/gr/products/bearings-units-housings/product-tables/index.html

https://www.kaydonbearings.com/RealiSlim_open_bearings.htm

http://www.kisssoft.ch/Manual/en/