The Conceptualisation, Development, Design and Optimization of an Integrated In-Hub Planetary Gearbox System for a Formula Student Race Car

Full text

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Master of Engineering in Automotive Engineering
3rd Year Dissertation
The Conceptualisation, Development, Design and
Optimisation of an Integrated In-Hub Planetary
Gearbox System for a Formula Student Race Car
School of Engineering at the University of Warwick
Executive Summary
This technical report explores the conceptualisation, development, design, and optimisation of an
integrated in-hub planetary gearbox system for a formula student race car successfully creating an
innovative and optimised electrical powertrain solution. Throughout the project a highly optimized
epicyclic gearset was designed, a thorough material and manufacturing selection has been performed
and Generative Design was employed to create an organic and lightweight design solution for the
gearbox casing. Furthermore, a dedicated development and design methodology, in line with the
systems approach, was created and implemented successfully, which allowed for the verification and
validation of the system. Finally, assembly procedures as well as renders were made to aid in building
and visualizing the system.
Student ID:
Pages:
Referencing:
Word Count:
Project Supervisor:
Date of Submission:
1920727
82
Harvard
22382
Dr. Ken Mao
March 16th, 2022

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Table of Contents
1.0 INTRODUCTION ........................................................................................................................ 1
2.0 PROJECT BACKGROUND ........................................................................................................... 1
2.1 USE CASES OF IN-HUB INTEGRATED GEARBOX SYSTEMS ........................................................... 1
2.2 EMPLOYING THE SYSTEMS APPROACH ......................................................................................... 1
3.0 DESIGN INTENT, REQUIREMENTS AND CONSTRAINTS ............................................................... 2
3.1 DESIGN INTENT ............................................................................................................................. 2
3.2 GEARBOX SYSTEM REQUIREMENTS .............................................................................................. 4
3.3 GEARBOX DESIGN CONSTRAINTS ................................................................................................. 4
4.0 GEARBOX CALCULATIONS, GEOMETRY AND DEVELOPMENT ..................................................... 6
4.1 OPTIMAL GEAR RATIO .................................................................................................................. 6
4.2 TYPES OF EPICYCLIC GEAR SYSTEMS AND EVALUATION ............................................................ 6
4.3 MATHEMATICAL FOUNDATIONS AND GEAR COMBINATIONS ...................................................... 7
4.3.1 Types of Gears ....................................................................................................................... 7
4.3.2 Gear Combinations for Planetary Systems ........................................................................... 8
4.4 MATERIAL SELECTION AND MANUFACTURING .......................................................................... 10
4.4.1 Material Choice ................................................................................................................... 10
4.4.2 Manufacturing Methods ...................................................................................................... 12
4.4.3 Surface Treatments .............................................................................................................. 13
4.4.4 Manufacturing Method for Project Gears ........................................................................... 14
4.5 ACTING FORCES, STRESSES, AND MACRO GEOMETRY ............................................................... 14
4.5.1 Gear Parameterization ........................................................................................................ 15
4.5.2 Tangential Force, Contact and Bending Stresses ............................................................... 16
4.5.3 Final Macro Geometry ........................................................................................................ 18
5.0 GEAR SYSTEM DESIGN, OPTIMIZATION AND ANALYSIS ............................................................ 19
5.1 GEAR SYSTEM DESIGN ................................................................................................................ 19
5.1.1 Gearbox Layout ................................................................................................................... 19
5.1.2 Input Shaft Design ............................................................................................................... 19
5.1.3 Carrier Design ..................................................................................................................... 20
5.1.4 Bearing Selection ................................................................................................................. 21
5.1.5 Gear System Construction in SMT MASTA ......................................................................... 22
5.1.6 Gear Lubrication ................................................................................................................. 23
5.2 GEAR SYSTEM OPTIMISATION, SIMULATION AND ANALYSIS .................................................... 24
5.2.1 Gear Optimisation ............................................................................................................... 24
5.2.2 Finite Element Analysis of Individual Gears ....................................................................... 24
5.2.3 Finite Element Analysis of the Input Shaft and Carrier ...................................................... 26
5.2.4 MASTA SMT Gear System Analyses .................................................................................... 27
6.0 GEARBOX DESIGN .................................................................................................................... 30
6.1 GEARBOX CONCEPTUALISATION ................................................................................................ 30
6.2 FORCE ANALYSIS ........................................................................................................................ 30
6.3 MANUFACTURING PROCESS AND MATERIAL SELECTION ........................................................... 31
6.4 GEARBOX DESIGN ....................................................................................................................... 31
6.4.1 Sealing and Casing Design ................................................................................................. 31
6.4.2 Wheel Shaft and Braking ..................................................................................................... 32
6.4.3 Lubrication System .............................................................................................................. 33
6.4.4 Sensors ................................................................................................................................. 34
6.4.5 Suspension Mounting Points ............................................................................................... 34
6.5 GENERATIVE DESIGN FOR UPRIGHT ........................................................................................... 35
6.6 GEARBOX ASSEMBLY .................................................................................................................. 35

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6.7 GEARBOX SYSTEM DISCUSSION .................................................................................................. 36
7.0 PROJECT OUTCOME, VERIFICATION AND VALIDATION ............................................................. 37
7.1 VERIFICATION AND VALIDATION ........................................................................................ 37
7.2 COMPARATIVE ANALYSIS .................................................................................................... 38
7.3 SUGGESTIONS FOR FUTURE IMPROVEMENT ........................................................................ 39
7.4 APPLICATION OF WORK ....................................................................................................... 39
7.5 CONCLUDING STATEMENT ................................................................................................... 40
8.0 BIBLIOGRAPHY .......................................................................................................................... I
APPENDICES ................................................................................................................................... V
APPENDIX A – CHAPTER 3 SUPPORTING INFORMATION .................................................................... V
APPENDIX B – CHAPTER 4 SUPPORTING INFORMATION .................................................................. VII
APPENDIX C – FINAL GEAR SET SPECIFICATIONS ......................................................................... VIII
APPENDIX D – FEA RESULTS OF INDIVIDUAL GEARS ...................................................................... IX
Appendix D.1 – Sun Gear FEA Results ........................................................................................ IX
Appendix D.2 – Planet Gear FEA Results ...................................................................................... X
Appendix D.3 – Ring Gear FEA Results ...................................................................................... XI
APPENDIX E – FEA RESULTS OF INPUT SHAFT AND CARRIER ........................................................ XII
Appendix E.1 – Input Shaft FEA Results ..................................................................................... XII
Appendix E.2 – Carrier FEA Results ......................................................................................... XIII
APPENDIX F – MACRO GEOMETRY ANALYSIS RESULTS REPORT ................................................. XIV
APPENDIX G – ADVANCED SYSTEM DEFLECTION RESULTS REPORT ............................................ XVI
APPENDIX H – LTCA RESULTS REPORT ..................................................................................... XVIII
APPENDIX I – GEARBOX SYSTEM ASSEMBLY ................................................................................ XXI
APPENDIX J – GEARBOX SYSTEM VISUALISATION ...................................................................... XXX
APPENDIX K – CHAPTER 7 SUPPORTING INFORMATION ............................................................ XXXV

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Table of Figures
Figure 1 – Example of Integrated Planetary Gearbox
Figure 2 – Example of Integrated Gearbox System
Figure 3 – Plettenberg Nova 15, RPM, Torque and Efficiency
Figure 4 – Project Methodology Flow Chart
Figure 5 – Available Build Volume
Figure 6 – Simple Spur Gear
Figure 7 – Helical Gear Set
Figure 8 – Double Helical Gear
Figure 9 – Gear Manufacturing Process Diagram
Figure 10 – Case Depth vs Diffusion Temperature
Figure 11 – Orthographic Front View of Macro Geometry
Figure 12 – Isometric View of Macro Geometry
Figure 13 – Layout Schematic
Figure 14 – CAD of the Input Shaft
Figure 15 – Stress (dotted line) Concentration Reduction Methods
Figure 16 – CAD of the Carrier Assembly
Figure 17 – Cross Sectional View of Carrier
Figure 18 – Output View in MASTA
Figure 19 – Cross Sectional View in MASTA
Figure 20 – Gearbox Oil Level
Figure 21 – Upright Layout
Figure 22 – Reference Frame Diagram
Figure 23 – Initial Casing Design
Figure 24 – Cross-Section of Casing and Casing Cover Design
Figure 25 – Engine Connection Plate Attached to Casing
Figure 26 – Wheel Shaft and Carrier
Figure 27 – Wheel Shaft and Carrier Assembly
Figure 28 – Cross-Section of Gearbox Design
Figure 29 – Top Oil Plug
Figure 30 – Lower Oil Plug
Figure 31 – Sensor Integration
Figure 32 – Suspension Mounting Points
Figure 33 – Generative Design Setup
Figure 34 – Generative Design Outcome
Figure 35 – Applied Loads and Static Stress
Figure 36 – Maximum Static Stress
Figure 37 – Maximum Static Stress; close-up of gear
Figure 38 – Maximum Displacement
Figure 39 – Maximum Reaction Force
Figure 40 – Applied Loads and Static Stress
Figure 41 – Maximum Static Stress
Figure 42 – Maximum Static Stress; Close-up of Gear Tooth
Figure 43 – Maximum Displacement
Figure 44 – Maximum Reaction Force

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Figure 45 – Applied Loads and Static Stress
Figure 46 – Maximum Static Stress
Figure 47 – Maximum Static Stress; Close-up of Gear Tooth
Figure 48 – Maximum Displacement
Figure 49 – Maximum Reaction Force
Figure 50 – Maximum Stress Angle 1
Figure 51 – Maximum Stress Angle 2
Figure 52 – Maximum Stress Close-up
Figure 53 – Regions of High Stress
Figure 54 – Setup and Maximum Stress
Figure 55 – Maximum Stress Angle 2
Figure 56 – High Stress Regions and Stress Reduction Zone (Red)
Figure 57 – High Stress Regions in the Carrier
Figure 58 – Stress Distribution in a Planet Carrying Shaft
Figure 59 – Torsional Stress along Shaft Profile
Figure 60 – Pressure Distribution along Gear Tooth Profile for Sun Gear
Figure 61 – Pressure Distribution along Gear Tooth for Sun-Planet Interface
Figure 62 - Pressure Distribution along Gear Tooth Profile for Sun-Planet Interface
Figure 63 – Number of Teeth in Contact between Sun and Planet Gears
Figure 64 – Number of Teeth in Contact between Planet and Ring Gears
Figure 65 – Front-Side Render of Gearbox System
Figure 66 – Back-Side Render of Gearbox System
Figure 67 – Front-Side Render of Gearbox System, 2
Figure 68 – Side Render of Gearbox System
Figure 69 – Cross-Sectional Render of Gearbox System
Figure 70 – Cross-Sectional Render of Gearbox System, Back Side
Figure 71 – Cross-Section Analysis of Gearbox System (Top View)
Figure 72 – Cross-Section Analysis of Gearbox System, Labelled
Figure 73 – Exploded View of Gearbox System (Front)
Figure 74 – Exploded View of Gearbox System (Back)

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Table of Tables
Table 1 – Electric Motor Data
Table 2 – Design Objectives
Table 3 – Pugh Matrix for Different Types of Epicyclic System
Table 4 – Valid Planetary Gear System Options
Table 5 – Common Gear Materials and their Properties
Table 6 – Properties of Steel Alloy EN36 Carburized and Oil Quenched
Table 7 – Preliminary Gear Parameters
Table 8 – Hand Calculation Results of Stress Analysis
Table 9 – Bearing Selection Parameters
Table 10 – Selected Bearings Specifications
Table 11 – Oil Types and Their Efficiencies
Table 12 – Optimised Gear Set Parameters
Table 13 – Duty Cycles
Table 14 – Force Analysis of Upright Gearbox Casing
Table 15 – Gearbox System Requirements
Table 16 – Gearbox System FEA
Table 17 – Number of Teeth of Involute Gear vs Lewis Form Factor
Table 18 – Final Gear Set Detailed Specifications
Table 19 – Fatigue Safety Factor Summary
Table 20 – Maximum Contact and Bending Stresses
Table 21 – Gearset Safety Factor Summary
Table 22 – Load Case for Gear System Input
Table 23 – Gear System Reliability Summary
Table 24 – Bearings Ratings
Table 25 – Input Shaft Analysis
Table 26 – LTCA for Sun-Planet Interface Numerical Simulation Results
Table 27 – LTCA for Planet-Ring Interface Numerical Simulation Results
Table 28 – Requirement Verification Traceability Matrix

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1.0 Introduction
As the automotive industry is gradually embracing sustainable alternatives to the petrol engine, electrical
drivetrains have become increasingly prominent. As a consequence, the research and development in
the area of electrical motors, batteries and conversion gearboxes has skyrocketed. Recognizing the
potential and importance of this ‘green revolution’ many motorsport classes are moving towards hybrid
and fully electric powertrains, for instance, formula student has added a new racing class (Electric
Vehicles or EV) to their tournament. The University of Warwick’s own formula student team (Warwick
Racing) has decided to exclusively participate in the EV class to show their commitment to a more
sustainable future. In this vein, the team has been looking into new innovative ways to design electric
powertrains. As a result, the researchers and engineers at Warwick Racing envisioned a system where
the electric motor and gearbox are directly integrated within the wheel hub. This greatly increases
packaging space within the car and enables each wheel to be controlled individually, thereby allowing
for torque vectoring. If this type of system is employed by the team it could greatly improve the overall
vehicle performance and the team’s overall competitiveness. The project presented hereby was
established to design precisely such an integrated in-hub gearbox system. Thus, to summarize, the aim
was to conceptualize, develop, design, and optimize a fully integrated in-hub planetary gearbox system
for the Warwick Formula Student Team race car.
2.0 Project Background
The Warwick Formula Student team has already developed an integrated motor-gearbox system for the
front wheel of the upcoming 2023 competing car as part of a 4th-year group project. This is the first time
the team has designed and created such a system, and therefore, there is a strong foundation to further
optimize and develop the system. This project will therefore attempt to design said system for the rear
wheel of the race car but will expand on the concept by making it lighter and more efficient than the
previously designed gearbox.
2.1 Use Cases of In-Hub Integrated Gearbox Systems
Integrated gearbox and electrical wheel hub systems are a relatively new concept and are currently
mainly employed by Formula Student teams and other classes of lightweight Formula like race cars.
Therefore, current research is limited, however, driven by the constantly self-innovating industry this
technology could soon find its way into other electric racing series, with the potential to be used in
motorcycles and other vehicle types as well.
2.2 Employing the Systems Approach
To be able to undertake the complex and difficult task of designing a fully integrated gearbox and
electrical motor upright, the systems approach was employed. This approach uses the V-model where
system and customer needs are captured and then converted to measurable system requirements, which

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are then implemented and integrated into the system. At each stage the chosen approach suggests
verifying its function to ultimately validate the overall system. Additionally, at the onset of the project
a Failure Mode and Effect Analysis (FMEA) was performed to identify which design aspects require
the greatest attention. The final and arguably most crucial aspect of this approach is that the results and
project outcomes are compared to the initial requirements and are thereby verified and validated to
ensure the final product meets its standards. In employing said approach for the project presented hereby,
the ISO standards for all aspects of the system design are considered to meet industry requirements and
standards.
3.0 Design Intent, Requirements and Constraints
3.1 Design Intent
3.1.1 Design Aim
To establish a design, intent or aim is one of the most crucial first steps in the development of the gearbox
system for the Formula Student car. The aim of this project was to conceptualise, develop, design and
optimize an integrated in-hub planetary gearbox system for the Warwick Racing Formula Student race
car. Therefore, the design intent for this project was to establish a CAD model of the entire gearbox
including planetary gears, sensors, brakes, bearings, drive shafts and full gearbox casing for the rear of
the race car, essentially creating a full electric drivetrain. The model had to be fully optimized, verified,
and readily constructable by the future Formula Student team. In creating this model all factors,
requirements and constraints as listed in Chapter 3.2 had to be implemented. Examples of the design
intent and gearbox are shown below in Figures 1 and 2.
3.1.2 Data and Supporting Information
The motors that are used to drive each individual wheel had been pre-determined by the Formula Student
team; concretely, these are Plettenberg’s Nova 15-50 water cooled engines of which Table 1 summarizes
the technical specifications. Additionally, the manufacturer supplied Figure 3, in which the left y-axis
depicts the engine’s rounds per minute (RPM), whilst the x-axis indicates the current input in Ampere
and the right x-axis both torque and engine efficiency. The red line represents RPM, the green line
Figure 2 – Example of Integrated Gearbox
System (White et al, 2019)
Figure 1- Example of Integrated Planetary
Gearbox (Bergman, 2018)

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displays the engine’s efficiency at different RPMs and current inputs whilst the blue line demonstrates
the torque output in Nm. This data will serve fundamentally for determining the optimal gearbox ratio.
The Formula Student team had also supplied CAD models needed for the project including rear uprights,
wheel hub and tire models, which were crucial in establishing a functional optimized design. The rims
of the WRe3 (Warwick Racing’s 3rd generation racing vehicle) will be similar in size and type as the
current 13-inch Team Dynamics 1.2 Pro Cast Alloy rims. It is important to note that these relatively
small rims hugely limited the space for packaging, as will be further discussed in Chapter 3.3.1.
3.1.3 Project Methodology
Chapter 2.2 introduced the systems approach taken in this project. For these purposes, a project
methodology flowchart had been created, as shown in Figure 4 below. This aids in the development and
splits the complex design task and aim into separate objectives, whereby parts are designed, integrated,
and then verified in fashion to the systems approach. The objectives had internal deadlines in accordance
with the Project Feasibility Study Gantt chart (Hoogeveen, 7).
Nova 15
Power Max
15 kW
Weight About
2,5 kg
RPM max
2.000-8.000 1/min
Torque max
30 Nm
Voltage Nominal
20-100 V
Efficiency max.
90% incl. controller
Figure 4 – Project Methodology Flow Chart
Figure 3 – Plettenberg Nova 15, RPM, Torque and
Efficiency (Motors - Nova Series 15, 2022)
Table 1 – Electric Motor Data (Motors -
Nova Series 15, 2022)

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3.2 Gearbox System Requirements
3.2.1 Objectives
Warwick Racing had set various objectives for the WRe3 in line with year-by-year innovation targets.
As WRe3 will feature an integrated motor and gearboxes in both the front and the back of the vehicle,
the objectives are similar in most aspects, though the surrounding geometry of the car and fact that the
rear suspension does not steer, slightly alters the final design objectives. The objectives for the rear
integrated gearbox system are summarised in Table 2 below.
3.2.2 Requirements
In line with the systems approach employed in this project various needs and objectives as set out in
Chapter 3.2.1 had been translated into system requirements as shown in Table 15 Appendix A. It should
be noted that only design and mechanical system requirements have been written as the control system
for the electrical motor as other electronics have already been developed as a separate project within
Warwick Racing.
3.2.3 Failure Mode and Effect Analysis
Another crucial aspect of the systems approach to maximize reliability is performing a Failure Mode
and Effect Analysis (FMEA) to determine what aspects of the gearbox require most attention and are
most prone to failure. Table 16 Appendix A summarizes the initial FMEA performed. The analysis
illustrates how particular focus had to be invested towards analysing, digitally testing, and verifying the
gears and planetary gear system to ensure strength and durability, for this MASTA was used. MATSA
is a CAE (Computer Aided Engineering) software package developed by SMT specifically for the
design, analysis and optimisation of gearboxes and drivelines.
3.3 Gearbox Design Constraints
3.3.1 Wheel Hub Packaging
One of the most constraining factors in the design of the integrated in hub gearbox is the space available
for the gearbox. Figure 5 above depicts a rough model of the rear wheel and rim geometry; the area
highlighted in blue illustrates the space available for the gearbox, which helps determine the packaging
Objective
Unit
Value
Vehicle Top Speed
Km/h
120
Gearbox Efficiency
%
> 95
Minimum Service Life
hours
100
Maximum Gearbox Mass
Kg
< 4kg
Maximum Wheel Hub/Upright Mass
Kg
< 8kg
Ingress Protection Rating [IP] (NEMA
vs IP Enclosure Protection, 2022)
65
Table 2 – Design Objectives
Figure 5 – Available Design
Volume

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volume available. The volume available is 160 mm wide, 245 mm high and 200 mm deep. Given the
restricted volume available it was concluded that almost all parts had to be custom-made and could not
be bought off the shelf.
3.3.2 Design for Manufacture and Assembly
A key constraint in the design of the integrated in hub gearbox were the manufacturing processes
available. The gearbox also had to be easy to assemble and maintain throughout its lifetime.
Additionally, using a minimal quantity of bolds and where possible, limiting the number of separate
parts would significantly reduce costs and facilitate an easier assembly.
For Design for Manufacture it was crucial to consider that various parts such as the gears would have to
be outsourced for manufacturing, whereas production of the wheel hub and gearbox cover could be
completed at the Warwick Manufacturing Group (WMG). This however also greatly depends on the
final type of manufacturing chosen for the gearbox casing, shaft, and other parts. Ideally, production of
parts like the gears is outsourced as these require specialised processes and sizing. Chapters 4.4 and 6.3
further investigate the manufacturing processes and treatments most suitable for the various parts. It
should be noted that Warwick’s Formula Student team disposes of a relatively small budget, hence, the
aim was to limit the cost of production of various parts or outsourcing thereof to a minimum. Thus, such
cost-awareness throughout the development of the concept and design stage of the gearbox system was
crucial for the project to remain viable.
Finally, considering Design for Assembly, it was important that the integrated gearbox system could be
assembled using standardised tools, nuts, bolds, bearings and gaskets. As such, upon designing
components it was essential to consider how these could be installed in the final assembly. To aid the
design process the appropriate constraints and tools were considered in the various CAD software
packages and renders were made to facilitate visualisation thereof.
3.3.3 Formula Student FSUK Regulations
The final constraining factor of the integrated gearbox system were the regulations set out by the
Formula Student governing body. The main rules that constrained the design include rule T 7.2.4
mentioning fully sealed lubrication systems, rule EV 4.2.1 specifying that every tractive system must be
appropriately labelled and finally, rule T 7.3.2 outlining the requirements for the protection of the
moving electric motor and gearbox parts. Apart from these regulations the current dimensions,
suspension geometry and wheel hub location remain the same. Therefore, the integrated gearbox system
design was constrained mainly by the current vehicle geometry and its parameters.

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Table 3 – Pugh Matrix for Different Types of Epicyclic Systems
4.0 Gearbox Calculations, Geometry and Development
4.1 Optimal Gear Ratio
The first step in designing the gearbox was to determine the optimal gear ratio. For these purposes, the
maximum required vehicle speed is used as well as the output range of the electrical engine. In order to
allow the engine to produce maximum RPM at maximum vehicle speed. This approach is used to ensure
that the engine provides plentiful torque up to the chosen top speed and does not reach its limit before
said speed is achieved. Based on the target top vehicle speed of 120 km/h (33.33 m/s), assuming that
the maximum electrical engine output is 8000 RPM and the tyre diameter is 521 mm, the optimal gear
ratio was determined using the below equations 4.0, 4.1 and 4.2.
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The optimal gear ratio (GR) is found to be 6.546, thus, implementing this GR meets requirement 1.0
(Table 15, Appendix A). For simplicity and further calculations, a GR of 6 was used to ensure the engine
would not reach speeds above 7500 RPM as a safety and engine preservation measure. The next step
was to find an epicyclic system within the packaging volume that would accommodate for this GR.
4.2 Types of Epicyclic Gear Systems and Evaluation
Various types of epicyclic gear systems exist. In order to decide on the best type of epicyclic gear system
for the purposes of this project, a Pugh matrix was used, as shown in Table 3. The first epicyclic system
that was considered is most common which features one fixed ring gear, three planetary gears and one
sun gear. The second system being similar but with four planet gears, and the third system with five
planet gears. Additionally, both a compound and a multi-stage planetary gear system were considered.
It should be noted that having more planet gears reduces the tangential force acting at each meshing
interface. However, it also increases friction and thereby reduces efficiency because of the greater
contact surface area resulting from more gears meshing per unit time (Arnaudov et al, 2019).
Type of Epicyclic gear
systems
Gear ratio
Range
Packaging
Efficiency (%)
Weight
Number of Parts
(assuming dual
planet carrier)
Overall torque
handling
capabilities
Simple 3 planet gear
3:1-12:1
>96
5
Simple 4 planet gear
3:1-12:1
>93
6
Simple 5 planet gear
3:1-12:1
>90
7
Compound gear system
3:1-12:1
>85
12
Multistage gear system
3:1-99:1
>75
14

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Based on Table 3 it was concluded that the planetary gear system consisting of three planet gears would
be most suitable as it offers the highest efficiency with the least number of parts, whilst also being the
lightest and most packageable option. Moreover, further research (What are the best reduction ratios,
2022) indicated that single stage 3 planet systems with a gear ratio of 6 are ideal and offer best
performance for both frequent acceleration and long-term running.
4.3 Mathematical Foundations and Gear Combinations
4.3.1 Types of Gears
The next step in the gearbox design is choosing the optimal gear type for the planetary system. For this,
three different types of gears are considered, namely, spur, helical, and double helical gears. Some of
the requirements that were considered throughout include: 2.0, 3.0, 3.1 4.0 and 8.5 (Appendix A).
4.3.1.1 Spur Gears
The simplest and most used gear type is the spur gear. Simple in design and implementation this type of
gear features in many modern-day gear-driven mechanical systems. The gear consists of straight-cut
teeth parallel to the axis of rotation, as shown in Figure 6. The
advantage of these gears is that they are easy to manufacture and are
highly efficient (97 – 99.5%) as the entire gear tooth face engages when
meshing. Additionally, the load imposed on the supporting shaft acts
only radially. Manufacturing methods include hobbing, shaping,
broaching, stamping, and sintering (Budynas et al, 2011, 733-783).
Spur gears are optimal for gear reduction ranges between 5-6:1 which
makes them highly suitable for this project as the required ratio is 6:1.
4.3.1.2 Helical Gears
Helical gears are somewhat more complex since the gear teeth are angled. Due to this structural attribute,
the gear teeth engage gradually, making these gears both smoother and quieter in operation as well as
capable of transferring higher loads whilst still being highly efficient at 95 – 98% (Budynas et al, 2011,
673-783). These gears can also operate at higher pitch line velocities (upwards of 25m/s), whereas spur
gears are limited to 20-25m/s. However, the main disadvantage of this gear type is that the load imposed
by the gear on the carrier and bearings produces both radial and thrust forces. This requires a thicker
and stronger carrier as well as heavier roller bearings to accommodate
for this, thus increasing overall gearbox weight. Apart from the types
of loading, helical gears are also tougher to manufacture, considering
that the only methods include hobbing, shaping, and milling
(Budynas et al, 2011, 733-783). It should also be noted that helical
gears require greater lubrication as result of the gradual teeth
engagement which causes greater contact surface stresses.
Figure 6 – Simple Spur Gear
(Spur Gears, 2022)
Figure 7 – Helical Gear Set
(Helical Gears, 2022)

8
4.3.1.3 Double Helical Gears
Double helical (herringbone) gears offer a hybrid between spur and helical
gears as it eliminates the thrust loading that occurs with single helical
gears whilst having higher loading capacities than spur gears. These types
of gears are highly efficient at 95 – 98% whilst reducing noise and being
capable of transferring loads at higher pitch line velocities. The main
disadvantage of these gears, however, is that within a planetary system
they are hard to implement, difficult to package and are the toughest of all
three types of gears to manufacture (Budynas et al, 2011, 733-783).
4.3.1.4 Final Selection
Having evaluated the three types of gears, it was ultimately decided to opt for the spur gear for three
main reasons. Firstly, spur gears are most efficient as compared to helical gears because helical gear
trains have sliding contacts between the teeth. This develops axial thrust forces on the gear shafts and
bearings, thereby generating more heat and greater wear and thus ultimately losing more engine power.
Secondly, since spur gears do not generate thrust forces, ball bearings can be used which are lighter and
more efficient compared to roller bearings because of less surface contact, which enhances overall
efficiency. Thirdly, spur gears allow for the simplest implementation (specifically, they allow for a small
packaging volume), manufacturing and assembly, making them cost-effective and more reliable. These
attributes are highly desirable for the Formula Student team. In contrast though it needs to be recognized
that spur gears will produce greater noise levels, have lower pitch line velocity capabilities and are less
smooth in operation (Radzevich et al, 2012, 177-187). However, since noise and smoothness do not bear
great importance to a race car and considering that pitch line velocities likely will not exceed 20m/s,
factors like ease of manufacture, cost and efficiency are more important. Thus, spur gears were selected
as the most suitable gear type for the planetary gear system.
4.3.2 Gear Combinations for Planetary Systems
To find the optimal macro geometry of the planetary gear system various requirements had to be met.
Most importantly, the gear ratio had to be roughly 6:1 and had to fit within the packaging volume. The
first aspect to be determined was the number of teeth per gear which was computed using six conditions.
The first condition is that the gear ratio is 6, the gear ratio in relation to number of ring gear teeth (Zr)
and number of sun gear teeth (Zs) is shown below (Gear Systems, 2015).
@A"#-!
-"C,#####################################################################40'05
Substituting 6 for GR and rearranging to find the number of sun gear teeth, equation 4.5 is obtained.
D."#/!
0##########################################################################40'*5
The second condition is that the gears’ centre distances must match for them to mesh and prevent
jamming. To satisfy this, the equation below had to be met (Rasmussen, 2022).
Figure 8 – Double Helical
Gear (Herringbone Gear
Prototype, 2021)

9
Table 4 – Valid Planetary Gear System Combinations
D1"D.C+ED################################################################40'B5
The third condition described in formula 4.7 is necessary to ensure that the planet gears are evenly
spaced around the sun gear, with N representing the number of planets (Gear Systems, 2015).
-"2-!
3"F87>#G><7H7%################################################################40'.5
The fourth condition ensures that the planet gears do not interfere with one another, which equation 4.8
describes (Gear Systems, 2015).
D#C+I
J
D.CD#
K
E3=>456
3########################################################40'65
The fifth condition that had to be met is that any gear had to have more than 18 teeth to prevent
undercutting and a thin tooth root radius (Spur Gears - Engineering Information, 2022). To be on the
safe side the constraint was set to 20.
D1$LD##LD.M+)#####################################################################40'/5
The sixth condition is to prevent high torsional fluctuation which occurs if the number of teeth on the
ring gear or sun gear divided by the number of planet gears is an integer [AGMA 6123]. Equation 4.10
was used to describe this.
D.
N"G><7H7%##1>2##D1
N"G><7H7%#################################################
4
0',)
5
To find the best solutions to all conditions a MATLAB script was written. The loop input was the
number of teeth of the planet gear set with a range between 90-140 as any value below or above would
likely not work within the specified packaging volume. The variable Zp or the number of teeth on the
planet gear is the input that was changed each run from 30-60. As the script ran it would check against
the six conditions; if all conditions were met the number of teeth of the ring gear would be stored as an
output. The gear ratio had an acceptable value range of ±0.2 to allow for more suitable gear system
combination outcomes. To prevent undercutting an important requirement is that the difference in teeth
between planet and sun or planet and ring gear is no less than 15 which was set as an extra condition.
As a final step the code would list the combination and calculate the gear ratio again. The final outcomes
of the code are summarized in Table 4.
From table 4 the combination highlighted in green was chosen as said combination would meet all
conditions. Additionally, this combination offered the best ratio between ring and sun gear teeth. Where
the number of sun gear teeth is maximised, which allows for good meshing, and ring gear teeth being
minimized to allow for a high diametral pitch and packaging capabilities. Such a higher diametral pitch
permits for stronger teeth and higher loading capabilities which are desirable for the gear system.
Gear ratio
Sun Gear Teeth (Zs)
Planet Gear Teeth (Zp)
Ring Gear Teeth (Zr)
Integer
6
20
40
100
40
6
22
44
110
44
6
23
46
115
46
6
25
50
125
50

10
Table 5 – Common Gear Materials and their Properties (Granta Edupack 2021)
To prevent significant undercutting the Hunting Tooth Factor must be considered. The Hunting Tooth
Factor Theory states that between meshing gears, the highest common ratio of gear teeth should be less
than 0.25. All the selected combinations have a Hunting Tooth Factor of 0.5 as the planet gear teeth are
directly divisible by the number of sun gear teeth. A way of preventing this is by setting condition 4.7
equal to uneven integers, which generates combinations with a low Hunting tooth factor but would also
result in the planets being unequally spaced. This could have detrimental effects on the load transfer
characteristics and vehicle driveability if the planets are not diametrically opposed. If this is the case,
conflicting mesh frequency harmonics would be generated, which are less likely to be supressed
naturally, thus causing more vibrations (Singh, 2010, 511-530).
A more common way of reducing the Hunting Tooth Factor is by adding or subtracting a tooth from the
gear which prevents the same tooth from contacting every revolution. This more evenly distributes the
wear pattern among the teeth. A tooth can be subtracted from the planet gear to create the final gear set
with teeth numbers 23, 45 and 115. Subtracting a tooth from the planet does not change the ratio or
affect any condition except for 4.6. This gearset was verified within MASTA to ensure that breaking
condition 4.6 would not cause the creation of an invalid gear set (Radzevich et al, 2012, 177-315).
Although breaking 4.6 would theoretically result in the gears not meshing properly, this consequence is
automatically overcome in MATSA by slightly altering the gear geometry.
4.4 Material Selection and Manufacturing
4.4.1 Material Choice
The gear set can be made from various types of materials including metals and polymers. For the
selection process common types of steel alloys, titanium and a high-performance polymer were
considered. Granta Edupack 2021 (material selection software) as well as Solvay’s polymer product
catalogues were used to find the most suitable materials and their properties. The results are summarized
in Table 5 below.
Material (Steel BS/AISI
codes)
Case Hardening or heat
treatment
Ultimate Tensile Strength
(N/mm^2) untreated
Brinell Hardness
(HB)
Density (g/cm^3)
Torlon Polyamide-Imide
-
220
205
1.48
Titanium Alloy Grade 5
Ti/6Al/4V
Ion-Nitriding
1050
336
4.51
EN8D/1040
Nitriding
690
220
7.85
EN24T/4340
Carb./Nitr./Ind. Hard.
940
302
7.84
EN36/9310
Carburizing
1000
341
7.85
EN19/4140
Induction/Nitriding
1050
302
7.85
EN362/8620
Carburizing/Nitriding
700
149
7.9

11
Some important factors to consider are the required strength and fatigue strength to withstand the high
contact and bending stresses that are likely to occur given the power input. Additionally, the material
had to have a high surface hardness and sufficient resistance to adhesive wear to prevent scuffing and
abrasion whilst running at intense duty cycles.
It should be noted that although the Torlon PPA polymer offers decent strength and high hardness at a
fraction of the weight of metals, the material will not have a sufficiently high surface strength to resist
the bending forces. This could lead to early fatigue failures and adhesive wear causing the gearbox to
jam and fail.
As listed in Table 5, steel alloys EN8D and EN362 can be removed from further consideration as they
compare weakly to the other steels in terms of strength and do not offer any significant benefits over the
others. EN24T is a low alloy medium carbon steel which can be case-hardened through carburizing,
nitriding or induction hardening. It has a high tensile strength and good Brinell Hardness. EN36 is a
high hardenability steel alloy due to its chromium contents, which is often carburized. The steel is
frequently used in industry for high stress heavy duty loading scenarios, although it needs to be noted
that it has a low core strength. The final material to consider is EN19, which is a high-quality steel alloy
with high tensile strength and is best known for its good ductility and shock resistance, therefore being
commonly used for shafts, rods, and shaft joints in many modern-day gearbox systems.
Titanium grade 5 alloy has superior properties compared to all other materials, weighing only half of
steel whilst still offering similar strength and hardness. However, the material’s costs as well as the
difficulty relating to its manufacturing and workability make it suboptimal for the Formula Student team.
Having considered all materials, EN36 was ultimately selected for its high surface strength and soft but
strong core, high loading and stress handling capabilities with high tensile strength and medium price.
Although it is the most expensive steel, it offers the best mechanical properties, explaining its frequent
use for modern day high stress gears, shafts, and couplings in the automotive industry.
To establish the maximum allowable stress, equation 4.11 can be used where SF is the safety factor and
Y is the yield strength of the material. For the purposes of this project, a safety factor of 1.3 was chosen
for the gearset calculations as this offers a good balance between optimized design and a low chance of
failure, especially since a steel material was selected.
?1O=?;?#1::9P1Q:7#3<%733 "# 7
89##########################################40',,5
All material properties of EN36 after carburization and oil quenching are summarized in Table 6, page
12 (EN36A Case hardening steel, 2022).

12
Table 6 – Properties of Steel Alloy EN36 Carburized and Oil Quenched (Granta Edupack 2021)
4.4.2 Manufacturing Methods
Manufacturing plays a crucial role in establishing the desired gear strength, thereby constraining the
gear geometry based on tooling and machining precision. Ideally, the manufacturing process will both
be affordable and precise. Fundamentally, the more precise the process, the larger the root fillets of the
teeth can be, which allows for greater loading capabilities of the gear.
4.4.2.1 Milling
Gears can be manufactured through milling, which is a process in which a tool or cutter is used to grind
away material. This process is rather limited and induces extensive heat transfers to the gear during
cutting. The advantages of this process include notably its stability and controllability with high
precision, as well as the fact that it is a highly efficient process that allows for single piece production.
The main disadvantage of this process is its cost intensity and the fact that it requires multiple tools to
manufacture different sizes of gears. Throughout the process, as result of the high heat transfer,
neighbouring teeth cannot be cut simultaneously to avoid gear defects. However, often small defects
occur anyway due to tooling defects or misalignments (Budynas et al, 2011, 733-783).
4.4.2.2 Shaping
Shaping is a manufacturing process in which a reciprocating pinion or rack cutter moves vertically,
cutting into the gear material and forming teeth as the gear stock rotates. The process often allows for
high precision gear manufacturing as machine tolerances are the only limitation. The advantages of this
process lay within its precision and the fact that one cutter or tool can be used to make various gears of
the same diametral pitch, regardless of the number of teeth. The disadvantage is that the process is not
as suitable for making internal gears and that the process can be time-intense, and hence, less efficient.
4.4.2.3 Hobbing
Hobbing is a process similar to shaping and milling whereby a worm gear resembling tool is rotated
around its centre axis whilst the gear material is moved at a direct angular velocity ratioed to that of the
hobbing tool. The advantages of this process include its time efficiency and ability to cut gears of varying
teeth numbers at good precision. The disadvantage of this process is that it is not optimised for the
manufacturing of internal gears or ring gears. Additionally, the process is not capable of machining
adjacent shoulders which are larger than the root radius of the gear (Budynas et al, 2012, 733-783).
Steel
Alloy
Ultimate
Tensile
Strength
(N/ mm^2)
Yield
strength
(N/ mm^2)
Maximum
allowable
stress
(N/mm^2)
Brinell
core Hard-
ness (HB)
Brinell
Surface
hard-ness
(HB)
Elonga
tion
(%)
Young’s
Modulus
(GPa)
Pois
-son
Rati
o
Cost
(pound
per kg)
Densit
y
(g/cm^
3)
EN36
1230
780
600
375
620
9
210
0.29
0.934
7.85

13
4.4.2.4 Wire Electrical Discharge Machining
Wire electrical discharge machining is a relatively new type of manufacturing process for gear making.
This process involves using a thin metal wire which discharges when in contact with the gear stock and
then cuts the material. The main advantage of wire electrical discharge machining is its very high
precision and ability to cut complex shapes; this would allow for greater root fillets on the gear teeth.
Additionally, the process does not impose any forces on the work piece and does not involve the need
for specialised tooling. On the other hand, the disadvantage of this process is the slow rate at which
material is cut, which can make the process more expensive and less efficient (Ho et al, 2004).
4.4.2.5 Selected Manufacturing Method
Through the aforementioned investigations into different types of manufacturing processes it became
clear that hobbing is an unsuitable process as it does not allow for the making of the ring gear. Although
the ring gear could be made separately from the planet and the sun gears, this could lead to varying gear
manufacturing accuracies, which in turn can lead to meshing issues. As precision plays a crucial role to
allow for maximum strength and given that residual material stresses due to tool cutting processes are
undesirable, the milling and shaping processes are equally unsuitable. Additionally, once the gear set
has been optimised the parameters will likely not conform to standardised ISO sizing, which is why
standard tooling used in the milling and shaping process will not be able to cut the custom gear geometry.
Therefore, the selected process is wire EDM, as this process will produce highly accurate gear
geometries with little to no manufacturing defects. Additionally, the process will leave only little
residual stresses in the gear due to the nature of EDM imposing low forces on the gear stock material.
4.4.3 Surface Treatments
A variety of surface treatments are available which allow further strengthening and hardening of the
gears and allow them to resist greater amounts of stress and loading. The processes considered were
limited by those available on the budget of the Formula Student team and can be performed by the gear
manufacturer. Therefore, the selection was limited to carburizing, nitriding and induction hardening.
Having chosen EN36 steel alloy for the gears, all the aforementioned surface treatments could be
performed. However, this steel is specifically engineered to benefit from the carburizing case hardening
technique, which is why this process is employed.
Carburizing is a process in which the steel workpiece is placed in a heated chamber. As the desired
temperature is reached (usually around 850-950˚C), the chamber is filled with carbon monoxide or a
combination of ethane and methane. The carbon of the gas is diffused into the surface of the steel work
piece, for this project, the gear, up to a certain case depth. After the diffusion is complete, the parts are
quenched in a liquid. The added carbon content to the exterior surface of the gear produces a hard casing
around the softer ductile core. This increases the surface strength, toughness, wear resistance and surface
hardness, which are all beneficial to the performance of the gears (Radzevich et al, 2012, 177-315).

14
4.4.4 Manufacturing Method for Project Gears
To achieve the highest quality gears using the EN36 steel alloy, a manufacturing method is set out, as
outlined in the Figure 9.
Initially, the material comes in an untreated rough state. After material inspection and preparation, the
gears can be cut using the wire electrical discharge process. Upon completion thereof, the gears can be
brushed and polished before they are moved to the case hardening facility, where the gears are gas
carburized using carbon monoxide. For high performance gears a case-depth of 1 mm is desirable, which
was equally found to be sufficient for the project gears (Machuta et al, 2018, 2441-2450).
To determine the carburizing process time and heat Figure 10 is used. The ideal temperature for
carburizing is 900˚C, which corresponds to a diffusion time of roughly 9.5 hours. (Mittemeijer et al,
2015, 485-553). Upon completion of the carburization process, the gears are oil-quenched as this best
controls the heat transfer and as compared to other coolants, minimizes the formation of transformational
gradients, cracks, and distortions. Finally, as part
of quality control, the gears could be inspected
using ultrasound testing equipment to ensure an
equally diffused 1 mm layer of carbon throughout
the gear’s surface, as well as examining any cracks
or distortions. This is a step beyond the
capabilities of the chosen manufacturer and is
therefore considered as a future failure mode
avoidance technique in Chapter 3.2.3 (Radzevich
et al, 2012, 243-515).
4.5 Acting Forces, Stresses, and Macro Geometry
The next step in establishing the macro geometry of the gear system was to establish the basic gearset
parameters. Once this step was completed, the forces and stresses acting on the gears could be
investigated using EN36’s mechanical material properties. The bending and contact stresses could
thereafter be used to determine the required face-width of the gears.
Figure 9 – Gear Manufacturing Process Diagram
Figure 10 – Case Depth vs Diffusion
Temperature (Mittemeijer et al, 2015, pp. 502)

15
Table 7 – Preliminary Gear Parameters
4.5.1 Gear Parameterization
To establish the 2D gear parameters, the maximum diameter the ring gear could have (depending on
maximum packaging space) was used to establish the diametral pitch. The maximum diameter found in
Chapter 3.3.1 is 130 mm, the ring gear will need to have 10 mm of rim thickness to allow for bolting to
the gearbox casing. Therefore, a diameter of 120 mm was used as the outer diameter (
R"
) to estimate
the diametral pitch using equation 4.12 where N is the number of teeth.
R=1?7<%1:#S=<TU# "#NC+#
R"######################################################40',+5#
The calculated diametral pitch (DP) is 24.788 which converts to a module of 0.975, however this does
not comply with ISO 56:1997 therefore a module of 1 was chosen which has a DP of 25.4. For gears to
mesh the diametral pitch must be the same for all gears, hence the DP of the planet and sun gears is also
25.4 (Spur Gears - Engineering Information, 2022). Other parameters like circular pitch, gear diameter
and tooth thickness were found for the sun, planet and ring gear using the module and number of teeth,
the results of which are summarized in Table 7.
Parameters (module = 1)
Ring Gear
Planet Gear
Sun Gear
Number of Teeth (N)
115
45
23
Diametral pitch (DP)
25.4
25.4
25.4
Pitch diameter :; < !
"= [mm]
114.985
44.999
22.987
Circular Pitch >? <$#$%&%'
"@$[inch]
0.123
0.123
0.123
Whole Depth >A(<)*)
"B CD CCE@$[mm]
2.25
2.25
2.25
Addendum >F <$ %
"@ [mm]
1
1
1
Dedendum :G <$A(+ H F= [mm]
1.25
1.25
1.25
Outer diameter :;,< ; B EF= [mm]
116.98
46.9994
24.987
Root Diameter :;-< ; H EG= [mm]
112.485
42.499
20.487
Tooth Height :A < F B G= [mm]
2.25
2.25
2.25
Tooth thickness >I < %*./,0
"@$[mm]
1.57
1.57
1.57
An important aspect to consider is that the sun gear teeth root diameter should have sufficient clearance
to the bore of the engine shaft. If this is not the case, this could lead to weak gears and cause cracks due
to high rim stress concentrations in the absence of sufficient space for stress dissipation. The standard
as set out by the American Gear Manufacturing Organisation [AGMA] is that the rim thickness should
be greater than 1.2 times the tooth height. To verify this, equation 4.15 must be satisfied where
RJ"1%
is
the diameter of the engine output shaft, which amounts to 10 mm in diameter.
R1VRJ"1% M,'+EU################################################################40',*5
This condition is satisfied where 12.487 > 2.7. Accordingly, the sun gear parameters are functional.

16
4.5.2 Tangential Force, Contact and Bending Stresses
Having identified the 2D gear geometry, the next step was to determine the face width of the gears using
the safety factor and material properties. To pre-determine a face width for stress calculations, a general
rule of thumb is that the face width should be 3 to 5 times the circular pitch (Budynas et al, 2012, 123-
783). The pre-determined face width is set at 16 mm. As the face width will have a great influence on
the loading limitation of the overall gear system, the tangential force, bending and contact stresses must
be investigated in order to determine the optimised face width. Firstly, the tangential force acting on a
single gear tooth is found using 4.14, where T is applied torque and D is the pitch diameter (Radzevich
et al, 2012, 177-315).
W!"#K666L
M###############################################################40',05
As per Newtons third law, each gear tooth poses an equal but opposite reaction onto the gear tooth of
the meshing gear. Therefore, and since torque is a factor of force and diameter, the tangential force
acting on the gear teeth at each interface is equal. The calculated tangential force is 869.3 newtons as
the load is shared between three planets. However, it should be noted that in real life the load usually is
not carried equally between planets due to manufacturing inaccuracies and periodic tooth stiffness
variations (Seager, 651-56) (Malkapure et al, 2014, 150-155). Thus, the hand calculations only serve as
a preliminary analysis.
One of the most fundamental tools in analysing the maximum allowable tooth bending stress in gears is
the Lewis Bending equation (Barth’s Revision) (4.15). This equation simplifies the gear teeth geometry
to that of a cantilever beam, thereby simplifying the calculation of the bending moment and stresses as
it uses the tangential force as a point load. In equation 4.15,
W!
is the tangential force (Nm), m the
module, W the face width (mm), Y the Lewis form factor and
XN
the dynamic loading factor (Radzevich
et all, 2012, 177-315). The Lewis form factor is a constant found using the pressure angle and number
of teeth, a standard pressure angle of 20˚ is used. According to Shigley’s Mechanical Engineering
Design handbook (Budynas et al, 2011, 738), the form factors are estimated to be 0.334, 0.4 and 0.45
for sun, planet, and ring gear respectively. Table 17 was used for this in (Appendix B).
Y"# W!#
P#Z?Z[#ZXN#################################################################40',*5
For cut and milled gears, the dynamic loading factor, also known as Barth Speed Factor, can be found
using the maximum pitch line velocity of the respective gear (Budynas et al, 2011, 739).
XN"#OD42N
OD4 ##########################################################################40',B5
8" !#ZP
K###########################################################################40',.5
The maximum pitch line of the sun gear is computed using the maximum RPM output of the engine and
equation 4.17. It is however more difficult to find the pitch line velocity of the planet gears, which
requires the use of the Willis equation (4.18) (Willis Equation For Planetary Gears, 2022). In this

17
Table 8 – Hand Calculation Results of Stress Analysis
equation
!#
,
!.
and
!Q
are the angular velocities of the planet, carrier and sun gear, and
R#
and
R.
are
the pitch diameters of the planet and sun gear, respectively.
!#ZR#"#!QZ
J
R#CR.
K
V!.ZR.###############################################40',65
!Q"!!"#########################################################################40',/5
Equation 4.19 recalls the result from equation 4.0 as the output angular velocity of the planetary gear
set is the same as the angular velocity of the planet carrier. It should be noted that the pitch line velocity
of the ring gear is 0 as this gear is fixed. Using the gear’s maximum pitch line velocities, the maximum
bending stresses can be found using equation 4.15, the results of which are shown in Table 8.
Having computed the bending stresses, the Hertz theory is used to investigate contact stresses, for which
equation 4.20 is used. Here
\#
is the elastic coefficient as defined by AGMA (Budynas et al, 2011, 733-
783), theta the pressure angle,
A#
the Radii of pitch of the driving gear and
A'
the radii of pitch for the
driven gear. This formula is computed for the sun to planet interface and planet to ring interface.
YQ" V\#
]
R#S9$
TSUVW
:
X
=^
4
Y%C4
Y&
_`
'
(###################################################40'+)5
The elastic coefficient is found using equation 4.21 where
F#
and
F'
are the young’s moduli of the gear
material (EN36), and
8#
and
8'
the poison ratio of the driving and driven gear material, respectively.
\#"
a
b
b
b
c
,
dZ
e
,V8#
K
F#C,V8'
K
F'
fg
h
h
h
i
4
K
##################################################40'+,5
The Radii of pitch of the driven and driving gear are calculated using equation 4.22 where
R#
and
R'
are the pitch diameters of the driving and driven gear, respectively.
A#"#R#Zjkl#4m5
+########A'"#R'Zjkl#4m5
+#####################################40'++5
Finally, it should be noted that equations 4.20 up to 4.22 employ the English system, therefore all units
were converted accordingly. The computed Hertzian contact stresses are summarized in Table 8 below.
Gear
Torque
(Nm)
Tangential
Force (N)
Maximum
bending
stress
(N/mm^2)
Maximum
contact stress
(N/mm^2)
Angular
velocity
(rad/s)
Maximum
pitch line
velocity
(m/s)
Dynamic
loading
factor
Face width
(mm)
(required)
Sun
30
869.3
418
1441
837.75
9.626
2.57
16 (18)
Planet
60
869.3
252
1441 (S-P)
1227 (P-S)
226.77
5.26
1.86
16 (18)
Carrier
180
-
-
-
127.94
-
-
-
Ring
-
869.3
120
1227
0
-
1.86
16

18
Figure 11 – Orthographic Front View of
Macro Geometry
Figure 12 – Isometric View of Macro
Geometry
Although the hand calculations are not sufficient to determine actual bending and contact stresses, they
allow for a rapid analysis to determine the required face width at maximum loading. It should be noted
though that the dynamic constant equation is based on experimental research and is not theoretically
proven. Additionally, the bending stress equation does not consider the acting radial forces which
generate an additional compressive stress (Budynas et al, 2011, 733-783). As noted in Chapter 4.4.1, the
maximum allowable stress of the material is 600 MPa. The maximum bending stress as experienced by
the sun gear is 418 MPa, this value is comfortably within the allowable stress limit of the material.
Since the fatigue strength or maximum contact stress of EN36 after the specified manufacturing process
is difficult to calculate, ISO standard 6336-5 is used. This standard computes the fatigue strength for
,)O
cycles using the steel, hardening type and quality grade. There are three quality grades, namely,
ML, MQ and ME (listed from lowest to highest). MQ is hereafter used as most manufactures conform
to this quality grade. Given that EN36 is a carburised alloy steel, the maximum allowable contact stress
is 1400 MPa.
The maximum contact stress as calculated between the sun-planet (s-p) interface is 1441 MPa, which is
above the aforementioned maximum allowable contact stress. Therefore, the face width is increased to
18 mm at which width the calculated contact stress is 1359 MPa, which is below the allowable stress
limit. The issue with calculating the contact stress is that various versions of the Hertz theory can be
used, for example, the equations used in this report are simplified and do not account for all factors,
which leads to only very rough estimates. Therefore, a proper analysis using MASTA was required to
ensure the contact and bending stresses do not exceed the material’s limits.
4.5.3 Final Macro Geometry
Having established, through hand calculations, the required face width of the gears the macro geometry
of the gear system was finalised. Using the 18 mm face width and gear parameters from Chapter 4.5.1,
a 3D model of the planetary gear system is created using MASTA, as shown in Figures 11 and 12.

19
5.0 Gear System Design, Optimization and Analysis
5.1 Gear System Design
5.1.1 Gearbox Layout
Before designing any of the individual components or
deciding the type of bearings, a cross sectional layout of
the gearbox was created. Having considered various types
of planetary gearbox designs and the requirements as stated
in Chapter 3, a preliminary technical drawing of the layout
as shown in Figure 13 was created. The drawing illustrates
how the power is transmitted through the input shaft
(purple) to the carrier (black), which outside of the gearbox
casing slots into the wheel shaft (orange), which is secured
using a bolt (dark blue) on the counter-threaded end of the
carrier shaft. The planet gears will be mounted to the
carrier using bearings (green) and are secured using a
carrier plate. For ease of interpretation the gears are not
shown.
5.1.2 Input Shaft Design
The input shaft of the gearbox system is manufactured by Plettenberg, the electrical motor manufacturer.
The standard shaft has a diameter of 18 mm, which can be custom machined to requirements.
Considering the fact that the Formula student team uses a 10 mm shaft diameter for the front gearboxes
and knowing that the face width of the gearset is 18 mm, the diameter and shaft length dimensions are
set. Additionally, 2x30x4 mm grooves are used to fix the gear to the shaft using two dowel keys, which
are easy and cheap to fix in case of failure. Having two keys reduces vibrations, micro backlash and
further reduces the stress acting per key. Therefore, two keys were used. Additional features like
chamfers and fillets are used to increase the shaft’s strength and to reduce local stress concentrations.
Since the shaft has such a small diameter, it is not
hollowed out to reduce shaft mass as strength is more
crucial. The preliminary version of the shaft is shown in
Figure 14, where a simple retaining clip is used to fix
the gear to the input shaft. A locational transition fit is
desirable for the shaft; hence, the H7/p6 tolerance is
applied according to ISO 282-6 (Budynas et al, 2011,
395-408).
Figure 14 – CAD of the Input Shaft
Figure 13 – Layout Schematic

20
5.1.3 Carrier Design
The carrier of the gear system is the component connecting the planets to the output shaft. In designing
the carrier various aspects required consideration, including the carrier plate thickness, Design for
Manual Assembly, connecting mechanism to the wheel shaft and design for stress concentration
reduction employing techniques similar to those shown in Figure 15.
Firstly, as can be seen in Figure 16 below, a double walled carrier was chosen over a single walled
carrier as this would distribute the load evenly over the bearings and planet carrying shafts. If a single
sided carrier is chosen, high stresses could build up at the carrier plate to bearing shaft connection,
leading to potential material, or bearing fatigue failures. As aforementioned, the carrier plate will be
connected to a shaft which, carried by a bearing, exits the internal part of the gearbox. The wheel shaft
will then slot on and will be secured using an M16 bolt through the counter threaded end of the carrier
shaft. Using Data from Shigley’s Standard Handbook of Machine Design (Shigley, 37.1-37.21), a shaft
thickness of 30 mm, adding 5 mm for safety, is used to accommodate for a torsional load of 180 Nm.
Moreover, a stress reduction zone is added to the carrier to guide the stresses from carrier plate to the
main output shaft, thereby reducing stress build-up at the connecting point, as visualized in Figure 17.
Further estimated shaft parameters are used for the initial design, which can be finalised when the wheel
shaft and casing geometry have been fully defined. A locational clearance fit is desirable for the wheel
shaft, hence requiring an H7/h6 tolerance, whereas the rest of the output shaft benefits from a locational
interference fit to allow for rigid and high accuracy mounting (Budynas et al, 2011, 397). Thus, an H7/p6
tolerance is used according to ISO 282-6. The material selected for the carrier is cold rolled AISI 4320
steel, which was selected for its strong mechanical properties and easy workability. The carrier will only
be heat-treated and polished as case hardening causes threads to be brittle, therefore making them likely
to fail. The initial design of the carrier is shown in Figures 16 and 17, whereby the latter figure highlights
the implemented design features.
Figure 15 – Stress (dotted line) Concentration Reduction Methods (Budynas, 2012, 372)
Figure 16 – CAD of the Carrier Assembly
Figure 17 – Cross-Sectional View of Carrier

21
Table 9 – Bearing Selection Parameters
5.1.4 Bearing Selection
The gearbox system requires the selection of three bearings, a bearing holding the input shaft, three
planet carrying bearings, and finally a bearing to support the carrier output shaft. To establish which
bearings are most suitable, the radial loading of each bearing as well as its required lifetime, type and
diameter must be identified. Utilizing this information as well as referring to SKF Bearings’ catalogue,
the preliminary bearing selection was performed. After which in Chapter 5.2.5, after further analysis
this could be verified and updated, if necessary. Firstly, the radial load is found using equation 5.1.
W1"#W!#Z<1>
4
m
5
######################################################################4*',5
The radial load, shaft diameter, radial velocity and required lifetime are summarized in Table 9.
Maximum velocity is taken as maximum electrical engine output.
Equation 5.2 is used to compare the required bearing rating to that of the SKF catalogue to find the most
suitable bearings.
W1#4n1>1B)5'
)"#WP#4nP>PB)5'
)########################################################4*'+5
Here
n1##
and
nP
are the rating life in hours,
>1
and
>P
the revolutions per minute,
WP
the catalogue
rating in kN and
o
is a constant experimentally found to be 3 for ball bearings and 3/10 for roller bearings
(Budynas et al, 2011, 549-610).
A deep groove ball bearing was chosen for the input shaft, the type of which was selected based on the
fact the shaft has a high speed and imposes low axial forces on the bearing as it does not carry the shaft.
Secondly, the bearing needed to be small in dimension to facilitate packaging it, considering the small
input shaft. Therefore, the SKF W 61703-2RS1 bearing was selected for its light weight at 4 grams,
small size and adequate dynamic loading capabilities of 0.559 kN considering the calculated radial load
is 0.424 kN. Another advantage of this bearing is that it is double shielded, which offers protection in
case any metal shavings or chips caused by internal damage are swung around. Additionally, if an oil
seal were to fail, the shields would, in such a case, prevent excessive oil draining via the input shaft,
reducing the chances of extensive damage.
Location
Tangential
Load (N)
Radial
Load (kN)
Shaft diameter
(mm)
Required
lifetime
(hours)
Velocity
(rad/s)
Constant a
Input Shaft
869.3
0.424
10
100
837.75
3
Planet Shaft
869.3
0.424
17
100
226.77
3
Carrier Shaft
869.3
-
35
100
127.94
3/10

22
Table 10 – Selected Bearings Specifications
Selecting the bearings for the carrier proved particularly challenging due to the trade-off between roller
and ball bearings, as the roller bearings offer higher radial load capabilities due to the greater contact
area. However, the geometry must be perfect to avoid skewing or misaligning of which measures to
prevent this add considerable weight. Ball bearings overcome this issue as they self-align, however,
even the smallest damage to a ball would seriously destabilise the bearing and thus also the carrier. Ball
bearings are chosen because potential damage to the balls can be reduced by selecting shielded bearings.
Using ball bearings will also reduce inertial forces and thus make for a more responsive and efficient
gear system. The SKF 62300-2RS1 was chosen due to its high load characteristics (8.06 kN), double
shielding and size, which allows it to fit well within the planet gears and on the planet carrying shafts.
Finally, the output shaft bearing is selected. Since this bearing will carry both the radial load imposed
by the carrier as well as the wheel shaft and therefore, the entire wheel under track conditions, the
bearing needs to withstand both high axial forces and radial forces. A tapered roller bearing is therefore
the only suitable option. The SKF 32007 X is chosen for its exceptionally high dynamic loading
capability at 52.3 kN, long lifetime and relative light weight weighing only 230 grams considering its
size. All bearings use a mounting tolerance P6 in accordance with ISO 14405-1. The details of the
bearings are summarized in Table 10.
5.1.5 Gear System Construction in SMT MASTA
Having designed the input shaft and carrier system and having selected the appropriate bearings, the
gear system is constructed in MATSA to analyse and optimise the system. The carrier geometry is
simplified to allow for easier analysis as the actual carrier geometry cannot be imported and used for
simulations within MASTA. The created model is shown in Figures 18, 19 and 20.
Shaft
Bearing
Name
Bearing
Type
Dynamic
Load Rating
(kN)
Static Load
Rating (kN)
Limiting
Speed
(rpm)
Inner
Diameter
(mm)
Outer
Diameter
(mm)
Width
(mm)
Weight
(kg)
Input
SKF W
61703-
2RS1
Deep groove
ball
0.559
4.75
38000
17
40
12
0.067
Planet
SKF
62300-
2RS1
Deep groove
ball
8.06
3.4
15000
10
35
17
0.06
Output
SKF
32007X
Tapered roll
52.3
54
8500
35
62
18
0.23

23
Figure 18 – Output View in
MASTA
Figure 19 – Cross Sectional
View in MASTA
Table 11 – Oil Types and Their Efficiencies
Figure 20 – Gearbox Oil Level
5.1.6 Gear Lubrication
To guarantee the efficient functioning and lasting lifetime of the gearbox, the appropriate lubricant
needed to be selected as well as its correct volume. Lubrication reduces friction and provides wear
protection to the gears and bearings. Since the bearings require a splash type of lubrication and the
system operates at medium pitch line velocities, Elastohydrodyanmic oil lubrication is chosen. This will
be most beneficial for parts that are in constant rolling contact like gears and bearings (Budynas et al,
2011, 603-669). The desirable viscosity of the oil can be found by using the operating temperature and
maximum pitch line velocity and comparing this to the ISO VG standard chart. At a maximum pitch
line velocity of 8000 RPM at the sun gear, operating temperature of 50 degrees Celsius, power input of
15 kW and gear ratio of 6 the optimal viscosity is between ISO VG 32 and 46, which translates to a
kinematic viscosity of 30 to 50
**(
.
.
However, to verify this, various other common gearbox oil types and their specifications were tested in
MASTA. An advanced system deflection simulation was run for all oil types to discover which was
most efficient. The results thereof are summarized in Table 11.
Oil Type
Manufacturer
Density at 20°
Celsius
Kinematic at 40°
Celsius
Kinematic at 100°
Celsius
Efficiency at peak
performance (%)
Default Lubricant
(SMT MASTA)
-
0.870
220
18.6
99.27
10W40
Motul
0.859
101.9
14.8
99.24
80W90
Mobil
0.90
136
14.5
99.19
75W80
Ravenol
0.844
43.1
8.5
99.16
Dexron VI ATF
Motul
0.843
30.5
6.1
99.1 (Failure)

24
Table 12 – Optimised Gear Set Parameters
From the above table and investigation, it can be concluded that the default lubrication offers the highest
efficiency at 99.27%. As can be observed from the data, there also seems to be a positive trend between
kinematic viscosity and efficiency, namely, the higher the viscosity, the higher the efficiency. Since the
most desirable oil is a default lubricant a manufacturer producing a similar oil can be found using the
density and ISO viscosity grade which is ISO VG 220. Liqui Molly Synth gear oil is chosen as it
conforms to the VG standard and has a similar density at 0.855 at 15 degrees Celsius. The higher
viscosity offers the advantage of less gearbox oil being required as the oil is more resistant to
deformation, thus keeping it on the gear teeth surface for longer. This in turn requires less oil in the
gearbox, thereby reducing unsprung vehicle mass. Using the built-in tools in MASTA, the appropriate
oil level is selected at 111 mm as shown in Figure 20, page 23.
5.2 Gear System Optimisation, Simulation and Analysis
5.2.1 Gear Optimisation
Having established the preliminary gear system macro geometry, it can thereafter be optimized using
MASTA. Utilizing the built-in optimization tool, the gear set is optimized in terms of profile shift,
pressure angle, Helix angle and tip thickness according to user-defined safety factors for contact,
bending, fatigue fracture and micro pitting. A general safety factor target of 1.2 was used. The
calculation of contact and bending safety factors were performed according to ISO 6336:2006. The
optimisation also aimed at reducing undercutting by increasing the profile shift coefficient and pressure
angle. This generates a greater load sharing capability of each tooth, thereby developing less wear. A
more extensive summary of the gear set parameters can be found in Appendix C.
5.2.2 Finite Element Analysis of Individual Gears
After having optimised the gear set, the next step was to investigate their strength using multiple finite
element analyses. It is important to note that after the optimisation the gear geometry of all three gears
had changed, as can be observed from the change in tip and normal thicknesses, hence why an individual
FEA of each gear is required. The FEA’s were set up fixing the inner surface of the gears, for the sun
gear three loads were applied at equally distanced teeth with a point load at the gear tooth tip. Since the
Property
Sun Gear
Planet Gear
Ring Gear
Teeth
23
45
115
Module
1.036
Pressure Angle
26.0418
Helix Angle
0.2987
Tip Thickness (mm)
0.318
0.704
0.875
Backlash (mm)
0.0721 (sun to planet)
0.072 (planet to ring)
Normal Thickness
1.512
0.961
3.733

25
FEA is a static simulation, the tangential force (870 N) is multiplied by the dynamic load factors (see
Table 10) to simulate the gears under dynamic loading. For the sun and planet gears the tangential force
is multiplied by 2.57 and for the ring gear by 1.86. For the planet gear FEA, two loads were applied
across from one another acting in opposing directions in order to simulate how the planet gear engages
with the sun and ring gear. Finally, for the ring gear FEA, three loads were applied at equally spaced
distances like the sun gear. A custom material was made in Fusion 360 using EN36’s mechanical
properties since EN36 is not in its default library. The setup and results of the FEA analyses are shown
in Appendix D.
The sun gear FEA (Appendix D.1) predicted a safety factor of 0.59 which seems rather low; however,
this is likely a result of loading the gear tooth at the tip line rather than applying the force across a
surface. This is further verified by the fact that the highest stress concentrations form along the tooth tip
edge with a maximum of 2140 MPa, as per Figure 36. Ignoring the small high stress regions, most stress
occurs near the tooth root fillets and tooth tip where the maximum stress is 1000 MPa. As can be seen
from Figure 37, the stress concentrations around the tip are rather random with higher stress at different
lengths along the tooth tip edge illustrating that perhaps the simulation is not as accurate in predicting
the dynamic load behaviour. The maximum reaction force is 92.1 newtons which occurs in the dowel-
key cut-out of the gear, as per Figure 39. Another important outcome is the maximum displacement,
which is 0.012 mm at the tooth tip, as can be seen in Figure 38. Both the safety factor and maximum
displacement raise design concerns, however, based on the above discussion it is important to first verify
the results with a MASTA ASD simulation.
The planet gear FEA (Appendix D.2) results predicted a safety factor of 1.57, which is significantly
higher than that of the sun gear despite both having been simulated using the same material. This is a
result of the difference in the optimised micro geometry of the different gears, as notably the tip
thickness of the planet and ring gears are much larger than that of the sun gear. Similarly, to the sun
gear, the highest stress concentrations occur at the tip of the tooth with a maximum of 808.3 MPa, as
Figures 41 and 42 illustrate. This is considerably less than the maximum stress at the sun gear; the
maximum displacement is also significantly lower at only 0.00957 mm. The maximum reaction force
occurs at the inner surface close to the location of the applied tangential load with a maximum of 77.93
newtons. Given these results it can be concluded that the design is strong, however, further MASTA
analyses could help to identify any other potential failure points.
The simulation results of the ring gear (Appendix D.3) were similar to that of the planet gear with a
maximum stress of 600.8 MPa and a safety factor of 2.12. The highest stress concentration occurs near
the tooth tip, as visualized in Figure 46 and 47. The tooth root fillets experience an average stress of 250
MPa, this concentration then dissipates into the rim of the gear, as can be observed from Figure 47. The

26
maximum displacement is low at 0.00588 mm (as per Figure 48) and the maximum reaction force equals
59.13 newtons. These results indicate a strong design and requires no further design enhancement.
Although the simulations can be useful combined with the hand calculations performed in Chapter 4 to
predict regions of high static stress and maximum bending and contact stresses, it also simplifies the
dynamic behaviour of the gears. Hence, the FEA and hand calculations are only useful as preliminary
design verification method after which MASTA can be used to perform analyses based on duty cycles.
This more adequately simulates and thereby predicts the strength of the gears under dynamic loading.
5.2.3 Finite Element Analysis of the Input Shaft and Carrier
With the FEA of the gears complete, it was crucial to also investigate the strength of the input shaft and
carrier. Especially, this is important for the carrier as the geometry and analysis tools in MATSA are not
suitable for the analysis of the complex carrier geometry. Firstly, the FEA for the input shaft was set up
where the two dowel-key slot’s side surfaces are fixed and a moment is applied at the opposite end of
the shaft of 30 Nm, which is the maximum torque. Additionally, at the centre of the bearing location, a
radial load of 0.424 kN is applied in the Y-direction, based on Table 10.
The Carrier FEA is setup fixing the planet carrying shafts and applying a moment at the wheel shaft
connection point of 180 Nm. A radial load of 0.424 kN is applied at the centre of the bearing location
on the planet carrying shafts. Finding the maximum radial load at the drive shaft connection point,
however, was difficult as a full simulation of the car under track conditions is necessary. Therefore it
was assumed the car experiences up to 3 times the force of gravity in the vertical plane. Since the car
weighs around 400kg and assuming each wheel carries this equally the maximum vertical load or radial
load is calculated at 100kg x 9.81
*
.(
x 3g ≈ 3 kN. All radial loads are applied in the same direction, to
simulate the weakest scenario. Additionally, the radial loads are applied such that it acts mainly on a
singular planet carrying shaft. The results of both simulations are shown in Appendix E.
The FEA simulation of the input shaft (Appendix E.1) illustrates how most stress concentrates between
the connecting fillet and start of the dowel key slot as shown in Figures 50, 51 and 52. The shaft
experiences a maximum stress of 498 MPa and has a safety factor of 1.27. Figure 53 illustrates the two
areas containing high stress concentrations. To improve the shaft strength and reduce stress building up,
the radius of the fillets could be increased, a stress reduction zone could be introduced as outlined in
Chapter 5.1.3 or the dowel key slots could be made shorter. However, this last technique could result in
the load being unequally transferred to the sun gear.
In the carrier FEA (Appendix E.2), a safety factor of 0.85 was predicted where the highest stress would
build up in the fillet between the carrier plate and planet carrying shaft as shown in Figure 54. To

27
Table 13 – Gear System Duty Cycles
overcome this local weakness, the radius of the fillet was increased from .4 mm to 1 mm which resulted
in a safety factor of 1.3. The second FEA simulation demonstrated how most stress concentrates inside
the planet carrying shafts, especially the connecting fillets, as per Figures 56, 57 and 58. The FEA also
verifies the function of the stress reduction zone where the highest stress concentration is within the
reduction zone, moving it away from the main shaft, as displayed in Figure 55. The maximum
displacement is found to be 0.216 mm however this is without considering the support the bearing or
wheel shaft offers. Therefore, no further design improvements are deemed necessary, especially since
the parts are made from a high-grade steel.
The weakness of this FEA is that it is a static simulation and therefore does not simulate the loading
under track/running conditions. Since MASTA is not able to import these specific components, a future
suggestion would be to experimentally verify the shaft’s strength using prototypes and servo hydraulic
test machines which could simulate varying amplitude cyclic loading.
5.2.4 MASTA SMT Gear System Analyses
With the FEA analyses complete the full system was investigated in MATSA which allows for the
simulation of various load-cases and life cycles. The analysis considers the whole system and therefore
was used to investigate the gears, bearings, and shafts. Firstly, a set of load-cases with specified lifetime
was created to establish duty cycles. It should be noted that since maximum power and torque are at
4770 RPM this was considered the worst-case loading scenario, additional low, medium, and maximum
RPM/torque load cases were established. The duty cycles are summarized in Table 13.
These duty cycles were used to perform a macro geometry analysis, an Advanced System Deflection
(ASD) analysis and a Loaded Tooth Contact Analysis (LTCA). MASTA automatically created
simulation reports, all of which can be found in Appendices F-H.
The macro geometry analysis provided a summary of the gear set’s maximum contact and bending
stresses and safety factors. All results are summarized in Appendix F. Table 19 summarizes the fatigue
Load Case Name
Duration (h)
Speed (RPM)
Torque (Nm)
Power (kW)
Low Torque
100
4770
5
2.5
Low Power
100
5000
4
2
Medium Torque
100
3180
15
5
Medium Power
100
4770
17
15
Maximum Power and RPM
100
8000
17.9
15
Maximum Torque and Power
100
4774
30
15

28
safety factors for the contact and bending stress under the worst load case. The lowest safety factor is
1.134, which is at the right flank of the teeth on the sun gear. Previously, a safety factor of 1.3 for all
parts was suggested, however, considering that the gears are made from case carburised steel and the
fact that this would occur after 100 hours under the worst-case load scenario, a design improvement is
not necessary. Additionally, it should be noted that the electrical engine inverter limits the engine power
to 80% of its maximum. Therefore, the gears will never actually be exposed to the worst-case load
scenario. Table 19 also illustrates how the third planet gear has a higher safety factor, which can be
explained by the fact that not all gears are engaged simultaneously. This is visualized by Figure 63
Appendix H, demonstrating that only a maximum of 2 planets are in full contact with the sun gear at
any time.
Table 20 summarizes the worst static and dynamic contact and bending stresses. The maximum static
and dynamic bending stresses are the same at 404.65, occurring at the planet’s gear teeth. In Chapter 4
the maximum bending stress was found to be 418, which yields a percentage error of 3.29%. The
maximum static and dynamic contact stresses are 1282.79, which again is close to the hand-calculated
value of 1441 obtained in Chapter 4, Table 8. The percentage error is 10.97%, indicating that the hand
calculations provided precise estimates. This can be explained by the fact that the bending stress
calculations involved the dynamic load factor as well as the accurate estimations of the Lewis form
factor. The contact stress calculations involved many mechanical properties of the material as well as
using the exact same load case as the worst load case in the MASTA study, thus ultimately yielding the
precise estimation of maximum stress.
Table 21 summarizes all safety factors for the gear set calculated in accordance with ISO 6336. The
worst safety factor for scuffing is 1.011 at the sun gear, followed by a safety factor of 1.116 for contact
stresses in the sun gear. The analysis has shown that the weakest link in the gear set is the sun gear, as
expected. As previously mentioned, the safety factors are deemed acceptable.
The Advanced System Deflection analysis results simulated the entire gearbox system under the duty
cycles, results of which are shown accordingly in Appendix G. Table 22 provides the gearbox efficiency
at the different load cases. The overall efficiency is 99.11%, which is an excellent value, with a minimum
of 98.85%. The table illustrates that there is a positive trend between power input and efficiency, the
higher the power input the more efficient the system becomes. Table 23 summarizes the system’s
reliability, which amounts to 99.5%, overall indicating that the system is highly unlikely to experience
any failure throughout its service life.
Table 24 summarizes the safety factors, lifetime and reliability for the different bearings used. The input
shaft carrying bearing, the SKF 62300 X, has the lowest safety factor and a reliability at 1.82 and

29
97.81%, respectively. Thus, the bearings are appropriate for use. Furthermore, it is important to note
that the output carrying bearing has a safety factor of 50 and a reliability of 100, which is logical as there
is no attached output shaft or wheel in the simulation which would generate substantial radial loads.
Therefore, the SKF 32007 X bearing should be verified via real world testing.
Table 25 summarizes the results of the input shaft simulation, yielding a reliability of 100% and a safety
factor of 2.837. The carrier could not be simulated as the complex geometry of it cannot be recreated in
MASTA as was mentioned in the carrier FEA. Figure 59 illustrates that the highest torsional stress
concentration in the input shaft is at the interface between the 18 mm and 10 mm section in similar
fashion to the input shaft FEA results.
The gear Loaded Tooth Contact Analysis analyses the behaviour of the gear teeth or micro geometry
under loading. The results of this study are summarized in Appendix H. Figure 60 from the simulation
illustrates the pressure distribution along the gear tooh profile between the sun and planet gear interface.
Moreover, Figure 61 represents the same interface, whilst Figure 62 depicts the pressure distribution
between the planet and ring gear interface. Figure 61 illustrates how most pressure is experienced by the
middle section of the tooth. Interestingly, it also shows a high-pressure section at the right side of the
tooth profile, which is likely a result of slight shaft deflection under high loads. Figure 62 demonstrates
that the highest pressure at the planet ring interface is again at the horizontal middle of the tooth. It can
also be observed that there is a small high-pressure area towards the left of the surface, likely as a result
of system deflection. The middle sections experiencing the highest pressure are most likely to experience
fatigue wear and micro pitting. However, since all safety factors are acceptable, as previously noted, no
re-design or further optimization is deemed necessary.
Tables 26 and 27 quantify the simulation outcomes which show that the maximum transmitted torque
at the sun-planet interface is 22.13 Nm and 61.91 at the planet-ring interface. Since there are three planet
gears the total torque is 185.7 Nm, which verifies that the gearbox produces the previously estimated
180 Nm of torque. Additionally, the results show that the maximum misalignment is 0.958 and -0.925
micrometre between the sun-planet and planet-sun interface respectively, the source thereof being
system deflection. This is low and acceptable, especially considering the diametral pitch and high load.
The simulation also shows that 100% of the contact area, face width and effective profile are utilized at
all gear interfaces. This maximum utilization effectively makes the gear system as efficient as it is.

30
Table 14 – Force Analysis of Upright and Gearbox Casing
6.0 Gearbox Design
6.1 Gearbox Conceptualisation
Having designed and verified the gear system, the final stage
of the project was to design the gearbox casing and upright. To
do so, Figure 13, introduced in Chapter 5, was used to envision
the upright structure, and create a layout sketch, as shown in
Figure 21. The objective for the gearbox upright was to make
it as light as possible thereby reducing the amount of unsprung
mass. A useful weight reduction technique called Generative
Design was employed using Autodesk Fusion 360. Before
using this technique, a force analysis had to be performed,
exclusion zones and features added, and mounting points had
to be identified and designed.
6.2 Force Analysis
To design the gearbox casing and upright, all the acting forces
had to be identified. The Warwick Formula Student team
provided specifications of various load scenarios, including a
force analysis of the brake calliper and engine mounting. These
were calculated by the team and are summarized in Table 14.
Figure 22 depicts the frame of reference (top right corner) to
demonstrate in which direction forces are exerted. In this
context, it is important to note that all loads are for a singular
upright, whereas the static load (last) is for two uprights/wheel-
hubs.
Load Description
Magnitude Fx (N)
Magnitude Fy (N)
Magnitude Fz (N)
Vertical 3G bump load with weight transfer from
1.5g of braking force (worst load scenario)
2169
500
6885
Lateral 1.5g cornering force
180
2300
430
Maximum force regenerative braking
-
1500
-
Maximum force acceleration
667
-
-
Force to resist motor torque input motor to
mounting plate (6 bolts)
-
102 per bolt
102 per bolt
Force to resist motor torque input mounting
plate to gearbox casing (5 bolts)
-
70 per bolt
85 per bolt
Force transmitted by brake calliper at maximum
braking
-
5364.94 per bolt
-
Static rear load of vehicle mass (total)
1268 (634 per upright)
-
-
Figure 22 –Reference Frame Diagram
Figure 21 – Upright Layout

31
6.3 Manufacturing Process and Material Selection
An important step in designing the gearbox upright is the material and manufacturing process selection.
Since generative design creates structures that can only be made using Additive Manufacturing (AM),
the gearbox upright could only be manufactured using Metal AM. There are various types of metal 3D
printing techniques, though the one commonly used in the automotive industry is Metal Power Bed
Fusion (MPBF). This printing type offers final part mechanical properties that can be of similarly high
quality as forged parts, are capable of manufacturing almost any structure, eliminate residual stresses
whilst producing highly accurate parts, and can be treated and machined like traditional metal parts
(Frazier, 1917-1928). The three methods of MPBF include Direct Metal Laser Sintering (DMLS),
Selective Laser Melting (SLM) and Electron Beam Melting (EBM). EBM involves two electrodes
melting metal producing rough parts that require intense post-processing and machining, hence making
it an undesirable option given the required precision. The difference between DMLS and SLM is that
DMLS involves welding the metal layers together on a molecular level, whereas SLM melts the metal,
resulting in differing grain structures. DMLS parts are therefore more porous but can incorporate alloys
with a broad range of different materials (Frazier, 917-1928). Since the upright is ideally made from an
alloy to improve strength and considering that the DMLS process is more cost effective and widely
available around the University, this AM process is chosen for the manufacture of the upright.
As for the chosen AM process, the material selection is limited to Aluminium, Steel and Titanium. Since
the AM process is already highly cost-intensive, Titanium is not an available option for budgetary
reasons. Steel is another alternative, however, compared to aluminium, it offers relatively low strength
per unit mass as well as requiring post processing to effectively resist outdoor race conditions. Hence,
aluminium is chosen, the specific type being Aluminium AISi10Mg as this is the only available type of
aluminium to be used in Fusion 360’s Generative Design environment. Once the upright is manufactured
through the AM process, the threads and bores will be machined separately using a CNC router.
6.4 Gearbox Design
Using the force analysis table and proposed layout, the casing could be designed. In creating the CAD
model, parametric modelling is used with an iterative approach to add features like brake mounting,
sealing and oil plugs. The aim was to design the gear system enclosure, suspension mounts and brake
mounts. This was followed by employing Generative Design to connect the enclosure to the mounting
points, thereby avoiding contact with any important features.
6.4.1 Sealing and Casing Design
Firstly, the enclosure for the gears was designed, whilst accounting for the IP65 rating (requirements
6.0 and 6.1), the mounting location for the engine, as well as the reaction forces exerted by the engine
and ring gear on the casing from Table 14. A simple casing model was created based on the engine

32
Figure 23 – Initial Casing
Design
Figure 24 – Cross-Section of Casing
and Casing Cover Design
Figure 25 – Engine Connection
Plate Attached to Casing
location and ring gear diameter, as shown in Figure 23. As an IP65 rating is required, two oil seals had
to be selected for the input and output shafts. The selection was performed using the shaft’s rotational
speeds, diameter, performance, and temperature rating, ensuring they are suitable for the outdoor race
car application. The oil seals selected for the input and output shafts are ISO type 1 seals or DIN 3760
Type A seals made from Acrylonitrile-butadiene rubber with a temperature rating of -30 to 100 degrees
Celsius. These seals are made specifically for high-performance automotive applications. To achieve a
good oil seal fit and comply with the IP65 rating an ISO h11 shaft tolerance and H8 casing tolerance
around the oil seal bores are required.
To assemble the casing and insert the gear system, the casing is split into two parts. To ensure that the
interface between these two parts also conforms to the IP65 rating, a custom gasket or rubber O-ring is
required. Since the manufacturing of a custom gasket is cost intensive due to high material costs, a
rubber O-ring was ultimately chosen to seal the casing cover interface. The casing is split in two parts
at the output shaft’s bearing centre location so that the radial loads are directly transmitted into the casing
cover walls. A model displaying the development up to this stage is shown in Figure 24. To mount the
engine a connecting plate was required, which was made using the bolting locations and imposed motor
reaction forces and subsequently optimised using Autodesk Fusion 360’s shape optimisation tool. The
final CAD of the plate is shown in Figure 25.
6.4.2 Wheel Shaft and Braking
Having developed a preliminary casing design, the wheel shaft was designed and added using the 3D
model of the rear tyre mounting pattern and that of the brakes and brake disc. The wheel carrying shaft
was designed around the previously proposed connection system to the carrier output shaft. The model
after implementation of these features is shown in Figure 26. The shaft is to be assembled using five
aluminium cylinders to keep the shaft rotationally locked. This mechanism is used as the shaft and
carrier will be easier to machine, as they only require a bore to accommodate the five cylinders.

33
Figure 29 – Top Oil Plug
Figure 30 – Lower Oil Plug
Additionally, the cylinders are cheap to buy, without requiring any manufacturing, thereby reducing
cost. Finally, an M16 nut bolts on to secure the system. The assembly procedure is shown in Figure 27.
The objective was to have the shaft be as light and strong as possible as well as being able to manufacture
it in house at the University to reduce cost and lead times. Therefore, it was decided to use 6000 grade
aluminium as it perfectly balances those two objectives. The shaft can be manufactured using the 3-axis
Emco Concept mill 260 CNC router available in the Engineering Build Space at the University of
Warwick. The Formula Student team had, as part of another project, designed their own brake calliper
with an externally supplied brake disc and holder. This model was imported to implement the brake disc
into the wheel shaft design and to integrate the calliper into the gearbox casing, which is shown in Figure
28.
6.4.3 Lubrication System
To lubricate the gear system, the casing design requires an oil draining and filling plug. These are added
at the bottom and top, as shown in Figure 29 and 30. The plugs are supplied by Gold Plug (Gold Plug
Magnetic Drain Plug – MP-12, 2022) which manufacture oil draining plugs with an integrated magnet
inside to capture any metal shavings or debris. When removing any of the two plugs the magnet will
allow for an easy way to inspect if the gearbox is suffering any damage and will prevent the metal
particles from mixing with oil and gears, preventing potential further damage.
Figure 26 – Wheel Shaft and
Carrier
Figure 27 – Wheel Shaft and
Carrier Assembly
Figure 28 – Cross-Section of
Gearbox Design

34
6.4.4 Sensors
The gearbox had to feature a thermal and a wheel speed sensor to monitor the gearbox’s behaviour,
including any potential failures, overheating or errors. Another speed sensor is incorporated within the
electrical engine, the advantage of this being that the two speed sensors combined will be able to detect
any errors in power transmission. Additionally, the wheel speed sensor will be part of the traction control
system. The selected temperature sensor is the Febi Bilstein Sensor 37782, weighing only 25 grams and
being capable of withstanding high temperatures. This sensor mounts easily to the gearbox via a M10
bore in the gearbox casing and has a simple male digital plug to connect to the wiring harness.
The chosen speed sensor is the Honeywell LCZ Series Hall effect digital speed sensor which, like the
temperature sensor, is easy to mount using an M10 threaded bore on the side off the casing. The speed
sensor will employ small, embedded magnets in the brake disc holder to measure the angular velocity
using the change in magnetic flux. This data will be fed back via the wiring loom exiting via the back
of the sensor. Considering the suspension mounts are above and below the casing, the two sensors are
placed on the back side of the gearbox, reducing aerodynamic drag and making them more accessible.
Figure 31 illustrates the sensors integrated within the gearbox casing model.
6.4.5 Suspension Mounting Points
With the casing complete, the suspension geometry and tyre dimensions were used to determine the
suspension mounting locations of the upright, creating two smaller 3D models, as shown in Figure 32.
The mounts are based of the current rear suspension concept envisioned by the formula student team. In
creating the mounting points, the inner rim diameter was considered to avoid any interference or contact
with the wheel.
Figure 31 – Sensor Integration
Figure 32 – Suspension Mounting
Points

35
6.5 Generative Design for Upright
Having finalised the gearbox casing, mounting locations and all features, these, in combination with the
force analysis, were used to perform the Generative Design process. Generative Design is a new
innovative tool in the engineering sector that via Artificial Intelligence and Machine Learning, using
user-defined design objectives and constraints, iteratively generates various organic design solutions.
Thereby significantly reducing the mass of a part compared to a conventionally designed part. Autodesk
Fusion 360 CAD software was selected to perform this process as it has a build in, intuitive Generative
Design environment.
The first step in the process was to create and select the appropriate obstacle geometry, in other words,
the areas or bodies to be avoided in creating the upright model. In front and behind the casing as well as
above any plugs or bores, obstacle geometry was created to ensure no geometry was generated around
the oil plugs, sensors, engine, and wheel hub assembly. With this complete, the preserve geometry was
set to the bodies to be included in the Generative
Design outcome. This included the casing,
suspension mounts and brake calliper mounts.
The third step was to add fix constraints which
were applied to the suspension mounting holes,
followed by applying the static loads in
accordance with Table 14. The material was set
to the aluminium selected in Chapter 6.3.
Finally, the objectives for the Generative Design
solution had to be set. The objective was to
reduce mass whilst keeping a safety factor of 2.
Figure 33 illustrates the generative design setup
which was cloud-solved using Fusion 360’s
servers.
The generative design study generated one outcome as shown in Figure 34. This outcome was converted
to a solid body and was edited in the form body workspace to smoothen and optimize the model further.
The final upright is shown in Appendix J. This design was ready to be implemented within the model
of the full gearbox system.
6.6 Gearbox Assembly
Once the upright with integrated gearbox and electrical motor was complete, the assembly procedure
had to be created for the team to be able to build the gearbox system. Appendix I outlines the assembly
procedure using engineering drawings which were created according to ISO 8888. The first drawing No.
Figure 33 –
Generative Design
Setup
Figure 34 – Generative
Design Outcome

36
1 (Appendix I) illustrates the assembly of the carrier and planetary gears. Drawing No. 2 depicts how
the ring gear and casing are assembled. Drawing No. 3 demonstrates how the electrical engine and
mounting plate are assembled. Drawing No. 4 shows how the engine assembly and casing are assembled,
and how the sun gear is to be installed. Drawing No. 5 illustrates how the casing and carrier bearing are
all assembled using a special cooling technique, the notes in regard to the cooling process are included.
Drawing No. 6 shows how the wheel shaft and brake disc are assembled separately after which Drawing
No. 7 illustrates how this assembly is connected to the casing and carrier and how the brake calliper is
installed. Finally, Drawing No. 8 specifies how the final parts and sensors are assembled. Each drawing
includes manufacturing requirements, including tolerancing, and assembly instructions. In each drawing
there is a note box comprising important information like assembly mass and revision details. Small
drawing revisions were denoted with A, B, C etc., and major revisions with 1, 2 etc., in order to keep
track of unfolding developments throughout the project.
6.7 Gearbox System Discussion
With the gearbox system complete and assembly procedure outlined, various renders and cross-sectional
views of the gearbox were made to visualize the final system (Appendix J, Figures 65-74). The final
model of the system which can be found via this link, includes all components sorted into sub-
components according to the assembly procedure, as outlined in Chapter 6.6. Figures 65 to 68 (Appendix
J) are renders of the entire gearbox system within Autodesk Fusion 360, and Figures 69 and 70 show
renders of a cross sectional view. Figure 71 shows a cross-sectional view of the system via a section
analysis. Figure 72 displays a labelled cross-section which gives a good overview of all components and
parts. Finally, Fusion 360’s animation tool was used to create Figures 73 and 74, which depict an
exploded view of the entire gearbox system from two different angles.
The final system weighs 7377 grams, which is very light, knowing that, for example, the same system
that was designed for the front tires by the aforementioned Warwick 4th year group project weighs three
kilograms more. The weight reduction is mainly due to the Generative Design tool used which reduced
weight of the original upright by half whilst offering equal strength and performance. Though all
components have been tested via FEA’s performing real world testing could be useful to find any defects
or manufacturing errors. The gearbox features many innovative design techniques such as a stress
reduction zone in the carrier, load transferring cover design, Generative Design for the upright and
magnetic oil plugs. Altogether this resulted in a highly advanced system that could allow the Warwick
Racing Team to greatly enhance their competitiveness within their class.

37
7.0 Project Outcome, Verification and Validation
7.1 Verification and Validation
As part of the systems approach employed in this project, the final step was to verify the results and
validate them. An important distinction to make between these two terms is that verification looks to
examine whether the system was built correctly, whereas validation ensures whether the correct system
was built. The purpose behind this dual process is to minimize the likelihood of any system failures or
risk of building an incompatible system as much as possible. Verifying the system throughout the
development and design stage reduces extensive costs in the later product life cycle, which is
quintessential for the Formula Student Team, given their restricted budget.
To verify a system, testing methods, so-called Design Verification Methods (DVMs), need to be
established and carried out, which test the system against the requirements. The chosen DVMs included
running various types of virtual simulations and analyses. Throughout Chapters 4 and 5, the gearset was
verified through finite element analyses, a macro geometry analysis, and a loaded tooth contact analysis
under maximum loading conditions. The results of these analyses verified that the gears were indeed
designed correctly and could handle all acting forces and stress. The carrier and input shaft were
individually verified through finite element analyses to ensure their resistance to the most extreme
loading conditions. The outcomes, in terms of safety factors and maximum stress again demonstrated
effectively that they had been designed correctly. Finally, the geartrain system was tested via an
advanced system deflection analysis which verified, through fatigue and life safety factors, that the
geartrain, bearings and input shaft were successfully designed to withstand all loading conditions.
The gearbox casing and upright as well as wheel shaft and engine connecting plate were verified through
finite element analyses to ensure their static strength. However, one weakness of these FEA’s is that it
does not simulate the dynamic loading that the upright/casing would experience, hence further testing
is recommended, as is mentioned in table 28.
A useful tool to ensure and inspect if all previous system requirements are met and all aspects of the
system are verified is a Requirement Verification Traceability Matrix (RVTM). Such matrix was created
for this project and is displayed in Table 28, Appendix K. The RVTM illustrates that almost all
requirements had been met except for Requirements 2.1, 6.1, 7.0 and 7.2 as these require real world
testing. Despite some further testing being required, it can be concluded that the system is well designed
and meets all tested requirements.

38
With the system almost fully verified, it can subsequently be validated. This, however, is less reliant on
pre-existing requirements as the validation process boils down to whether the correct system was built
to begin with. The validation of the project was conducted by comparing the final system to the customer
needs, in this case, the objectives of the Formula Student Team. Recalling Table 2, the design objectives
can be compared to the outcomes. All the objectives of the system as outlined in Table 2 have been met,
though the IP rating needs further verification. In particular, the maximum mass objectives were well
below the maximum, demonstrating how not only the requirements were met but exceeded. Since all
the team’s needs/objectives have been met and since all interface requirements have been met the correct
system has been built. Thus, the integrated in-hub planetary gearbox system developed in the report has
been validated.
7.2 Comparative Analysis
Having designed the gearbox system, a comparative analysis was completed to investigate the quality
of the work performed. As part of a 4th year group project at the University of Warwick (Khonat et al,
2021, 1-255) a similar planetary gearbox system was developed and despite the considerable depth of
the report created by this group, various aspects were not analysed in sufficient detail. For example,
whilst the report (Khonat et al, 2021, 1-255) did consider the Hunting Tooth factor and its effects, it
chose an unevenly spaced epicyclic system to avoid a high hunting tooth factor which is however
unfavourable for the load transfer behaviour of the gearbox (Parker, 561-573). Additionally, it failed to
determine the correct material properties, leading to the use of an ISO standard for material properties
rather than using the properties as indicated by the steel suppliers. This thereafter led to an unreliable
FEA analysis. Subsequently, it should be noted that the report used a MATLAB code for stress
calculations and failed to examine how its calculations were performed and did not mention the
outcomes, resulting in a weak analysis.
Comparing this work to a similar report by students from the University of Belfast (White et al, 2021,
1-7) and students from Chalmers University of Technology (Danielsson et al, 2021, 1-51), it can be
observed that this report goes into much greater depth in establishing and providing a full comprehensive
guide through all development and design stages of the gearbox system. Both reports investigate
simplified aspects and draw most conclusions from previously performed work by other student groups.
The second mentioned report (Danielsson et al, 2021, 1-51) looks at the development of the same system
but does not have any mathematical background except for efficiency calculations and discusses only
superficially the development of the planetary system.
The aim of this report was to perform a full analysis and employ the systems approach to be able to
cover all aspects of the gearbox design, which is oftentimes missing from other published technical
papers. Such as those mentioned above. A technical report written by Oriol Tort (2016) –“Design of a
gearbox for an electric FSEA vehicle” – made a good attempt at doing a full systems approach; however,

39
it touches just the surface of gearset analysis and optimisation and fails to investigate the material science
appropriately by only using the basic mechanical material properties of a given steel. Additionally, it
failed to investigate contact and bending stresses thoroughly.
What has made this report unique is the extensive detail presented in designing the gearbox system by
employing a thorough systems approach and design methodology. This report also demonstrated a more
critical and in-depth analysis and discussion of simulation and optimisation results. Furthermore, this
paper discusses innovative engineering solutions, such as Generative Design, explaining in full detail
how the tool was employed and the benefits it offered.
7.3 Suggestions for Future Improvement
Though this report went into considerable depth regarding the conceptualisation, development, and
design stages of gearbox system, various future improvements are suggested. Firstly, more extensive
research could be performed to identify the benefits and potential of epicyclic gear systems with more
than three planets, as this was only briefly discussed in Chapter 4. Undoubtedly, there is further potential,
through optimisation, to create an even lighter system.
Secondly, the focus of the project was to develop and design the system, and although manufacturing
and assembly procedures were outlined and defined, the project could benefit from a more profound
examination and perfection of these stages. Specifically, to evaluate the feasibility of building the
system, more closely involving local manufacturers and suppliers of individual parts should be given
greater consideration overall.
Finally, the project could be improved by establishing an improved inter-communication and
collaboration between the person conducting the project and the Formula Student Team. The more
involved the team is, the more accurately the system requirements can be grasped and understood,
thereby reducing the need for system adjustments in later stages of the project life cycle. For example,
at the onset of this project, the exact suspension mounting locations had yet to be released by the team,
likely necessitating some final adjustments when building the physical system.
7.4 Application of Work
As was mentioned previously in this technical report, integrated wheel-hub drivetrain systems are
currently predominantly found in Formula Student cars or other lightweight racing classes. Therefore,
the hereby presented research will likely materialize only in this class of motorsport. However, it could
be used to develop any type of tightly packaged gearbox system which could be useful, for example, to
develop new motorcycle drivetrain systems or even future automotive powertrain systems. More
importantly, the conceptualisation, development and design methodology employed within this project

40
might prove helpful to develop other types of drivetrain systems, especially those aiming to be highly
optimized and efficient.
7.5 Concluding Statement
The aim of the project was to conceptualise, develop, design, and optimize an integrated in hub planetary
gearbox system for the Warwick Racing Formula Student race car. The aim of the project has been
achieved successfully as evidenced by the numerical, simulation and analysis results embedded in this
report. Furthermore, the project has:
• Developed and implemented a unique and comprehensive design methodology, incorporating
the systems approach, to successfully design an integrated in-hub planetary gearbox system;
• Extensively employed various Computer-Aided-Engineering and Computer-Aided-Design
software programs and their simulation, analysis, and optimisation tools to design and optimize
a highly efficient (99.1%) and lightweight (7.4 kg) gearbox system;
• Created an innovative and advanced design solution, acknowledging and embedding all
constraints and system requirements, and employing techniques like Generative Design to
create an organic lightweight design solution;
• Thoroughly analysed and selected materials and their treatments, manufacturing methods and
assembly techniques to establish a readily manufacturable system;
• Critically evaluated and employed data, simulation, and analysis results to assess system
reliability (99.5%), efficiency (99.1%), functioning and performance (maximum torque
conversion of 30 Nm to 185 Nm) under numerous loading conditions;
• Conducted a critical self-assessment of the project outcomes and discussed the application of
the undertaken research and development and its industrial application;
• Verified and validated the gearbox system through various Design Verification Methods and
relying on a Requirement Verification Traceability Matrix, demonstrating how the ambitious
project objectives were not only met, but partially exceeded.
In conclusion, the achievement of this project, and its development and design methodology is a highly
optimised, innovative, and verified in-hub integrated planetary gearbox system with a reliability of
99.5%, efficiency of 99.1%, total mass of only 7.4 kg whilst producing 185 Nm of torque. The system,
as well as the methodology employed to design said system will greatly enhance the Formula Student
team’s performance and competitiveness. Altogether this report serves as a foundation for further
research and development, and the design and implementation of such systems in light-weight electric
(racing) vehicles, electric motorcycles, and potentially the automobile of the future.

I
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McGraw Hill, pp. 14-340.
Singh, A., (2010). Load sharing behaviour in epicyclic gears: Physical explanation and generalized
formulation. Mechanism and Machine Theory, 45(3), pp.511-530.
tec-science. (2022). Willis equation for planetary gears. [online] Available at: https://www.tec-
science.com/mechanical-power-transmission/planetary-gear/willis-equation-for-planetary-gears/
[Accessed 2 March 2022].
Tort, Orial Sanfeliu. (2016). Design of a gearbox for an electric FSAE vehicle. Illinois, United States of
America. Armour College of Engineering, Illinois Institute of Technology. Available at:
https://upcommons.upc.edu/bitstream/handle/2117/113957/TFM-%20Oriol%20Sanfeliu%20Tort-
%2039405240F.pdf?sequence=1&isAllowed=y [accessed 7 October 2021].
White, G., Cunningham, G., & Doyle, D. (2019). Design of an Electric Drive Transmission for a
Formula Student Race Car. In Advances and Current Practices in Mobility: SAE International
Conference Proceedings: WCX SAE World Congress Experience. Detroit, United States. Available at:
https://doi.org/10.4271/2019-01-1295 [Accessed 10 October 2021].
Zhang, C., Wang, Z., Song, Q. (2019). Matching Design and Optimization Research of Gearbox for
Electric Vehicle. DEStech Transactions on Environment, Energy and Earth Sciences, (iceee)
https://www.researchgate.net/publication/336928543_Matching_Design_and_Optimization_Research
_of_Gearbox_for_Electric_Vehicle [Accessed 14 October 2021].
Zhang, S., (2018). Parameter Study and Improvement of Gearbox Whine Noise in Electric
Vehicle. Automotive Innovation, 1(3), pp.272-280 https://link.springer.com/article/10.1007/s42154-
018-0029-5 [Accessed 27 October 2021].

V
Appendices
Appendix A – Chapter 3 Supporting Information
Objective
Requirement
Type of requirement
Requirement
Code
Vehicle top
speed
The gearbox system should be geared in such way that at
120km/h the engine is providing 7500rpm (full power).
Functional
1.0
The gearbox system should be capable of transferring the
maximum torque of 30Nm without mechanical failure.
Functional
1.1
Gearbox
efficiency
The gearbox system shall be able to transfer maximum
torque at an efficiency of minimum 90% from shaft output
of the electrical motor.
Non-Functional
2.0
The gearbox should be able to transfer at least 90% of the
input torque by the motor to the wheels whilst
maintaining an operating temperature below 60 degrees
Celsius.
Non-Functional
2.1
Maximum
Service Life
The gearbox should be able to endure 100 hours of
running time at 50% of maximum torque.
Non-Functional
3.0
The gearbox should be easy to maintain and assembly.
Non-Functional
3.1
The gearbox should feature easy to access oil fill and drain
plugs in appropriate positions.
Non-Functional
3.2
Maximum
Gearbox Mass
The mass of the gearbox system should be below 4Kg.
Non-Functional
4.0
Maximum
Wheel Hub
Mass
The entire wheel hub assembly should have a total mass
below 8Kg.
Non-Functional
5.0
Ingress
Protection
Rating
The entire gearbox assembly should have an IP rating of
65.
Non-Functional
6.0
The assembly should be fully protected against dust as
well as against low pressure water jets from all directions
with limited ingress [IEC 60529].
Non- Functional
6.1 IEC
Non-Objective
Based
Loading
Scenarios
The gearbox system shall be able to withstand vertical
and horizontal accelerations of 3g.
Non-Functional
7.0
The gearbox should be able to endure 2 minutes of 25Nm
of electrical engine input with 150Nm of wheel output.
Non-Functional
7.1
The full wheel hub gearbox system should be able to
withstand dynamic loading of 2g cornering, 2g braking, 2g
acceleration and 3g bump loading.
Functional
7.2
Interface
Requirements
The gearbox system should be able to be mounted directly
to the electrical engine using 6 M5 bolts.
Interface
8.1
The full gearbox system should be fully compatible with
the Warwick Racing Manufactured brake callipers.
Interface
8.2
The full gearbox system should be fully compatible with
the 250mm standard cast iron floating braking discs.
Interface
8.3
The rims should be able to be directly bolted onto the final
output shaft of the gearbox system using the standard
wheel pattern of the Team Dynamics 1.2 Pro Cast Alloy
Rims.
Interface
8.4
The full gearbox and engine system should be packaged
with the specified rims and suspension geometry.
Interface
8.5
The gearbox system should feature a 10 mm threaded
hole allowing for the mounting of a temperature sensor.
Interface
8.6
Table 15 – Gearbox System Requirements

VI
Part and/or
Function
Potential
Failure Mode
Effect Mode
S
E
V
Potential
Causes
O
CC
Current Process
Control
D
E
T
RP
N
Recommended
Further Action
Gear Teeth
Breaking of
gear teeth due
to high
loading
Jamming of
gearbox,
loss of
complete
function
10
Incorrect
calculations and
or simulations
due to wrong
loading
3
Verifying results by
comparison to
similar projects
3
90
Running matlab
code to perform
calculations
Gear Teeth
Breaking of
gear teeth due
to material
failure
Jamming of
gearbox,
loss of
complete
function
10
Incorrect
simulations and
or material
selection
2
Ensure simulations
are run at maximum
load and correct
safety factor
2
40
Ensuring the
appropriate
material simulator
is used as well as
material inspection
Gear Teeth
Breaking of
gear teeth due
to
manufacturing
defects
Jamming of
gearbox,
loss of
complete
function
10
Incorrect
machining by
manufacturing
or material
defect
2
Ensure all
manufactures work
according to ISO or
BS standards
3
60
Ensure material
has gone through
proper inspection
which could
include ultrasonic
inspection
Gear Teeth
Fatiguing of
gear teeth
surface due to
high loading
Jamming of
gearbox,
loss of
complete
function
10
Incorrect
analysis and
simulation of
contact stresses
3
Ensure appropriate
preliminary
calculations are
performed and cross
verified with FEA and
simulation results
3
90
Gear Teeth
Fatiguing of
gear teeth due
to high
loading
Jamming of
gearbox,
loss of
complete
function
10
Wrong or in
proper material
selection
2
Ensure material
calculations and
selection is done to
an appropriate level
and verified to
industry standards.
3
60
Gear Teeth
Fatiguing of
gear teeth
surface due to
high loading
Jamming of
gearbox,
loss of
complete
function
9
Un equal
penetration of
case hardening
causing week
spots in surface
3
Ensure the
manufacturer uses
and operates case
hardening technique
to industry standards
2
54
Inspect the surface
of the gear using
an ultrasound
transducer
ensuring equal
depth of case
hardening
Gearbox
Grinding of
gear teeth
Build-up of
material
pieces in
gearbox
resulting in
jamming
8
Incorrect
parameters set
in CAD software
3
Verifying
measurements
through CAD and
SMT MASTA
2
40
Output
Shaft
Overloading of
shaft due to
unforeseen
stresses
Potential
bending
and miss
alignment
of wheels
7
Incorrect
simulations and
or material
selection
2
Running varies FEA
simulations,
considering the
safety factor and
material selection
2
21
Investigation
acting forces of
racing cars and
comparing those
for analysis
Oil
Reservoir
High internal
gearbox
pressure as
result of
inserting too
much oil
Reduced
efficiency
and
leakages
6
Incorrect
volumetric
calculations
having
considered
thermal
expansion of oil
2
Investigating the
thermal expansion of
oil used adding a
safety factor
3
36
Gearbox/W
heel Hub
Interference
with
suspension
and other
geometry
Poor
vehicle
dynamics
and
damage of
suspension
5
Incorrect
analysis of
suspension
geometry when
coilover are
under full
compression
1
Analysing movement
of suspension in CAD
with finalized
gearbox/wheel hub
model
2
10
Table 16 – Gearbox System FMEA

VII
Appendix B – Chapter 4 Supporting Information
Table 17 – Number of Teeth of Involute Gear vs
Lewis Form Factor (Budynas et al, 2011, 738)
Table 18 – Gearbox System FMEA

VIII
Table 18 – Final Gear Set Detailed Specifications
Appendix C – Final Gear Set Specifications
Cylindrical Gear Set
Name
Planetary Gear Set
Planetary Gear
Set\Sun
Planetary Gear
Set\Planet
Planetary Gear
Set\Annulus
Number of Teeth
z
23
45
115
Face Width (mm)
b
18
18
18
Normal Module (mm)
mn
1.036
Flank Name
Both Flanks
Normal Pressure Angle (°)
αn
26.0418
Helix Angle (°)
β
0.2987
Centre Distance (mm)
aw
34.5
34.5
Speed Ratio A to B
0.5111
0.3913
Torque Ratio A to B
1.9565
2.5556
Default Cylindrical Gear
Material ISO
Default Material

IX
Figure 35 – Applied Loads and Static
Stress
Figure 36 – Maximum Static Stress
Figure 37 – Maximum Static Stress;
close-up of gear tooth
Figure 38 – Maximum Displacement
Figure 39 – Maximum Reaction Force
Appendix D – FEA Results of Individual Gears
Appendix D.1 – Sun Gear FEA Results

X
Figure 40 – Applied Loads and Static
Stress
Figure 41 – Maximum Static Stress
Figure 42 – Maximum Static Stress;
Close-up of Gear Tooth
Figure 43 – Maximum Displacement
Figure 44 – Maximum Reaction Force
Appendix D.2 – Planet Gear FEA Results

XI
Figure 45 – Applied Loads and Static
Stress
Figure 46 – Maximum Static Stress
Figure 47 – Maximum Static Stress;
Close-up of Gear Tooth
Figure 48 – Maximum Displacement
Figure 49 – Maximum Reaction Force
Appendix D.3 – Ring Gear FEA Results

XII
Figure 50 – Maximum Stress Angle 1
Figure 51 – Maximum Stress Angle 2
Figure 52 – Maximum Stress Close-up
Figure 53 – Regions of High Stress
Appendix E – FEA Results of Input Shaft and Carrier
Appendix E.1 – Input Shaft FEA Results

XIII
Figure 54 – Setup and Maximum Stress
Figure 55 – Maximum Stress Angle 2
Figure 56 – High Stress Regions and
Stress Reduction Zone (Red)
Figure 57 – High Stress Regions in the
Carrier
Figure 58 – Stress Distribution in a
Planet Carrying Shaft
Appendix E.2 – Carrier FEA Results

XIV
Table 19 – Fatigue Safety Factor Summary
Table 20 – Maximum Contact and Bending Stresses
Appendix F – Macro Geometry Analysis Results Report
Fatigue Safety Factor
Summary
Name
Bending Safety Factor
for Fatigue
Contact Safety Factor
for Fatigue
Left Flank Rating
Right Flank
Rating
Left Flank Rating
Right Flank
Rating
Planetary Gear Set\Sun
50
2.5141
50
1.134
Planetary Gear Set\Planet
(Planet 1)
1.7803
2.0771
2.2889
1.2478
Planetary Gear Set\Planet
(Planet 2)
1.7803
2.0771
2.2889
1.2478
Planetary Gear Set\Planet
(Planet 3)
2.6257
3.1525
2.7117
1.5002
Planetary Gear Set\Annulus
Not Rateable
Not Rateable
2.3164
50
Name
Maximum
Bending
Stress
(MPa)
Maximum
Contact
Stress
(MPa)
Maximum
Static
Bending
Stress
(MPa)
Maximum
Static
Contact
Stress
(MPa)
Left
Flank
Rating
Right
Flank
Rating
Left
Flank
Rating
Right
Flank
Rating
Left
Flank
Rating
Right
Flank
Rating
Left
Flank
Rating
Right
Flank
Rating
Planetary
Gear Set\Sun
0
400.9418
0
1282.7905
0
400.9418
0
1282.7905
Planetary
Gear
Set\Planet
(Planet 1)
404.6529
346.8306
711.4809
1269.3831
404.6529
346.8306
711.4809
1269.3831
Planetary
Gear
Set\Planet
(Planet 2)
404.6529
346.8306
711.4809
1269.3831
404.6529
346.8306
711.4809
1269.3831
Planetary
Gear
Set\Planet
(Planet 3)
274.3587
228.5167
594.4606
1047.4428
274.3587
228.5167
594.4606
1047.4428
Planetary
Gear
Set\Annulus
Unknown
0
711.4809
0
Unknown
0
711.4809
0

XV
Table 21 – Gearset Safety Factor Summary
Compon
ent
Description
Safety
Factor
Required
Normalised
Reliabilit
y (%)
Damage
(%)
Time to
Failure (hr)
Planetar
y Gear
Set\Sun
ISO/TS 6336-20:2017, Scuffing
(Flash Temperature Method)
1.1011
1
1.1011
N/A
N/A
N/A
ISO 6336:2006, Contact
1.116
1
1.116
N/A
2.63
68568.5429
ISO 6336-4:2019 according to Witzig
thesis, Tooth Fatigue Fracture
1.4776
1.2
1.2314
N/A
N/A
N/A
ISO/TS 6336-22:2018, Micro pitting
1.4801
1
1.4801
N/A
N/A
N/A
ISO 6336:2006, Static Contact
1.8406
1.2
1.5338
N/A
N/A
N/A
ISO 6336:2006, Bending
2.4433
1
2.4433
N/A
0
8765760
ISO/TS 6336-21:2017, Scuffing
(Integral Temperature Method)
3.4016
1
3.4016
N/A
N/A
N/A
ISO 6336:2006, Static Bending
6.2978
1.6
3.9361
100
N/A
N/A
Planetar
y Gear
Set\Plan
et
(Worst
Safety
Factors)
ISO/TS 6336-20:2017, Scuffing
(Flash Temperature Method)
1.1011
1
1.1011
N/A
N/A
N/A
ISO 6336:2006, Contact
1.2312
1
1.2312
N/A
0.48
251946.496
6
ISO 6336-4:2019 according to Witzig
thesis, Tooth Fatigue Fracture
1.4776
1.2
1.2314
N/A
N/A
N/A
ISO/TS 6336-22:2018, Micro pitting
1.4801
1
1.4801
N/A
N/A
N/A
ISO 6336:2006, Static Contact
1.8601
1.2
1.55
N/A
N/A
N/A
ISO 6336:2006, Bending
1.7559
1
1.7559
N/A
0
8765760
ISO/TS 6336-21:2017, Scuffing
(Integral Temperature Method)
3.4016
1
3.4016
N/A
N/A
N/A
ISO 6336:2006, Static Bending
5.8841
1.6
3.6776
100
N/A
N/A
Planetar
y Gear
Set\Ann
ulus
ISO 6336-4:2019 according to Witzig
thesis, Tooth Fatigue Fracture
2.3563
1.2
1.9635
N/A
N/A
N/A
ISO 6336:2006, Contact
2.2959
1
2.2959
N/A
0
8765760
ISO/TS 6336-22:2018, Micro pitting
2.6224
1
2.6224
N/A
N/A
N/A
ISO 6336:2006, Static Contact
3.3434
1.2
2.7861
N/A
N/A
N/A
ISO/TS 6336-20:2017, Scuffing
(Flash Temperature Method)
4.7579
1
4.7579
N/A
N/A
N/A
ISO/TS 6336-21:2017, Scuffing
(Integral Temperature Method)
5.2383
1
5.2383
N/A
N/A
N/A

XVI
Table 22 – Load Cases for Gear System Input
Table 23 – Gear System Reliability Summary
Table 24 – Bearings Ratings
Appendix G – Advanced System Deflection Results Report
Efficiency
Load Case Name
Power Lost
(kW)
Energy
Input (MJ)
Energy Output
(MJ)
Energy Lost
(MJ)
Efficiency
(%)
Medium Torque in Gearbox Load
Cases - Initial
0.0573
1800
1779.3731
20.6269
98.85
Medium Power in Gearbox Load
Cases - Initial
0.08434
3600
3569.6386
30.3614
99.16
Maximum RPM and Power in
Gearbox Load Cases - Initial
0.1106
5400
5360.1956
39.8044
99.26
Maximum Torque and Power in
Gearbox Load Cases - Initial
0.1092
5400
5360.6767
39.3233
99.27
Low Torque in Gearbox Load
Cases - Initial
0.04692
1080
1063.1084
16.8916
98.44
Low Power in Gearbox Load Cases
- Initial
0.03437
720
707.6275
12.3725
98.28
Overall
99.11
Reliability
Rating Type for Bearing Reliability
ISO 281:2007
Shaft Rating Method
SMT
Rating Type for Shaft Reliability
Fatigue For Infinite Life
Overall Duty Cycle Bearing Reliability (%)
100
Overall Duty Cycle Shaft Reliability (%)
100
Overall Duty Cycle Gear Reliability (%)
99.5
Overall System Reliability (%)
99.5
Name
Bearing
Design
Component
Detailed
Analysis
Misalignment
Summary
Designation
ISO
281:2007
Modified
Rating Life
Safety
Factor
ISO 281:2007
Modified
Rating Life
Time (hr)
ISO/TS
16281:2008
Modified
Reference
Rating Life
Damage (%)
ISO/TS
16281:2008
Modified
Reference
Rating Life
Time (hr)
Worst ISO
76:2006
Safety
Factor,
Static
Equivalent
Load
Capacity
Ratio
ISO
281:2007
Basic
Rating
Life
Reliability
(%)
Maximum
Value (mrad)
Formula Student
Gearbox\Bearing
1 (using mean
load and load
sharing factor)
62300-
2RS1
1.8224
3631.6958
17.63
3403.6555
1.5986
97.81
-
Formula Student
Gearbox\Bearing
1 (Planet 1)
62300-
2RS1
2.4486
8808.1981
7.28
8240.0815
1.9663
99.29
0.2489
Formula Student
Gearbox\Bearing
1 (Planet 2)
62300-
2RS1
2.4486
8808.1986
7.28
8240.0818
1.9663
99.29
0.2489
Formula Student
Gearbox\Bearing
1 (Planet 3)
62300-
2RS1
2.4486
8808.1979
7.28
8240.0812
1.9663
99.29
0.2489
Formula Student
Gearbox\Bearing
2
W 61703-
2RS1
20.1157
4883784.4278
0.0015
8765760
50
100
5.556E-06
Formula Student
Gearbox\Bearing
3
32007 X
50
8765760
0
8765760
50
100
1.495E-06
Maximum
-
-
1303.9092
412.5613
-
-
-

XVII
Table 25 – Input Shaft Analysis
Figure 59 – Torsional Stress along Shaft Profile
Shaft Analysis
Shaft Rating Method
SMT
Worst Static Safety Factor
2.8347
Worst Fatigue Safety Factor
3.7796
Worst Fatigue Damage (%)
0
Worst Fatigue Safety Factor For Infinite Life
3.7796
Worst Reliability For Finite Life (%)
100
Worst Reliability For Infinite Life (%)
100

XVIII
Figure 60 – Pressure Distribution along Gear Tooth Profile for Sun Gear
Table 26 – LTCA for Sun-Planet Interface Numerical Simulation Results
Appendix H – LTCA Results Report
Gear Mesh Transmission Error Analysis Sun to Planet
Analysis Name
Basic LTCA
Peak-To-Peak TE (µm)
2.5645
Active Flank
Right
Apply Application and Dynamic Factor?
Yes
Name
Sun
Planet (0°)
Nominal Torque (N
⋅
m)
9.9978
19.4746
Torque (Scaled by Application and Dynamic Factors) (N
⋅
m)
11.365
22.1379
Equivalent Misalignment (µm)
fsh
0.9585
Misalignment Source
System Deflection
ISO 6336:2006 Mesh Stiffness Across Face Width (N/m)
2.9E+08
ISO 6336:2006 Single Stiffness Across Face Width (N/m)
2.069E+08
ISO 6336:2006 Mesh Stiffness (N/(µm
⋅
mm))
cγ
16.1099
ISO 6336:2006 Single Stiffness (N/(µm
⋅
mm))
c'
11.4953
Maximum Contact Stress (MPa)
918.4439
Index of Roll Angle with Maximum Contact Stress
2
Minimum Force Per Unit Length (N/m)
0
Maximum Force Per Unit Length (N/m)
72094.773
Calculated Face Load Factor (Contact)
KHβ
1.2161
Percentage of Potential Contact Area Loaded (%)
100
Face Utilization Load Cutoff Parameter (%)
0
Utilization Force Per Unit Length Cutoff Value (N/m)
0
Percentage of Potential Contact Area Utilized (%)
100
Percentage of Effective Face Width Utilized (%)
100
Percentage of Effective Profile Utilized (%)
100
Theoretical Total Contact Ratio
1.5641
Actual Total Contact Ratio
1.75
Peak-to-Peak Moment About Centre (N
⋅
m)
3.302

XIX
Figure 61 – Pressure Distribution along
Gear Tooth Profile for Sun-Planet
Interface
Figure 62 – Pressure Distribution along
Gear Tooth Profile for Sun-Planet
Interface
Table 27 – LTCA for Planet-Ring Interface Numerical Simulation Results
Gear Mesh Transmission Error Analysis Planet to Ring
Analysis Name
Basic LTCA
Peak-To-Peak TE (µm)
1.1952
Active Flank
Left
Apply Application and Dynamic Factor?
Yes
Name
Planet (0°)
Annulus
Nominal Torque (N
⋅
m)
19.4441
49.5839
Torque (Scaled by Application and Dynamic Factors) (N
⋅
m)
24.2797
61.915
Equivalent Misalignment (µm)
fsh
-0.9256
Misalignment Source
System Deflection
ISO 6336:2006 Mesh Stiffness Across Face Width (N/m)
3.393E+08
ISO 6336:2006 Single Stiffness Across Face Width (N/m)
2.273E+08
ISO 6336:2006 Mesh Stiffness (N/(µm
⋅
mm))
cγ
18.8497
ISO 6336:2006 Single Stiffness (N/(µm
⋅
mm))
c'
12.6282
Maximum Contact Stress (MPa)
446.8043
Index of Roll Angle with Maximum Contact Stress
17
Minimum Force Per Unit Length (N/m)
0
Maximum Force Per Unit Length (N/m)
57543.831
Calculated Face Load Factor (Contact)
KHβ
1.2657
Percentage of Potential Contact Area Loaded (%)
100
Face Utilization Load Cutoff Parameter (%)
0
Utilization Force Per Unit Length Cutoff Value (N/m)
0
Percentage of Potential Contact Area Utilized (%)
100
Percentage of Effective Face Width Utilized (%)
100
Percentage of Effective Profile Utilized (%)
100
Theoretical Total Contact Ratio
1.6857
Actual Total Contact Ratio
2.1875
Peak-to-Peak Moment About Centre (N
⋅
m)
3.5628

XX
Figure 63 – Number of Teeth in Contact between Sun and Planet Gears
Figure 64 – Number of Teeth in Contact between Planet and Ring Gears

XXI
Appendix I – Gearbox System Assembly
The Assembly Engineering Drawings follow on the next page.

XXII
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





 





 



 


 


    
   
   
   



  



 




XXIII



  











   
 
 
  






 





    





  



  


  



 





 



 



XXIV



  











   
 
 
  






 





    
   
   
  






 




XXV



  











   
 
 
  






 





    
  




   
  









  







 



 


 


 


XXVI



  











   
 
 
  






 





  
  
  



   
  
















  




  













 


 


 

 



 







XXVII



  











   
 
 
  






 





    
   
  






  




 




 



 


XXVIII



  











   
 
 
  






 





    
  



  




   












 


 


 




XXIX



  











   
 
 
  






 





    
  




   
  


 








 


 



XXX
Appendix J – Gearbox System Visualisation
Figure 65 – Front-Side Render of Gearbox System
Figure 66 – Back-Side Render of Gearbox System

XXXI
Figure 67 – Front-Side Render of Gearbox System, 2
Figure 68 – Side Render of Gearbox System

XXXII
Figure 69 – Cross-Sectional Render of Gearbox System
Figure 70 – Cross-Sectional Render of Gearbox System, Back Side

XXXIII
Figure 71 – Cross-Section Analysis of Gearbox System (Top View)
Figure 72 – Cross-Section Analysis of Gearbox System, Labelled

XXXIV
Figure 73 – Exploded View of Gearbox System (Front)
Figure 74 – Exploded View of Gearbox System (Back)

XXXV
Appendix K – Chapter 7 Supporting Information
Requir
ement
ID
Requirement Description
Require
ment
Type
DVM
Outcome
Conclusion/Recommend
ations
1.0
The gearbox system should be geared in
such way that at 120km/h the engine is
providing 7500rpm (full power).
Function
al
Verified
through hand
calculations
Passed
Weak DVM, could be
improved by real world
track testing.
1.1
The gearbox system should be capable of
transferring the maximum torque of 30Nm
without mechanical failure.
Function
al
DVM 1: FEA
DVM 2: Macro
Geometry
Analysis
DVM 3: ASD
DVM 4: LTCA
Passed
Strong DVM’s, verified in
many ways, could still
benefit from bench test
and track test.
2.0
The gearbox system shall be able to transfer
maximum torque at an efficiency of
minimum 90% from shaft output of the
electrical motor.
Non-
Function
al
ASD Simulation
Passed
Excellent DVM,
outcomes showed a
>99% system efficiency
meeting its requirement
2.1
The gearbox should be able to transfer at
least 90% of the input torque by the motor
to the wheels whilst maintaining an
operating temperature below 60 degrees
Celsius.
Non-
Function
al
10 hours on
bench test at
maximum
power
Not
conducted
DVM can only be
performed with physical
system
3.1
The gearbox should be able to endure 100
hours of running time at 50% of maximum
torque.
Non-
Function
al
ASD Simulation
Passed
The results showed
excellent system
behaviour and resilience
3.2
The gearbox should feature easy to access oil
fill and drain plugs in appropriate positions.
Non-
Function
al
Optical Model
Inspection
Passed
Simple DVM but the
model does verify plugs
are easy to access
4.0
The mass of the gearbox system should be
below 4Kg.
Non-
Function
al
CAD Inspection
of model
properties
Passed
CAD showed gear system
weighing just under 3.8
kilograms
5.0
The entire wheel hub assembly should have
a total mass below 8Kg.
Non-
Function
al
CAD Inspection
of model
properties
Passed
CAD showed entire
system weighing 7.37
kilograms
6.0
The entire gearbox assembly should have an
IP rating of 65.
Non-
Function
al
Selection of
appropriate
sealing
techniques
Passed
Weak DVM as correct
parts can be selected but
could still fail to pass IP
65 rating, see Req. 6.1
6.1 IEC
The assembly should be fully protected
against dust as well as against low pressure
Non-
Function
al
Mounted rig
with water jets
testing
Not
conducted
DVM can only be
performed with physical
system

XXXVI
water jets from all directions with limited
ingress [IEC 60529].
7.0
The gearbox system shall be able to
withstand vertical and horizontal
accelerations of 3g.
Non-
Function
al
DVM 1: FEA
DVM 2: Track
Testing
Passed
Not
Conducted
Only partially verified,
physical system required
7.1
The gearbox should be able to endure 2
minutes of 25Nm of electrical engine input
with 150Nm of wheel output.
Non-
Function
al
DVM 2: Macro
Geometry
Analysis
DVM 3: ASD
DVM 4: LTCA
Passed
Strong DVM’s, verified in
many ways the system,
could still benefit from
bench test and track test.
7.2
The full wheel hub gearbox system should
be able to withstand dynamic loading of 2g
cornering, 2g braking, 2g acceleration and 3g
bump loading.
Non-
Function
al
DVM 1: FEA
DVM 2: Track
Testing
Passed
Not
Conducted
Only partially verified,
physical system required
8.1
The gearbox system should be able to be
mounted directly to the electrical engine
using 6 M5 bolts.
Interface
Optical CAD
Model
Inspection
Passed
CAD model shows the
interface mounting
8.2
The full gearbox system should be fully
compatible with the Warwick Racing
Manufactured brake callipers.
Interface
Optical CAD
Model
Inspection
Passed
The CAD model shows
the perfect integration of
the brake calliper
8.3
The full gearbox system should be fully
compatible with the 250mm standard cast
iron floating braking discs.
Interface
Optical CAD
Model
Inspection
Passed
The CAD model shows
the perfect integration of
the brake disc
8.4
The rims should be able to be directly bolted
onto the final output shaft of the gearbox
system using the standard wheel pattern of
the Team Dynamics 1.2 Pro Cast Alloy Rims.
Interface
Optical and
Geometric CAD
Model
Inspection
Passed
The wheel bolts perfectly
to the designed wheel
shaft
8.5
The full gearbox and engine system should
be packaged with the specified rims and
suspension geometry.
Interface
Optical and
Geometric CAD
Model
Inspection
Passed
The final CAD model fits
perfectly within the blue
design volume (Chapter
3.3.1)
8.6
The gearbox system should feature a 10 mm
threaded hole allowing for the mounting of
a temperature sensor.
Interface
Optical CAD
Model
Inspection
Passed
The temperature sensor
is easily mounted to the
casing
Table 28 – Requirement Verification Traceability Matrix