1. 1
Optimisation of a Sustainable Flywheel Energy
Storage Device
Prepared by:
Carl Ronald Schoombie
Department of Electrical Engineering
University Of Cape Town
Prepared for:
Dr Azeem Khan
Department of Electrical Engineering
University Of Cape Town
October 2014
Submitted to the Department of Electrical Engineering at the University of Cape Town in partial
fulfilment of the academic requirements for a Bachelor of Science degree in Electrical Engineering
Key Words:
Axial Flux; Brushless DC machine; Flywheel; Permanent Magnet

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Declaration:
1. I know that plagiarism is wrong. Plagiarism is to use another's work and pretend that it is
one's own.
2. I have used the IEEE convention for citation and referencing. Each contribution to, and
quotation in, this thesis report from the work of other people has been attributed, and has been
cited and referenced.
3. This thesis report is my own work.
4. I have not allowed, and will not allow, anyone to copy my work with the intention of passing it
off as their own work.
Name: Carl Ronald Schoombie
Student Number: SCHCAR042
Signed:_____________ on __________

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Acknowledgements:
I would like to thank the following people for their invaluable input and guidance throughout the
project:
 My father, Deon Schoombie, for the help and practical tips on the building of the machine
used in the project.
 Mr Chris Wozniak, for the practical guidance and mentoring throughout the building and
testing of the electrical components of the project.
 My supervisor, Dr Azeem Khan, for his input and knowledge throughout the project.

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Abstract:
There is an ever growing need for a method of storing energy efficiently for the “on demand” use at
a later stage. One way to satisfy this need is to use a flywheel based energy storage systems (FBESS).
This system uses an electrical machine to transfer energy into the flywheel where it gets stored in
the form of rotational mechanical energy, and then use this stored kinetic energy to later create
electrical energy again. In order to achieve this, an electrical machine together with a bidirectional
power converter is required. Flywheel based technologies are most suited to applications which
require numerous cycles of power boost and are able to create numerous cycles of charging (putting
energy into the flywheel). Flywheel efficiency is dependent on the materials used in the construction
of the system, shape of the flywheel, bearing efficiency, the type of electrical machine and the
power converter used. Examples of applications of flywheel based energy storage systems are:
hybrid power systems, hybrid vehicles, space satellites applications and power smoothing
applications [1]. This report deals with the flywheel and electric machine of a scrap-based FBESS.

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Table of Contents
Optimisation of a Sustainable Flywheel Energy Storage Device.............................................................1
List of figures...........................................................................................................................................8
1 Introduction .......................................................................................................................................11
1.1 Background of the Project ..........................................................................................................11
1.2 Objectives of the Project Report.................................................................................................11
1.3 Scope and Limitations of the Project Report..............................................................................11
1.4 Plan of Development ..................................................................................................................12
2 Literature Review...............................................................................................................................13
2.1 FBESS justification and applications............................................................................................13
2.2 The electric machine topologies.................................................................................................14
2.2.1 Permanent Magnet Machines .............................................................................................14
2.2.2 Axial Flux PM Machine.........................................................................................................16
2.2.3 Brushless DC Electrical Motor..............................................................................................18
2.2.4 Power Generation................................................................................................................18
2.3 Mechanics of a FBESS..................................................................................................................19
2.4 Permanent Magnets (PM)...........................................................................................................20
2.4.1 Magnetic Materials..............................................................................................................21
2.4.2 Magnet Orientation .............................................................................................................22
2.5 Electronics of a FBESS .................................................................................................................22
3 Theoretical base of Flywheel Based Energy Storage System (FBESS)................................................23
3.1 Flywheel Theory..........................................................................................................................23
3.1.1 Kinetic Energy.......................................................................................................................23
3.1.2 Materials of the flywheel.....................................................................................................24
3.1.3 Geometry of the flywheel....................................................................................................25
3.2 Axial Flux Machine Theory..........................................................................................................26
3.2.1 Windings ..............................................................................................................................26
3.2.2 Magnetic Flux.......................................................................................................................34
3.2.3 PM Generating.....................................................................................................................44
3.3 Mechanical Theory......................................................................................................................46
3.3.1 Bearings................................................................................................................................46
3.4 Magnetic Circuit......................................................................................................................48
3.5 The electronics............................................................................................................................50
4 Design & Simulations .........................................................................................................................51

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4.1 Flywheel......................................................................................................................................52
4.2 Electric machine..........................................................................................................................54
4.2.1 Topology...............................................................................................................................54
4.2.2 Motoring Mode....................................................................................................................56
4.2.3 Generating Mode.................................................................................................................59
4.3 Mechanical Considerations.........................................................................................................60
4.3.1Bearings.................................................................................................................................61
4.3.2 Windage Losses....................................................................................................................62
4.3.3 Total Rotational Losses ........................................................................................................63
4.4 ELECTRONICS...............................................................................................................................64
4.4.1 Angular Sensing....................................................................................................................64
4.4.2 BLDC Commutation..............................................................................................................66
4.4.3 Phase coil connection ..........................................................................................................69
4.4.4 BLDC motoring simulation ...................................................................................................69
4.5 Final Design.................................................................................................................................70
5 Construction of the final FBESS design ..............................................................................................71
6 Testing and Analysis of the Flywheel based Energy Storage System.................................................74
6.1 Microcontroller signal, voltage and current waveform tests .....................................................74
6.2 Voltage vs. Speed and current vs. speed tests............................................................................76
6.2 Initial no-load open-circuit run down testing .............................................................................78
6.3 Tests done with increasing airgap lengths..................................................................................81
6.3.1 Eddy Current Braking ...........................................................................................................82
6.3.2 Voltage smoothing circuit used for run down curve ...........................................................83
6.3.4 Run-down efficiency improvement .....................................................................................84
6.3.5 Effect of increased airgap on motoring and generating......................................................85
6.4 Windage loss tests ......................................................................................................................86
6.4 Resistive delta-connected load tests ..........................................................................................88
6.5 High speed test ...........................................................................................................................89
7 Conclusions ........................................................................................................................................90
8 Recommendations.............................................................................................................................91
9 List of Acronyms and Symbols ...........................................................................................................94
8 Appendices.........................................................................................................................................99
i) BLDC control code..........................................................................................................................99
ii) 3 Phase MOSFET Driver schematic .............................................................................................102

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iii) MOSFET Driver Notes................................................................................................................103
iv)Hazard Identification and Risk Assessment ................................................................................105
v) Assessment of Ethic in Research Project ....................................................................................106
Bibliography ........................................................................................................................................107

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List of figures
Figure 1: Flow diagram of a basic FBESS [3]..........................................................................................13
Figure 2: Torque-Speed Quadrants of a DC motor [5]..........................................................................14
Figure 3: Flux Direction of RFM and AFM [8]........................................................................................15
Figure 4: i) Single-Rotor-Single-Stator ii) Single-Rotor-Double-Stator..................................................16
Figure 5: Magnetic flux paths for i) NN Double-Rotor and ii) NS Double-Rotor AFPM [7]...................17
Figure 6: Triple-Rotor-Double-Stator Multi-Disc AFPM........................................................................17
Figure 7: AFPM topology variations [10] ..............................................................................................18
Figure 8: Direction of force handling capabilities of:............................................................................20
Figure 9: PM shapes and North-South Orientation ..............................................................................22
Figure 10: Flywheel shape with corresponding value of constant K [1]...............................................26
Figure 11: AFPM Single-layer winding with m=3, p=6, S1=36, y1=Q1 and q1=2 [19]...........................28
Figure 12: 3-Phase overlapping concentrated coils..............................................................................29
Figure 13: i) 3-Phase phase group coil configuration (n=2) ii) 3-Phase ungrouped configuration (n=1)
[20]........................................................................................................................................................29
Figure 14: Type 1 concentrated coil [20] ..............................................................................................30
Figure 15: Type 2 concentrated coil [20] ..............................................................................................32
Figure 16: Coil shape and dimensions ..................................................................................................34
Figure 17: First order system response curve [23] ...............................................................................36
Figure 18: Equivalent Circuit of one phase on an BLDC machine (Rs= Stator Resistance, Ls= Stator
Inductance, Is= Stator Current) [24] .....................................................................................................37
Figure 19: i) Switch arrangement for 3-phase Y-connection ii) Switch "On Time" current iii) Switch
"Off Time" current [19].........................................................................................................................37
Figure 20: Phase current and torque sequence....................................................................................38
Figure 21: Phase conduction and Back EMF wave form [5]..................................................................39
Figure 22: Torque-speed relationship of an BLDC AFPM motor [19] ...................................................41
Figure 23: Equivalent circuit of an AFPM generator [19] .....................................................................45
Figure 24: Bearing load capabilities as a function of shaft diameter and angular speed [29] .............46
Figure 25: Bearing frictional losses as a function of friction coefficient and rotational speed ............47
Figure 26: Bearing friction losses as a function of load and angular speed..........................................47
Figure 27: Graph illustrating how the average airgap flux density varies with remanence of PM ......49
Figure 28:Graph illustrating how the average airgap flux density varies with length of airgap...........50
Figure 29: Rotor Position (i) with corresponding current path (ii) .......................................................51
Figure 30: Flywheel energy as a function of speed and i) increasing radius ii) increasing mass..........52
Figure 31: Flywheel Dimensions ...........................................................................................................53
Figure 32: Energy stored in flywheel vs. speed.....................................................................................54
Figure 33: AFPM machine, with stator core, flux density plots at different depths in the airgap ii)
2mm from face of the magnet iii) 8mm from the face of the magnet.................................................55
Figure 34: AFPM coreless machine flux density plots at different depths in airgap ii) 2mm from the
face of magnet iii) 8mm from the face of the magnet .........................................................................55
Figure 35: Phase resistance as a function of i) Wire Diameter ii) Number of turns per phase ............57
Figure 36: Magnet dimensions and polarity.........................................................................................58

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Figure 37: Winding factor as a function of average radius at which the PM's are placed on the rotor
..............................................................................................................................................................59
Figure 38: EMF generated as a function of average airgap flux density (T) and rotational speed (RPM)
..............................................................................................................................................................60
Figure 39: EMF generated as a function of average airgap number of turns per phase (N) and
rotational speed (RPM).........................................................................................................................60
Figure 40: Flywheel/rotor mounting options........................................................................................61
Figure 41: Graph of designed machine's frictional losses in Watt (W).................................................62
Figure 42: Graph of designed machine's windage losses in Watt (W) .................................................63
Figure 43: Graph of designed machine's total rotational losses in Watt (W).......................................64
Figure 44: Angular position sensor 1 ....................................................................................................65
Figure 45: Angular position sensor 2 ....................................................................................................65
Figure 46: Angular positions sensor circuit diagram.............................................................................66
Figure 47: Six repeated rotor positions ................................................................................................67
Figure 48: Current path for the six different rotor positions................................................................67
Figure 49: Phase excitation scheme......................................................................................................68
Figure 50: 12 coils, 3-phase Y-connection ............................................................................................69
Figure 51: Line-to-line voltage waveform.............................................................................................69
Figure 52: Phase current waveform......................................................................................................70
Figure 53: Final design and assembly model ........................................................................................71
Figure 54: Coil dimensions....................................................................................................................72
Figure 55: Stator coil assembly.............................................................................................................72
Figure 56: Epoxy resin fill illustration....................................................................................................72
Figure 57: Rotor assembly ....................................................................................................................73
Figure 58: Photograph of Final Product................................................................................................73
Figure 59: Firing angle calibration plot .................................................................................................74
Figure 60: Line-to-line voltage waveforms ...........................................................................................75
Figure 61: Phase current waveform......................................................................................................75
Figure 62: Output voltage waveform in generating mode. ..................................................................76
Figure 63: Decreasing voltage amplitude with decreasing angular speed ...........................................76
Figure 64: Voltage vs. speed in motoring mode...................................................................................77
Figure 65: Current vs. speed in motoring mode...................................................................................77
Figure 66: Voltage vs. speed and calculated Back EMF vs. speed ........................................................78
Figure 67: Initial no-load open-circuit run down test...........................................................................79
Figure 68: Plate causing high eddy current losses under freewheeling conditions .............................81
Figure 69: Voltage vs. speed with varying airgap length ......................................................................82
Figure 70: Open-circuit no-load run down curve of different airgap lengths.......................................82
Figure 71: Eddy current braking characteristics from a study done in [36]..........................................83
Figure 72: Signal smoothing circuit.......................................................................................................84
Figure 73: Run down Curve from 790 RPM with 20mm airgap............................................................84
Figure 77: i) 35mm Airgap between face of PM's and steel plate ii) Flux density plot at20mm..........86
Figure 74: Ring gear identification........................................................................................................87
Figure 75: Reduced windage run down curve vs. unmodified run down curve...................................87
Figure 78: Delta-load run down curves.................................................................................................88
Figure 79: Power dissipation of 30 ohm delta load for i) 2mm and ii) 20mm airgaps .........................89

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Figure 80: Angular sensor malfunction plot .........................................................................................90
Figure 81: High speed angular sensor failure .......................................................................................90
Figure 82: Double-rotor-single-stator flux density plots ......................................................................92
Figure 83: Recommended topology (double-rotor-single-stator) and mounting orientation .............92
Figure 84: Recommended topology to avoid high eddy current losses with single thrust bearing .....93
Figure 85: MOSFET Driver Schematic (Received from Mr Chris Wozniak of the Machines Lab at the
Electrical Department of the University of Cape Town).....................................................................102
Figure 87: MOSFET Driver Schematic (Received from Mr Chris Wozniak of the Machines Lab at the
Electrical Department of the University of Cape Town).....................................................................104

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1 Introduction
This project comes about as a requirement for a Bachelors of Science degree in Mechatronics
engineering. Each final year Mechatronics engineering student needs to undertake a final year
project in order to prove his or her competency as an engineering graduate. The project counts a
significant amount towards a student’s mark for the year. This particular project topic was selected
due to my keen interest in the field of electrical machines and renewable energy.
1.1 Background of the Project
The large drive for sustainable energy around the world has seen many institutions doing research
and development (R&D) into a means of storing energy in both an economic and efficient manner.
The University of Cape Town is one such institution, with individuals from undergraduate to PhD
level, undertaking in such R&D.
This project ties into the research being done by UCT in the search for a sustainable wind generator
system. A particular area of interest is using the flywheel as a mechanism to store energy and then
release the energy, on demand in short intervals. A typical Flywheel Based Energy Storage System
(FBESS) will consist of a DC-DC bidirectional power converter, an electric machine which performs
both as a motor and generator, and the flywheel itself which is used as the mechanical energy
storage device. The idea is that any excess energy produced by the wind generator will be stored in
the flywheel device until it is required at a later stage.
Two such undergrad projects have already been developed at UCT; however both systems had flaws
and inefficiencies. Thus this project topic comes about as a result of trying to learn from the previous
flaws and improve on them.
1.2 Objectives of the Project Report
The objectives of the project report are to:
 show an in depth understanding of the mechanical and electrical operation of a flywheel
 demonstrate the redesign of the existing flywheel system
 document the building of a prototype of the new FBESS design
 test and make improvements to the system
 show the results of tests undertaken
 analyse the data gathered during the tests
 draw conclusions to the results obtained from the tests
 make recommendations on how to improve the system further
1.3 Scope and Limitations of the Project Report

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This project includes a basic literature review of the mechanics and electronics involved in using the
flywheel as a storage device. It also includes details of the theory behind the design of flywheels and
a specific electric machine used to sink and source the energy into and out of an FBESS. The electric
machine used in the project is a Brushless DC (BLDC) motor and only this type of motor’s topology
and control will be considered in the report. In generating mode however, the machine operates as
a synchronous generator and therefore a brief discretion synchronous generation is included.
The project report is not involved in the design of AC to DC or DC to AC converters (it is not within
the scope for this project) and a variable DC bus voltage is assumed to be available. The flywheel
system will be predominantly designed and built out of scrap and other readily available materials.
For this reason the report will consider only low to medium speed flywheel based energy storage
devices. A sophisticated control system is also not in the scope of this project.
1.4 Plan of Development
The project report begins with a literature review of the basic components of a FBESS and then goes
on to detail the theory behind these components. The report continues into the design and
simulations of the FBESS. The simulations will detail expected voltage and current waveforms as well
as magnetic flux paths in the electric machine. After the designs have been dealt with the report
deals with the details of construction of the designed FBESS.
The results of the testing phase of the project are then considered and compared to the expected
results. An in depth analysis of the data gathered during the testing phase is integrated into the
testing section of the report. Conclusions are then drawn with regard to the efficiency of the design
and finally recommendations are made on how the system could be improved by future designers.

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2 Literature Review
This section of the report is an overview of the flywheel based energy storage system components
and its capabilities. It deals with a broad look at the potential for design variations and the basic
theory thereof.
2.1 FBESS justification and applications
A FBESS combines mechanical theory with electrical theory in order to create a system which is able
to store kinetic energy (as mechanical rotational energy) and then make this energy available, on
demand, in the form of electrical energy, in the most efficient manner possible [2].
In Figure 1 below, the block diagram is illustrates the energy flow of a basic FBESS:
Figure 1: Flow diagram of a basic FBESS [3]
The block diagram illustrates how energy is passed to and from the flywheel (blue arrows) with
various losses in the system illustrated in red. This diagram brings forward some of the key concepts
which need to be considered in the design of such a system. Efficiency is of utmost importance
therefore losses need to be minimized, the electrical machine and flywheel optimized, while the
electronics need be capable of maximizing the potential of the system.
Flywheel technology has recently seen an increase in attention due to the drive for higher
efficiencies in all lines of industry. An example of a highly tuned flywheel is that of a design by
Beacon Technologies. The flywheel uses cutting edge technology and materials (such as carbon fibre
used for flywheel construction) to produce a flywheel which spins between 8000 and 16000 rpm in a
vacuum sealed chamber. It makes use of magnetic bearings and produces up to 15kW for 15
minutes. The mechanics of this system are 97 % efficient and the system as a whole is around 87%
efficient [2]. This is one example of the potential of the FBESS. Many other examples including the

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hybrid motor vehicle, used in Formula One cars, make use of high tech FBESSs but the key to its
effectiveness is a well-engineered system.
Advantages of the FBESS over other energy storage systems such as batteries are:
 Efficiency
 Fast Response
 Long Lifetime
 Low maintenance [4]
2.2 The electric machine topologies
The first requirement for the electric machine chosen for the FBESS is that it must be able to
efficiently accelerate the flywheel from different speeds while in motoring mode. Secondly the
machine must be able to efficiently recapture the energy stored in the flywheel by transferring
mechanical kinetic energy into electric energy while in generating mode. Various electrical machines
can be used for this purpose, each with their strengths and weaknesses in different operating
conditions. One such machine which is well suited to both high speed and low speed FBESS is the
permanent magnet (PM) machine.
2.2.1 Permanent Magnet Machines
The conventional radial flux (RF) brushed DC motor/generator makes use of permanent magnets
(PM) on the stator with rotor windings and a brush split-ring commutator combination providing the
path for electrical energy transfer. An electrical current is passed through the rotor winding creating
a magnetic field. The motors electric field interacts with the permanent magnets on the stator of the
motor, creating a torque on the shaft of the motor. In generating mode the magnetic field of the
stator PM’s interacts with the rotor coils inducing a voltage. If the generator is connected to a load
the energy flow is in the opposite direction as to when in motoring mode. For a FBESS the flywheel
would be providing the mechanical rotational energy.
The figure below demonstrates the four quadrants of operation of a PM machine:
Figure 2: Torque-Speed Quadrants of a DC motor [5]

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i) Positive speed, positive torque (Forward Accelerating)
ii) Negative speed, positive torque (Reverse Braking)
iii) Negative speed, negeative torque (Reverse Acclerating)
iv) Postive speed, negative torque (Forward Braking)
In the first and third quadrant, the forward voltage is greater than the back EMF resulting in forward
and reverse motoring respectively. The difference is the direction of current flow, noting that torque
is a function of current while speed is a function of voltage. In the second and fourth quadrant the
back EMF is greater than the forward voltage and as a consequence the machine will be in
generating mode. Once again the difference is the direction of current flow. [5]
A brief review of the PM motor as opposed to electromagnetic excitation reveals that PM excitation
produces higher torque and output power per unit volume. This allows for more compact designs.
The PM also doesn’t require any external energy supply in order to create the excitation. This
translates into a more efficient machine. PM motors offer simple construction and reduced
maintenance as opposed to wound machines (stator and rotor wound). The maintenance is further
decreased if the PM is on the rotor, thereby eliminating the need for a slip ring commutation set up.
One major disadvantage however, is the inability to adjust the flux density of the PM. [6]
Furthermore PM RFM are well known to have to high torque capabilities and high efficiencies
compared to other machines such as the induction machines [7].
Two major types of PM DC motors/generators exist, firstly the more traditional radial flux machine
(RFM). It produces magnetic flux in a radial direction (perpendicular to shaft) and is very well
understood and documented. However, the less common PM DC machine configuration is the axial
flux machine (AFM). This configuration produces magnetic fluxes which points in an axial direction
(parallel to shaft) as opposed to a radial direction in the machine above. This is illustrated below:
Figure 3: Flux Direction of RFM and AFM [8]

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The figure above shows how the flux directions differ between the two major categories of electrical
machine. The AFM is not as common as the RFM and therefore not as well documented however it
has its place in industry.
The machine used for this project is the axial flux permanent magnet (AFPM) Brushless DC (BLDC)
machine. Therefore only this topology will be dealt with in detail.
2.2.2 Axial Flux PM Machine
The AFM has some distinct advantages over the RFM in a FBESS. One such advantage is that the
rotor can easily be used as the flywheel itself. This has many practical and efficiency advantages such
as a more compact machine, fewer moving parts (e.g. fewer bearings) and easy to maintain. It can
therefore be designed to have a higher power-to-weight ratio. AFMs are generally built out of thin
disc like rotors resulting in a significantly better torque-to-volume and torque-to-weight ratio
compared to the traditional RFM structure. They also have planar airgaps which are easy to adjust
and optimise. The noise and vibration levels are also less than RFM’s. One disadvantage of the AFM
is the large forces present in the axial direction. [7].
The AFPM works by having magnets on the rotor instead of the stator. This allows for various stator-
rotor configurations, for example a single-rotor- single- stator, single-rotor-double-stator or even a
multistage configuration. Furthermore the AFPM machines can be built with slotted or slotless
stators and core or coreless stators. Slotless stators have the advantage of no cogging torque while
coreless stators minimize the eddy current losses of the machine. The next few paragraphs will
highlight some of the variations of AFPM’s design parameters and key concepts which need to kept
in mind. [7]
Topology
The most basic AFPM is the single-rotor-single-stator topology which are generally easy to construct,
however their torque production capabilities are however lower than other topologies [9]. A servo
drive is a typical application of a single sided AFPM machine [7].
Figure 4: i) Single-Rotor-Single-Stator ii) Single-Rotor-Double-Stator
The figure above indicates a single-rotor-single-stator (i) as well as a single-rotor-double-stator (ii)
configuration. Double sided machines can be built with a single internal rotor and a double external

17. 17
stator or a single internal stator and a double external rotor. Advantages of the “double
configuration” are that the forces in the axial direction are balanced and torque is increased.
In the case of double-rotor-single-stator configurations, another variation is the choice of adjacent
rotor pole polarities. The choice between these two configurations will influence the magnetic flux
paths; this is demonstrated in Figure 5 below. The choice between the two variations influences the
direction of forces on the two rotors themselves as well as the stator coil configuration. In the case
of the NN set-up the rotors will be forcing each other apart while the in the NS case the will be
attracted towards one another.
Figure 5: Magnetic flux paths for i) NN Double-Rotor and ii) NS Double-Rotor AFPM [7]
The mechanical integrity of the machine does however put a limit on the double sided machines.
The ability of the machine to withstand the large centrifugal forces on the rotor at high speed and
limited torque are examples of limits which the machine may face. If more torque is required one
option the AFM offers is to use a multidisc configuration. An example can be seen below in Figure 6:
Figure 6: Triple-Rotor-Double-Stator Multi-Disc AFPM

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The example above is a triple-rotor-double-stator machine but there is no theoretical limit as to how
many cascaded rotor and stator the AFPM can have. Practicality and weight are the most likely
limitations to the number of cascades.
The different topologies can be summarized as follows:
Figure 7: AFPM topology variations [10]
It must be noted that, due to the high centrifugal forces on the PM’s of the AFPM machine, it is more
suited to low speed applications unless a non-ferromagnetic holder can be built into the design to
contain the PM’s [11].
2.2.3 Brushless DC Electrical Motor
The brushless DC (BLDC) motor is a more modern motor technology which has the PM on the rotor
with its windings on the stator (this is opposite to the conventional DC motor). A brushless DC motor
requires an angular position sensor and a means of commutation. This type of machine therefore
requires a driver circuit in order to operate it; making it a more complex machine but according to
[5] some of the advantages of BLDC motors are: ease and accuracy of control, high power density
and small size.
2.2.4 Power Generation
The theory behind generating electricity is based on Faraday’s Law of Induction [12]. This law states
that a changing magnetic flux across a conductor will create an electromotive force (EMF) (or
developed voltage) between the two ends of the conductor according to:
(1) | | | |

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Where, = induced voltage
= magnetic flux
In the simple case of a wire coil moving perpendicularly through a magnetic field the equation is:
(2)
Then,
Where B = magnetic field
= Peak induced voltage
= area of coil
= time for magnet to pass over coil
According to formula (2) (2) the induced voltage can be increase by either increasing
the strength of the magnetic field, increasing the area of the coil or the increasing the speed at
which the wire travels through the magnetic field. [12]
2.3 Mechanics of a FBESS
FBESS’s generally don’t have too many moving parts. Traditionally the only moving parts of the
system are the components of the electrical machine (rotor, shaft and bearings) and flywheel
together with its bearings. Thus the bearing choice is an important source of efficiency (or
inefficiency).
Further important mechanical considerations are strength of materials, due to the stresses in the
system, of which two primary force directions are of most importance namely, the radial direction
and the axial direction.
Bearings can have various forms, and depending on their structure, can either support linear motion
or rotary motion. Since this project involves only rotary motion, only rotary motion bearings will be
discussed. Further categorization can be made namely, contact bearings (sliding, rolling or flexing)
and non-contact bearings (fluid or magnetic) where contact bearings have varying friction
coefficients and non-contact bearings are almost frictionless [13]. A system of mixed bearings is also
an option-where both mechanical and magnetic bearings are used.
FBESS’s need to be as efficient as possible, therefore one way of reducing losses is to reduce friction.
By using magnetic bearings (non-contact), friction (and wear) is eliminated by levitating the flywheel
shaft resulting in efficiency of 100% (or very near). A drawback of magnetic bearing is however their
availability and price. For these reasons it may be worthwhile using conventional mechanical
bearings of which there are many available.

20. 20
Two main categories of mechanical contact bearings exist: thrust bearings where the primary forces
act in an axial direction and radial bearings where the primary forces act in a radial direction. Both of
these have their advantages and disadvantages for any given system. In the case of the FBESS a
thrust bearing would likely lead to a vertically orientated flywheel axis where as a radial bearing
would likely lead to a horizontally orientated flywheel axis.
Load, speed and friction are all factors to consider when choosing a bearing. Generally the roller
class of bearing can handle larger forces in the radial direction while ball bearings are more suited to
axial forces [13].However multi-directional loading can be accommodated too. These bearings are
called angular contact bearings and are able to withstand forces in both the radial and axial
directions. Examples of force direction together with the appropriate bearing are illustrated below:
Figure 8: Direction of force handling capabilities of:
i) Roller Bearing ii) Ball Bearing iii) Angular Contact Ball Bearing [13]
i) Roller bearing with radial force
ii) Ball bearing with axial force
iii) Angular contact bearing with radial and axial force
According to [13], in the case of the angular contact bearing, the greater the angle the higher the
axial load carrying capacity the bearing has.
Bearings are designed to have as little friction as possible however contact bearings suffer from
small amounts of friction even under ideal operating conditions. The speed of a bearing is limited by
the temperature it can withstand. Bearings which run with less friction are able to run at higher
speeds. Thrust bearings are generally not able to run at speeds as high as roller bearings or ball
bearings as consequence of their design [13]. Furthermore, in general ball bearings run with lower
frictional losses than roller bearings [13]. If super low friction is required SKF have a range of Energy
Efficient (SKF E2) bearings which run with at least 30% less frictional moment. Another consequence
of friction is wear and tear. Thus higher friction not only leads to lower efficiencies but also higher
maintenance.
2.4 Permanent Magnets (PM)

21. 21
The magnetic circuit of an electrical machine directly affects its performance. It is therefore a very
important performance parameter regardless of the type of PM machine or its topology. Permanent
magnets tend to be expensive but are however a crucial part in the PM electric machine. It is
therefore important to source magnets with strong enough magnetic field to achieve the
performance levels required.
The following two sections briefly discuss some of the common modern permanent magnet
materials and orientations in order gauge the options available for design.
2.4.1 Magnetic Materials
i) Ceramic (ferrite) magnets
These magnets are made from barium carbonate or strontium carbonate. They are widely available
and relatively low cost. They are brittle and difficult to shape. These magnets have a good balance
between resistance to demagnetizing and magnetic strength. They are also able to handle high
temperatures however have a low mechanical strength and the surface can have a tendency to rub
off. [14]
ii) Alnico magnets
Alnico magnets are made from an alloy made of mainly aluminium nickel and cobalt. They have a
high resistance to corrosion, high mechanical strength and can work in high temperatures
environments but tend to demagnetize under certain conditions. [14]
ii) Rare Earth magnets
These magnets are made out of alloys from the Lanthanide group of elements. There are various
alloy combinations under this group of magnets including samarium-cobalt and neodymium-iron-
boron.
Samarium-cobalt magnets can operate in temperatures up to 350° C according to [14]. They are
however brittle, prone to chipping and cracking and are high cost. They therefore are usually chosen
for high temperature conditions where corrosion isn’t important. They have low mechanical
strength.
Neodymium-iron-boron (Neo) magnets have a stronger mechanical strength than Samarium-cobalt
magnets. The materials making up this magnet are costly in a “per mass” but has the highest flux
density out of the magnets discussed. The high energy product makes them suitable for compact
applications making it preferable for electric machine operation. They are however prone to
corrosion if not protected (there are protective measures which make them suitable for most
applications). [14]
iii) Polymer Based magnets
These magnets are a mix of the magnets discussed above. In this way you are able to create a range
of magnetic and mechanical properties.

22. 22
2.4.2 Magnet Orientation
Magnets can be manufactured in different shapes and different north-south pole orientation. The
following figures are taken from [14] and show some of the possible magnet orientations:
Figure 9: PM shapes and North-South Orientation
2.5 Electronics of a FBESS
In the block diagram in Figure 1, a crucial element of the FBESS is highlighted, namely the power
electronics used to sink and source electrical energy through the system. The choice of power
electronics used is dependent on whether the machine will operate with DC or AC. For this project
the machine will perform as a 3-phase DC motor (square wave motoring) but as a synchronous
generator. DC PM Motors can be commutated with a split-ring brush combination (as was done for
the motor developed in [15]). The other option is to use a brushless set-up where the angle of the
rotor is sensed and the phase coils excited accordingly.
For a BLDC setup, 3 important components are required - the angular sensor, the switches (used to
commutate) and a device to fire the various switches at the correct moment. Many different angular
sensing options are available such as the Hall Effect sensor, rotary potentiometer, resolvers as well
as various encoded disc configurations. The modern switch used in this type of application is the
power transistor. These come in different forms of which 4 are very well known-the Bipolar Junction
Transistor (BJT), Darlington Transistor, Insulated Gate Bipolar Transistor (IGBT) and the Metal-Oxide-
Semiconductor Field-Effect Transistor (MOSFET) [16]. The choice of transistor is dependent on the
application and operating characteristics of the transistor. For example; the BJT’s are current
controlled switches while the MOSFET’s are voltage controlled. Transistors have maximum current
and voltage ratings and therefore also have to be chosen with regard to the load requirements. [17]
In summary to the literature review, the table below gives some idea of typical characteristics of low
speed versus high speed FBESS’s:

23. 23
Table 1: Typical characteristics of FBESS's [7]
3 Theoretical base of Flywheel Based Energy Storage System (FBESS)
There are many different configurations options, and variations of these, which are well known and
well documented for FBESSs. However, the basic concepts will be highlighted in the following text as
well as specific details related to the final design of the FBESS. Basic examples will be used to help
clear up certain theory. A BLDC AFPM machine is assumed from this point onward. Furthermore in
Figure 1, only a DC-DC bidirectional power converter is shown (does not include an AC-DC/DC-AC
conversion). This is due to the limited time with which to complete the project. Thus the literature
includes details from the rectified DC electrical supply to the flywheel itself only.
3.1 Flywheel Theory
No matter the level of technology behind a flywheel design, there is certain theory common to all
designs. The most important design considerations are brought to light in this section of the report:
3.1.1 Kinetic Energy
The key concept behind FBESS’s is the ability of the flywheel to store energy. The flywheel stores
energy as kinetic rotational energy which is dependent on the angular velocity as well as the
moment of inertia of the flywheel [1]:
( )
Where, = Kinetic Energy,
LOW SPEED HIGH SPEED
Flywheel
Material
Steel
Composite
Materials
Electrical
Machine
Asynchronous,
syncronous,
reluctance
machines, PM
machines
Sycnronous,
reluctance, PM
machines
Operating
Environment
Partial Vacuum, air,
light gas
Vacuum
Flywheel
Weight
Medium-heavy
weight
Light weight
Bearings
Mechanical or
magnetic
Magnetic
Typical
Application
Power Smoothing
applications
Aerospace
Cost Low High

24. 24
= Inertia of the flywheel,
= angular velocity of flywheel.
The moment of inertia of a flywheel depends on its mass and its geometry:
(4) ∫
For example the moment of inertia of a cylindrical shell shaped flywheel is:
(5)
Where, = moment of inertia of an object,
= distance of each particle of mass from the axis of rotation
= mass
The above formulae show that the amount of energy stored in the flywheel at any given time is
dependent on the moment of inertia (high = high ) and the square of the angular velocity (high
= high ). Furthermore, according to equations (4) & (4), the higher the mass and the further
away from the axis of rotation that mass is, the higher the energy storage capability. However there
are limitations, such as friction and windage which limit the angular velocity a flywheel is capable of
maintaining.
Continuing with a cylindrically shaped flywheel, the energy stored will be:
(6)
3.1.2 Materials of the flywheel
The maximum angular velocity of the flywheel is further determined by the ability of the material,
with which the flywheel is constructed, to withstand the large centrifugal forces it experiences
(putting the material under tensile stress) [1]. The centrifugal forces created by the high angular
velocity are proportional to mass, radius and the square of rotational speed of the material in
question. These forces are the highest at the rim of the flywheel. Therefore a flywheel’s maximum
tensile stress, for a given angular velocity and radius can be approximated by [18]:
(7)
Or
( )
Where, = mass density of material.
=maximum tensile stress of a material

25. 25
This leads to a concept known as specific energy which relates the energy available “per unit of
mass” of the flywheel as follows:
( )
Where, = specific energy
Continuing with the cylindrical example:
(10)
Now subbing in equation ( ) and given that is the materials maximum tensile stress and is its
density, the maximum specific energy is for a cylinder is:
(11)
This suggests that the ideal material for the cylindrical shell should be of low density and high tensile
strength thereby increasing the energy per unit of mass of the flywheel [18].
3.1.3 Geometry of the flywheel
In equation ( ) above, it is shown that the higher the speed of the flywheel, the more energy it
contains (stored). This is true, but higher speeds bring problems such as increased friction, vibration
and possible degradation of the material of which the flywheel is built. It is therefore important to
design the flywheel such that it minimizes friction and vibration but is also able to withstand the
centrifugal forces it is exposed to at its maximum operating speed. Thus the shape of the flywheel
also has a significant part to play in its maximum energy storage capabilities.
In the same way density has a “per unit of mass” effect on the ideal flywheel; shape also has a “per
unit of volume” effect on its energy of storage capabilities. This is known as energy density. The
equation for energy density is given below [18]:
( )
Where, = energy density
= constant, dependent on the shape of the flywheel
The formula above suggests that in order to achieve high energy per unit of volume, a high value of K
is required. ( ) The constant K is determined by the shape of the object. The higher K
is, the higher the maximum energy density of a particular flywheel is. The figure below demonstrates
some possible shapes and their values of K:

26. 26
Figure 10: Flywheel shape with corresponding value of constant K [1]
As stated in [1] the top two shapes are generally used when metal is the material of choice for the
flywheel ,and is appropriate for low to medium speeds applications, while the bottom two are
typical of composite high speed flywheels.
The table below makes a comparison between the characteristics of different possible choices of
materials used to construct the flywheel:
Table 2: Material and its corresponding density, tensile stress rating,
energy density and specific energy. [1]
It is clear from the table above that the composite materials such as graphite outperform the
metallic materials such as steel and aluminium on both the energy density and specific energy
fronts, even though they have lower densities. The reason behind this is that they have very high
tensile strengths and are therefore better able to withstand the high centrifugal forces at very high
rotational speeds.
3.2 Axial Flux Machine Theory
As was briefly mentioned in the literature review, AFPM come in many different topologies each
with their pros and cons. This section of the project will however go into more specific technical
detail of AFPM machines:
3.2.1 Windings
Material ρ [kg/m^3] σ [MPa] ev [MJ/m^3] em [kJ/kg]
Aluminium 2700 500 251 93
Steel 7800 800 399 51
Glass E/Epoxy 2000 1000 500 250
Graphite HM/Epoxy 1580 750 374 237
Graphite HS/Epoxy 1600 1500 752 470

27. 27
There are many different winding configurations available for AFPM machines some of which are
discussed here. The relationship between the number of poles, radius and coil configuration is
known as the winding factor. The winding factor ( is a very important parameter in electrical
machine design; it directly affects the performance of the machine therefore a few AFM winding
configurations will be considered and their respective winding factors provided from [19]. The
winding factor consist of two primary terms namely the distribution factor ( and the pitch factor
( . The distribution factor is a measure of how the windings are distributed on the stator while the
pitch factor is a measure of how the dimension of the phase coils relates to the number poles on the
rotor:
 Three-phase windings, distributed in slots:
The distributed winding is a configuration which has each phase distributed in a number of slots. In a
single layer winding, one coil side is located in a single slot. In the case of double layer windings two
sides of different coils are located in a single slot. For single layer winding the number of coils per
phase is:
(13)
While the number of slots for a double layer is:
(14)
Where, = number of coils per phase
= number of slots
= number of poles
=number of phases
In order to calculate the pitch factor further information and calculations are required:
(15)
(16)
A full coil pitch can be expressed as
Where,
While a short pitch coil can be expressed as:
(17)
Where,
(18) = coil-pitch to pole-pitch ratio
= coil pitch in unit of length as a function of r

28. 28
= pole pitch in the same units as coil pitch (also a function or r)
Then the distribution factor can be calculated as follows:
(19)
And the pitch factor is:
(20) ( )
Then the winding factor is:
( )
The diagram below is taken from [19] and is an example of such a distributed winding configuration:
Figure 11: AFPM Single-layer winding with m=3, p=6, S1=36, y1=Q1 and q1=2 [19]
 Concentrated Coreless stators:
Concentrated windings are configurations where phase coils are concentrated in a single slot.
Coreless stators have their coils wound and stuck straight on a non-magnetic and non-conductive
stator backing. These coils are usually held in place by a composite of epoxy resin and hardener and
are often trapezoid in shape according to [19]. An advantage of a coreless stator is that cogging
torque is eliminated, according to [19] . AFPM machines with coreless stator windings have the
advantage of not having to put the windings in slots thereby making better use of stator space, no
iron losses and eddy currents are minimized [20]. For these reasons coreless windings are examined
further.

29. 29
According to [20]there are various coreless concentrated configurations some of which will be
examined in detail:
The first major variation is the overlapping concentrated coil. This is demonstrated below with 3
coils of different phases overlapping.
Figure 12: 3-Phase overlapping concentrated coils
This configuration’s winding factor is not detailed in this paper, however [20] does provide the
numerical formulas needed to analyse such configurations.
The non-overlapping concentrated-coil stators also have variations of their own:
Concentrated coils can be grouped in phases or stand alone. The difference is easily seen below
where, in (i) from Figure 13 below, more than one coil of the same phase is grouped together to
form a phase group (n= number of coils in a group). In this case n=2. The second diagram is an
example of a non-overlapping ungrouped (n=1) 3 phase coil concentrated coil configuration.
Figure 13: i) 3-Phase phase group coil configuration (n=2) ii) 3-Phase ungrouped configuration (n=1) [20]
The winding factor of two 2 differing non-overlapping concentrated coils configurations is discussed
below:
 Type 1: The layout of the non-overlapping concentrated coreless stator of the first type (with
dimension) is taken from [20] and illustrated below:

30. 30
Figure 14: Type 1 concentrated coil [20]
Where, =coil width at radius r (radians)
= outer radius of stator winding (m)
= inner radius of stator winding (m)
= active length of stator coil (
= width of coil side
The calculation for winding factor of a slotless machine is slightly different too (as opposed to slotted
stators) in that slot numbers cannot be used in the formulae to calculate the winding factor. The
steps to calculating the winding factor of the first type of concentrated winding are derived in [20]
and given below with reference to the diagram in Figure 14 above.
(22)
Where, = coil pitch (in electrical radians)
= number of coils
Then the pitch factor of the first type of slotless winding is given by:
(23)
Where,
(24)
(25)

31. 31
( )
= Gap length between magnets of disks (meters
And distribution factor:
(27)
Where, = number of coils in a phase group
Then the winding factor of type 1 concentrated windings is:
(28)
Furthermore there is a relationship which exists between the winding factor ( ) and a value ,
called the concentrated stator factor:
(29) (the following must hold: )
(30) = concentrated stator factor = √
Therefore,
(31)
√
The table below is taken and adapted from [20]. It gives the concentrated stator factors ( ) (from
which the winding factor can be calculated) for various combinations of poles, phase-groups and coil
numbers for fixed values of .
Where,
(32) √

32. 32
Table 3: Pole and coil numbers with corresponding stator factors [20]
The highest stator factors are highlighted in red for a given value of which, according to [20],
produces the highest torque when . It must also be noted that the highest torque is
produced when the stator factor is highest. From equations ( ) & (30) the stator factor is clearly a
function of the radius and radial length of the coil. This in turn affects the winding factor of the axial
flux machine from equation (31).
 Type 2: The coils of type 2 concentrated windings are not placed perfectly side by side (as
can be seen below in Figure 15).
Figure 15: Type 2 concentrated coil [20]
Once again the winding factor is calculated differently:
Pitch Factor:
σr = 0.6 Kr= 1.28
Poles n Q Ksc
2 12 0.509
14 4 12 0.441
5 15 0.452
1 12 0.545
16 2 12 0.472
5 15 0.486
18 1 27 0.372
1 12 0.53
20 1 15 0.545
3 18 0.496

33. 33
(33)
Distribution Factor:
(34)
Where, (35)
(36)
= number of coils in a phase group
Then,
(37)
Further details regarding these coil configurations can be seen in [20].
Coil Dimensions
The coil shape and dimensions are a function of the number of coils distributed around the
stator, the amount of spacing between the coils, the average radius (Ro-Ri) of the PM’s on
the rotor and the number of turns in the coil.
The length of the arc in the middle of the coil should thus be:
(38)
Below is an example of a commonly shaped stator coil. It is based on a 12 coil stator, with no spacing
between the coils (i.e. concentrated non-overlapping type 1 coil). Therefore the outer dimensions
limits need to span 360/12=30°. The thickness of the coils is shown to be 10mm which will
determine the number of turns that can fit into a single coil while the length of the magnet
determines the coil length (in the example below it is shown to be mm).

34. 34
Figure 16: Coil shape and dimensions
3.2.2 Magnetic Flux
Another important factor in the design of PM machines is the flux in the airgap. It too directly affects
the performance parameters of the machine. The average airgap flux density for an AFPM machine
is approximated (assuming stator plate has infinite permeability and leakage flux is neglected) in [9]
to be:
(39)
Where, = average airgap flux density
= Magnet remanence
= relative permeability
= airgap (includes winding width for slotless stators)
=Thickness of magnet
It is clear that the larger the airgap g, the lower the average airgap flux density is. Conversely the
higher the flux remanence of the PM is, the higher the average flux density is. Therefore in order to
improve the performance of an AFPM machine the airgap needs to be minimized and the flux
remanence figure of the PM maximized.
Then the peak airgap flux density is:

35. 35
(40) ̂
Where, ̂ = peak airgap flux density
= magnet span in electrical degrees
3.2.3 Motor Mode
A crucial step in creating an economical FBESS is to match the size requirements of the
motor/generator to the energy storage capabilities of the flywheel. The maximum speed at which
the flywheel will operate, determines the motoring requirements needed. In other words, the rated
speed of the motor must be at least equal to the maximum speed of the flywheel (assuming that the
flywheel is directly coupled to the motor shaft).
Furthermore the torque requirements of the motor are also partly determined by the flywheel. In
motoring mode the torque required by the motor is as follows [21]:
(41)
̇
Where, = angular velocity of flywheel (rad/s)
̇ = angular acceleration of flywheel (rad/s^2)
=gearing ration between flywheel and motor shaft (a = 1 for direct coupling)
= moment of inertia of motor
= moment of inertia of flywheel
= torque developed from the working load
= damping factor of motor
= damping factor of flywheel
The torque the motor is able to develop must therefore match the requirements of the operating
conditions of the flywheel. The damping factor of the machine (and flywheel) is a crucial parameter
with regard to the performance of the FBESS. In order to determine the damping factor an electric
machine a no load run down curve can be plotted and used to derive the damping coefficient as
follows [22]:
(42)
Where, = equivalent viscous friction constant of the system
= equivalent inertia of the system
= mechanical time constant

36. 36
For a first order system, such as the one plotted below, the mechanical time constant can be
calculated by taking the time it takes the system to reach of its initial value A. That
is . [23]
Figure 17: First order system response curve [23]
The run down cure is then characterized by:
(43)
Where, = angular speed (rad/s) as a function of time. [22]
= time (seconds)
Square wave motoring
It was decided to focus of one type of motoring namely BLDC (or square wave motoring) for this
project. This section of the report will go in to specific details of the motoring mode of an AFPM DC
controlled machine. It includes the following topics of square wave motors specifically:
 BLDC 3 phase motor control explanation
 Terminal voltage calculation
 Back EMF calculation
 Developed torque production calculation
 Magnetic flux calculation
 Torque speed relationship
 Stator current calculation
 Power Losses

37. 37
 Efficiency
In order to analyse the machine in motoring mode an equivalent circuit for the BLDC can be
used. The figure below shows a single phase’s equivalent circuit:
Figure 18: Equivalent Circuit of one phase on an BLDC machine (Rs= Stator Resistance, Ls= Stator Inductance,
Is= Stator Current) [24]
 BLDC 3 phase motor control explanation
A common 3 phase connection scheme will be used in this project namely, the 3 phase Y connection
(as can be seen in figure 19 below). For BLDC operation only two phases conduct at any given time.
For example, in the diagram below, the state shown indicates switches T1 & T4 to be on, and
conducting, while the rest are off. Current will flow through the positive terminal of the phase A
winding, through the neutral point of the Y connection, and out of the negative terminal of the
phase B winding. In this state both phase A and B will be contributing a positive torque to the motor
while phase C provide zero torque (See figure 20 below).
The dashed line and black arrows show the current path in between switching phases. The coil
inductance forces current to flow (acts as a current source) even though the switches are off. Flyback
diodes are placed in the circuit as seen in the diagram to allow the freewheeling current to flow
safely and prevent any damage to the circuit. In the example below, when phase A is turned off, the
current will freewheel through diode D2. When both phases are turned off the current freewheels
through diodes D2 and D3 [21]. For more on switching see [21].
Figure 19: i) Switch arrangement for 3-phase Y-connection ii) Switch "On Time" current iii) Switch "Off Time" current [19]

38. 38
It must also be noted that the “squarewave” is not genuinely square. The switches are not ideal and
take a short amount of time to turn on and turn off [21] [19]. This is also demonstrated in ii & iii
above.
Figure 20: Phase current and torque sequence
A three phase Y-connection switching scheme is seen above, showing which phase conducts in a
“positive direction” with it corresponding “phase partner” conducting “negative current”. At any
given time two phases will be on (both producing positive torque) and one off (providing zero
torque).
 Terminal voltage calculation
The terminal voltage of the Y connected BLDC machine (square wave motor) is derived in [19]:
(44)
Where, = sum of the two phase EMF’s in series
= the resistance of the two phase windings in series
= DC current through the two phase windings in series
(Switch voltage drops are neglected)
 Back EMF calculation
The back EMF for a square wave machine (Y-connection), where 2 phases are conducting at any
given time, is also derived in [19]:
(45) =

39. 39
Where = rotational speed of rotor (RPS)
= Square wave EMF constant
= number of turns per phase
Shown below, in Figure 21, is the per-phase Back-EMF wave pattern. It is clearly shown to be in
phase with the phase current. It must be noted that in motoring mode and when
generating . [5]
Figure 21: Phase conduction and Back EMF wave form [5]
 Torque Production
A major difference in theory between AFPM and RFPM machines is the torque production formulae.
The radius at which the forces act on the rotor is not uniform in AFM’s (as is the case for RF’s). The
pole pitch and pole width become a function of the radius. This is confirmed by the formulae given in
the windings section of the report.
Furthermore the flux density and thus the flux generated in the airgap by the PM’s, are functions of
the shape of the magnet’s dimensions (which may or may not be a function of radius as well)
according to [19]. [19] Continues to derive formulae for sinusoidal and non-sinusoidal flux
distributions. The developed average electromagnetic torque equation for an AFPM machine is then
derived to be:
The torque developed is:
(46)
Where, = Square wave torque constant.

40. 40
 Magnetic flux calculation
For a rectangular distribution of peak magnetic flux which is constant with the pole shoe width, the
flux exciting the coils can be calculated as follows:
(47)
For,
Where, = Outer radius of PM
= Inner radius of PM
=pole shoe width
=pole pitch (m) [25]
= = effective pole arc coefficient (shoe width-to-pole pitch ratio)
= peak magnetic flux density in airgap
= excitation flux [19]
 Torque-speed relationship
The speed torque relationship is APPROXIMATED to be:
(48)
Where
= rotational speed (RPS)
= no load speed (RPS)
= EMF constant
= locked rotor current
= produced when output rotational speed is zero (or the torque load that causes the
output rotational speed of a device to become zero - i.e. to cause stalling)
The figure below shows speed-torque relationships of a practical AFPM square wave driven motor. It
can be seen that the motor is able to generate a higher torque for a given speed when a duty cycle is
used to control the current through the windings.

41. 41
Figure 22: Torque-speed relationship of an BLDC AFPM motor [19]
The continuous duty torque is limited by the temperature rating of the machine. In other words the
motors performance is limited by the temperature the coil windings are able to handle. [19]
 RMS Current
The RMS current of a BLDC motor with 120° square wave is derived in [19]:
(49) √ ∫ √ ∫ √ √
Where, = period of square wave.
=RMS phase current
= peak square wave current
 Power Losses
Total power losses is include stator winding losses, stator core losses (negligible in coreless stators
according to [19]), rotor core losses, permanent magnet losses, rotational losses and eddy current
losses to give total losses of:
(50)
Where, = total losses
= rotational losses

42. 42
= stator winding losses (copper losses)
= stator core losses
= rotor core losses in the solid steal backing holding the magnets (NB permeability of
steal)
= Permanent magnets losses
= eddy current losses [19]
Only rotational losses and copper losses will be derived here; however the derivations for the rest of
the losses components are available in [19].
Stator winding losses
For DC current the stator resistance can be calculated as follows:
(51)
Where, = number of turns per phase
= average length per turn
= number of parallel current paths
= number of parallel conductors
= electrical conductivity of conductor
= conductor cross section [19]
The copper losses in a DC motor are then:
(52)
The higher the copper losses are, the lower the efficiency of the machine and the higher the
temperature of the coils become (thus limiting the torque generation capability).
To reduce copper losses either the current can be reduced or the resistance of the can be lowered.
From formula (51) (51) the resistance can be reduced in numerous ways: decreasing
the number of turns, decreasing the average length of each turn or by increasing any of or
.
Rotational losses (mechanical losses)

43. 43
The two mechanical losses are due to friction and drag (or windage). Together they constitute the
rotational losses as follows:
(53)
According to [19] a rough estimate of the bearing frictional losses can be calculated as follows:
(54)
Where = bearing frictional constant (varies from 1 to 3 m2
/s2
)
=mass of rotor
= mass of shaft
Windage losses for a rotating disc can be estimated from
(55)
Where = specific density of the cooling medium
= outer radius
= shaft radius
√
= drag coefficient
= Reynolds number (dimensionless quantity used to help predict fluid flow patterns)
The Reynolds number for a rotating disc with outer radius is:
(56)
The density of air at 1 atmosphere and 20°C is and the dynamic viscosity is
. [19]
Formula (54) suggests that frictional losses can be lowered, for a given rotational speed, by reducing
the bearing frictional constant, the shaft mass or rotor mass. According to formula (55) the windage
losses can be reduced, for a given rotational speed, by decreasing any of , , or by increasing
the shaft radius Reducing any of the losses discussed above, without reducing the speed, will
increase the efficiency of the AFPM motor.
Efficiency
Then efficiency can be calculated to be:
(57)

44. 44
3.2.3 PM Generating
In generating mode, torque is applied to the shaft of the electrical machine. This torque causes a
rotation of the PM rotor which, in turn, creates alternating magnetic fields across the coils in the
stator. The alternating magnetic field induces a voltage in the stator coils. The more turns there are
per coil, the higher the induced voltage (see formula (45) for line-to-line EMF). Based on the
principals from formulae (39), (45) and (47) the closer the magnets are to the coils, the higher the
voltage induced in the coils. It is therefore important to reduce the airgap between the rotor
magnets and the stator coils. Lastly the faster the rotor spins the higher the induced voltage (see
formula (45).
The current generated dependent on the torque produced on the shaft of the machine. The higher
the torque, the higher the current. Current can however be controlled by the resistance of the load
connected to the terminals of the generator. The higher the resistance the lower the current that
will be produced. [26]
The current per phase can be calculated by rearranging the torque formula:
(58)
(59)
Where, = torque produce on the shaft
= Number of phases
= Number of turns per phase
= Winding factor
= Average flux density
= Current per phase [27]
When a load is connected to the generator, the induced EMF will cause a current to flow through the
load and create a force on the rotor (opposite to the direction of rotation) according to:
(60)
Where, = force (N)
= Current through the conductor
= Length of conductor

45. 45
In the case where the generator is power by the torque produced by a flywheel, this opposing force
will cause the flywheel to slow down and therefore lose kinetic energy.
The diagram below is the equivalent circuit of an axial flux permanent magnet (AFPM) generator.
Figure 23: Equivalent circuit of an AFPM generator [19]
In the equivalent circuit represents eddy current losses, is the resistance of the stator, is
the inductance of the stator while and are the generated voltage and load resistance
respectively. [12]
An advantage of PM generators are their efficiencies; they do not require energy to excite rotor
coils; which is case for non PM generators. Furthermore, three phase generators tend to be more
efficient than single phase generators. [28]
The AFPM machine in generating mode cannot produce square output waveforms. It therefore
operates as synchronous generator. The waveforms are thus sinusoidal and can be rectified using a
simple diode rectifier to achieve a positive waveform (or any other applicable rectifier).
Current per phase (neglecting eddy current losses) produced in the armature can be calculated using
the following formula:
(61)
√
and output terminal voltage:
(62) √
Where, = Stator / load curent
= EMF per phase
= phase volteg
= per phase resistance
= Load resistance
= Stator Coil Inductance

46. 46
= Load Inductance
= Load capacitance [19]
Topology of the machine also plays an important role in the operation of the synchronous generator.
For a given speed of rotation, the number of poles determines the frequency of the sinusoidal
output. The more poles, the higher the frequency. [11]
3.3 Mechanical Theory
Generally there aren’t many moving parts in an FBESS however designing the mechanics of the
system carefully can lead to a highly efficient energy storage device.
3.3.1 Bearings
The most efficient bearings with very low losses are magnetic bearings. However they are costly and
may not be suited to all systems. Therefore a closer look at mechanical bearings will highlight some
further options.
Figure 24: Bearing load capabilities as a function of shaft diameter and angular speed [29]
The diagram above is taken from [29]and shows the load capabilities the various types of mechanical
bearings are able to handle as a function of speed n (RPS) and shaft diameter.
It can be seen that for higher speeds the fluid bearings generally outperform the rest. However they
are more suited to very clean environments which may be a drawback for some applications. [29]
Formula (54) from the power losses section of the report shows that the frictional losses of a bearing
are dependent on the mass of load it is carrying, the rotational speed and the frictional constant ,

47. 47
which is dependent on the specific bearing. This constant generally ranges from 1 to 3 [19]. The
graphs below demonstrate the characteristics of mechanical bearings:
Figure 25: Bearing frictional losses as a function of friction coefficient and rotational speed
Figure 26: Bearing friction losses as a function of load and angular speed
The graphs clearly show how the frictional losses of the bearing increase with speed, load mass and
the bearing specific frictional coefficient. It is thus important to keep the load mass as low as
possible and choose the bearing with the lowest frictional coefficient in order to achieve the lowest
losses at the highest speeds.

48. 48
3.4 Magnetic Circuit
As was briefly mentioned in the literature review an important factor in the performance of the
AFPM machine is the magnetic circuit created by the magnetic field of PM’s. Two important factors
will be discussed here namely, the materials in the magnetic circuit and the PM’s themselves.
The magnetic circuit will be made up of the PM’s themselves, the airgap and the material which the
PM’s are mounted on. Thus the material chosen to mount the magnets on becomes an important
factor in the design of the machine. The higher the permeability of the material the more efficient
the magnetic field will be. The table below gives some values of relative permeability of readily
available materials.
Table 4: Relative permeability of readily available materials [30]
The remanent (or residual flux) of a PM will also help determine the airgap flux density (therefore
the airgap flux) according to formula (39). This in turn will affect the performance parameters of the
machine. It is thus important to choose the magnets with the highest remanent flux in order to
achieve the best performance from the machine. The shape of the magnet is also an important
factor as it also has an effect on airgap flux density. The table below gives a few residual flux values
for different magnet types and grades as well as their maximum operating temperatures.
Material μr
Iron 200 000
Cobalt-Iron 18000
Iron 5000
Electrical Steel 4000
Ferritic Stainless Steel 1000-1800
Carbon Steel 100
Neodymium Magnet 1.05
Aluminium 1.000022
Wood 1.00000043
Air 1.00000037
Vacuum 1

49. 49
Table 5: Magnet Residual flux and working temperature [14]
(Note: 1T = 104
g)
As mentioned before the airgap flux density is an important design parameter and has a large effect
on the performance of the machine. The two graphs show how the PM grade and airgap influence
the average airgap flux density. The graphs are based on formula (39).
Figure 27: Graph illustrating how the average airgap flux density varies with remanence of PM
Magnet
Residual Flux
Density Br (g)
Working
Temperature
°C
Ceramic 5 3950 400
Sintered Alnico 5 10900 540
Cast Alnico 5 8200 540
Samarium Cobalt 20 (1,5) 9000 260
Samarium Cobalt 28 (2,17) 10500 350
Neodymium N45 13500 80
Neodymium 33UH 11500 180
0.6
0.7
0.8
0.9
1
1.15 1.2 1.25 1.3 1.35 1.4 1.45
FluxDensity(Tesla)
Remanence Flux (Tesla)
Average Airgap Flux Density-Varying
PM Remanence Flux
Average Airgap Flux
Density

50. 50
Figure 28:Graph illustrating how the average airgap flux density varies with length of airgap
3.5 The electronics
As mentioned earlier this project only involves BLDC motoring (therefore it is assumed that a DC bus
is available) but the machine also operates as a synchronous generator. In order to control the
direction of power as well as the amount of power the system is transferring at any given time it is
necessary to control the polarity of the voltage across motor windings and direction of current at a
given operating condition. That is the electric machine will either be operating in motoring or
generating mode or free to run under the control of angular momentum of the flywheel, friction and
windage. The power converter must be able to operate in all three modes.
A sophisticated power electronics is not in scope of this project. Pulse width modulation (PWM) can
therefore be used to control the amount of power flow in both motoring and generating modes. To
achieve all of the above a simple DC to DC bidirectional converter with a simple 3-leg scheme is
applicable.
For 3 phase square-wave motoring, a common wiring scheme is the Y connection. The 3 phases are
controlled by 6 switches (T1,T2,T3,T4,T5,T6) with flyback diodes in parallel with each switch in order
to handle the freewheeling current in between switching cycles (see [21] for more on switching) . An
example of the switching required for a 4 pole, 6 coil, 3 phase machine is shown below:
0
0.2
0.4
0.6
0.8
1
1.2
0 0.01 0.02 0.03
FluxDensity(Tesla)
Airgap (m)
Average Airgap Flux Density-Varying
Airgap
Average Airgap Flux
Density

51. 51
Figure 29: Rotor Position (i) with corresponding current path (ii)
In this position the current would flow through the first switch (T1) and through phase A’s coils in a
“positive” direction to the neutral point. The same current then flows through the phase C coils in a
“negative” direction and finally through switch T6. In this state phase A and C are contributing
positive torque while phase B is left off. For each position of the rotor similar current paths will be
taken but with different switches and phases operating. The switching scheme is however different
for different pole-coil combinations.
Important considerations when designing the power electronics are the DC bus voltage, the electric
machine current and voltage ratings. The various components such as transistors and diodes need to
be able to handle and perform efficiently under the harshest operating conditions. A typical
motor/generator used in a FBESS application could have the following rating: 230V DC, 20 A, 1500
rpm (ratings taken from a machine in the Machines Lab at UCT).The power electronics of the system
would therefore have to handle a normal operating power figure of 4.6kW.
The power handling capabilities of the individual components in the bridge have significantly
improved over the years. An example of a switch which could be used is the MOSFET transistor
(IRFB4233PbF-data sheet attached in appendix).
As was mentioned earlier in the text; which switches are on (and conducting current) at any given
time, is dependent on the position of the rotor. An angular position sensing device, together with a
control system, is therefore required to switch the appropriate switches on and off. More specific
details into the choice of sensing device are given in the design section of the report below.
4 Design & Simulations
The design of the FBESS is based on the theory discussed above. The FBESS will incorporate the
flywheel into the electric machine itself. In other words the flywheel will be the rotor of an axial flux
machine. (See Figure 53 at the end of the chapter for a scale for a 3-D model of the final design).
Furthermore the machine will be operating in both motoring and generating modes.
The justifications for the chosen topology, keeping in mind the FBESS is based on scrap materials, are
listed:

52. 52
 adjustable airgap
 topology is ideal to easily adjust and maintain
 high efficiency
 simple construction and ideal for prototyping
 Stator coils can easily be wound and adjusted [6]
 RFM has issues with heat removal [6]
 compact
 minimal moving parts (i.e. low wear and tear)
4.1 Flywheel
The deliverables for this project included a working scrap-based prototype of the designed FBESS.
Noting that the higher the angular speed of the flywheel is, the more energy it has stored, it was
important to ensure the flywheel is well balanced in order to achieve the highest speed possible. It
was decided to use a scrapped flywheel, from a piston driven engine, of a Warrior truck. These
flywheels are inherently balanced and are ultimately designed for the same purpose as for this
project (periodic storage of energy).
Based on formula (6) for the energy stored in a cylindrical flywheel it is apparent that the energy
stored for a given rotational speed, can be increased in two manners: i) increase the mass for a given
radius or ii) increase the radius for a given mass (or both). One way to increase the mass of the
flywheel, and thus the energy storage capabilities, is to place two (or more) flywheels side by side.
However, choosing a flywheel with a larger radius, for a given mass, has a larger impact on the
energy storage of capability of the flywheel, due to the radius term being squared in formula (6)
(that is a per unit of mass vs. per unit of radius length). Thus the reason for choosing a single
flywheel with a larger radius, as opposed to cascading smaller flywheels, is based on formula (6) and
supported by the graphs below:
Figure 30: Flywheel energy as a function of speed and i) increasing radius ii) increasing mass
The two graphs above demonstrate how radius and mass affect the energy storage capability of the
flywheel respectively. The graphs were derived from realistic flywheel options.
The properties of the chosen flywheel are roughly as follows:

53. 53
Figure 31: Flywheel Dimensions
The diagram above shows the cylindrically shaped flywheel with dimensions given. Based on the
shape of the flywheel the “K” values is roughly 0.305 which is not very high compared to Laval, solid
or ring shaped flywheels but is typical of a metallic flywheel.
The flywheel was weighed and has a total mass of:
A rough estimate of the MMI is:
(63)
Where, = flywheel outer radius
= shaft slot radius
The shaft also adds to the mass and MMI of the rotor/flywheel, thus the properties of the shaft are:
Dimensions: 40mm Diameter x 330mm Length
(64) Mass = = ( )
Shaft MMI =
Thus:
The energy storage capability of the rotor/flywheel design is graphed according to formula (6):

54. 54
Figure 32: Energy stored in flywheel vs. speed
4.2 Electric machine
There are many factors to consider when designing an electric machine of which power, torque,
Back EMF and efficiency are the most important for this project. All of these factors are influenced
by various parameters of which the most important will be discussed in depth.
The first major decision for the design of the machine is the decision between using AC or DC to
drive the motor. For this project DC is chosen as it is easier to control and simpler to build. No
further comparisons will be made regarding the choice between AC and DC but the details of BLDC
motoring will be highlighted.
4.2.1 Topology
Section 2.2.2 of the report showed that AFPM machines have many possible topologies however, in
the quest for ease of construction and compactness two topologies were considered. The first
topology is the single-rotor-single-stator topology which can be seen in Figure 4(i). This design is
easy to construct but suffers from two main disadvantages. Firstly the rotor and stator suffers from
unbalanced axially directed forces and secondly, this topology generally has lower torque production
relative to the other topologies.
The second topology considered is the single-rotor-double-stator configuration and can be seen in
Figure 4 (ii). This machine will generate a higher torque compared to the above machine and would
achieve balanced axial forces on the rotor. The design would however require more magnets and
more coils. For this reason the single-rotor-single-stator option was chosen.
A second major decision was the choice between a stator with a core and a coreless stator. The
advantage of a coreless stator is the lack of core losses. However, the Finite Element (FE) analysis
done in FEMM 4.2 reveals that the magnetic circuit is improved by having a ferromagnetic stator

55. 55
plate used as a core. The figures below demonstrate this by showing the flux density plots of both
core and coreless machines:
Figure 33: AFPM machine, with stator core, flux density plots at different depths in the airgap ii) 2mm from face of the
magnet iii) 8mm from the face of the magnet
The flux density plots above show the how the flux density varies around the circumference of the
AFPM machine at the mean radius of the PM’s . In the diagram above, the first plot (ii)
shows the flux density at the face of the coils (2mm from face of the PM’s) and the second plot (iii)
the flux density in the middle of the coil (in the axial direction) at 8mm from the PM’s.
The same simulation was repeated for the coreless stator and illustrated below in Figure 34:
Figure 34: AFPM coreless machine flux density plots at different depths in airgap ii) 2mm from the face of magnet iii)
8mm from the face of the magnet
From both sets of flux density plots it is clear, that for a single-rotor-single-stator topology, a
machine with a stator core will improve the magnetic circuit and thus increasing flux reaching the

56. 56
stator coils. To reduce eddy current losses the original design was to have layers of laminated
ferromagnetic material as the stator core, however this would have increase costs and added to
construction complexities. The final design included a steel core (8mm thick, without laminations)
which would be placed 17mm from the face of the magnets. The coils could safely be brought up to
within 2mm from the face of the PM’s. Lastly a slotless stator is chosen to eliminate cogging torque
[9].
4.2.2 Motoring Mode
The primary goal of this specific machine, in motoring mode, is to accelerate the flywheel while
when energy is to be stored. The torque required by the machine is based on formula (41). On the
other hand the torque the machine is able to produce is characterized by formula (46). According to
the formula the torque generated by the machine can be increase in numerous ways:
Increasing the phase current is one means of delivering more torque. Torque is proportional to
current however; increasing the current also increases the power consumption of the machine.
Careful design of the machine can lead to higher torque capabilities with little or no increase in
power consumption. Increasing the number of poles, number of turns per phase or the remanence
flux of the PM magnet will all contribute to an increase in the torque the motor is able to generate.
All of these factors will have their own limits as to how much they can be increased due to their
physical properties and/or physical size.
The topology of the AFPM machine is also a contributor to torque production. As discussed earlier, a
higher number of rotor-stator faces can lead to a higher torque capability. Lastly the winding factor
is a very important characteristic of any motor with regards torque production.
 Number of turns per phase
Rearranging formula (44) shows that the current a BLDC motor is drawings at any given time, is a
function of the back EMF (or the speed of the rotor), terminal voltage as well as the coil resistance.
In order to reduce the heat produced for a given value of current (i.e. reduce the copper losses) the
resistance of the copper wire can be reduced by increasing the diameter of the wire strand.
Furthermore there is a trade-off between the length of copper wire per phase (i.e. number of turns
per phase which directly influences torque produce in motoring mode and the voltage induced in
generating mode) and copper losses. The equation of resistance for a wire strand is given below:
(65)
( )
Where, = coefficient of resistivity
= length of copper conductor
= Area of wire cross section
= diameter of wire cross section

57. 57
The two graphs demonstrate how varying the diameter and the length of the copper
(number of turns per phase) wire influence’s the resistance of the wire (and thus the copper losses):
Figure 35: Phase resistance as a function of i) Wire Diameter ii) Number of turns per phase
It was decided to use a relatively large diameter of copper wire (0.9mm).This reduces copper losses
(and heat losses) but results in a larger coil winding for a given number of turns. Using a larger
diameter allows for more turns per phase, thus increasing the torque and induced voltage, for a
given loss value. 100 turns per coil (or 400 turns per phase) was used in the final design resulting in a
measured resistance per phase of 2.1 ohm (this is in accordance with the calculated value).
 PM Selection
A higher flux density in the air gap of the motor will increase the force on the rotor (all other
parameters being constant). Formula (39) indicates that, in order to increase the flux density in the
airgap, the remanent flux of the PM needs to be increased (or by reducing the airgap length). Thus it
is necessary to choose magnets which have a high flux remanence but at the same time are robust.
The Rare Earth Metal magnet types meet the requirements. More specifically the Neo magnets are
most well suited. The N35 (with a flux remanence of 1.21T) was the highest grade available in the
dimensions required. The dimensions and polarity orientation of the chosen magnets is shown
below:

58. 58
Figure 36: Magnet dimensions and polarity
 Winding factor
For square wave operations common winding types are salient winding or concentrated winding
[19]. There are various tried and tested coil configurations which have differing impacts on
performance parameters such as torque, power and losses. For this project however the simple
concentrated non-overlapping ungrouped (n=1) coil is the chosen configuration.
The advantages of this coil configuration include simple analysis and construction. Furthermore it is
well a well-known configuration for DC motoring as well as generating and allows for a relatively
low-complexity power electronics system.
Once again looking at the formula for torque production, formula (46), the more poles placed on the
rotor the higher the torque. It is however not this straight forward as changing the pole number also
changes the pole pitch and coil pitch and hence the winding factor. The effect of changing the
number of poles and coils can be seen in Table 3.
The final number of coils and poles (12 and 16 respectively) was chosen based purely on maximizing
the winding factor. Looking at Table 3 it can be seen that this this combination provides the highest
stator factor for a given value of thus maximising the winding factor . The final design
produced a winding factor of 0.946.
A disadvantage of an increase in the number of poles is that it becomes more expensive (magnets
aren’t cheap) and potentially more complicated to control the commutation of the motor (see
electronics for more details). A 16 pole machine was finally chosen to achieve a balance between
complexity, cost and size but most importantly to achieve a high winding factor and therefore an
efficient torque production and voltage generation.

59. 59
Once the number of coils and poles are decided on, another important factor in the winding factor
calculation is the average radius at which the PM’s are placed. The graph below shows how the
winding factor changes as the average radius changes (all other factors kept constant):
Figure 37: Winding factor as a function of average radius at which the PM's are placed on the rotor
It is clear that the further the PM’s are place from the axes of rotation the higher the winding factor.
The average radius of the final design was chosen to be 0.13 m.
4.2.3 Generating Mode
The most important factors to consider when in generating mode are current and induced EMF on
the stator windings. According to equation (45) the important parameters to consider, with regard
to the line-to-line EMF created while generating, are similar to the torque production formula
namely; number of poles, turns per phase, winding factor and flux. The rotational speed of the rotor
is also influential. The graphs below demonstrate the effect the number of turns per phase (N) and
the average flux density in the airgap have on the induced EMF:

60. 60
Figure 38: EMF generated as a function of average airgap flux density (T) and rotational speed (RPM)
From the graphs above, the higher airgap flux density, the higher EMF induced in the phase
windings. The graph below shows a similar trend with the number of turns per phase, where an
increase in the number of turns leads to an increase in EMF.
Figure 39: EMF generated as a function of average airgap number of turns per phase (N) and rotational speed (RPM)
As mentioned earlier, the final design included 400 turns per phase while the average flux density in
the airgap was around 0.33T. This average flux density is lower than it could be but due to the lack of
stock in the country, the highest grade magnet that could be sourced was the N35 Neo magnets.
4.3 Mechanical Considerations
The scope of this project does not include a detailed mechanical design, however, two mechanical
factors are very important with regard to the efficiency of the system namely, the bearing choice
and the shape of the rotor.

61. 61
4.3.1Bearings
The targeted speed of the flywheel will be in the range of 1000-2000 rpm while the load on the
bearing/bearings is the mass of the shaft plus the mass of the flywheel/rotor (43.35kg). The
coefficient of friction for a contact sliding bearing may be around 0.05 to 0.1 while that of a rolling
element (ball bearing for example) is typically 0.005 according to [29]. Furthermore the shaft of the
motor will be exposed to both axial and radial forces. Taking all of this into consideration the ball
bearing is chosen as the most suitable. It has a relatively low coefficient of friction and is able to
withstand a fair amount of force in both the radial and axial direction.
The next step in the design, with regard to bearings, is the method used to mount the flywheel
within its frame structure. The figure below shows various mounting options. A single bearing can be
used which will reduce costs however, if the load creates a moment about the about the bearing, it
is a good idea to put a bearing on each side of the flywheel in order to evenly distrubute the forces
across the bearing:
Figure 40: Flywheel/rotor mounting options
Out of the four bearing configuration options above it was decided to use two bearings, one on
either side of the flywheel (as can be seen in (iv) in figure above).This will result in the load being
shared between the two bearings and minimize the moment about each bearing (two bearings may
however be more inefficient).