Paper submitted within the scope of the Master’s Thesis Master of Industrial Sciences GROUP T – Leuven Engineering College – 2009-2010 Abstract—Is it possible to place in-wheel motors in the front wheels of a racing kart as part of a KERS 1 , how can this be done, what order of acceleration gain can be achieved and what is the total cost of converting a regular kart to a kart with an in-wheel KERS? To answer these questions, a prototype of a wheel rim and an in-wheel electromotor were developed and produced. A controller and energy source were also selected and the motor specifications will soon be checked against the predicted specifications. When looking at the conception, design and production phase of this project, one can conclude that it is possible to implement a KERS using in-wheel motors in the front wheels of a kart as described in this paper. In the speed range of 0 to 80 km/h, the designed prototype can accelerate 6,4% faster than a conventional kart and the conversion cost of a regular kart is approximately 3450 Euros. Index Terms— In-wheel motor, kart, KERS (kinetic energy recovery system), motor design, wheel rim design, electronic differential, unsprung mass I. INTRODUCTION The so called KERS is a recent automotive development that enables temporary storage of braking energy by means of a flywheel, batteries or supercapacitors. The stored energy is used for extra acceleration when desired. This system found its first application in some of 2009’s Formula One vehicles. Research about implementation of this system in racing karts has been done as well. In 2009, on request of Campus Automobile, a thesis was written about a KERS with two electromotors positioned next to a kart’s front wheels [1]. Successful elaboration of this project pointed out the scarcity 1 Kinetic Energy Recovery System, a system storing and releasing braking energy of available space in the front section of a kart. It also revealed how a next-to-wheel placement of the motors in a KERS leads to mechanical complexity. This paper explains the development of a KERS with two in-wheel motors in order to reduce size and mechanical complexity. Section II explains the mechanical design of this prototype. Section III handles about the electrical aspects of this system. A short discussion about the finances of the project can be found in section IV and section V highlights two important extra considerations that have to be done when implementing an in-wheel KERS in a Formula One vehicle instead of in a kart. II. MECHANICAL DESIGN A. Demands Since front wheel rims of a conventional kart do not provide enough space to place an electromotor in (see Figure 1), a new wheel rim concept has to be made. Fig. 1. Conventional front wheel rim of a kart with little inner space for in- wheel motor placement Requirements concerning the new wheel rim are the possibility of mounting original tires, the possibility of mounting the rim on an original kart without the requirement of heavy modifications, an adaptable distance between the front wheels and a reasonable production cost. Design of an in-wheel kinetic energy recovery system for a kart Fabrice Boon*, Jan Revyn*, Pierre Detré**, Marc Nelis**, Frederic Duflos°, Kristof Goris° *Master student electromechanical engineering focus intelligent manufacturing, GROUP T – Leuven Engineering College, Vesaliusstraat 13, 3000 Leuven **Automotive development, Campus Automobile, Route du Circuit 60, 4970 Francorchamps °Unit energy, GROUP T – Leuven Engineering College, Vesaliusstraat 13, 3000 Leuven, [email protected]
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Paper submitted within the scope of the Master’s Thesis
Master of Industrial Sciences
GROUP T – Leuven Engineering College – 2009-2010
Abstract—Is it possible to place in-wheel motors in the front
wheels of a racing kart as part of a KERS1, how can this be done,
what order of acceleration gain can be achieved and what is the
total cost of converting a regular kart to a kart with an in-wheel
KERS?
To answer these questions, a prototype of a wheel rim and an
in-wheel electromotor were developed and produced. A
controller and energy source were also selected and the motor
specifications will soon be checked against the predicted
specifications.
When looking at the conception, design and production phase of
this project, one can conclude that it is possible to implement a
KERS using in-wheel motors in the front wheels of a kart as
described in this paper. In the speed range of 0 to 80 km/h, the
designed prototype can accelerate 6,4% faster than a
conventional kart and the conversion cost of a regular kart is
approximately 3450 Euros.
Index Terms— In-wheel motor, kart, KERS (kinetic energy
recovery system), motor design, wheel rim design, electronic
differential, unsprung mass
I. INTRODUCTION
The so called KERS is a recent automotive development
that enables temporary storage of braking energy by means of
a flywheel, batteries or supercapacitors. The stored energy is
used for extra acceleration when desired. This system found
its first application in some of 2009’s Formula One vehicles.
Research about implementation of this system in racing karts
has been done as well. In 2009, on request of Campus
Automobile, a thesis was written about a KERS with two
electromotors positioned next to a kart’s front wheels [1].
Successful elaboration of this project pointed out the scarcity
1 Kinetic Energy Recovery System, a system storing and releasing braking
energy
of available space in the front section of a kart. It also revealed
how a next-to-wheel placement of the motors in a KERS leads
to mechanical complexity.
This paper explains the development of a KERS with two
in-wheel motors in order to reduce size and mechanical
complexity. Section II explains the mechanical design of this
prototype. Section III handles about the electrical aspects of
this system. A short discussion about the finances of the
project can be found in section IV and section V highlights
two important extra considerations that have to be done when
implementing an in-wheel KERS in a Formula One vehicle
instead of in a kart.
II. MECHANICAL DESIGN
A. Demands
Since front wheel rims of a conventional kart do not provide
enough space to place an electromotor in (see Figure 1), a new
wheel rim concept has to be made.
Fig. 1. Conventional front wheel rim of a kart with little inner space for in-
wheel motor placement
Requirements concerning the new wheel rim are the
possibility of mounting original tires, the possibility of
mounting the rim on an original kart without the requirement
of heavy modifications, an adaptable distance between the
front wheels and a reasonable production cost.
Design of an in-wheel kinetic energy recovery
system for a kart
Fabrice Boon*, Jan Revyn*, Pierre Detré**, Marc Nelis**, Frederic Duflos°, Kristof Goris°
*Master student electromechanical engineering focus intelligent manufacturing, GROUP T – Leuven Engineering College,
Vesaliusstraat 13, 3000 Leuven
**Automotive development, Campus Automobile, Route du Circuit 60, 4970 Francorchamps
°Unit energy, GROUP T – Leuven Engineering College, Vesaliusstraat 13, 3000 Leuven, [email protected]
2
B. Description of the design
In this section the final wheel rim design is explained
together with the way of mounting the wheel rim onto the
kart’s body. Earlier concepts in the design process that were
considered but rejected are shown in a conceptual report (see
Addendum A). The motor design of the customized
electromotor that is developed for this application is
elaborated further in paragraph III. Technical drawings of all
designed parts can be found in Addendum B.
Figure 2 illustrates a kart with adapted front wheel rims and
custom made BLDC2 in-wheel outer rotor electromotors. It
gives a first visual impression of what this thesis project is
about.
Fig. 2. Kart’s body with adapted wheel rims and in-wheel motors
Figure 3 shows a detailed view of both sides of an adapted
front wheel.
Fig. 3. Left and right side of a front wheel
Figure 4 shows the axle of the right front wheel. The part
pictured in blue is based on the part of the original kart. The
only adjustment is the groove indicated on the picture. This
groove is required to avoid rotation of the motor’s stator due
to the torque exerted by the rotor on the stator (see Figure 5).
The axle’s dimensions and material are based on those of the
original axle. This ensures the axle is stiff enough for this
application and does not imply dimensional adaptations to the
original part shown in Figure 4b. The end of the axle is M14
thread. This is dimensioned in such a way that the nut pictured
on Figure 3 can be mounted in the cavity also indicated in the
same figure.
2 BLDC, BrushLess Direct Current
Fig. 4. Axle of the right front wheel (a) and view of the groove (b)
Figure 4 also shows three spacers. Putting zero to three of
these spacers on the axle, results in different distances
between the front wheels of the kart with a range of 30 mm
per wheel. A higher range would result in a design in which
the axle would stick out from the wheel rim or in a smaller,
less stable distance between the two used bearings in the
motor (for bearing placement see further). A compromise is
made between an acceptable distance between the bearings
(47 mm) and an acceptable adjustablity of the distance
between the front wheels (30 mm per wheel). The spacers on
picture 4 are designed in such a way that they slide easily over
the axle and that they avoid the stator of the motor from
rotating. Figure 5 shows the stator of the in-wheel motor
attached onto the axle (see paragraph III.E. for more
information about the electrical design of this stator).
Determining the fitting between stator and axle, is making a
compromise between the ease of adjusting the distance
between the front wheels, for which loose fittings are wanted,
on the one hand and avoiding a variable airgap between the
stator and the rotor, for which fixed fittings are desirable, on
the other hand.
Fig. 5. Two views of the stator attached on the axle
In Figure 6 a spacer is slided over the axle. This ring makes
contact with the stator and the inner ring of the bearing on the
axle (see Figure 6b). The spacer is needed to avoid contact
between the rotating outer ring of the bearing and the fixed
stator. The outer diameter of this ring is dimensioned
according to the design recommendations for SKF bearing
spacers [2]. More information about the bearings used in this
design is given in section II.C.1. A spacer tube is placed
between the two bearings to obtain a fixed distance between
the inner rings of these bearings (see Figure 7).
nut
cavity
groove
axle
a b
M14
thread
spacers
groove
3
Fig. 6. Spacer to avoid contact between rotating outer ring of bearing and
stator (a) and view of bearing (b)
Fig. 7. Spacer tube obtaining fixed distance between inner rings of two
bearings
The rotor of the motor acts as part of the wheel rim and is
pictured in Figure 8. It is composed of two welded parts made
of low carbon steel (CS-1010 steel). A motivation for this
material choice is given in paragraph III.D.1. This rotating
part makes contact with the outer rings of two bearings as
illustrated in Figure 10. Into the grooves 28 magnets are
placed as pictured in Figure 9. More information on these
magnets is given in section III.D.3.
Fig. 8. Rotor composed of two welded parts, acting as part of a wheel rim
Fig. 9. Rotor with magnets
Figures 10 and 11 show the rotor mounted on all previously
mentioned parts.
Fig. 10. Visualisation of connection between rim/rotor and rotating outer
rings of bearings
Fig. 11. Rotor placed on axle together with all previously mentioned parts
Another spacer is placed next to the left bearing (see Figure
12a) in order to avoid contact between the fixed nut (see
Figure 12b) and the rotating outer ring of the left bearing.
Fig. 12. Spacer to avoid contact between the self locking nut and the
rotating outer ring of bearing (a). Self locking nut (b)
All the components discussed so far, are axially held
together by the nut pictured in red. This is a M14 self locking
nut that does not come off by vibrations when driving the kart.
In order to make it possible to (dis)mount tires on this wheel
rim, the rim is composed of two easily detachable main parts.
One of those parts is the setup shown in Figure 12. The second
part contains a hole for air flow and is attached to the first part
as indicated in Figure 13. This figure pictures the entire wheel
rim.
Fig. 13. Both wheel rim parts mounted together
spacer
a b
spacer tube
groove
connection rotor-bearings bearing
weld
connection
nut
a b Spacer
bearing
magnets
spacer
left
bearing
fixed nut
a b
two wheel rim parts
air hole
4
Since no inner tires3 are used for kart applications, a sealing
ring between both main parts is required to avoid air leakage
from the tire (see Figure 14). This sealing ring has standard
dimensions [3]. The groove in the wheel rim part in which the
sealing ring is positioned is calculated considering a
compressed state of the ring.
Fig. 14. Sealing ring to avoid air leakage from the tire
The two main parts of the wheel rim are held together with
five M6 bolts. Both of the parts contain five holes for air
cooling of the windings on the stator (see Figure 15).
Fig. 15. Holes for cooling and bolts to fasten the two main parts of the
wheel rim
Mounting a tire on the rim can be done by successively
unscrewing the five bolts, sliding the tire over the wheel rim
part of Figure 14 and attaching the two rim parts together
again.
C. Strength considerations and material selection
1) Bearings
The bearings are single row deep groove ball bearings from
SKF (type 61903-2RS1) (see Figure 16). This type of bearings
is eligible for the kart because they can handle loads in both
radial as axial direction. Furthermore, they are suitable for
high speeds, are robust in operation and require little
maintenance. Lifetime calculations were executed to quantify
the strength of the considered bearings (see Addendum C)
[2][4]. A compromise is made between big bearing
dimensions involving a high lifetime and little space for the
stator of the motor on the one hand and small bearings
involving a low lifetime and more space for the stator on the
other hand. A life expectancy of approximately 10000 hours is
obtained by using bearings with an outer diameter of 30 mm.
3 Inner tire, an inflatable rubber tube that fits inside the tire
Fig. 16. Single row deep groove ball bearing
2) Bolts and nuts
Five M6 bolts are used to hold the two main rim parts
together (see Figure 17). M6 bolts with strength class 5.8 are
able to carry dynamic axial loads of 2.5kN [4]. Five bolts can
therefore carry up to 12,5kN dynamic load. Since the forces
exerted on these bolts are only caused by the axial forces that
the track exerts on the kart when cornering and the force
needed to squeeze the sealing ring between both main rim
parts, no further strength verifications are done for the bolts.
Also the M14 nut (see Figure 12b) can carry loads of more
than 10kN.
3) Weld connection
The mechanical design of the in-wheel KERS is developed
for karts with tubeless tires. Therefore, the two rotor parts (see
Figure 8) are welded together by means of a continuous
welding line. Spot welding is not possible because this would
lead to air leakage from the kart’s tire. Additionally, spot
welding would induce an unbalance in the rotor. In
consultation with Campus Automobile’s welding instructor it
was decided that a continuous weld of 3mm is strong enough
to carry the loads exerted on the rotor (gravitational force,
acceleration force and torsion). A V-shaped welding groove is
foreseen in both parts to be welded (see Addendum B).
4) Material choice
As mentioned earlier, part 2 indicated in Figure 17 consists
of two subparts that are welded together. Because the subpart
where the magnets are placed in, which is preferably made of
CS1010-steel (see section III.C.1), is to be welded together
with the subpart containing the grooves (see Figure 17), this
last subpart is also made of this type of steel. Part 1 indicated
in Figure 17, the spacer tube between the bearings (see Figure
7), the spacers in Figures 6a and 12a and the spacers with
groove (see Figure 4a) all are made of aluminum. This
material is used because of its combination of relatively low
weight (2,7 g/cm3), relatively high yield strength (200-600
MPa) and stiffness (E = 70 GPa), low price and machinability.
For reasons mentioned earlier (see section II.B.) it is decided
to produce the axle (see Figure 4a) from steel with dimensions
based on the original kart’s axles.
D. Vibration considerations
1) Centering of the two rim parts
As shown in Figures 17 and 18, the two main rim parts are
fixed to each other using five bolts. These bolts however do
not guarantee an accurate alignment of part 1 with the axle. To
avoid vibrations due to a possible unbalance in the rotor, part
1 and part 2 (see Figure 17) fit by means of a groove. The
sealing ring
bolt
cooling
hole
5
dimensions and tolerances of this groove are detailed on the
technical drawings in Addendum B.
Fig. 17. Fitting between the two main rim parts to avoid heavy vibrations due
to rotor unbalance
Fig. 18. Fitting between the two main rim parts to avoid heavy vibrations due
to rotor unbalance (other view)
2) Consideration of resonance due to rotor unbalance
In order to check whether or not an unbalance in the rotor
can cause resonance of the kart, a simplified kart model is
considered in which the body is replaced by two beams made
of steel (see Figure 19a). By calculating the deflection of point
A caused by the driver’s mass (see Figure 19b), an
approximation of the kart’s stiffness is achieved. This leads to
a certain resonance frequency, to which the driver will be
subjected (see Addendum D). The simplified system of
Figure 19 has a resonance frequency of 98,5Hz. Since the
wheels of the kart have a maximum angular speed of 2550rpm
(maximum kart velocity is 120 km/h), an unbalance in the
rotor is not able to cause resonance due to its frequency of
42,5Hz (= 2550rpm). From this point of view, balancing the
wheel rims is not required. It does however have a positive
influence on drive comfort and handling.
Fig. 19. Simplified car model from above (a) and from aside (b)
3) Torsion resonance
The torque delivered by BLDC electromotors is not
perfectly constant. This phenomenon of harmoniously varying
torque is referred to as torque ripple. The ripple is transmitted
from the motor’s stator to the kart’s frame and can cause
torsion resonance of the axle indicated in Figure 20. However,
since the axle on which the torque variation is exerted has a
small moment of inertia, this ripple does not lead to problems
such as axle rupture.
Fig. 20. Torque ripple transmitted from stator to kart’s frame
E. Manufacturing aspects
The wheel rim and in-wheel motor consist of custom made
parts and standard parts. The custom made parts are the parts
shown in addendum B. Used standard parts are the bearings,
bolts, washers, nuts, electric wire and magnets. Machinability
of all custom made parts was taken into account from the
beginning of the design phase. In that aspect, part 2 (see
Figure 17) is made out of two initially separate parts that are
welded together in a later stage of the manufacturing process
(see Figure 8). Since this enables an electric wire to go
through the entire part, it is possible to cut the grooves (see
Figure 8) by means of electric discharge milling. The custom
made parts have tolerances as shown on their technical
drawings (see Addendum B). Determination of these
tolerances is making a compromise between manufacturing
costs and part accuracy. Important is to guarantee there is no
contact between stator and rotor of the motor due to
dimensional errors of the parts and to obtain the required fits
(running fit, push fit). The fabrication of the custom made
parts is done by specialized companies. The stator however is
partly manufactured by the authors in order to get a better
understanding of the manufacturing process of EDM. Figure
21 shows how the stator is produced.
Fig. 21. Subsequent steps of the stator’s production
groove for
fitting
goes into
the groove
part 1
axle
part 2 ΔT
ΔT
axle subjected to
torque variation
stack of 100
laminates
clamped
together drilling
placement
clamping the two
parts together
EDM wire cutting,
followed by glueing
6
III. ELECTRICAL DESIGN
In this section the motor design and choice of the energy
source and controller are discussed. As indicated, some of the
formulas for the motor design are based on previous work [7].
A. Motor selection
As the dimensions of the motor should match the dimensions
of the designed wheel rim (section II), a custom electromotor
is developed. Due to the fact that no transmission is used, a
specific torque/speed curve for the electromotor has to be
obtained. The available motors on the market do not satisfy
these requirements. The developed motor is a radial flux
BLDC motor, because this type of motor has a high efficiency
and power to size ratio and does not require a lot of
maintenance compared to several other motor types [5]. A
BLDC motor has a rotor with permanent magnets and a stator
with windings. The brushes and commutator have been
eliminated and the windings are connected to a controller,
which replaces the function of the commutator and energizes
the proper winding. Radial flux BLDC motors can work as
outer rotor motors, where the rotor is situated on the outside of
the stator [6]. As a result, the rotor of the motor can directly be
used as wheel rim, which eliminates the need for a
transmission between the rotor and the wheel.
B. Energy source
1) Choice of energy source
The contract giver4 demanded, if possible, to reuse
supercapacitors from a previous project. The (dis)advantages
of this technology were investigated in order to verify the
suitability of these supercapacitors. Compared to
electrochemical batteries the use of supercapacitors for the
KERS of the kart offers these following advantages:
Higher number of charge/discharge cycles
Higher efficiency
Higher specific power output5
However, the supercapacitors also have a number of
disadvantages compared to electrochemical batteries:
Lower energy density
Lower voltage
Higher self-discharge
Since these limitations are less critical for the KERS of the
kart, the conclusion is made that supercapacitors are suitable
for the application (see Addendum E). In this project
supercapacitors from Maxwell are used (type BMOD0250)
from which the main characteristics are given in Table 1.
4 Campus Automobile Spa-Francorchamps 5 Specific power output, amount of power a component can deliver per kg
Table 1: Specification of the Maxwell BMOD0250 supercapacitor module
Parameter Value
Capacity 250F
Voltage 16,2V
Max continuous current 115A
Max peak current for 20s 200A
Weight 4450g
2) Maximum output current
When the kart is driving, the electromotors are only used
when accelerating and decelerating before and after a turn.
One can assume that this always takes less than 20s. The
motors can thus take advantage of the maximum peak current
of 200A.
3) Configuration
Two of these capacitors are placed in series (see Figure 22).
A first reason is the higher voltage obtained compared to the
use of only one capacitor, or the use of two capacitors in
parallel rather than in series. This results in a lower current for
the same power and thus less Joule losses in the motor, which
increases efficiency. A second reason is that a cheaper
controller can be used, since controllers with lower current
limit are less expensive. Only two supercapacitors are used,
because of limitations in price, weight and available space on
the kart. In this configuration the two capacitors have enough
energy to drive both motors at maximum power for 10s (see
Addendum E).
Fig. 22. Two supercapacitors in series connected to the controllers of the left
and right front wheel
4) Voltage drop
When the capacitors release their energy, their voltage
drops. With a lower voltage the motor cannot accelerate to its
maximum angular velocity anymore. If, for instance, the two
capacitors are only half charged, the voltage of the capacitors
drops from 32V to 23V. This results in a drop of the maximum
angular speed of the electromotors from 2130rpm (see section
III.E.3) to 1500rpm, which corresponds to a speed drop for the
kart from 100km/h to 70km/h. In this situation the
electromotors are not able to provide an acceleration gain to
the kart at speeds above 70km/h (see Addendum E).
7
C. Controller
1) Choice of controller
A controller from Kelly Controls is selected (type
KBL72101). These controllers are relatively cheap and fit all
the requirements. The controllers can handle the maximum
peak current of 100A from the capacitors (see Table 2).
Table 2: Specification of the Kelly Controls KBL72101 controller
Parameter Value
Input Voltage 18V – 90V
Output Voltage 18V – 90V
Max continuous current 50A
Max peak current for 1min 100A
Weight 2270g
2) Commutation
Three bipolar hall sensors are used for the commutation.
These hall sensors detect the position of the rotor magnets and
based on this information the controller determines which coil
needs to be energized. They are installed with a phase shift of
120° on the stator of each of the motors.
3) Regenerative braking
The controller allows regenerative braking at all speeds.
This means that the capacitors can still be charged when the
back EMF6 generated by the motor is lower than the voltage of
the capacitors.
.
4) Temperature control
A maximum operating temperature for the motor can be set.
When this temperature is exceeded, the controller
automatically shuts down the motor. In order to measure the
temperature of the motor, a thermistor is used. The placement
of this thermistor on the motor and the value of the shut down
temperature is chosen so that each individual component of
the motor never exceeds its maximum operating temperature.
5) Maximum number of poles
The controller can handle a maximum of 40.000 electrical
rpm. The maximum speed of the kart is 120km/h, which
corresponds to a front wheel angular speed of 2550rpm. For
this application the motors can have a maximum of 15 pole
pairs (see Formula 1).
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒 𝑝𝑎𝑖𝑟𝑠 =𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑟𝑝𝑚
𝑚𝑒𝑐 𝑎𝑛𝑖𝑐 𝑎𝑙 𝑟𝑝𝑚 (1)
𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒 𝑝𝑎𝑖𝑟𝑠 = 15
D. Rotor design
1) Material
The rotor is made from low carbon steel 1010 (CS 1010). It
contains between 0,08% and 0,13% of carbon. Steel is a
ferromagnetic material and is commonly used in motor
construction [6]. Due to the low carbon content this type of
steel has desirable magnetic properties.
6 EMF, electromotive force
2) Number of poles
In general terms, a higher number of poles creates a higher
torque for the same current level, however at the cost of a
lower space for each pole. Eventually, a point is reached
where the spacing between rotor magnet poles becomes a
significant percentage of the available space on the rotor and
the torque no longer increases. The optimum number of
magnet poles is a complex function of motor geometry and
material properties [6]. In literature motors with 14 poles are
common for high torque applications and therefore this
number of poles is selected.
3) Magnets
NdFeB7 magnets are among the strongest permanent
magnets available on the market and are popular in high
performance applications. The selected magnets have grade
N42. The letter N means that the maximum operating
temperature is 80°C. The number 42 implies that the
maximum energy product8 equals 42 MegaGauss Oersteds,
which corresponds to 334kJ/m³.
Two magnets per pole are used in order to reduce the
variation of the airgap and therefore increase efficiency. The
magnets are placed side by side and slightly oblique (see
Figure 23a).
Fig. 23. Magnet placement (a) and grooves on rotor’s inner surface (b)
To be able to fit the magnets more easily during installation,
grooves are made on the rotor’s inner surface (see Figure 23b).
These grooves also ensure that the magnets stay in place
during rotation of the motor. The magnets are glued to the
rotor’s inner surface. For more information about this glue see
Section III.E.1.
By using magnets with a width of 10mm, a magnetic
coverage of 85% is obtained (see Addendum F). In literature
can be found that the magnetic coverage is usually situated
between 65% and 85%.
4) Dimensions
The rotor’s outer diameter 𝐷𝑜𝑟 equals the diameter of the
wheel rim of 123mm.
By increasing the airgap flux density 𝐵𝑔 , one can increase
the force generated. This can be done by decreasing the
effective airgap length 𝑔𝑒 , which takes the extra flux path
distance over the slot into account. Manufacturing tolerances
do not allow physical airgap lengths 𝑔 lower than
7 NdFeB, Neodymium-Iron-Boron 8 Maximum energy product, a measurement for the maximum amount of
energy stored in the magnet
a b
groove
airgap
8
approximately 0,3mm [6]. In addition, decreasing 𝑔 increases
the undesirable cogging torque9. According to the
manufacturing tolerances of the designed wheel rim, 𝑔 is set
to 1mm. This results in 𝑔𝑒 equal to 5,6mm (see Formula 2).