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, Kristof.Goris@groept.be

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).

𝒈 = 𝒑𝒉𝒚𝒔𝒊𝒄𝒂𝒍 𝒂𝒊𝒓𝒈𝒂𝒑 𝒔𝒊𝒛𝒆, [𝒎] = 𝟎,𝟎𝟎𝟏𝒎 𝒈𝒆 = 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 𝒂𝒊𝒓𝒈𝒂𝒑, [𝒎] 𝒍𝒎 = 𝒎𝒂𝒈𝒏𝒆𝒕 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔, [𝒎] = 𝟎,𝟎𝟎𝟓𝒎 µ𝒓 = 𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒑𝒆𝒓𝒎𝒆𝒂𝒃𝒊𝒍𝒊𝒕𝒚 𝒎𝒂𝒈𝒏𝒆𝒕𝒔 = 𝟏,𝟏

𝑔𝑒 = 𝑔 +𝑙𝑚µ𝑟

(2)[7]

𝑔𝑒 = 0,0056𝑚

The remanent magnetic flux density 𝐵𝑟 of the N42 grade

permanent magnets equals 1.3T. As a result, the airgap flux

density 𝐵𝑔 equals 0,6T (see Formula 3).

𝑩𝒈 = 𝒂𝒊𝒓𝒈𝒂𝒑 𝒇𝒍𝒖𝒙 𝒅𝒆𝒏𝒔𝒊𝒕𝒚, [𝑻]

𝑩𝒓 = 𝒓𝒆𝒎𝒂𝒏𝒆𝒏𝒕 𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒄 𝒇𝒍𝒖𝒙 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒎𝒂𝒈𝒏𝒆𝒕𝒔 =𝟏,𝟑𝑻

𝐵𝑔 =𝐵𝑟

1 + µ𝑟 .𝑔𝑒𝑙𝑚

(3)[7]

𝐵𝑔 = 0,6𝑇

Saturation is a limitation occurring in ferromagnetic cores.

Initially, as the current is increased the flux increases in

proportion to it. At some point however, further increases in

current lead to progressively smaller increases in magnetic

flux. Eventually, the core can make no further contribution to

magnetic flux growth and any increase thereafter is limited

[8]. This is the reason why the thickness of the material

between the rotor’s outer surface and the magnets must be

sufficient. The purpose of the rotor back height (see Figure

24a) is to provide a return path for the flux from the magnets.

The flux from one magnet splits equally and couples to the

two adjacent magnets (See Figure 24b). For common electrical

steels, hard saturation is reached at flux densities between

1.7T and 2.3T [6].

Fig. 24. Rotor back height and pole pitch (a) and magnetic flux lines through

rotor back height (b)

The pole pitch 𝜏𝑝 is the distance between two successive

poles (see Figure 24a). For a saturation flux density of 1.7T,

𝜏𝑝 equals 25,6mm (see Formula 4).

9 Cogging torque, the torque due to the interaction between the permanent

magnets and the stator’s teeth [6]

𝝉𝒑 = 𝒑𝒐𝒍𝒆 𝒑𝒊𝒕𝒄𝒉, [𝒎]

𝒑 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒐𝒍𝒆𝒔 = 𝟏𝟒 𝑩𝒊𝒓𝒐𝒏 = 𝒊𝒓𝒐𝒏 𝒃𝒂𝒄𝒌 𝒔𝒂𝒕𝒖𝒓𝒂𝒕𝒊𝒐𝒏 𝒇𝒍𝒖𝒙 𝒅𝒆𝒏𝒔𝒊𝒕𝒚, 𝑻 =𝟏,𝟕𝑻

𝜏𝑝 =𝜋.𝐷𝑜𝑟

𝑝 +𝜋.𝐵𝑔𝐵𝑖𝑟𝑜𝑛

(4)[7]

𝜏𝑝 = 0,0256𝑚

Knowing 𝜏𝑝 , the rotor back height 𝑕𝑟𝑟 can be calculated.

According to Formula 5, 𝑕𝑟𝑟 should be at least 4,4mm.

𝒉𝒓𝒓 = 𝒓𝒐𝒕𝒐𝒓 𝒃𝒂𝒄𝒌 𝒉𝒆𝒊𝒈𝒉𝒕, [𝒎]

𝑕𝑟𝑟 =𝜏𝑝 .𝐵𝑔

2.𝐵𝑖𝑟𝑜𝑛 (5)[7]

𝑕𝑟𝑟 = 0,0044𝑚

Using the free finite element software package for magnetic

simulations FEMM, a view of the magnetic flux through the

motor is obtained (see Addendum G). From this simulation it

is determined that the maximum flux density in the rotor back

height equals 2,2T, which is smaller than the upper hard

saturation limit of 2,3T.

Based on Formula 6, the rotor’s inner diameter 𝐷𝑖𝑟 equals

104,2mm.

𝑫𝒊𝒓 = 𝒊𝒏𝒏𝒆𝒓 𝒓𝒐𝒕𝒐𝒓 𝒅𝒊𝒂𝒎𝒕𝒆𝒓, [𝒎] 𝑫𝒐𝒓 = 𝒐𝒖𝒕𝒆𝒓 𝒓𝒐𝒕𝒐𝒓 𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓, [𝒎] = 𝟎,𝟏𝟐𝟑𝟎𝒎 𝒉𝒓𝒓 = 𝒓𝒐𝒕𝒐𝒓 𝒃𝒂𝒄𝒌 𝒉𝒆𝒊𝒈𝒉𝒕, [𝒎] = 𝟎,𝟎𝟎𝟒𝟒𝒎 𝒍𝒎 = 𝒎𝒂𝒈𝒏𝒆𝒕 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔, [𝒎] = 𝟎,𝟎𝟎𝟓𝒎

𝐷𝑖𝑟 = 𝐷𝑜𝑟 − 2. 𝑙𝑚 − 2. 𝑕𝑟𝑟 (6)[7]

𝐷𝑖𝑟 = 0,1042𝑚

E. Stator design

1) Material

For the stator electrical steel is used. This steel type

contains a small percentage of silicon, which is a

semiconductor. The presence of silicon increases the

resistivity of the steel, thereby reducing eddy current losses.

Eddy current losses are caused by induced electric currents

within the ferromagnetic material under time-varying

excitation. These induced eddy currents circulate within the

material, dissipating power due to the resistivity of the

material. It is common to build the stator using laminations of

materials. These thin sheets of material are glued together. The

glue forms a resistive layer between the laminations. Although

glues specially developed for this application are available, for

practical reasons Pattex Contact glue is used. This glue has the

following desirable properties:

a b

rotor back height

pole pitch

9

Well suited for steal to steal contact

Maximum operation temperature of 110°C

High resistance to moisture

By stacking these laminations together, the resistivity of the

material is dramatically increased in the direction of the stack

[6].

Since nonconductive material is also nonmagnetic, it is

necessary to orient the lamination edges parallel to the desired

flow of flux. It can be shown that eddy current loss in

laminated material is proportional to the square of the

lamination thickness. Thus thin laminations are required for

lower loss operation [6]. Laminations with a thickness of

0,35mm are used.

2) Dimensions

According to Formula 7 the stator’s outer diameter

𝐷𝑜𝑠 equals 102,2mm.

𝑫𝒐𝒔 = 𝒐𝒖𝒕𝒆𝒓 𝒔𝒕𝒂𝒕𝒐𝒓 𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓, [𝒎] 𝒈 = 𝒑𝒉𝒚𝒔𝒊𝒄𝒂𝒍 𝒂𝒊𝒓𝒈𝒂𝒑 𝒔𝒊𝒛𝒆, 𝒎 = 𝟎,𝟎𝟎𝟏𝒎

𝐷𝑜𝑠 = 𝐷𝑖𝑟 − 2.𝑔 (7)[7]

𝐷𝑜𝑠 = 0,1022𝑚

In literature a stator with 12 teeth in combination with a

rotor with 14 poles is a common configuration for high torque

applications and is therefore selected.

The tooth width 𝑏𝑡𝑠 must be large enough, so that they are

not saturated when the magnetic flux passes through them (see

Figure 25a). Based on Formula 8, 𝑏𝑡𝑠 should be at least

7,9mm.

𝒃𝒕𝒔 = 𝒕𝒐𝒐𝒕𝒉 𝒘𝒊𝒅𝒕𝒉, [𝒎]

𝑏𝑡𝑠 =𝜋.𝐷𝑜𝑠 .𝐵𝑔

𝑝.𝐵𝑖𝑟𝑜𝑛 (8)[7]

𝑏𝑡𝑠 = 0,0079𝑚

Fig. 25. Magnetic flux lines in the teeth (a) and the pole shoe (b)

Using FEMM, the maximum flux density through the teeth

is determined. The maximum flux density in a tooth is the

highest when the center of the tooth is aligned with the center

of a magnet, this tooth position is thus critical for the analysis.

As indicated in Addendum G, the maximum flux density in

this tooth equals 1,9T. This value lies between the upper and

lower saturation limit.

The end of a tooth, which is adjacent to the airgap, is called

the pole shoe. The pole shoe is larger than the tooth. This

results in a lower flux density in the airgap. The resistance for

the magnetic flux through the airgap is therefore reduced [9].

The value of the shoe tips depends on the permeability of the

ferromagnetic material composing the shoes and teeth.

Similarly as with the rotor back height and the stator teeth, the

pole shoe should not become saturated. Using FEMM, the

shape and dimensions of the shoes are optimized. The

magnetic flux density in the shoes is the highest when a shoe

is situated between two poles (see Figure 25b). This shoe

position is thus critical for the analysis. As indicated in

Addendum G, the maximum flux density through the shoe

equals 1.6T, which is smaller than the lower hard saturation

limit of 1.7T.

The inner stator diameter 𝐷𝑖𝑠 must be large enough, to be

able to incorporate the required bearings. For the selected

bearings a 𝐷𝑖𝑠 of 45mm is used.

When winding the stator with emailed copper wire10

, the

insulating coating on the wire can be damaged by sharp edges

on the stator. This is why a sheet of fiberglass is applied

between the teeth of the stator. The sheet prevents the wire to

come in direct contact with the stator.

3) Windings

In Addendum H the torque constant 𝐾𝑡 of the motor is

determined. This is the ratio of the torque over the current (see

Formula 10). The optimal 𝐾𝑡 for the KERS of the kart equals

0,145𝑁𝑚 𝐴 . This 𝐾𝑡 results in a maximum motor speed of

223 rad/s or 2130rpm, which corresponds to a kart speed of

100km/h.

𝝎𝒎𝒂𝒙 = 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅, [𝒓𝒂𝒅 𝒔] =𝟐𝟐𝟑𝒓𝒂𝒅 𝒔

𝑽𝒔 = 𝒗𝒐𝒍𝒕𝒂𝒈𝒆 𝒎𝒐𝒕𝒐𝒓, [𝑽] = 𝟑𝟐,𝟒𝑽

𝐾𝑡 =𝑉𝑠

𝜔𝑚𝑎𝑥

= 0,145𝑁𝑚 𝐴 (9)[7]

Increasing 𝐾𝑡 in order to obtain a higher maximum motor

speed, is not suitable. This is because the KERS of the kart is

mostly used at speeds below 100km/h. By selecting a higher

𝐾𝑡 , the maximum speed decreases, however the maximum

torque increases (see Addendum H). The motor produces

14,5Nm of torque if the maximum current of 100A, delivered

by the supercapacitors, flows through the stator’s windings

(see Formula 10).

10 Emailed copper wire, a wire with an insulating coating

a b

10

𝑲𝒕 = 𝒕𝒐𝒓𝒒𝒖𝒆 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 = 𝟎,𝟏𝟒𝟓 𝑰𝒎𝒂𝒙 = 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒂𝒍𝒍𝒐𝒘𝒆𝒅 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝑨 = 𝟏𝟎𝟎𝑨

𝑻𝒎𝒂𝒙 = 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒕𝒐𝒓𝒒𝒖𝒆 𝑵𝒎

𝐾𝑡 =𝑇

𝐼 (10)

𝑇𝑚𝑎𝑥 = 𝐾𝑡 . 𝐼𝑚𝑎𝑥 = 14,5𝑁𝑚

For a compact motor design, a high surface current loading

(S) is desirable [7]. The windings of each phase are distributed

in a number of slots. Since the EMFs in different slots are not

in phase, their phasor sum is less than their numerical sum.

This reduction factor is what is called winding factor 𝑘𝑤 . Most

of the three-phase machines have winding factor value

between 0.85 and 0.95 [10]. We suppose a 𝑘𝑤 of 0,9.

The machine active length 𝐿 is determined (see Figure 26).

This is the length of the stator’s teeth. Increasing 𝐿 increases

the generated force [6]. The additional length of the copper

windings that reach out of the stator (see Figure 5) should be

taken into consideration when determining the available space

inside the wheel rim. The maximum 𝐿 that can be achieved is

40mm.

Fig. 26. Machine active length

To avoid the demagnetization of the permanent magnets,

the current loading 𝑆 must always be smaller than the

maximum allowed current loading 𝑆𝑚𝑎𝑥 [7]. This is because

if the external magnetic field opposes that developed by the

magnets and drives the operating point into the third quadrant

past coercivity, it is possible to irreversibly demagnetize the

magnet [6]. 𝑆𝑚𝑎𝑥 for N42 grade NdFeB magnets equals

225kA/m (see Addendum I) and 𝑆 equals 62kA/m (see

Formula 11).

𝑺 = 𝒔𝒖𝒓𝒇𝒂𝒄𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒍𝒐𝒂𝒅𝒊𝒏𝒈, [𝑨 𝒎]

𝑻 = 𝒕𝒐𝒓𝒒𝒖𝒆, [𝑵𝒎] = 𝟏𝟒,𝟓𝑵𝒎

𝒌𝒘 = 𝒘𝒊𝒏𝒅𝒊𝒏𝒈 𝒇𝒂𝒄𝒕𝒐𝒓 = 𝟎,𝟗 𝑳 = 𝒎𝒂𝒄𝒉𝒊𝒏𝒆 𝒂𝒄𝒕𝒊𝒗𝒆 𝒍𝒆𝒏𝒈𝒕𝒉, [𝒎] = 𝟎,𝟎𝟒𝒎

𝑆 =3

2.

2.𝑇

𝜋.𝐷𝑜𝑠2 .𝐵𝑔 . 𝐿. 𝑘𝑤

(11)[7]

𝑆 = 62 𝑘𝐴/𝑚

Since 𝑆 is smaller than 𝑆𝑚𝑎𝑥 , the magnets are not

demagnetized by the external magnetic field.

According to Formula 12 the total number of wires in the

motor equals 202.

𝒁 = 𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒊𝒏𝒅𝒊𝒏𝒈𝒔 𝑲𝒕 = 𝒕𝒐𝒓𝒒𝒖𝒆 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕[𝑵𝒎 𝑨 ] = 𝟎,𝟏𝟒𝟓𝑵𝒎 𝑨

𝑍 =3.𝐾𝑡

𝐷𝑜𝑠 . 𝐿.𝐵𝑔 . 𝑘𝑤 (12)[7]

𝑍 = 202

Based on Formula 13 the number of windings per tooth

𝑛𝑠 equals 17.

𝒏𝒔 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒊𝒏𝒅𝒊𝒏𝒈𝒔 𝒑𝒆𝒓 𝒕𝒐𝒐𝒕𝒉

𝒒 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒕𝒆𝒆𝒕𝒉 = 𝟏𝟐

𝑛𝑠 =𝑍

𝑞 (13)[7]

𝑛𝑠 ≅ 17

In Addendum J, the diameter of the emailed copper wire is

determined. The total available area for this wire, visible in

Figure 27, equals 120mm².

Fig. 27. Available area for wire

Because of the empty space between the wires and the

space required for the winding process, only about 60% of the

area can be used by the windings. This is called the fill factor.

Therefore, only 72mm² is available for the wire itself. To

obtain the area of the cross section of one wire, this area is

divided by the number of wires. The diameter of one wire

equals 2,32mm. However, because a wire with this diameter is

not flexible enough, it is difficult to wind around the teeth of

the stator without damaging the teeth or the insulating coating

of the wire. Instead, multiple smaller wires in parallel are

used. Furthermore, due to the skin effect11

, wires with smaller

diameters can have a higher current density. This allows a

higher current to flow through the same area. Wires with a

diameter of 0,85mm are used. By placing seven of these wires

in parallel, the maximum allowed current through the motor

equals 180A (see Addendum J).

11 Skin effect, the tendency of an alternating electric current to distribute

itself within a conductor so that the current density near the surface of the conductor is greater than at its core

machine active length

available area

11

Because the maximum current through the motor equals

100A, a lower number of wires in parallel could be used.

However, by using more wires in parallel, the resistivity of the

wires drops and the motor dissipates less heat, which increases

efficiency.

The motor is winded in abBCcaABbcC configuration:

The number of letters equals the number of teeth

The letter A corresponds to the first phase

The letter B corresponds to the second phase

The letter C corresponds to the third phase

Uppercase means wind in clockwise direction

Lowercase means wind in counterclockwise

direction

As shown in Figure 28, the three phases are connected in Y.

This is because with all else being equal, ohmic losses are

50% greater in Δ than in Y connection. However, Y

connections require 1,5 times more magnetic material [11].

F. Performance

Figure 28 shows the electrical scheme of the energy

source, the controller and the motor.

Fig. 28. Electrical scheme of energy source, controller and motor

With:

𝑳 = 𝒊𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆 𝑽𝒎 = 𝒃𝒂𝒄𝒌 𝒆𝒎𝒇

𝑹 = 𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆

Figure 29 represents the equivalent scheme of one phase of

the circuit.

Fig. 29. Equivalent scheme of one phase

For the motor performance calculations, a simplified

scheme is used. As shown in Figure 30, this scheme does not

take the inductance of the motor into account.

Fig. 30. Simplified equivalent scheme of one phase

Due to the commutation, the current is always divided over

two phases. At any time, the currents in two of the phases are

equal in magnitude and the current in the third phase is zero.

This means that only two phases are contributing to torque

production at any one time [6].

Formula 14 gives the back EMF as function of the angular

speed (see Figure 31).

𝑽𝒎 𝝎 = 𝒃𝒂𝒄𝒌 𝒆𝒎𝒇 𝒑𝒆𝒓 𝒑𝒉𝒂𝒔𝒆, [𝑽] 𝑲𝒕 = 𝒕𝒐𝒓𝒒𝒖𝒆 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 = 𝟎,𝟏𝟒𝟓

𝝎 = 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒕𝒉𝒆 𝒎𝒐𝒕𝒐𝒓, [𝒓𝒂𝒅 𝒔]

𝑉𝑚 (𝜔) = 𝐾𝑡 .𝜔 (14)

Fig. 31. Back EMF in function of the angular speed

One can see that at the maximum speed of the electromotors

of 2130rpm, the back EMF equals the voltage across the

capacitors, which is 32,4V. At this point there is no potential

difference across the windings, so no current flows through

them. This means that the motor produces no torque and is not

able to accelerate anymore. The motor has reached its

maximum angular speed, which is called the no load speed. In

reality there is always a small potential difference across the

windings because of the friction losses in the motor. A small

current flows through the windings. This produces a small

torque, which is just enough to overcome the friction losses so

that the angular speed of the motor remains constant. If the

angular speed of the motor is higher than 2130rpm, the back

EMF of the motor is higher than the voltage of the capacitors.

In that case, the motor acts as a generator and the capacitors

are charged. If the back EMF is lower than the voltage of the

capacitors, they would normally not be charged. The

controller however, allows generative braking even when the

back EMF generated by the motor is lower than the voltage of

the capacitors. This is achieved by means of power electronics

in the controller.

According to Formula 15, the theoretical line current

through the motor is calculated. This is the current that flows

through two phases of the motor, without limitation by the

0,05,0

10,015,020,025,030,035,0

0 500 1000 1500 2000B

ack

EMF

(V)

Rpm

12

controller (see Figure 32). The RMS12

value for the current

equals the maximum amplitude of 100A, because the

controller uses square waves. The resistance of one phase

equals 32mΩ (see Addendum K).

𝑽𝒔 = 𝒔𝒐𝒖𝒓𝒄𝒆 𝒗𝒐𝒍𝒕𝒂𝒈𝒆, [𝑽] = 𝟑𝟐,𝟒𝑽 𝑰𝒍𝒊𝒏𝒆,𝒕𝒉𝒆𝒐 𝝎 = 𝒕𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍 𝒍𝒊𝒏𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕, [𝑨] 𝑹𝒆𝒒𝒖𝒊𝒗,𝒑𝒉𝒂𝒔𝒆 = 𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒏𝒆 𝒑𝒉𝒂𝒔𝒆, 𝜴 = 𝟑𝟐𝒎𝜴

𝐼𝑙𝑖𝑛𝑒 ,𝑡𝑕𝑒𝑜(𝜔) =(𝑉𝑠 − 𝑉𝑚 (𝜔))

2.𝑅𝑒𝑞𝑢𝑖𝑣 ,𝑝𝑕𝑎𝑠𝑒

(15)

Fig. 32. Line current in function of the angular speed

As mentioned in the section III.C.1, the controller limits the

current to 100A. For this reason the actual line current curve is

flattened (see Figure 32). Between 0rpm and 1700rpm the

current is limited to 100A by the controller. At speeds above

1700rpm, the current is lower than 100A and is not longer

limited by the controller.

In order to limit the current through the motor, the

controller adapts the line voltage, as shown in Figure 33 (see

Formula 16). At speeds above 1700rpm, the line voltage

equals the source voltage.

𝑽𝒍𝒊𝒏𝒆,𝒄 𝝎 = 𝒍𝒊𝒏𝒆 𝒗𝒐𝒍𝒕𝒂𝒈𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍𝒍𝒆𝒓, [𝑽]

𝑰𝒍𝒊𝒏𝒆,𝒂𝒄𝒕𝒖𝒂𝒍 𝝎 = 𝒂𝒄𝒕𝒖𝒂𝒍 𝒍𝒊𝒏𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕, [𝑨]

𝑉𝑙𝑖𝑛𝑒 ,𝑐 = 𝑉𝑚 (𝜔) + 𝐼𝑙𝑖𝑛𝑒 ,𝑎𝑐𝑡𝑢𝑎𝑙 (𝜔). 2.𝑅𝑒𝑞𝑢𝑖𝑣 ,𝑝𝑕𝑎𝑠𝑒 (16)

Fig. 33. Line voltage in function of the angular speed

12 RMS, root mean square, a statical measure of the magnitude of a varying

quantity

The electrical power, theoretical mechanical power and

Joule losses shown in Figure 34 are given by Formulas 17, 18

and 19 respectively. The theoretical mechanical power only

takes the Joule heating into consideration. The actual

mechanical power is lower due to iron losses, magnetic losses

and friction losses.

𝑷𝒆𝒍𝒆𝒄 𝝎 = 𝒆𝒍𝒆𝒄𝒕𝒓𝒊𝒄𝒂𝒍 𝒑𝒐𝒘𝒆𝒓, [𝑾] 𝑷𝒎𝒆𝒄𝒉,𝒕𝒉𝒆𝒐 𝝎 = 𝒕𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍 𝒎𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍 𝒑𝒐𝒘𝒆𝒓, [𝑾] 𝑷𝑱𝒐𝒖𝒍𝒆 𝝎 = 𝑱𝒐𝒖𝒍𝒆 𝒉𝒆𝒂𝒕𝒊𝒏𝒈, [𝑾]

Pelec (𝜔) = 𝑉𝑙𝑖𝑛𝑒 ,𝑐(𝜔). 𝐼𝑙𝑖𝑛𝑒 ,𝑎𝑐𝑡𝑢𝑎𝑙 (𝜔) (17)

Pmech ,theo 𝜔 = 𝑉𝑚 𝜔 . 𝐼𝑙𝑖𝑛𝑒 ,𝑎𝑐𝑡𝑢𝑎𝑙 𝜔 (18)

PJoule 𝜔 = 2.𝑅𝑒𝑞𝑢𝑖𝑣 ,𝑝𝑕𝑎𝑠𝑒 . 𝐼𝑙𝑖𝑛𝑒 ,𝑎𝑐𝑡𝑢𝑎𝑙2 𝜔 (19)

Fig. 34. Power in function of the angular speed

The maximal electrical and theoretical mechanical power

are reached at 1700rpm and equal 3240W and 2610W

respectively. The maximal Joule heating occurs between 0rpm

and 1700rpm and equals 630W.

Based on Formula 20, the theoretical torque of the motor is

calculated (see Figure 35). The theoretical torque is based on

the theoretical mechanical power and is thus lower than the

actual torque.

𝑻𝒕𝒉𝒆𝒐 𝝎 = 𝒕𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍 𝒕𝒐𝒓𝒒𝒖𝒆, [𝑵𝒎]

𝑇𝑡𝑕𝑒𝑜 (𝜔) =Pmech ,theo (𝜔)

ω (20)

0100200300400500600

0 500 1000 1500 2000

Cu

rre

nt

(A)

Rpm

Theoretical line current

Actual line current

0,05,0

10,015,020,025,030,035,0

0 500 1000 1500 2000

Vo

ltag

e (

V)

Rpm

0500

100015002000250030003500

0 500 1000 1500 2000P

ow

er

(W)

Rpm

Electrical power

Theoretical mechanical power

Joule losses

13

Fig. 35. Theoretical torque in function of the angular speed

Between 0rpm and 1700rpm, the motor can deliver a

constant torque of 14,5Nm.

According to Formula 21, the theoretical efficiency of the

motor is calculated. This theoretical efficiency only takes the

Joule heating into account.

𝜼𝒕𝒉𝒆𝒐 = 𝒕𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍 𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚, %

𝜂𝑡𝑕𝑒𝑜 =𝑃𝑚𝑒𝑐 𝑕 ,𝑡𝑕𝑒𝑜

𝑃𝑒𝑙𝑒𝑐. 100 (21)

The maximum electrical power is reached at 1700rpm and

goes together with an efficiency of 81%.

When the KERS of the kart is used and the capacitors are

fully charged, the two motors produce a constant torque of

29Nm between 0rpm and 1700rpm (see Figure 35). This

translates in an acceleration force from the front wheels to the

ground of 232N, which is a gain in acceleration force of 22%

over a kart without the KERS. If the extra weight of 22kg of

the KERS is taken into consideration, a kart with KERS can

accelerate 6,4% faster from 0km/h to 80km/h, compared to a

kart without KERS. Between 80km/h and 100km/h the gain in

acceleration decreases linearly (see Addendum L).

IV. FINANCES

The cost of this research is approximately 1300 Euros (see

Addendum M). This amount covers the production of one

adapted wheel rim with one custom made in-wheel

electromotor and the purchase of one controller and the

needed components to test the motor. The selected

supercapacitors are reused from a previous project at Campus

Automobile and are therefore not included in this price.

The price of one KERS including two in-wheel motor rims,

two controllers and two supercapacitor modules is 3450 Euros.

However, the cost of this conversion kit will lower as the size

of the production badge raises. Since the price of an average

racing kart is 3000 Euros, a prototype kart with in-wheel

KERS will cost 2,15 times the price of an unmodified kart.

See Addendum M for financial details about machining costs

of the KERS’ parts and other purchased equipment.

V. CONSIDERATIONS WHEN USING THE DESIGN FOR FORMULA

ONE VEHICLE

In this paper the design of an in-wheel motor is made for a

kart. The mechanical concept and the motor’s design method

could also be used to implement in-wheel motors in a Formula

One vehicle. However, a kart can be seen as a simplified

version of a Formula One vehicle. Two important

simplifications in a kart are the absence of suspension and the

absence of a differential. The aim of this paragraph is to

explain what extra considerations have to be taken into

account when implementing the developed design in a

Formula One vehicle.

1) Electronic differential

To keep the complexity of a kart limited, there is no

mechanical differential. This means that on a kart, which has

rear wheel drive, one rear tire must slide while cornering. This

is achieved by designing the chassis so that the inner rear tire

lifts up slightly when the kart turns. This allows this tire to

slide or lift off the ground completely [12]. The KERS of the

kart drives the front wheels, which do not lift up when

cornering. If the KERS is used in corners, the two front wheels

have the same angular speed. This means that the inner wheel

causes drag, this can result in unpredictable handling, damage

to tires and roads, strain on (or possible failure of) the entire

drivetrain.

A solution for this problem is the implementation of an

electronic differential. An electronic differential uses the

vehicle speed and steering angle as input variables and

calculates the required inner and outer wheel speeds. In a

straight trajectory, the two wheels rotate at exactly the same

speed. When the vehicle arrives at the beginning of a corner,

the driver applies a steering angle on the wheels. The

electronic differential acts immediately on the two motors,

reducing the speed of the inner wheel and increasing the speed

of the outer wheel [13].

However, to reduce the complexity of the design of the

KERS for a kart, an electronic differential is not implemented.

To overcome this absence the KERS of the kart is only used at

the end of a corner, where the difference between inner and

outer front wheel speed is relatively low. Regenerative braking

should only occur before a corner and not in the corner. While

cornering, the front wheels are not driven, but can rotate

freely. This means that the front wheels can rotate at different

speeds and do not cause damage or affect the kart’s handling.

This design of a KERS for a kart could be transposed to a

Formula One vehicle. In this case the ability to use the KERS

in corners could potentially have great benefits, for instance

when overtaking other vehicles. Hence it is worth to take a

look at the implementation of such a system in a Formula One

vehicle.

0,0

5,0

10,0

15,0

20,0

0 500 1000 1500 2000

Torq

ue

(N

m)

Rpm

14

Figure 36 illustrates a Formula One vehicle, equipped with

an in-wheel KERS, taking a corner.

Fig. 36. Overview of the vehicle in a corner

According to Formula 22 the radius of the curve depends on

the wheelbase and the steering angle:

𝑹 = 𝒓𝒂𝒅𝒊𝒖𝒔 𝒄𝒖𝒓𝒗𝒆 𝑾 = 𝒘𝒉𝒆𝒆𝒍𝒃𝒂𝒔𝒆 𝜹 = 𝒔𝒕𝒆𝒆𝒓𝒊𝒏𝒈 𝒂𝒏𝒈𝒍𝒆

𝑅 =𝑊

𝑡𝑎𝑛𝛿 (22)

With the vehicle speed, the angular speed of the vehicle is

calculated (see Formula 23):

𝝎𝒗 = 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅 𝒗𝒆𝒉𝒊𝒄𝒍𝒆 𝒗 = 𝒗𝒆𝒉𝒊𝒄𝒍𝒆 𝒔𝒑𝒆𝒆𝒅

𝜔𝑣 =𝑣

𝑅 (23)

Based on Formula 24 and 25 the distance from the center of the turn to the left and right front wheel is calculated:

𝑥 = 𝑊2 + 𝑅 +𝑇

2

2

(24)

𝑦 = 𝑊2 + 𝑅 −𝑇

2

2

(25)

Formula 26 and 27 give the speed of each front wheel:

𝒗𝒍 = 𝒍𝒆𝒇𝒕 𝒇𝒓𝒐𝒏𝒕 𝒘𝒉𝒆𝒆𝒍 𝒔𝒑𝒆𝒆𝒅

𝒗𝒓 = 𝒓𝒊𝒈𝒉𝒕 𝒇𝒓𝒐𝒏𝒕 𝒘𝒉𝒆𝒆𝒍 𝒔𝒑𝒆𝒆𝒅

𝑻 = 𝒕𝒓𝒂𝒄𝒌

𝑣𝑙 = 𝜔𝑣 . 𝑊2 + 𝑅 +𝑇

2

2

(26)

𝑣𝑟 = 𝜔𝑣 . 𝑊2 + 𝑅 −𝑇

2

2

(27)

According to Formula 28 and 29 the angular speed of each

wheel equals:

𝝎𝒍 = 𝒍𝒆𝒇𝒕 𝒇𝒓𝒐𝒏𝒕 𝒘𝒉𝒆𝒆𝒍 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅

𝝎𝒓 = 𝒓𝒊𝒈𝒉𝒕 𝒇𝒓𝒐𝒏𝒕 𝒘𝒉𝒆𝒆𝒍 𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒔𝒑𝒆𝒆𝒅

𝜔𝑙 =𝑣𝑙𝑅

(28)

𝜔𝑟 =𝑣𝑟𝑅

(29)

By substituting Formula 24, 25, 26 and 27 in Formula 28

and 29, the angular speed of each front wheel is obtained:

𝜔𝑙 =𝑣. 𝑊2 +

𝑊𝑡𝑎𝑛𝛿

+𝑇2

2

. 𝑡𝑎𝑛2𝛿

𝑊2 (30)

𝜔𝑟 =𝑣. 𝑊2 +

𝑊𝑡𝑎𝑛𝛿

−𝑇2

2

. 𝑡𝑎𝑛2𝛿

𝑊2 (31)

When the vehicle takes a corner, the electronic differential

calculates the right angular speed of each front wheel by using

two variables: the steering angle and the speed of the vehicle.

2) Unsprung mass

Implementing motors in the wheels of a Formula One

vehicle results in a higher unsprung mass. This has an

undesirable influence on drive performance. To explain this a

quarter car model of a suspended Formula One car is

considered (see Figure 37) [14].

Fig. 37. Quarter car model

Using the conventional techniques described in [15][16],

following equations are obtained describing the dynamics of

this model:

15

𝑑

𝑑𝑡 𝑀𝑧 + 𝑘𝑠 𝑧𝑢 − 𝑧 −1 = 𝐶𝑠 𝑧 𝑢 − 𝑧

𝑑

𝑑𝑡 𝑚𝑧 𝑢 + 𝑘𝑠 𝑧𝑢 − 𝑧 + 𝑘𝑡 𝑧𝑢 − 𝑧𝑟 = 𝐶𝑠𝑧 − 𝐶𝑠𝑧 𝑢

Where:

𝑴 = 𝒔𝒑𝒓𝒖𝒏𝒈 𝒎𝒂𝒔𝒔 𝒎 = 𝒖𝒏𝒔𝒑𝒓𝒖𝒏𝒈 𝒎𝒂𝒔𝒔 𝒌𝒕 = 𝒔𝒑𝒓𝒊𝒏𝒈 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕𝒊𝒏𝒈 𝒕𝒉𝒆 𝒕𝒊𝒓𝒆 𝒌𝒔 = 𝒔𝒖𝒔𝒑𝒆𝒏𝒔𝒊𝒐𝒏 𝒔𝒑𝒓𝒊𝒏𝒈 𝑪𝒔 = 𝒔𝒖𝒔𝒑𝒆𝒏𝒔𝒊𝒐𝒏 𝒅𝒂𝒎𝒑𝒊𝒏𝒈

In the Laplace domain, this can be written as follows:

𝑀𝑠2𝑍 + 𝐶𝑠𝑠𝑍 + 𝐾𝑠𝑍 = 𝐶𝑠𝑠𝑍𝑢 + 𝐾𝑠𝑍𝑢 𝑚𝑠2𝑍𝑢 + 𝐶𝑠𝑠𝑍𝑢 + 𝐾𝑠 + 𝐾𝑡 𝑍𝑢 = 𝐶𝑠𝑠𝑍 + 𝐾𝑠𝑍 + 𝐾𝑡𝑍𝑟

From these equations an expression for the response of the

car body due to an acceleration of the road can be determined.

After conversion to the frequency domain the following

expression for the gain between road acceleration and sprung

mass acceleration is obtained (see Addendum N):

𝑍

𝑍 𝑟=

𝐾𝑡𝐾𝑠 + 𝑗𝜔𝐾𝑡𝐶𝑠𝑚𝑀𝜔4 − 𝑚 + 𝑀 𝐾𝑠 + 𝑀𝐾𝑡 𝜔

2 + 𝐾𝑡𝐾𝑠 − 𝑗𝐶𝑠 𝑚 + 𝑀 𝜔3 + 𝐾𝑡𝜔

By evaluating the real and imaginary parts of the numerators

and denominators and by taking the square root of the sum of

the squares of the real and imaginary parts [14], the graph

shown in Figure 38 can be drawn (see Addendum O). The red,

green and blue graphs represent respectively the gains for an

unsprung mass of 40 kg, 80 kg and 120 kg. This visualization

shows that the bigger the unsprung mass, the more the second

resonance frequency of the system shifts to the left. Since it is

easier to isolate high-frequency vibrations in a car, a lighter

unsprung mass is desirable [14]. The use of in-wheel motors

results in a higher unsprung mass which therefore results in

less isolation of the wheel-hop resonant frequency and hence

relatively poor driving comfort.

Fig. 38. Response gain of car body for 3 different unsprung masses

VI. CONCLUSION

In this paper is shown how a KERS (Kinetic Energy

Recovery System) for a kart can obtain a lower mechanical

complexity and leads to less space occupied on the front area

of a kart if two electromotors are placed inside the front

wheels instead of next to the wheel. This is done by the design

and manufacturing of an adapted wheel rim. A customized

BLDC (BrushLess DC) motor intended to be placed inside this

adapted wheel rim is developed and is being produced. A

controller is selected. For energy storage two supercapacitor

modules are used. A kart containing this in-wheel KERS

accelerates approximately 6,4 percent faster in a speed range

of 0 to 80 km/h. Between 80 and 100 km/h this percentage

decreases quasi linearly. The cost of the entire KERS

prototype is 3450 Euros. Subsequent to the development and

production phase of the KERS, the specifications of the BLDC

in-wheel motor will be tested against the predictions by means

of a test bench available at Campus Automobile. Possible

improvements of the KERS are either reducing its cost by

bigger production amounts or by achievement of better

accelerations. This can be done by further optimization of the

electromotor. To end with, it is explained in this paper that

implementing the designed KERS for a kart cannot directly be

integrated into a formula one vehicle because of the need for

an electronic differential on the one hand and the problems a

high unsprung mass can cause on the other hand.

ACKNOWLEDGMENT

We want to thank Pierre Detré and Marc Nelis from

Campus Automobile for their help and for shearing their

knowledge in automotive technology and their experience in

project engineering. Thanks also to Campus Automobile for

their financial support. We also thank Frederic Duflos and

Kristof Goris for their support and guidance during this thesis

project. For reviewing this paper prior to publication, we want

to thank Tiene Nobels and Cédric Boon. Finally we want to

say thank you to our parents for being supportive throughout

this entire thesis project and for giving us all the means needed

to succeed in this education.

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