Concept for a modular assembly direct drive permanent magnet generator

UPTEC ES10 003

Examensarbete 20 p Januari 2010

Concept for a modular assembly direct drive permanent magnet generator

Development of model and winding scheme

Henric Skoog

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress:

Box 536 751 21 Uppsala Telefon:

018 – 471 30 03 Telefax:

018 – 471 30 00 Hemsida:

http://www.teknat.uu.se/student

Abstract

Concept for a modular assembly direct drive permanent magnet generator

Henric Skoog

In this thesis, a concept for a modular assembly direct drive permanent magnet generator is presented. The maximum forces that act on the different parts of the generator during normal operation have been calculated and used in solid mechanic simulations in SolidWorks. The result is a rough first draft of a generator design where the stator has been divided into five modules and the rotor into six modules.

This division is done in order to avoid symmetries in the generator that could lead to problems with self-oscillation.

The modulization of the stator brings about certain difficulties, both for the magnetic circuit and for the winding scheme. Different solutions for optimization of the magnetic circuit are analyzed from both a physical and a construction technical perspective. A winding scheme is produced and the winding process tested in a winding dummy produced according to the conceptual generator design.

ISSN: 1650-8300, UPTEC ES10 003 Examinator: Ulla Tengblad

Ämnesgranskare: Hans Bernhoff Handledare: Sandra Eriksson

Sammanfattning

Energisystemet i de industrialiserade länderna står sannolikt inför en drastisk förändring.

När de fossila bränslena sinar tvingas vi hitta nya energikällor och det är väldigt troligt att vindkraften kommer att spela en relativt stor roll i den framtida energiförsörjningen.

Vindkraftsbranschen utvecklas fortfarande för att kunna möta den kommande

utmaningen. Den allmänna trenden har varit att bygga allt större vindkraftverk i stora parker. För att undvika NIMBY-problematiken (Not In My Back Yard) placeras dessa vindkraftsparker på avlägsna platser. Detta faktum medför logistiska problem för vindkraftverkens olika delar, inte minst för de långa turbinbladen.

Flertalet av dagens vindkraftverk har horisontalaxlade turbiner, HAWT (Horisontal Axis Wind Turbine), men forskarna vid Uppsala universitet har valt en annan design, nämligen VAWT (Vertical Axis Wind Turbine).¹ Att kombinera en vertikalaxlad turbin med en direktdriven generator ger en väldigt enkel konstruktion med endast en rörlig del.

En stor fördel med att ha en direktdriven generator är att man kan utesluta användandet av en växellåda. Detta är gynnsamt eftersom en stor del av de mer allvarliga mekaniska felen hos vindkraftverk uppkommer till följd av att växellådan går sönder.² En nackdel med denna konstruktion är dock att generatorn blir väsentligt mycket större. Generatorns ökade vikt är egentligen inte något problem för vindkraftverkets uppbyggnad, eftersom den kan placeras på marken i ett vertikalaxlat vindkraftverk. Den höga vikten och stora diametern på generatorn medför dock transportproblem.

Diametern på en direktdriven generator med en märkeffekt i megawattklassen kan vara upp till mellan 10 och 15 meter, beroende på generatorns andra parametrar. Det är uppenbart att en sådan generator blir svår att transportera i ett stycke. De flesta vattenkraftsgeneratorerna i samma storlek byggs ihop på plats. Genom att införa ett modulbaserat koncept för generatorn så är det dock möjligt att överkomma detta logistiska problem.

I det här arbetet har ett första steg mot realiseringen av en modulbaserad generator tagits.

De maximala krafterna som verkar på generatorns olika delar under normal drift har beräknats och använts för hållfasthetssimuleringar i SolidWorks. Resultatet är ett grovt första utkast på en generatordesign där statorn har delats upp i fem delar och rotorn i sex delar. Detta är för att undvika symmetrier i generatorn som skulle kunna medföra självsvängningsproblem.

Statorns uppdelning medför vissa svårigheter, både för den magnetiska kretsen och för lindningsschemat. Olika lösningar för optimering av den magnetiska kretsen har analyserats ur både ett fysikaliskt och ett konstruktiontekniskt perspektiv. Ett

lindningsschema har tagits fram och lindningsprocessen testats i en för syftet framtagen lindningsattrapp.

1 Deglaire et al., 2007

2 Ribrant et al., 2007

Contents

1 Introduction... 3

1.1 Background ... 3

1.2 Aim ... 4

1.3 Method ... 4

2 Theory ... 5

2.1 Electromagnetic theory ... 5

2.2 Solid mechanics ... 6

2.3 Generators ... 10

2.4 Software ... 13

3 Mechanical construction ... 14

3.1.1 Development of the basic concept ... 14

3.1.2 Discussion ... 15

3.2.1 Construction of the concept ... 16

3.2.2 Discussion ... 24

4 Winding scheme... 25

4.1.1 Winding of a stator module... 25

4.1.2 Discussion ... 26

4.2.1 Construction of winding dummy ... 26

4.2.2 Arrangement of coil ends and winding... 29

4.2.3 Discussion ... 32

5 Conclusions... 34

6 Future work ... 35

7 Acknowledgements... 36

References... 37

Appendix 1 – Generator blueprints... 38

Appendix 2 – Forces used in simulations ... 50

Appendix 3 – Winding dummy blueprints... 55

List of Symbols and Abbreviations

2D Two dimensional

3D Three dimensional

CAD Computer-aided design

EMF Electromotive force

FEM Finite element methods

HAWT Horizontal axis wind turbine

MMF Magnetomotive force

NIMBY Not in my back yard

VAWT Vertical axis wind turbine

oe Electrical degrees

A m² Area

B T = Vs / m² Magnetic field

ε V Electromotive force

E J = Nm Energy

e J / m³ Energy density

ΦB Wb = Tm² = Vs Magnetic flux

F N = kg m / s² Force

f Hz = s^-1 Frequency

h m Length

I A Electrical current

l m Length

µ0 Vs/Am Permeability

µr Vs/Am Relative permeability

M Nm Torque

N N Normal force

N_c - Number of turns in a coil

P W = VA Power

PM Permanent magnet

q - Slots per pole and phase

R Ω = V / A Resistance

Rm H^-1 = A / Wb Reluctance

rpm Rotations per minute

σ N/m² Stress

S ^oe Coil pitch

τ N/m² Shear stress

τp o

e Pole pitch

t s Time

U V = Nm / As Voltage

ω rad / s Angular frequency

w m Length

1 Introduction

1.1 Background

The energy system in the industrialized countries is most likely about to change

drastically. With the fossil fuels running out, we have to look elsewhere for energy and it is very likely that wind power will play a relatively big role in the future energy supply.

The wind power business is still evolving in order to face the upcoming challenge. The general trend has been towards wind power plants of increasing size in large farms. In order to avoid the NIMBY-attitude (Not In My Back Yard) of the population, the wind power farms are often located in desolate places. This fact brings about problems with transport of the different parts of the wind power plants, especially for the very long turbine blades.

Most of today’s wind turbines are of the horizontal axis type, HAWT (Horizontal Axis Wind Turbine), but the researchers at Uppsala University have chosen another design, namely VAWT ( Vertical Axis Wind Turbine). They have chosen to combine the VAWT with a direct drive generator, which gives a very basic wind power plant with only one moving part.³ The two different types of turbines can be seen in figure 1.1.

Figure 1.1 A small VAWT to the left and a HAWT to the right

A big advantage of having a direct driven generator is that one can avoid the use of a gear box. This is favorable because a large part of the major failures in wind power plants occur due to a fault in the gear box.⁴ However, a drawback is that the generator needs to be a lot bigger. The weight of the generator is no real problem with regard to the structure of the wind power plant, as it can be placed on the ground in a VAWT. It does however bring us back to the logistical problem, mentioned above.

The radius of a direct driven generator with a maximum power rating in the range of megawatts can be between ten and fifteen meters, depending on other parameters of the

3 Deglaire et al., 2007

4 Ribrant et al., 2007

generator. It is obvious that such a generator will be rather difficult to transport in one piece. Most hydropower generators with a similar size are assembled on site. By applying a modular assembly concept, it is possible to overcome this logistical problem.

It is very difficult to find any literature on the subject of modular assembly generators, but some research has been done previously to this thesis work.⁵ The concept suggested here is however very different from the already existing design.

1.2 Aim

The primary aim of this thesis is to find a viable concept for the construction of a modular assembly direct drive permanent magnet generator. This should be achieved in order to make transport of the relatively large generator to site easier. With ease of transport comes the possibility to centralize production and thus enable serial production. Having the generator built in modules can also facilitate repairs as a single faulty module can be replaced or removed for repairs.

A secondary aim is to find an example of a winding scheme for the stator modules and to build a winding dummy in order to test the winding process.

1.3 Method

The modelling of the generator will be done in the CAD software SolidWorks. Solid mechanics simulations will be carried out in the same program, using the built in FEM calculation toolbox.

The winding dummy will be designed in SolidWorks as well, and the construction of the dummy will be carried out in a work shop, using materials funded by the Göran

Gustafsson Foundation.

5 Spooner et al., 1995

2 Theory

2.1 Electromagnetic theory The magnetic circuit

The magnetomotive force, MMF, is the force that drives the magnetic flux, Ф = BA, much as a voltage drives the current in its electrical analogy. The “Ohm’s law” of a magnetic circuit is⁶

Φ

= m

cI R

N (2.1)

NcI is the MMF and its unit is ampere turns. A permanent magnet also has a certain MMF, depending on its remanent magnetic field. This MMF has a fixed value, as long as the magnet is not demagnetized. The magnetic resistance, Rm, is known as reluctance.

Reluctance of a magnetic “conductor” of length l and area A is described by⁷

A R l

r m

µ0

= µ (2.2)

where µ₀ is the permeability and µ_r the relative permeability of the material.

Induction

The induced electromotive force, EMF, in a solenoid can be described by the following formula:⁸

dt N_c dΦ

−

ε = (2.3)

If we now recall equation 2.1, we can se that if we have a magnetic circuit with a fix MMF and the reluctance is somehow enlarged, the magnetic flux is reduced. This would in turn cause the magnitude of the EMF to get smaller.

Magnetic force

Energy density in a magnetic field, when µr is constant, can be described by⁹

2 0

1 2

1 B

e

rµ

= µ (2.4)

6 Nordling et al., 2004, page 213

7 Ibid., page 213

8 Ibid., page 214

9 Ibid., page 210

In an air-gap µr = 1, so we get

2

2 0

1 B

e⁼ µ ^(2.5)

The total energy in the air-gap is then given by the equation

Al B

E ²

2 0

1

= µ (2.6)

where A is the cross-sectional area of the air-gap and l its length.

In order to find the force acting between the stator and the rotor we can turn to the concept of virtual work. Assuming that the change of the air-gap is infinitesimal, so that the force does not change, we can apply a formula for force in a conservative force field:¹⁰

dl

F =dE (2.7)

By combining equation 2.6 and equation 2.7, we get

A B Al

dl B d dl

F dE ²

0 2

0 2

1 2

1

µ µ ^⁼





= 

= (2.8)

and can thus get an expression for the attractive radial force between two magnetically conducting materials, for example the stator and the rotor in a generator.

2.2 Solid mechanics

Von Mises Stress and yield criterions

A rather basic way of illustrating stress in a material is looking at a cross-section of a homogenous axially loaded rod, as seen in figure 2.1. It has a constant cross-sectional area, A, along its entire length. The forces applied, F, are equal in magnitude but have the opposite direction, which entails that the rod is in steady state. In an imaginary cross- section, the normal force, N, would have to be of the same magnitude as the force, F, or that specific part would not be in steady state.

10 Nordling et al., 2004, page 165

Figure 2.1 Top: Axially loaded rod with the cross-section area A Middle: Normal force in the cross-section Bottom: Tensile stress in the cross-section

With the normal force evenly distributed over the surface of the cross-section, the stress, σ, is defined as

A F A N =

σ = (2.9)

The positive sign of the stress defines it as tensile stress. If the forces applied would have had the opposite direction we would get

A F A N = −

σ = ^(2.10)

The negative sign of the stress shows us that we have compressive stress in this case.¹¹ In a more general case, the stress could vary in both direction and magnitude over the surface of the cross-section. Any stress tangential to the surface of the cross-section is known as shear stress, τ. The magnitude of the stress is known as effective stress and in accordance to von Mises is defined as¹²

2 2 2 2

2

2 _{y z x y y z z x} 3 _xy 3 _yz 3 _zx

x

e σ σ σ σ σ σ σ σ σ τ τ τ

σ = + + − − − + + + (2.11)

where x, y and z denotes the three axes in a Cartesian coordinate system. τ_xy is, for example, the shear stress in the y-direction on the plane with normal direction x.

Yield strength and fatigue

A good estimate of the effective stress is essential in solid mechanics when dimensioning structures to be resistant to breaking and fatigue. A material-specific parameter called the yield strength, σs, is compared to the highest effective stress in the part being designed, when it is exerted to the highest occurring force. If the yield strength is exceeded, the part

11 Lundh, H., 2007, page 5

12 Nordling et al., 2004, page 386

will deform plastically and possibly break if the effective stress reaches the tensile strength, σB. Plastic deformation means that the material will not go back to its original shape as the forces on it are removed. Most often a certain degree of safety is applied during construction, setting the maximum effective stress as half or a third of the yield strength for the material in question.

Fatigue is another solid mechanics phenomenon that is crucial to avoid. It is caused by a load varying over time, giving rise to micro cracks where the local effective stress is highly increased due to small geometrical or material defects. The cracks expand over time during repeated load cycles and finally result in a material failure.

There is another material parameter which is called the fatigue limit, σ_u. This parameter can be used if the load continuously changes sign. For most construction steel the relation between the fatigue strength and the tensile strength is in the interval¹³

60 . 0 35

.

0 < <

B u

σ

σ (2.12)

With an offset of the periodically changing stress, where it varies between zero and some other defined value without ever changing sign, the fatigue strength gets slightly lower and is denoted as σup. A somewhat simplified Haigh diagram can be seen in figure 2.2. It visualizes the relation between the materials yield strength and the two mentioned types of fatigue strength. It can be used for dimensioning a part in order to avoid material failure due to fatigue.

Figure 2.2 A generic Haigh diagram. σm is a static amount of stress and σa is a periodically changing stress. Grey area shows acceptable values.

13 Lundh, 2007, page 247

If the applied stress is within the grey area, the lifetime of the part is more than 10⁶ cycles and defined as infinite. It is common to take some precautions to keep the maximum stresses well within the borders of the grey area by multiplying the values received from the diagram by a factor lower than one before using it to dimension the part.¹⁴

Table 2.1 Examples of solid mechanics parameters¹⁵

Material σ_s [MPa] σ_B [MPa] σ_u [MPa] σ_up [MPa]

Carbon steel 141450-1 290 470 ±140 130±130

Carbon steel 141550-01 360 540 ±180 160±160

Cast steel 141505-2 - >490 ±220 -

Natural frequency

If an object is set in motion by an impulse force, the frequency with which it vibrates afterwards is its natural frequency, also called fundamental frequency. If the object is exerted to a periodical force with that same frequency it will vibrate ever more strongly, until the power lost to friction (and possibly electromagnetic losses) is equal to that of the power added to the object from the periodical force. This observable fact is called

resonance. The vibration can however become so violent that the object or its fixation is destroyed before the described equilibrium appears.

Not only forces varying with the objects natural frequency can cause this behavior, but also a force varying with a frequency that is multiple of n and the fundamental frequency, where n is a natural number. These higher frequencies are called overtones or harmonics.

The phenomenon can be visualized by the vibration of a string, as seen in figure 2.3.

Figure 2.3 The natural frequency of a string and the five first overtones

14 Lundh, 2007, page 243

15 Sundström, B., 2007, page 372

2.3 Generators General facts

Generators are used to convert kinetic energy into electrical energy. One of the most basic equations that are used for generators was presented in chapter 2.1:

dt N_c dΦ

−

ε = (2.3)

The flux in this equation is calculated as the magnetic field times the active area, A. The active area is therefore defined as the area through which the magnetic flux passes and contributes to the EMF. It is possible to dive even deeper into generator theory to get a more detailed equation for the induced EMF, but that will not be necessary in this thesis.

The stator core is in place to help conduct the magnetic flux through the winding. A negative side effect of having the stator steel present is that the varying magnetic flux induces currents in it, not only in the windings. By laminating the stator, these unwanted eddy currents can be reduced with very little reduction of the active area.

The power output is dependant on both the voltage and the current from a phase and how many phases there are. Another way to look at the power from the turbine is to analyze it from a mechanical point of view. The equation describing the power output is then:¹⁶

ω M

P= (2.13)

where P is the power, M the applied torque and ω the mechanical angular frequency.

As can be understood from equations 2.1 and 2.8, if the length of the air-gap varies, so will the radial force. These unbalances in force can come to be very big with only

moderate deviation from a perfectly round rotor and stator or if the rotor is eccentric. This will not only greatly affect the mechanical structure, but it will also give a poorer electric quality as the induced EMF will be affected by the unsymmetrical magnetic field.

Cogging is an unwanted effect from the fact that the reluctance of the air-gap will vary as the rotor is turned. If no external force is applied, the force between the rotor and stator would strive to make the reluctance of the air-gap as low as possible. In figure 2.4, we can see how the magnetic flux passes between a pole and a stator tooth. If the rotor was to turn counter-clockwise, the reluctance for this particular part of the air-gap would first increase and give rise to an increasing force trying to hold the rotation back. As more and more flux would change path and starts flowing through the next stator tooth, the force would decrease until it starts pulling the rotor counter-clockwise as most of the flux has changed to the path through the second tooth. The force ripple that occurs is what is known as cogging.

16 Nordling et al., 2004, page 231

Figure 2.4 Magnetic flux between a pole and a stator tooth Cogging is closely linked to harmonics in the electrical output. As the MMF in a

magnetic circuit has a ripple, so will the EMF in the linked electrical circuit. As a result, overtones will be present in the voltage output.

Windings

There are numerous ways to wind a stator. As the standard in electricity generation is having 3 phases, it is exclusively this kind of winding that will be presented here.

The first parameter that must consider, when winding a stator, is whether to have an integer number or a fractionary number of slots per pole and phase, q. Examples of the two can be seen in figure 2.5, where τp is the pole pitch in electrical degrees, ^oe.¹⁷

Figure 2.5 Lines mark out coil ends, dotted lines mark out coil pitches I ) Winding with integer q, q = 2, S = τp =180^oe II ) Winding with fractionary q, q = 5/4, S1 = 144^oe, S2 = 192^oe

17 Lagerkvist, S., 1960, page 34

If the rotor is rotated so that two poles pass a specific point, the output voltage from the generator will be one period of a sinus. Therefore, τp is always equal to 180^oe. As can be seen in figure 2.5 I, for an integral slot winding the coil pitch, S, is equal to the pole pitch.

For a fractional slot winding the coil pitch will vary. This will reduce cogging effects and lower the amount of harmonics, but at the cost of slightly lower amplitude of the output voltage. This has to do with how much of the overtone that is present in the coil pitch. An example for the fifth overtone can be seen in figure 2.6.¹⁸

Figure 2.6 Coil pitches from figure 2.5 versus fundamental tone and fifth overtone For a winding with an integer q, the fifth overtone will have its maximum possible value;

the area under one half wave. For S₂, the grey area is subtracted from the odd half wave and as a result, the contribution to the fifth overtone from this coil is about two thirds of what a coil pitch of 180^oe would give. The cut in the fundamental tone is however not as noticeable. We can see that in S1, the fifth overtone is totally cancelled out due to

symmetry; the negative area cancels out the positive area. There is a lot more to say about overtones, but it will not be addressed in this thesis.

With more than one cable per slot, it is also possible to have a wider phase belt than τ_p/3 as seen in figure 2.7. In this figure, the winding to the right has each phase spread out in three of the six slots that corresponds to one pole pitch. For other windings, a different width of the phase belt could be applied.¹⁹

Figure 2.7 Phase belt of τ_p/3 to the left and τ_p/2 to the right

By having a phase belt wider than τp/3, the amount of harmonics can be somewhat reduced, much as in the case of a fractionary q.

18 Lagerkvist, 1960, page 23

19 Ibid., page 34

There are several ways to connect the coil ends. Two basic concepts are depicted in figure 2.8. The wave winding is done by only letting the coil ends move in one direction, going all the way around the stator, in this case, two times. The lap winding is done by winding an entire coil before moving on to the next one, thus effectively only winding once around the stator.²⁰

Figure 2.8 The stator has been cut up and spread out, showing two types of windings. Wave winding at the top and lap winding at the bottom

2.4 Software

SolidWorks is a CAD-program used for feature based parametric modeling of massive bodies. It has a graphical user interface, seen in figure 2.9, in which 2D-sketches are drawn and can be transformed to 3D-shapes by a diverse selection of features. It is possible to create fully associated 3D-models with or without restrictions. It can also be used to create blueprints quick and easy from the models. More product information can be found on www.solidworks.com.

Figure 2.9 SolidWorks’ user interface

20 Lagerkvist, 1960, page 52

3 Mechanical construction

3.1.1 Development of the basic concept

The starting point for this thesis was a vaguely defined idea of a generator being split into pieces containing both a part of the stator and a part of the fully permanent magnetized rotor, as schematically can be seen in figure 3.1. These pieces should be possible to transport separately and easily be put together on site.

Figure 3.1 Schematic picture of a modular assembly generator One major concern is to obtain a good enough magnetic circuit, i.e. low reluctance, bridging between the modules. A suggested way to obtain a low reluctance between the stator modules can be seen in figure 3.2. The yoke-teeth would consist of several layers of stator sheets.

Figure 3.2 A possible solution to lower the reluctance in the transition between stator modules

Another solution to keep the reluctance between the stator modules low would be to keep the air-gap between them as short as possible.

An iron ring is needed to conduct the magnetic flux inside the rotor and the air-gap between rotor and stator should be kept as small as possible in order to get a high magnetic flux.

3.1.2 Discussion

A definite deviation from the original idea, depicted in figure 3.1, is having the amount of stator modules to differ from the amount of rotor modules. If the amounts of the different types of modules would be the same, the symmetry would risk causing a ripple in both the torque and the normal force as the modules radially aligns with each other repeatedly.

Except from the heightened risk of material fatigue this causes, the roundness of the stator could be compromised if the rotational frequency times the amount of stator or rotor modules coincides with the natural frequency of either the stator or the rotor. This cogging effect would also have a negative influence on the electrical quality.

A second deviation from the original idea is having the generator magnetized after installation on site. This is partly brought on from the previous deviation mentioned above, but also because the large magnetic forces could be hazardous during the assembly of the generator. It would furthermore complicate the sensitive process of making sure that both the rotor and stator are near perfectly round and centered, during installation.

One concern with the interlacing of the stator modules is that the stator sheets in the yoke-teeth may sprawl and thus preventing the joining unless they first are compressed.

This could however be avoided by using wedges between the teeth, as seen in figure 3.3.

The modules would first be put together and the wedges put into place afterwards, after which compressing bolts can be put in and tightened.

Figure 3.3 A possible way of compressing the sprawling stator sheets by leaving room for and inserting wedges after putting the stator modules together

The interlacing would also require some space and thus reducing the amount of active area. This would complicate the development of a winding-scheme and risk causing unsymmetrical forces between the rotor and stator during operation.

Even though the idea of joining the stator modules by a moderate interlacing of the stator sheets would provide a low reluctance, the idea was rejected. This was due to the fact that the assembly on site would be too difficult. Very high precision would be needed as the pieces are put into place, even though the yoke-teeth would consists of several stator sheets as a compromise between low reluctance and ease of assembly.

The relatively simple idea of keeping the air-gap between stator modules as low as possible seems as a more viable one. It is however not clear how much the air-gap could come to affect the efficiency of the generator.

3.2.1 Construction of the concept

In table 3.1, a few generator specific parameters are presented. They were provided by the supervisor of this thesis and are a result from simulations in the in-house FEM- program Kalk.²¹ The number of poles and slots are selected to make sure that it is possible to split the rotor and stator into six and five pieces, respectively.

Table 3.1 Specified generator parameters

Parameter (unit) Value Parameter (unit) Value

Power (MW) 2 Slots per pole and phase 3

Voltage, VLL (kV) 7 Magnet height (mm) 28

Rotational speed (rpm) 19.1 Magnet width (mm) 200

Current (A) 165 Iron ring (mm) 50

Electrical frequency (Hz) 9.55 Cables per slot 4 Stator inner diameter (mm) 5200 Cable area (mm²) 100 Stator outer diameter (mm) 5500 Current density (A/mm²) 1.65

Generator length (mm) 2023 Load angle (^o) 9.1

Air-gap width (mm) 16 B air-gap (T) 0.85

Cable length (m) 5493 B tooth (T) 1.8

Weight PM (k kg) 5.283 B yoke (T) 1.3

Weight stator steel (k kg) 23.402 B iron ring (T) 1.5

Weight cable (k kg) 6.182 Losses Cu (kW) 32.05

Weight total (k kg) 48.187 Losses Fe (kW) 8.18

Number of poles 60 Efficiency (%) 98.0

The following section gives a short description of the construction of the generator in the CAD-program SolidWorks. More detailed drawings can be found in appendix 1.

21 Eriksson et al., 2008

The construction of the generator is partly an iterative process, where several simulations are carried out for the different parts to make sure that they can withstand the forces they are exerted to.

Rough estimation of the forces acting on the different parts has been calculated and can be seen in table 3.2. For full calculations, see appendix 2.

Table 3.2 Forces per unit of area

Force Value

Magnetic tangential force, between rotor and stator 11.8 kN / m² Magnetic normal force, between rotor and stator 287 kN / m² Magnetic normal force, between adjacent stator modules 672 kN / m²

Gravity was also included, as well as the weight from other components weighing down on the simulated parts.

The cable area of 100 mm² suggests a diameter of the cable, including isolation, of approximately 18 mm. Since no specific make of the cable has been chosen, this approximated value has been used in the construction of the stator.

In order to maximize the amount of magnetic material in the teeth of the stator, every other slot is somewhat radially displaced, see figure 3.4. This will allow a slightly smaller radius for the construction without having the teeth magnetically saturated.

Figure 3.4 Stator sheet seen from above

The stator would normally be made out of a large quantity of electrically isolated stator sheets. In order to keep the memory usage of the computer at an acceptable level, the stator was drawn as a solid piece, as seen in figure 3.5.

The inner diameter is according to the specifications given in table 3.1. The outer

diameter has been somewhat enlarged to supply room for the dove-tails without reducing the available amount of magnetic material for the magnetic flux through the stator. There are 108 slots in each of the five stator modules, adding up to 540 slots for all the modules.

Figure 3.5 Stator module without winding and support structure

The support beams together with the dove-tails, shown in figure 3.6, are constructed to be used as stabilization when putting the stator sheets in place. They will also play a role in counteracting the forces between the rotor and stator. These forces, especially the torque, will however be greatly reduced due to the friction between the stator and its base

support.

Figure 3.6 Dove-tail to the left and support beam to the right

It is critical that these support beams don’t give way for the forces that they are exerted to. The results from a static simulation, with all of the magnetic forces acting between the rotor and the stator applied, can be seen in figure 3.7. The displacement of the beam comes to a maximum in the middle and is no greater than 0.38 mm.

Figure 3.7 Result of a simulation on the support beam from SolidWorks. Green arrows denote boundary conditions and purple arrows denote forces. The arrow on the scale to the right shows the lowest stress level represented in the plot.

On top of and underneath the stacked stator sheets, a spacer is placed. The spacer is depicted in figure 3.8. It protects the winding from the otherwise sharp metal edges of the slots in the stator. It also acts as a big reluctance between the stator and the carrying structure.

Figure 3.8 Spacer used between the stator and the carrying structure

The part of the carrying structure that is closest to the stator can be seen in figure 3.9. To be able to refer to it later, we call it the support stator interface. It has a total height of 180 mm in order to give room for the coil ends. The big holes, used for bolting this part together with the rest of the carrying structure, are over-dimensioned to make it possible to shift the stator module’s position somewhat in relation to the other stator modules. A metal plate, acting as a washer, will be used to distribute the force from the bolt to the surrounding material.

Figure 3.9 Support stator interface

The structure beams, seen in figure 3.10, connects the support stator interface to the rotor bearings. The upper structure beams are first and foremost in place to counteract any radial forces. The bottom structure beams are connected to the foundation, as well as the lower rotor bearing and the structure stator interface. These structure beams have the important function of stabilizing everything above in the axial direction.

Figure 3.10 Top: Upper structure beams Bottom: Lower structure beams together with the mounting elements sticking up from the foundation

The bearings have only been schematically drawn with one part to be attached to the support beams and the other to the rotor axis. They are however very essential to the generator and great care must be taken when dimensioning them.

Figure 3.11 A stator module with only the winding missing

The fully assembled stator module can be seen in figure 3.11. Only the stator winding is missing in the figure. The upper structure beam will be mounted after the rotor is put into place.

A sturdy axis is needed to keep the rotor in place and to withstand the forces it is subjected to. In figure 3.12 it can be seen that the axis is hollow to reduce the weight.

There are two rims for mounting of the rotor modules and the inner part of the schematically drawn bearings are placed outside of these rims. At the very top of this axis, the connection towards the turbine axis is placed.

Figure 3.12 Rotor axis

The rotor modules are identical to each other and an exploded view of one can be seen in figure 3.13.The magnets are due to practical reasons not made out of one single piece as shown in the picture. They will instead consist of several smaller magnets that are put into place after the entire generator is otherwise completely assembled and adjusted for roundness. The magnetization is done by pressing the magnets into the rotor from above.

There are ten poles on each of the six rotor modules.

Figure 3.13 Exploded view of a rotor module

Figure 3.14 Result of a simulation on a piece of the rotor from SolidWorks. Green arrows denotes boundary conditions, purple arrows denote forces and the red arrow denote gravity. The arrow on the scale to the right shows the lowest stress level represented in the plot.

A multitude of simulations have been run in order to properly configure the rotor module’s construction. The final result, as seen in figure 3.14, shows that the von Mises stress barely exceeds 80 MPa, which is well within the tolerance limit.

The fully assembled generator is shown in figure 3.15.

Figure 3.15 Fully assembled generator

3.2.2 Discussion

To split the stator into five pieces gives modules that should be small enough for relatively easy handling. Another number of modules could be used as well, but

preferably not any fewer for this particular generator, as it would make the modules too large. As a consequence of this choice, it was decided to split the rotor into six pieces.

6 can only be divided with the prime numbers 2 and 3. And as 5 is a prime number in itself, the choices of number of different modules make sure that they can never align and should therefore not risk adding another rotational frequency to be avoided due to the stator’s or rotor’s natural frequencies.

The magnetic normal force between adjacent stator modules are calculated for the maximum value of the magnetic flow in the yoke. This force will be concentrated not in the split tooth but in the yoke, so the simulations made for the stator will have a greatly exaggerated von Mises stress level. Still, the stress level was well below the upper limit.

The support beams for the stator sheets was drawn partially to be easy to construct. Initial simulations indicated that there needed to be lots of support beams. By using a solid piece of steel, as thick as the stator, to distribute the forces along the dove-tail instead of having the forces applied directly on the dove-tail, a more realistic scenario was achieved, where the support beam wasn’t as deformed as in the previous case. This simulation shows that six support beams should be enough.

4 Winding scheme

4.1.1 Winding of a stator module

A modular assembly generator cannot be wound using a regular wave winding, unless one wants an immense amount of cable joints. Instead a modified lap winding is

suggested. This keeps the cable joints to a minimum of two per stator module and phase.

Figure 4.1 Schematic 2D-figure of the suggested lap winding

According to the generator parameters given in table 3.1, the winding will have three slots per pole and phase. Furthermore the phase belt will be equal toτp⋅4 9, as seen in figure 4.2.

Figure 4.2 Cross-section of the winding through the stator. A dot denotes cables coming up and an X denotes cables going down.

4.1.2 Discussion

The coil-ends are rather hard to figure out how to organize practically, and will thus be handled in a following chapter, arrangement of coil ends and winding.

Even though the resistance of a single cable joint is relatively low, having a regular wave winding with a great amount cable joints could significantly increase the resistance of each phase winding. It was therefore decided to keep the amount of cable joints to a minimum, using the modified lap winding shown in figure 4.1.

The suggested winding does however bring about a possibly serious problem. If the generator would be short circuited somewhere along one of the windings, the forces due to the high currents could be very unevenly distributed and thus deform the stator. This problem needs to be studied further, but it falls outside the scope of this thesis.

As a winding with an even number of slots per pole and phase gives rise to a relatively big amount of harmonics, the phase distribution is bigger than it would be for the simplest type of winding. This phase distribution will inhibit the harmonics to a certain degree. However, no calculations regarding the amount of harmonics have been carried out.

4.2.1 Construction of winding dummy

In order to test the winding, a winding dummy was built in the work shop of the Division for Electricity Research at Uppsala University. At an initial step, the dummy was

constructed in the CAD-program SolidWorks.

The winding dummy was scaled down from the original dimensions to be suitable for winding with a cable diameter of 8 mm. The scaling factor was chosen as 1:2.255 in order to make the cable fit loosely in the slots.

The assembly was drawn to have a total height of 850 mm. As can be seen in figure 4.3, the plywood sheets are fixed together at seven places. More exact dimensions are given in appendix 3.

Figure 4.3 Winding dummy

First a template of a stator module as seen from above, according to the previously mentioned scaling, was printed out using six A3 papers. The paper template was glued onto a piece of plywood and left to dry. Using a jigsaw, the piece was roughly cut out.

Two more pieces of plywood “stator sheets” was subsequently cut out using the first one as a template.

The three pieces of plywood was fixed together by using a couple of clamps, after which the holes for the bolts was drilled. The clamps were removed and six bolts with washers and nuts were used to fix the plywood pieces together instead.

With the pieces of plywood securely fixed in place, a belt sander was used to remove any plywood extending beyond the contours of the glued on paper template. The holes in the slots were drilled according to the markings in the paper template using a pillar drill, as seen in figure 4.4. Finally the slots were cut open radially, using the jigsaw once again.

Figure 4.4 Drilling of the slots

Spacers were cut out directly from dimensional lumber, measuring 45 mm x 70 mm, and the holes were drilled lengthwise through each piece separately. A template was used to make sure that the holes were correctly placed.

Round cast iron bars were put in a lathe and the thinner section of the bars was cut out, after which the outermost 18 mm were threaded to be able to fit washers and nuts.

With most of the winding dummy complete, all pieces were put together, as seen in figure 4.5. The processed round cast iron bars were welded onto pieces of flat iron bars, with the intention of stabilizing the construction.

Figure 4.5 Welding of the stabilizing “feet”

4.2.2 Arrangement of coil ends and winding

Several short pieces of grey, blue and brown cable were used to represent the coil ends.

The cables were put in one phase at the time, starting with the split-coil phase which marks both the start and end of largest unique piece of the winding, called the repeatable group. That is, the following coils in the stator module will be wound in the same way.

When the grey phase coil ends had been properly arranged, a different phase’s coil ends were put in, followed by the last phase’s coil ends. See figure 4.6 for further clarification.

Figure 4.6 Left: Placing of the second phase’s bottom coil ends.

Right: Top coil ends.

The top coil ends was done first, and the result can be seen in figure 4.7. When the upper coil ends were finished, the order of threading of the winding could be determined and the bottom coil ends be arranged thereafter. In figure 4.8 we can see the arrangement of the bottom coil ends. They are spread out to make it easier to see how the winding should be done. The two figures mentioned above were printed out together with the scheme of the winding order, seen in figure 4.9, and used when the actual winding test was done.

Figure 4.7 Arrangement of the top coil ends as seen from above

Figure 4.8 Arrangement of the bottom coil ends as seen from underneath

Figure 4.9 Winding order of the three phases. Equal numbers and colors are connected by the top coil ends and the winding is done in numerical order. X denotes where the winding of a coil is started from above

Two repetitions of the repeatable group were wound in the winding dummy. This is enough to visualize how the entire winding will look, including transitions between the repeatable groups. Figure 4.10 and 4.11 shows the result.

Figure 4.10 The part of the winding that was wound

Figure 4.11 The same winding as in figure 4.10, seen from above and underneath, respectively

4.2.3 Discussion

There was a rather large amount of cable of the diameter 8 mm left from earlier projects, which made this choice of winding cable good for use in the winding dummy. The scaling factor of 1:2.255, that makes the cables fit loosely in slots, ensures that the winding process will go rather smoothly.

The spacers are used to make the winding through the stator visible and to give it some length. The middle plywood sheet is there to stabilize the winding through the winding dummy. This setup makes it easier to see how the winding is done.

The height of the dummy was chosen in order to make it possible to perform the winding sitting down on a chair.

Both cables with few and many strands have been tested for winding. The winding of the stator is made easier with the latter because of its higher flexibility, but either one can be used. Combining the two for different phases is not recommended, however. This would likely cause the resistance of the windings to differ. With the make of cable that was used here, Draka©, it will also be more likely that damage is caused to the isolation of cables during the winding when using different amount of strands for the different phases. This is due to the fact that their respective protective coating have different hardness.

By first using a winding dummy, the winding of the real generator would likely go a lot smoother as any mistakes done here are easily corrected and gives valuable experience.

Obviously, other winding schemes could be used. For example, an altered version of a wave winding could be done with the cable going back over the module instead of being joined to the next module, except for the very last parts of the winding in the specific module. This would keep the cable joints to a minimum, but it would greatly increase the amount of cable needed and thus increase the winding’s resistance. It is also possible to arrange the coil ends differently; the way shown in this thesis is but one of many.

5 Conclusions

The stator and the rotor should be divided into different amount of modules. Otherwise a periodical force ripple may occur between the rotor and the stator as the different

modules align with each other. This could come to negatively affect the mechanical stability of the generator as well as the quality of the electrical output.

In order to have a low reluctance between the stator modules the distance between adjacent modules should be kept as short as possible. No interlacing should be used, as this would make the installation of the generator more difficult and time consuming.

The magnetization of the rotor needs to be done as the final step of the installation. The big forces that arise with the magnets present could make the assembly dangerous for the personnel that put the different parts into place. Premagnetization would obviously also make the calibration of the stator roundness more difficult.

A rather basic winding scheme can be used, even with the segmentation of the stator.

Before applying a winding scheme in a real generator, it is advantageous to test it in a winding dummy. Preferably, cables with many strands should be used.

Finally, it can be concluded that the concept developed in this thesis is possible to implement, even though a lot of research still remains to be carried out. Work that is still left to be done is described further in chapter 6; Future work.

6 Future work

Simulations and experiments ought to be carried out in order to find how much the distance between the stator modules affect the efficiency of the generator. Perhaps the effect is marginal and less effort can be put on getting the modules to fit as tightly as possible.

The concept should be worked over in order to make construction of the modules, transport and assembly easier. This process depends on what machinery will be available during production.

An effective way of magnetization, as well as demagnetization, should be developed.

The bearings of the rotor need to be carefully dimensioned before the concept is applied.

This should not be done too early on, as the forces applied to the bearings can come to differ as the concept matures.

The winding still needs to be electromagnetically simulated and a study regarding the forces that can occur during different fault modes needs to be carried out. With the knowledge gained from such a study, the construction could be modified for increased structural survivability.

7 Acknowledgements

Thanks to...

...the Göran Gustafsson Foundation for making this thesis work possible.

...Sandra Eriksson for her patience and valuable input.

...Hans Bernhoff for reviewing my ideas.

...Mats Leijon for the productive discussions.

...Senad Ferhatovic for his input regarding the writing of the paper.

...Ulf Ring for his help with processing of the metal parts of the winding dummy.

...the people who have been present in the "thesis work-room" during my time there, making it an enjoyable one. I would especially like to thank Hjalmar Nyström and Anders Nilsson for their help when I tried to figure out how to use SolidWorks properly and Tobias Semberg for practical tips regarding the winding.

...to the many PhDs at the division for electricity who has been there for me when there was something I needed to ask or helped by pointing me in the right

direction.

References

Deglaire, P., Eriksson, S., Kjellin, J., Bernhoff, H., Experimental results from a 12 kW vertical axis wind turbine with a direct driven PM synchronous generator, EWEC 2007 – European Wind Energy Conference & Exhibition, Milan, Italy, 2007

Eriksson, S., Bernhoff, H., Leijon, M., FEM simulations and experiments of different loading conditions for a 12 kW direct driven PM synchronous generator for wind power, Renewable Energy, 33(4):674-681, 2008

Lagerkvist, S., Asynkrona och synkrona maskiners lindningar, Göteborg, 1960.

Lundh, H., Grundläggande hållfasthetslära, Instant Book AB, Stockholm, 2007. ISBN 978-91-972860-2-2

Nordling, C., Österman, J. Physics Handbook for Science and Engineering, Studentlitteratur, Lund, Seventh edition, 2004. ISBN 91-44-03152-1

Ribrant, J., Bertling, L.M, Survey of failures in wind power systems with focus on swedish wind power plants during 1997-2005, IEEE Transactions on Energy Conversion,

22(1):167-173, 2007

Spooner, E., Chen, Z., A modular, permanent magnet generator for variable speed wind turbines, Electrical Machines and Drives, Conference Publication No. 412, 1995

Sundström, B. (editor), Handbok och formelsamling i Hållfasthetslära, Instant Book AB, Stockholm, Fifth edition, 2007.

Appendix 1 – Generator blueprints

The materials used for the different parts in this appendix are listed in table a1.1 below.

They do not exactly correspond to the materials that should be used in the construction, but they do have similar properties and can be considered to be representative of the actual materials used. The material used for the magnets are chosen to have similar weight only. Material specific parameters can be found in SolidWorks documentation.

Table a1.1 Materials used for the different parts in simulations

Part Material

Stator segment 1023 Carbon Steel Sheet (SS) Stator end plate PVC Rigid

Dove-tail 201 Annealed Stainless Steel (SS) Support beam 1023 Carbon Steel Sheet (SS) Support stator interface 1023 Carbon Steel Sheet (SS) Upper structure beam 1023 Carbon Steel Sheet (SS) Lower structure beam 1023 Carbon Steel Sheet (SS) Rotor axis 1023 Carbon Steel Sheet (SS) Rotor segment 1023 Carbon Steel Sheet (SS)

Band 1060 Alloy

Magnet 1023 Carbon Steel Sheet (SS)

The stator end plates have the same dimensions, except for the height that is set to 20 mm instead of 2023 mm.

Appendix 2 – Forces used in simulations

In order to be able to simulate the generator’s different parts properly, the forces applied to them had to be calculated. This appendix contains calculations for both magnetic and gravitational forces.

Force due to mass

Given the values of the parts’ different masses, the force they exert due to weight can easily be calculated according to:

Force [N] = Mass [kg] * Acceleration [m/s²] (a2.1) Where the acceleration = g = 9.81 m/s². The values are presented in table a2.1.

Table a2.1 Forces due to mass

Part Mass* (kg) Force (N)

Stator segment 7 892 77 420

Stator end plate 203 1 991

Dove-tail 48 471

Support beam 107 1 050

Support stator interface 376 3 689

Upper structure beam 726 7 122

Lower structure beam 709 6 955

Rotor axis 4 484 43 990

Rotor segment 3 353 32 890

Band 11 107.9

Magnet 87 853.5

Winding cable 6 182 60 650

* Values from SolidWorks except for the cable, which is specified in the generator parameters

Magnetic forces

The different magnetic field densities that will contribute to the forces acting on the parts of the generator can be seen in table a2.2.

Table a2.2 Magnetic field densities Parameter Value* (T)

B air-gap 0.85

B yoke 1.3

* Values according to generator specifications provided by the supervisor of this thesis work

To calculate the magnetic force per unit of area, the following equation can be used:

2

2 0

1 B A

F

= µ (a2.2)

With µ₀ =4π⋅10⁻⁷Vs Am and the values from table a2.2, we get the two values for the normal forces given in table a2.4. The magnetic field density in between two stator modules’ yoke will however be lower than the one listed, as the reluctance is greater here.

The value gives a worst case scenario, with regard to the force.

The magnetic tangential force between the rotor and the stator can be approximated by first looking at the rated power output, P, from the generator:

M mech

P= ω (a2.3)

Where M is the torque and ωmech is the mechanical angular frequency. By rearranging equation a2.3 we get an expression for the torque:

mech

M P

=ω (a2.4)

The torque can be divided into a tangential force, F_t, and a lever length equal to the radius of the rotor, R_rotor. The rotor radius is chosen instead of the stator inner radius in order not to underestimate the force.

rotor tR F

M = (a2.5)

Assuming that the force acts on the rotors active area,A_active,rotor =2πR_rotorH_rotor (where Hrotor is the rotors height), instead of the stators active area, we get the maximum value for the tangential force. By combining equation a2.4 and a2.5 we get:

rotor rotor mech

rotor active rotor mech active

t

H R f

P A

R P A

F

2 2

, 4 π

ω ⁼

≥ (a2.6)

By inserting the values from table a2.3 into equation a2.6 we get the value for the tangential force per unit of area shown in table a2.4.

Table a2.3 Generator parameters Parameter (unit) Value*

Power (MW) 2

Mechanical frequency (Hz) 0.318

Rotor radius (m) 2.584

Rotor height (m) 2.023

* Values according to generator specifications provided by the supervisor of this thesis work

The magnetic forces are presented in table a2.4 as force per unit of area.

Table a2.4 Forces per unit of area

Force Value (kN/m²)

Magnetic normal force, between rotor and stator 287 Magnetic normal force, between adjacent stator modules 672 Magnetic tangential force, between rotor and stator 11.8 Forces acting on the different parts

In the following section, the forces on the different parts will be estimated from the values given in table a2.1 and a2.4.

A stator segment will be exerted to forces from above equal to that of an entire support structure interface, a stator end plate and no more than two thirds of an upper structure beam. This adds up to 10.4 kN.

With an active area (A_active =2πR_stator,innerH_stator 5) of 6.57 m², the total magnetic normal force between rotor and a stator module is 1.89 MN and the magnetic tangential force is 77.5 kN.

The area facing an adjacent stator module (the stator segments height times its radial depth) is equal to 0.384 m². This area gives a greatly exaggerated force of 258 kN. The magnetic flux would normally only pass through the yoke and not be distributed as suggested by this calculation.

A summary of the forces on the stator segment can be seen in table a2.5.

Table a2.5 Forces on stator segment

Force Value (kN)

Axial force on top surface 10.4

Normal force towards rotor 1 890

Tangential force on active area 77.5

Force towards adjacent modules 258

The dove-tail and support beam will be treated as one single part here. They will

counteract the magnetic tangential and normal force that acts on the stators active area. A solid piece of metal of the same thickness as the stator was created and the dove-tail fitted into it. The forces mentioned, and listed in table a2.5, were divided by five, even though there are six support beams per stator module. This ensures that the forces are not

underestimated. Both forces were applied to the solid piece of metal in the simulation. No weight is assumed to be held up by the support beams. A summary of the forces on the part is shown in table a2.6.

Table a2.6 Forces on dove tail and support beam

Force Value (kN)

Radial force 378

Tangential force 15.5

The lower support stator interface is the one that will be exerted to the highest forces due to the mass of the structure above. Therefore, the part was dimensioned for those

conditions.

It will carry the weight of six support beams and dove-tails, a stator end plate, a stator module and its part of the winding plus the weight carried by the stator module itself. It all adds up to 109 kN.

Furthermore, the magnetic tangential and half of the normal force between the stator module and rotor will be transferred to this part. A summary of the forces is listed in table a2.7.

Table a2.7 Forces on support stator interface

Force Value (kN)

Radial force on top surface 945 Tangential force on top surface 77.5 Axial force on top surface 111

The forces on the lower structure beam are a bit more complicated to estimate. Part of the weight of the structure above will be carried up by the bearing attached to the structure beam’s innermost part, while the forces applied from the lower support stator interface will rest on the support beam’s outermost part. These forces are in turn mostly

counteracted by the base support, only a small part of the radial force will be transferred to the central bearing from the structure beam.

The force due to weight, applied to the outermost part of the structure beam, adds up to 115 kN.

The force due to weight, applied to the innermost part of the structure beam, consists of one fifth of the axis and rotor, including bands and magnets, plus no more than two thirds of an upper structure beam. The weight of the bearings has not been included due to uncertainty of their mass. It would most likely have an insignificant impact on the design of the structure beam. The forces add up to 64.6 kN.

Table a2.8 Forces on structure beam

Force Value (kN)

Outermost axial force on top surface 115

Innermost axial force on bearing contact surface 64.6

Outermost radial force on top surface 945

Outermost tangential force on top surface 77.5 The axis will have approximately half of the total inward radial force applied to the contact area for the upper bearing, which also carries the weight of no more than two thirds of the upper structure beams. The contact area for the lower bearing will see a significantly reduced radial force, which is neglected in this simulation. It will however transfer all of the force due to the weight to the lower structure beams. The middle part of

the axis will carry the weight of the rotor modules and be exerted to a large part of the radial outward force. It is not exactly clear how much of this force that will be transferred directly between the rotor modules and therefore the simulations are done with the full radial force. The tangential force that is applied to the rotor module mounting surface equals that of the tangential force acting on all five stator segments.

The force at the upper bearing contact surface adds up to 23.7 kN axially and 9450 kN radially. At the lower bearing we have an axial force of 323 kN. Axial force due to the weight of the rotor modules is 255 kN and the tangential force is 388 kN. The forces are listed in table a2.9.

Table a2.9 Forces on axis

Force Value (kN)

Axial force on upper bearing contact surface 23.7 Radial force on upper bearing contact surface 4 725 Axial force on rotor module mounting surface 255 Radial force on rotor module mounting surface 9 450 Tangential force on rotor module mounting surface 388 Axial force on lower bearing contact surface 323

The forces on a single rotor segment will be greatest in the radial direction towards the stator, equal to one sixth of the radial force on the rotor module mounting surface of the axis. There will be an axial force corresponding to the weight of ten magnets and ten bands applied to the rotor surface facing the stator, 9.61 kN. The forces are shown in table a2.10.

Table a2.10 Forces on rotor module

Force Value (kN)

Normal force towards stator 1 575

Tangential force on surface towards the stator 64.7 Axial force on surface towards the stator 9.61

Appendix 3 – Winding dummy blueprints

The winding dummy was drawn in SolidWorks and put together in the assembly hall of the Division for Electricity at the Ångström Laboratory, Uppsala University. The material used was funded by the Göran Gustafsson Foundation.