Design and Construction of High
Current Winding for a Transverse
Flux Linear Generator Intended for
Wave Power Generation
AHMED AMINE RAMDANI
SEBASTIAN RUDNIK
KTH ROYAL INSTITUTE OF TECHNOLOGY
High Current Winding for a
Transverse Flux Linear
Generator Intended for Wave
Power Generation
AHMED AMINE RAMDANI
SEBASTIAN RUDNIK
Master in Electrical Power Engineering Date: September 6, 2018
Supervisor: Anders Hagnestål Examiner: Oskar Wallmark
Swedish title: Design och Framtagning av Lindning Ämnad en Linjär Transervsalflödesgeneratorprototyp
Abstract
There is currently a high demand for electric power from renewable sources. One source that remains relatively untapped is the motion of ocean waves. Anders Hagnestål has been developing a uniquely efficient and simplified design for a point-absorb buoy generator by converting its linear motion directly into alternating electric power us-ing a linear PM engine. To test this method, a smaller prototype is built. Its characteristics present some unusual challenges in the design and construction of its winding.
Devices of this type typically use relatively low voltage (690V typ-ically for a wind turbine, compared to the 10kV range of traditional power plants). To achieve high power, they need high current, which in turn requires splitting the conductors in the winding into isolated parallel strands to avoid losses due to eddy currents and current crowd-ing. However, new losses from circulating currents can then arise. In order to reduce said losses, the parallel conductors should be trans-posed in such a way that the aggregate electromotive force the circuits that each pair of them forms is minimized.
This research and prototyping was performed in absence of ad-vanced industrial means of construction, with limited space, budget, materials, manpower, know-how, and technology. Manual ingenuity and empirical experimentation were required to find a practical im-plementation for: laying the cables, fixing them in place, transferring them to the machine, stripping their coating at the ends and establish-ing a reliable connection to the current source.
Using theoretical derivations and FEM simulation, a sufficiently good transposition scheme is proposed for the specific machine that the winding is built for. A bobbin replicating the shape of the engine core is built to lay down the strands.
The parallel strands are then organized each into their respective bobbin, with a bobbin rack and conductor funneling device being de-signed and constructed to gather them together into a strictly-organized bundle. An adhesive is found to set the cables in place.
Problems with maintaining the orientation and configuration of the cables in the face of repeated torsion are met and solved. A chemi-cal solution is used to strip the ends of the conductors, and a reliable connection is established by crimping the conductors into a bi-metal Cu-Al lug.
crimping lugs.
Keywords: Wave-power, transverse flux generator, winding, alu-minum conductor, magnetic flux leakage, ocean energy, wave energy, wave energy generator, electromotive force, parallel strands, circu-lating currents, crowding effects, skin effect, proximity effect, eddy currents, racetrack effect, cable twisting, AlCu connection, enamel, polyamide-imide, dicloromethane.
Sammanfattning
Efterfrågan på el från förnybara källor är hög och inget tyder på att det kommer ändras den närmsta tiden. En källa till förnybar el som än idag står relativt orörd är den där man använder energin från havsvå-gor. Det är denna förnybara källa Anders Hagnestål haft i åtanke när han nu bygger en unikt effektiv generator med syftet att i ett senare skede utvinna el med hjälp av flytande punktabsorberande vågkraft-system. Generatorn är av den linjära typen och omvandlar det punk-tabsorberande systemet rörelse till el. För att testa denna generator-modell så påbörjades bygget av två fullskaliga prototyper 2017. Denna uppsats behandlar specifikt arbetet med generatorlindningen till pro-totyperna och innefattar processen från design till själva byggnatio-nen. Lindingen består av flertalet mindre och isolerade lindningsleda-re med uppgift att bland annat minska skinneffekt och virvelströms-förluster. När man använder denna metod så uppkommer dock ett nytt problem vilket härstammar från att lindningsledarna är samman-kopplade i vardera ända och bildar på så sätt n2slutna strömkretsar. Konsekvensen kan vara stora förluster från cirkulerande strömmar på grund av det magnetiska ströflöde som finns runt järnkärnan som lindningen omsluter. Utgångspunkten för att minimera dessa cirkule-rande strömmar är att transponera alla lindningsledare på ett sätt så att den resulterande elektromotoriska spänningen för varje strömkrets blir så liten som möjligt.
Med hjälp av förenklade modeller samt FEM simuleringar så be-stämdes ett lämpligt sätt att transponera lindningstrådarna utifrån oli-ka kriterier. Lösningen blev att lindningstrådarna endast transponera-des en gång med en så kallad 180 grader transponering.
Detta ger en tillräckligt god minimering av de cirkulerande ström-marna, men den stora fördelen med denna lösning är att det är möjligt att linda maskinen med de små resurser projektet hade tillgång till, dock var detta till en stor nackdel då väldigt mycket tid gick till att hitta egna tillvägagångsätt för att utföra byggandet av lindningen på ibland okonventionella sätt.
Acknowledgments
We would like to thank our supervisor Anders Hagnestål for the op-portunity to work with this project and for all the encouraging words we got to believe in our work and ideas.
Jesper Freiberg and Stefan Bosniak for their help with the material and tools to execute our designs.
Brian Timmer, Post Doc at the Organic Chemistry division of the De-partment of Chemistry of KTH, who helped us test a chemical solution to quickly and safely strip the enamel from the cable, which is indis-pensable in preparing the extremities of the bundles for safe connec-tion.
Hendrik Klein, our contact at Elpress AB, who helped us find an ap-propriate solution for a bi-metal connection between the aluminum winding and the copper bus bars of the power electronics.
Malin Nordgren, of Gleitmo Technic AB, who sent us multiple types of glue for the assembly of the winding.
Zachary Ross and the rest of the staff at the Model Workshop of the School of Architecture of KTH, who kindly allowed us to use the CNC milling machine at the school and gave us the guidance to program and handle it.
1 Introduction 1
1.1 Background . . . 1
1.2 Aim and Purpose . . . 4
1.2.1 Research Questions . . . 4 1.3 Limitations . . . 5 1.4 Delimitations . . . 8 1.4.1 Literature . . . 8 1.4.2 Simulation . . . 9 1.4.3 Testing . . . 10 1.5 Assumptions . . . 10 1.5.1 Scientific Consensus . . . 10 1.5.2 FEM Simulation . . . 11 1.5.3 Winding Choice . . . 11 1.5.4 Construction . . . 11
1.6 Choice of Conductor Material . . . 11
1.7 Literature Review . . . 12
1.8 Current Crowding . . . 12
1.8.1 Joule effect and conductor section: . . . 13
1.8.2 Conductor bending . . . 14
1.8.3 Skin and proximity effects . . . 15
1.8.4 Eddy Currents: . . . 17
1.8.5 Circulating Currents: . . . 18
1.9 Transposition . . . 19
1.9.1 Defining the language . . . 19
1.9.2 Minimization . . . 24
1.9.3 Flux Density Distributions And Transposition Schemes 27 1.9.4 Linear Magnetic Field In Both Transversal Direc-tions . . . 29
1.9.5 Generalized Magnetic Flux Density . . . 29
2.3.1 The Ideal Solution . . . 38
2.3.2 One Transposition per Run . . . 39
2.3.3 The simplest solutions . . . 40
2.4 Winding Choice . . . 42
2.5 Winding construction method . . . 43
2.5.1 Building the Core-Replica Bobbin . . . 44
2.5.2 Winding the bobbin . . . 45
2.5.3 Damage to the Insulation: Prevention and Cor-rection . . . 52
2.6 Stripping The Wires . . . 53
2.7 Aluminum Conductor Terminations . . . 56
2.7.1 AlCu Bundle-Electronics Termination . . . 56
2.7.2 Al-Al Wire-Wire Connection . . . 57
3 Results 63 3.1 Material . . . 63
3.1.1 Materials . . . 63
3.2 Construction: Materials and Methods . . . 64
3.3 Bobbin Construction . . . 65
3.3.1 The Core-Replica Bobbin . . . 65
3.3.2 Raw Materials . . . 65
3.3.3 Ideal Bobbin Construction Method . . . 66
3.3.4 The Stadium-Shape . . . 70
3.4 Winding Construction . . . 72
3.4.1 Final and Working Winding Method . . . 72
3.5 Cable-Stripping . . . 78
4 Discussion and Conclusions 79 4.1 Simulation . . . 79
4.2 Winding Choice . . . 80
4.2.1 Aluminum or Copper . . . 80
4.2.2 Cross-Section Shape . . . 80
4.2.4 Current crowding effects. . . 81
4.2.5 Insulation . . . 81
4.2.6 Safer Handling of the Winding . . . 82
4.2.7 Cable-stripping . . . 82
4.3 Transposition . . . 82
4.4 Construction . . . 83
4.4.1 Connections and Resistances . . . 83
4.4.2 The CRB Construction . . . 83
4.5 Instrumental improvements . . . 85
4.6 Conclusion . . . 87
References 89 A Appendix 93 A.1 Statistical Fitting of Data . . . 93
A.2 Importing and Fitting the Goodness of Data . . . 93
A.3 Configuring the Geometric Parameters in COMSOL . . . 95
A.4 Tools . . . 97
A.4.1 Drawing and Measuring Instruments . . . 97
A.4.2 Holding Tools . . . 101
A.4.3 Boring Tools . . . 101
A.4.4 Cutting Tools . . . 103
A.5 Schematics . . . 105
A.5.1 Cores . . . 105
A.5.2 Bobbin . . . 106
A.6 Cable Lug instructions . . . 107
A.7 Datasheet for hot-melt adhesive . . . 112
A.8 Datasheet for low viscous hot-melt adhesive . . . 113
A.9 Datasheet for LCR bridge . . . 114
A.10 Datasheet for Micro-ohmmeter . . . 115
A.11 Datasheet for infrared camera . . . 116
Bundle - The collection of parallel strands that carries the total current in one phase of the winding
Conductor - The aluminum core of each strand
Core Replica Bobbin, CRB - A bobbin that is designed so that the wind-ing can be constructed around it, then removed and taken away to be incorporated into the electrical machine on its own.
Electromotive force - The voltage generated between the extremities of one loop of conductor by the variation along time of the mag-netic flux that traverses the surface that the loop is the border of. Magnet Wire - Also known as winding wire or enameled wire. The material constituting the strands; an aluminum conductor coated with insulating enamel.
Solidary Bobbin - A bobbin that is designed so that the winding, once constructed around it, remains fixed to it. The bobbin, contain-ing the windcontain-ing, is then added into the electrical machine as an integral part thereof.
Strand - Each individual insulated magnet wire
Translator - The column of steel and magnets that moves up and down the center of the device.
Introduction
1.1
Background
Since the industrial revolution, energy demand increased exponen-tially. While it was possible to rely on the combustion of fossil fu-els for a time, they are a non-renewable, finite resource, and burning them results in the release of gasses that increase the greenhouse ef-fect in the atmosphere, causing a man-made global warming with po-tentially catastrophic and irreversible consequences. As the problem became more urgent, economies around the globe sought to transi-tion to renewable energy sources. The use of hydraulic, wind, solar, biomass, and even geothermal power is abundant and growing expo-nentially, as shown in Fig. 1.1. The energy of the oceans, however, remains largely untapped to this day in comparison; the insignificant sliver that it represents in the previous graph is expanded upon in Fig. 1.2.
Based on possibly the highest quality global database available at present[3], it is estimated that the global gross resource is about 3.7 TW, which lies in the range of earlier evaluations (1-10 TW). However the exclusion of areas with very low energy (P ≤ 5kW/m) and in par-ticular areas impacted by sea ice decreases this resource by about 20%, resulting in 2.985 TW globally.
The total flux of ocean wave energy resource that goes through a line 30 nautical miles away from the coast is estimated to be 18 484 TWh, of which only 850 TWh (4.6%) can be extracted with state-of-the-art generators[4]. This represents 3.5% of the total electricity generated in 2015 is estimated to be 24 255 TWh [5].
Figure 1.1: Total Renewable Energy Installed Capacity[1]
On the other hand, [6] makes a similar estimate of the net theoret-ical energy resource at 2.985 TW, that is, 26148.6 TWh excluding areas where the wave power is below 5kW/km and areas with ice coverage. At the present time and on a global scale it is a very respectable energy source. This is even more the case when considering its local significance in the high-latitude countries where it reaches the highest levels. Currently, waves provide a gross power of 120 kw/m in the South Indian ocean, 90 kw/min the South Pacific, and 80 and 90 kw/m in the North Atlantic between 40°and 60°of latitude.
Furthermore, due to the effects of global warming, these magni-tudes can be expected to increase. 1 due to man-made global warming have consequences that drastically affect this status-quo.
1Since 1948, "the regions in the Southern Hemisphere with highest values
of wave energy are increasing at the highest rates with values from 0.4 to 0.8 kW/m/yr", while "North Atlantic and North Pacific are experiencing a moderate increase of 0.2 kW/m/yr". Furthermore, the impact of rising ocean levels, which should be expected to [7] ocean levels are between 30 and 180 cm by 2100, relative to levels in 1990
Figure 1.2: Total Ocean Energy Installed Capacity[2]
Nevertheless, the imminent threat of said global warming is the very reason governments and private entities are investing in devel-oping all available forms of renewable energy. The current project ap-proaches the extraction of the wave energy by approximating perfect extraction of the wave front’s energy as it traverses the buoy’s location. The main purpose of the thesis is to design and manufacture a suit-able winding for a transverse flux machine that is intended for wave-power generation. The specific type of transverse flux generator that the will be contributed to is the idea and work of Anders Hagnestål, researcher at the Royal Institute of Technology in Stockholm. He has come up with a design making it possible to convert the unusually slow motion of the waves to electricity in an efficient and low-cost way.[8] [9] [10]
To be specific, the task undertaken in the thesis was the design and construction of windings for a prototype to test the machine. Said pro-totype involves both a generator and a motor. They are identical in every dimension save the thickness of the cores, where the motor’s are wider, as shown in Fig. A.13.
The problem is complex; many interlocking parameters need to be considered in the design of the winding. A (non-exhaustive) break-down into smaller tasks and problems that had to be addressed in the work therefore can be seen in 1.2.
way as to minimize or eliminate the losses caused by circulating cur-rents through parallel winding due to magnetic flux leakage around the iron core, and how to construct the physical winding, or a proto-type thereof, in practice.
This research should help the reader better understand the problem of flux-leakage-induced circulating currents in machines that use par-allel conductors in their winding to conduct large currents, as well as the practical challenges that building and connecting such a winding raises.
Solving this problems allows for the construction of any similar machine with greater efficiency and power density, thus increasing the viability of any similar application, where energy needs to be extracted from a movement with a very wide and low range of frequency, and where the conditions require the usage of a high-current, low-voltage configuration.
In particular, it should establish the fundamental guidelines and tools for the completion of the construction of the winding for this specific prototype, as well as provide an example on how to proceed with the construction of windings for similar machines in the future, saving the reader time in exploration and experimentation.
1.2.1
Research Questions
The following questions were explored in this thesis, with an answer being proposed for each of them, and tested whenever possible:
• What is the shape and magnitude of the magnetic flux density field around the magnetic core in the areas occupied by the wind-ing?
• How to best transpose the windings to reduce induced voltages between parallel windings to a negligible level?
• Does this solution remain the optimal alternative in practice, given the challenges of its construction and maintenance?
• How to easily, cheaply, and quickly strip the insulation enamel from the extremities of the conductors that are going to connect to the power electronics?
• How to best connect the aluminum conductors of the generator with the copper bus bars of the power electronics?
• How to construct the winding in such a way that it can easily be fastened around both sides of the iron core of the electric ma-chine, which are physically separate from each other?
• How to construct a physical live-sized model of said iron core to function as a bobbin around which to build and consolidate the winding previous to its insertion?
• How to ensure that the winding holds its configuration once in the machine and subjected to the thermal and mechanical con-straints of its nominal functioning conditions?
• How much manpower would it take to construct the winding according to the method that we designed using the materials available? What changes in design or construction would im-prove this construction time?
1.3
Limitations
Technique and Know-how: Neither we nor anyone in the school had any experience winding machines of this size and characteristics nor the knowledge of the materials needed to do it correctly. The winding of forty parallel conductors in a single bundle around each core posed a peculiar challenge.
Time Constraints: Access to the lab and workshop were limited to only specific hours of the day. Due to continually trying new techniques, it was difficult to plan how long each task would take until it was well underway. Many unexpected difficulties in planning were encountered. Simulations were intensely time-consuming.
Budget: The project assigned to this team has been assigned very lim-ited resources, which led to most of the following limitations.
• There were no wire-stripping tools suitable for the type of magnet wire that was given. After many different tries, the best solution found was chemical: after research and exper-imentation, a combination of chemical solvents was found that could reliably and quickly dissolve the cable’s coating. • The stands that were used to support the bobbins in the
pro-cess of unwinding them had structural flaws in the shape of the shaft, the inertial, balance, and the friction, that made the process unwieldy and complex. Manual additions had to be implemented in order to make them functional, see Fig. 1.3.
(a) Right side fix (b) Left side fix
Figure 1.3: Bobbin Stand Fix
• To contain the conductor needed for each strand in the si-multaneous winding solutions, new bobbins had to be ex-pressly constructed, as shown in Fig. 1.4.
Figure 1.4: Bobbins to be wound with single strand
• To hold said bobbins in position, a dedicated rig had to be set, as shown in Fig. 1.5
Figure 1.5: Bobbin rack
Manpower: It was not possible to hire manual labor for the time-consuming tasks, or for those that would be physically demand-ing or require manual skill.
Logistics: It was not possible to order any products with significant lead time in a project where needs were discovered in an ex-ploratory way. Any acquisitions in addition to the pre-existing materials needed to be made from nearby distributors using the transportation means available. Much of the materials was recy-cled from the school’s workshop leftovers.
Space: It took a lot of time to get space to work in. From a small desk in a shared office, to a spot at the bottom of the stairs, to a corri-dor area between power cabinets and heavy electrical machinery in the building’s basement.
Due to the limitations as seen in 1.3, the priorities set by the thesis supervisor are as follows:
• Design build one functional winding that can be used for testing the electrical machine.
• Come up with a transposition method that can be reasonably ex-pected to minimize the winding losses.
• Stay within budget, finish on time, with the means at your dis-posal.
Therefore, the following choices were made:
• Instead of a detailed, dynamic, 3D simulation of the behaviour of the machine, including different types of winding transposition methods, a rudimentary 2D simulation of the machine and its flux leakage at different current phase angles was deemed suffi-cient.
• Instead of building the six winding pairs needed for the ma-chines, only one pair of windings was deemed enough.
• Instead of going into extreme detail on the Calculus and electro-physics involved in the phenomena here covered, an introduc-tory overview within the fundamentals was deemed sufficient. Instead, the focus of the thesis was directed towards the practi-cal considerations of the winding’s construction.
1.4.1
Literature
There’s a number of avenues of investigation that were deemed un-necessary or non-pertinent.
Most literature regarding losses in conductors due to eddy currents and/or current-crowding phenomena that reduce the effective cross-section of the conductors, is developed for frequency and/or high-voltage applications, and therefore does not apply to the problem at hand.
There’s a certain amount of debate regarding estimations of the to-tal wave potential, both locally and globally. There’s also a large body of literature regarding present experiments in the ocean wave energy sector and the state of the art therein. This was not explored beyond the broad strokes needed for the Background section (1.1).
1.4.2
Simulation
COMSOL Multiphysics was used for electromagnetic simulations. It might have been possible to make a more detailed simulation of the behaviour of the conductors.
• On COMSOL, the large, uniformed conductor could have been split into parallel strands of solid aluminum, linked in series ac-cording to each chosen transposition method. Running the sim-ulation could have then yielded more exact distributions of the current in the winding, and a more exact estimation of the losses. • The original COMSOL simulation could have been changed from a series of stationary simulations that identify a phase shift in the current with a position shift in the translator, to a time-dependent simulation that has the current be organically caused by the move-ment of the translator, rather than imposed as a simulation pre-condition.
• The whole machine could have been simulated in full 3D detail. All three suggestions share the same problem, in increasing levels: it is very time-consuming to do, be it in terms of implementing and configuring the simulation, or in terms of running it, as they require considerable processing power. Even the simple simulations that were actually run could leave our computers running at full power for sev-eral hours.
Because those simulations weren’t performed, it was not possible to obtain the parameters necessary to perform a full analytic model al-lowing a reasonably quick study of the different transposition schemes
In short, while more detailed simulation work would have been indispensable to obtaining an optimal result, the lack of time and re-sources, or, in other words, the urgency of building the physical bob-bins within a short time and with a small budget...
1.4.3
Testing
Given that by the time the winding were constructed and the thesis’ time was coming to an end, there was no magnetic core around which the materials could be tested, it was not possible to obtain the empiri-cal parameters of the circuit other than the resistance of the cables and of the lug connection.
Furthermore, as of the time of this writing, there isn’t a power source or sink available to provide or absorb the 180 kVA needed to simulate the circuit’s behaviour, and it is uncertain that the instrumen-tation available would be up to the task of measuring its behaviour.
1.5
Assumptions
The study begun with a number of assumptions, which were neces-sary to move forward. While some of them were tested, challenged, and rejected during the project, others remained in place, either be-cause it was impractical or impossible to verify them before the end of the project, or because doing so falls far beyond its scope.
1.5.1
Scientific Consensus
Well-established theoretical foundations such as Maxwell’s Laws and their correlates are taken as a given. Likewise, practical formulae, re-sults, and estimations, that were found in peer-reviewed scientific pa-pers and graduate theses, are treated as credible, and taken at face value. While it is not uncommon for published, peer-reviewed scien-tific papers to contain serious errors, verifying them falls outside of the
scope of this thesis, as such verification efforts can constitute enough work to be publications and theses in their own right.
1.5.2
FEM Simulation
• The geometry and characteristics of the simulated machine is considered to be sufficiently close to that of the finished machine, even though the simulation employs a uniformly distributed cur-rent density.
• It is assumed that the COMSOL simulation is a sufficiently accu-rate representation of the behaviour of the electromagnetic field around the magnetic core.
1.5.3
Winding Choice
• It was assumed that the winding would bend easily around the desired direction, and maintain straight orientation.
• It was also assumed that it would be a simple matter to keep track of forty parallel conductors and place them well.
• Aluminum was chosen because of its low cost, and issues relat-ing to the quality of terminations were not put into question. • It was assumed that the removal of the magnet wire’s polymer
coating would be a simple task.
1.5.4
Construction
• It was assumed that the methods employed for bonding the wind-ings together were sufficiently robust.
• The initial construction was made with the assumption that the windings would be forming large bundles.
1.6
Choice of Conductor Material
Some of the properties of copper and aluminum are compared in Table 1.1
resistance per length
The cost of the winding is estimated to be in the order of 5-10% of the total cost of the machine, but the winding losses represent 0.5% of the total power, in the order of 200 W per coil. This is also the reason why cooling is not a big concern: the windings produce barely more heat than a light-bulb. Therefore, the increased cost of using copper rather than aluminum is not justified by the corresponding increase in ampacity 1.6.
1.7
Literature Review
There is a fair amount of literature on topics resembling what is cov-ered in this thesis. Two common traits have emerged:
• The literature presents a solution but skips steps on how they got there, making replication difficult.
• The literature covers a specific topic which is close to the subject at hand. However, the methods presented in the former do not generalize to the latter.
In conclusion, the most crucial elements in this thesis build upon documents [12] and [11].
1.8
Current Crowding
The selected cabling given at the beginning of the thesis was chosen in consideration of the following effects:
• Joule effect. • Skin effect.
• Proximity effect.
• Leakage-driven eddy currents. • Racetrack effect.
However, this created a new concern, circulating currents. Minimiz-ing it it is the topic of this thesis. Below is a more detailed review of each of these effects and how they affect this specific problem.
1.8.1
Joule effect and conductor section:
Figure 1.6: Current Flux Through Conductor Section
dQ dV = J · E = J · J σ = J2 σ (1.1)
600V), and the power rating envisioned (180kVA), the current needed to be increased to a relatively large 300A. Consequently, in order to reduce Joule losses, it was decided that the total conductor section of one phase needed to be as large as possible.
The maximization of filling factor and power density of the wind-ing determined the choice of a quadrangular section shape.
Regardless of section shape, however, such a thick conductor would not only be difficult to bend and wield, but would leave a lot of room for eddie currents of different kinds to circulate within it, which would result in the various types of unnecessary losses listed above, and ex-panded upon below.
1.8.2
Conductor bending
Racetrack effect: When a conductor is bent with a small bend radius, current density increases towards the axis around which it is bent, as the current seeks to take the shortest path1.9. The sharper the turn, the stronger the effect, as seen in Fig. 1.8.
Figure 1.9: Current Density Variation[14]
1.8.3
Skin and proximity effects
Skin effect: The frequency of alternating current causes a synchronous change in the magnetic field within conductor (Fig. 1.10), which causes current density to migrate to the edges of the conductor (Fig. 1.11).
Figure 1.10: Skin Effect Cause[15]
The avoidance of the skin effect determined the splitting of the con-ductor in multiple parallel wires of equal section.
According to [16], the generic equation for skin effect depth, below which the current density drops below 1/e = 0.37 of the current at the
Figure 1.11: Skin Depth δ[15]
surface in a circular conductor, as long as the current is at frequencies far below fmin = 2π/(ρAlAlis given by 1.2.
δ =r 2ρ
ωµ (1.2)
Constant Value Unit Source
ρAl 2.82E-08 Ω · m [17] σAl 3.54E+07 S/m [17] r,Al 1.7 [18] epsilon0 8.85E-12 F/m [19] f 1 < f < 40 Hz µr,Al 1 [20] µ0 4π · 10−7 H/m δ 13.36 < δ < 84.5 mm
Table 1.2: Skin Depth Of Aluminum At 1 to 40 Hz
Table 1.2 shows all the relevant properties of Aluminum and esti-mates a skin depth above 13mm. The 4x2 mm aluminum conductors chosen are more than small enough for the skin effect to be negligible. The magnitude of the external magnetic flux leakage is in turn large enough that what little internal flux leakage there is might be entirely drowned out[21]. verifying this would be a topic for further research.
This separation in parallel strands reduces how far the current in the winding can migrate away from the center of the cross section,
leaving only a proximity effect.
Proximity effects: The fluctuating magnetic field caused by the alter-nating main current of one conductor causes in a nearby conduc-tor a back EMF which makes current density migrate away from said other conductor, as illustrated in Fig. 1.12.
Figure 1.12: Graphic Representation for the Proximity Effect[22] The increase in apparent resistance due to this effect is assumed to be negligible at the application’s frequency range.
1.8.4
Eddy Currents:
The need to reduce leakage-driven eddy currents determined the choice of a rectangular section, which was originally oriented so that the longer side would be parallel to the direction where the flux leakage density was expected to be largest, namely, transversal to the magnetic core. Construction constraints overrode that choice when it came to the in-dividual conductors: see 2.5.2.
Eddy Currents: Fluctuating magnetic field leakage coming from the magnetic core causes eddy currents in the conductor section plane perpendicular to the field, as seen in Fig. 1.13
Figure 1.13: Eddy Current In Flat Conductor Due To Transversal Mag-netic Flux[23]
1.8.5
Circulating Currents:
Circulating currents: A bundle of parallel conductors under a fluctu-ating magnetic flux form a mesh of conducting loops through which the flux induces a back-EMF and circulating currents that leave the total current entering and leaving the bundle unchanged.
Figure 1.14: Circulating Current One Pair Of Flat Conductors Due To Transverse Magnetic Flux[23]
It is possible to minimize the magnitude of said currents by trans-posing the conductors so that each pair of conductors crosses each other in the plane orthogonal to the direction of the leakage flux, in such a way the surface that is defined between each pair of parallel conductors is divided in two areas, where the flux traverses them in opposite directions. Thus, the EMF generated along the perimeter of one surface is equal and opposite that of the other, resulting in a
suffi-ciently small EMF that the circulating current is negligible, and so are the losses it causes.
The purpose of this assignment is, given all the previous design decisions, to generate a suitable transposition method and implement it in practice while constructing the winding.
1.9
Transposition
1.9.1
Defining the language
Bundled Wires
The construction of this linear generator requires the usage of a low-voltage, high current configuration.
In this configuration, the cable section needs to become very large to reduce Joule Losses (see 1.8.1). However, this opens it up to skin effect (1.8.3) and eddy current (1.8.4) losses.
In order to avoid this, the current is divided among parallel strands, the sum of the sections of conductor therein adding up to the desired total section.
Hereafter, the following terminology will be used: bundle refers to the collection of parallel conductors that carries the total current, while strand will refer to the individual conductors, and cable to the conduc-tor plus its insulating layer. In this section, conducconduc-tors will be treated as idealized to a single line, so they will be named ’strand’, ’cable’, or ’conductor’ interchangeably.
Time as a spatial metaphor
By envisioning the layout of the strands in terms of the process of winding them, one can phrase their spatial progress as a temporal one. One then says that the cable "spends time" in a position to say that it is laid at that position during a given spatial interval, or that the spatial regions between the bundle positions need to be "covered" by a pair of cables (that is to say, encircled or delimited) "for an equal amount of time".
Hereafter, this temporal language will be used alongside the spa-tial to facilitate ease of understanding. This temporal terminology is not to be confused with the time variable in the electrical machine’s
Figure 1.15: 180° transposition
movement. In this document, save for the formulation of the electro-motive force as a time derivative of the flux, the time variable will only be used in the context of phase angle when examining the state of the system at specific instants, as a perfectly regular periodic functioning is assumed.
Transposition Types
[11] helps us define two main transposition patterns, for a bundle made of two columns:
Rotation/Continuous The conductors switch places at regular inter-vals. Each conductor moves one slot above until it reaches the bottom, then rises up to the top of the next column.
360° transposition The rotation is at 360° each wire is back to the position in the bundle that it occupied at the beginning of the transposition, so that the bundle’s disposition is the same it was originally. See Fig. 1.16 and 1.17, as well as Fig 1.21 (c).
180° transposition The rotation is at 180° when the topmost wire at left column has reached the bottom of the same column. In other words, each wire occupies the opposite position to the one it was originally in, relative to the center of the bun-dle. See Fig. 1.15.
Mirroring/Discrete The positions are flipped alongside either the hor-izontal or the vertical symmetry axis of the bundle. See Fig. 1.18, as well as Fig 1.21 (a) and (b).
Figure 1.16: 360° transposition
Figure 1.19: Strand Circuit [24]
Circulating Currents And The Losses They Cause
The splitting of the current into a bundle of strands, however, cre-ates a new problem. As shown in 1.19 each pair of parallel strands forms its own closed circuit, and any variation of an electromagnetic flux traversing the surface the circuit encloses results in an electromo-tive force (emf) that propels a circulating current through that circuit, adding itself to the main current on the strand in which they share a direction, and subtracting itself to it in that in which their directions are opposite, as seen in (1.3) and (1.4).
I1 = i1 + I/n .. . In = in+ I/n (1.3)
In those parallel strand circuits, there is very little to impede the current caused by each emf. The resistance of the cable is small to be-gin with, and the reactance is likewise very small at the expected fre-quencies. Therefore, even small emfs due to otherwise negligible flux leakage can cause relatively large currents, and, therefore, relatively large losses, which may create heat problems in the generator.
From the perspective of the stator’s electric terminals, where all the bundle’s conductors come together, those electric currents end up cancelling out; they increase the current in one conductor the same as they decrease it in the other, and so they amount to a null sum (1.5). However, the Joule effect heat losses are proportional to the square of
k=1 Ik = k=1 (ik+ I/n) = I (1.4) n X k=1 ik = 0 (1.5) X P = XIk2R (1.6) = RX(ik+ I/n)2 (1.7) = R X i2k | {z } ≥0 + 2XikI/n | {z } 0 +X(I/n)2 (1.8) X P ≥X(I/n)2R (1.9)
In the present case, the magnetic flux leakage outside the motor core is sufficiently large that the circulating currents in the parallel strands resulting from it cannot be neglected, and require a counter-measure.
1.9.2
Minimization
In general, the method employed is to minimize the emf by setting the parallel strands in such a way that the magnetic flux leakage traversing the surface enclosed between them is made as small as possible, if not null.
Each circuit’s emf can be cancelled out by crossing the cables over in such a way that the flux leakage causes a positive emf in one region and a negative emf in the other, the latter cancelling the former out.
As the total flux encircled by the circuit is a result of the linear ad-dition of each component of the flux density, the problem is made more tractable by looking into each Cartesian component separately, as shown in 1.20 and (1.10).
Figure 1.20: Flux Density Decomposition Vs. Surface Normal Vector Z S ~ B·d ~S = Z S (Bx, By, Bz)·(dSx, dSy, dSz) = Z S BxdSx+ Z S BydSy+ Z S BzdSz (1.10) Furthermore, in the case of electrical machines, in the relatively small regions containing the electric conductors, and given the rel-atively small magnitude of the flux density, the original assumption was that it would be fair to approximate the variation of said flux den-sity as linear in the space the conductors occupy. In that local context, it was estimated to be diminishing linearly as the distance from the air gap and from the iron core increases. This was the approach used in [12].
The following subsections show how the problem was approached theoretically with increasingly-complex behaviour of the flux. Figure 1.21 is used as reference.
1.9.3
Flux Density Distributions And Transposition Schemes
Uniform Flux DensityWhen the normal flux density component is constant along the plane, each pair of parallel conductors must, as seen from that plane, cross each other in such a way that two regions so enclosed are of equal surface. The first region will have a normal vector pointing out of the plane, the second pointing in, and the sum total of the flux over each surface will therefore be equal and opposite.
To compensate the flux, it is enough that each pair of cables cover the same total area in positive and negative.
The simplest solution is then to perform one single transposition in the middle, where all cables will change position to the one opposite the occupied originally. Case (b) in Fig 1.21 is an example of such a solution. This is also the rationale behind twisted pair cables, as seen in Fig 1.22 and Fig 1.23.
Flux Density Variable On The Cross-Section But Constant Along The Bundle Length
This is the case when the transversal flux density is constant alongside the length of the bundle, but varies relative to height or depth.
It is trivial to generalize from the case where the flux density will vary along the ’depth’ or ’height’ but not both at the same time. The bundle is then modeled as flat, with all the cables existing in one plane. The greyscale transition in Fig. 1.21 represents how the flux density normal to the plane is constant along the "length" coordinate and
upon, on the next step, it will return to the "top".
When the conductors are bus bars and are stacked in a single col-umn, the resulting type of bundle is known as Roebels Bar. In the liter-ature, we have found it most commonly associated with long cylindri-cal engines. However, this method can be generalized to cases when we have more than one "column" of conductors, and the field varies along the "depth" as well as along the "height". Once the "first" con-ductor, that was initially at the top of the first column, reaches the bottom rung, it will then move on to the "top" of the next column, with the one at the bottom of the deepest/last column taking its place in the first, and so on. The process, whereby the "first" conductor undergoes such a journey until it is back in its original "position" in the bundle section, will be hereafter known as a 360° transposition sequence.
Several approaches present themselves:
• The simplest and roughest is to assume that the field is unifrom and apply a simple mirroring. All emfs won’t be cancelled, but if the average flux across the plane is non-null, the component of the emf due to said average flux will be cancelled out.
• The most complex one is to modify the separation between ca-bles accordingly so that the flux enclosed between two successive cable positions remains identical. If so, then a simple mirroring would work well. This would be possible only if the linear distri-bution of the flux density remains constant: as soon as the gradi-ent changes, the spacing among the cables would need to change accordingly. Furthermore, it is quite difficult to space conductors this way in practice. This approach is therefore plainly impracti-cal.
• The most effective approach is to have each pair of parallel con-ductors enclose each "height" interval of the plane in equal amounts, both "in positive" (with the normal component of flux density pointing in the same direction as the surface vector) and "in neg-ative" (with the flux density pointing in the opposite way), so
that the total sum of normal flux density over surface amounts to zero. If one were to envision the layout of the strands in terms of the process of winding them, one could also say that the re-gions need to be covered "for an equal amount of time". This can be achieved by having each cable spend an equal amount of ’time’ at each ’position’. This can be achieved by using:
– A 180° transposition sequence. (see Fig. 1.21 (d)).
– If the number of conductors is a power of two, a main mir-ror transposition of all wires in the bundle’s midpoint, then two secondary mirror transpositions for the top and bottom subsets of cables at the quarter- and there-quarter-point, etc. (see Fig. 1.21 (c)).
The mirror transposition method (Fig 1.21 (a) and (b)) remains suf-ficient if there is only one pair of cables.
1.9.4
Linear Magnetic Field In Both Transversal
Direc-tions
So far, the different possibilities have been be examined from the per-spective of a single plane, upon which the bundle is laid flat, and where only the magnetic flux density perpendicular to the plane will be taken into account. Because the total emf is a linear combination of the projection of the magnetic flux on each direction alongside the plane between cables, as long as the behaviour of the magnetic field is con-stant alongside the longitudinal axis of the bundle, it is possible to consider each plane separately, and freely combine the corresponding transpo-sition solutions defined for each plane.
This is roughly the case inside the slots of long electrical machines, such as the turbines studied in [11]. However, this doesn’t apply if the flux density does not behave according to this assumption, which turns out to be the case in the machine studied in this report.
1.9.5
Generalized Magnetic Flux Density
When the flux density varies alongside the longitudinal axis of the bundle, things become much more difficult. It becomes essential to find symmetries and regularities for which to design ad-hoc transpo-sition schemes. In the worst case scenario, the field may turn out to be
1.9.6
The usefulness of the simple crossing:
It is common practice to twist cables in pairs to increase electromag-netic compatibility by reducing electromagelectromag-netic radiation and cross-talk between neighboring pairs, and to improve rejection of external electromagnetic interference, as seen in 1.23.
In fact, the simple crossing remains useful when dealing with a two-wire bundle, in every instance where the magnetic field’s compo-nent normal to the plane containing the wires presents an even sym-metry relative to the plane that’s transversal to the cables’ direction and bisects them at the middle of their length. It also remains useful if the flux density is spatially periodic along the length of the bundle and the wires are made to cross at regular intervals equal to the spatial period. This can further be generalized to apply in
Methods
The study was performed in the Department of Electrical Power Engi-neering at the Royal Institute of Technology in Stockholm between Jan-uary and August 2018. The materials used include, in the exploratory phase, digital CAD software SolidWorks®, FEM simulation software COMSOL®, and mathematics software MATLAB®. This allowed the determination of the optimal transposition system. In the secondary and most important phase, implementation was performed manually, including the construction of relatively complicated systems to attempt the winding without interruption.
2.1
FEM Study Of The Magnetic Flux
On [11] and [12], methods are proposed for the analysis of the be-haviour of circulating currents between parallel strands, and for the study of how one current would interact with another. However, a fea-sibility difficulty was met immediately: while these studies dealt with 10 and 16 strands at a time respectively, the current design was ini-tially meant to be 100 parallel strands. This increased the difficulty of both formulating the problem mathematically and processing the sim-ulations numerically, to the point that the hardware we were granted couldn’t even handle a CAD sketch of 100 rectangles together, let alone solid figures with twisting and winding.
A later downsizing of the machine made the number of parallel windings in one bundle to be revised downward, settling at 40 parallel strands.
Nevertheless, the simulation results ended up suggesting a method
On the COMSOL model of the machine provided by the supervisor, the simulation results suggested symmetries in the electromagnetic field in the core, that could be exploited for a simple generic solution using only one twist, no matter how many layers of winding are used.
Figure 2.1: Magnetic Flux Density and Flux Lines Across the Whole Model.
The figures suggest the following:
• The magnetic flux density’s magnitude, as well as the magnetic flux lines, form a mirror symmetry alongside the middle plane of the machine.
Figure 2.2: Magnetic Flux Density and Flux Lines: detail.
penetrate the other side with the same intensity in the horizontal axis, but the opposite one in the vertical.
• This is true within the space occupied by the conductor itself. That is to say, this applies to the flux leakage.
This hypothesis is tested by taking a large number of measuring points of the magnetic flux leakage in the conductors, and exporting the Bx and By values, as shown in Fig 2.4 and 2.5 into tables. The
Figure 2.3: Magnetic Flux Density: magnitude and vectors plot within the conductors.
tables were then imported into Matlab, where they were separated by axis, and a statistical estimation of the data fit between the following values was made. If one sets the origin of coordinates at the center of the machines, then the hypothesis being tested is
Figure 2.4: Magnetic Flux Density: vectors plot within the conductors.
Figure 2.5: Magnetic Flux Density: vectors plot within the conductors, meshing quality test.
Bx(x, y) = Bx(−x, y) (2.1) By(x, y) = −By(−x, y) (2.2) The relevant Matlab code is referred to in the Appendix.
• The magnetic field’s horizontal component presents an even sym-metry along the x axis, relative to the middle plane 2.1.
• Its axial/horizontal component presents an odd symmetry along the y axis, relative to the middle plane 2.2.
Other than that, the magnetic field is very irregular and far from linear, especially as one draws close to the middle of the machine (see Fig. 2.3 and others in 2.2).
2.3.1
The Ideal Solution
Assuming that the field is constant along the z dimension (the one per-pendicular to the plane in wich the COMSOL 2D simulation is made), one can propose treating each "run" that the bundle does across the top or the bottom of the core like one would a slot in a rotating ma-chine, with the transition between top and bottom treated here as that between two slots is treated there. Fig. 2.6 shows a similar transition as one bundle leaves one layer and enters another in a lower position. According to the results found in [11], a transposition method con-sisting of a 360° process performed once for each pass above or below the core, with a mirror-flip transition in the "end" side, would practi-cally eliminate all circulating currents.
However, as seen later in 2.5.2, even winding a single bundle with all cables straight and parallel was impossible to in a timely manner do while keeping all cables properly oriented, within the limitations of this project. Doing so with the cables performing a full transposition in a uniform and orderly fashion was not at all within the realm of practicality.
It should be noted that, for the solution to be entirely perfect, the cable should be laid on the core along the edge (the shortest side) to reduce eddy current losses. This is further discussed in 2.3.3.
Figure 2.6: Ending of a double layer of winding in a rotating machine, flattened
2.3.2
One Transposition per Run
Keeping the cables in the same order during one run and transposing them between runs would be a reasonable method if the magnetic flux were uniform along the length as well as the height. In that case, the simple transposition methods discussed in [12] would suffice in deal-ing with such a field.
However, that is not the case: transpositions based on the logic of "each pair should spend an equal amount of time in each region" break down when the region’s field varies along the length.
Then one needs to consider the symmetries of the field.
By’s odd symmetry for two-column vertical bundle configurations, each pair of cables’ φy is cancelled so long as the layers remain at the same height when they are in the same turn (at the same distance relative to the center), and undergo a mirror flip over the vertical plane. With more than two columns, however, this becomes less and less true as the number of columns increases.
Bx’s even symmetry As long as the bundles are in narrow vertical columns, the y field is cancelled so long as the layers remain at the same height and don’t cross.
like a helix around the core, the vertical flux leakage cannot create cir-culating currents: the only remaining concern are the eddy currents.
Conversely, when the bundle is designed to be a single horizontal file, wrapped around the core like a spiral, the horizontal flux leakage is similarly disarmed, leaving eddy currents as the only concern.
Since the vertical field is estimated to be an order of magnitude larger than the horizontal, a vertical configuration was chosen for the construction.
Single-transposition solutions
Single-transposition solutions are the simplest to achieve: they require transposing the cables only once, when making the jump from the left core to the right one. However, when combining with symmetry ef-fects in the flux, the results can be tricky. Nevertheless, the rule of thumb is as follows:
• When faced with odd symmetry in the flux, mirroring the config-uration across the symmetry axis has the best chance of roughly reducing the total flux across each pair. This entails performing no transposition between the cores.
• When faced with even symmetry, doing the opposite is what is required, and a mirror transposition between the cores is recom-mended. This is achieved by folding the bundle around the Y axis.
It is possible to combine both solutions by interlacing the wind-ings as they are being folded. In the device built for this project, this could have been achieved by opening the funnel and interchanging the cables’ positions alongside the the machine’s X axis (which, in the rig, happens to be the vertical direction, because the bobbin is being wound on its side). In simple terms, open the rig, and trade the cables’ positions vertically, two by two.
However, combining both solutions undermines the cancellation of the vertical flux, as the vertical flux is not uniform along the vertical axis (on average, it drops significantly as one moves away from the core), and thus the flux each horizontal pair is exposed to is no longer cancelled. However, it is better than not doing it at all.
Edge vs. Flat
Bending the cable around the edge side is much more difficult and del-icate to do well than bending it around the flat side. However, when it comes to avoiding eddy current losses, bending it around the edge side is preferable. The flux density in the winding is much larger in the vertical than the longitudinal direction, by an order of magnitude (see 2.1).
For equal magnetic flux density, the losses due to eddie current are proportional to the transversal dimension of of the cable that is orthogonal to the magnetic field, squared. Here it is called the width. Given that the conductor’s flat side is twice as wide as its edge side, as shown in Fig 2.7, when the conductor is turned, from lying on its edge relative to the core, to lying on its flat instead, the eddy currents are expected to quadruple (2.6) [26].
2.4
Winding Choice
Magnet wire is the winding material commonly used in electrical ma-chines that needs tight coils of insulated conductors. There are a lot of different types of magnet wires with different kinds of shapes, sizes and heat properties. By reading into the price and physical differences between aluminum and copper magnet wires of different kinds to-gether with the practical knowledge we gained during the construc-tion work of the winding we would say that it would be smart to choose something that is square instead of rectangular. The aluminum strands we used were very pliable but at similar sizes even copper would be pliable
Below are some given/wanted specifications from the thesis super-visor: VLL = 750V ILN = 300A f = 4to40Hz Bmax = 1.7T Sf e = 0.0531m2 ΦB = B · S = 0.09027Wb
While the power electronics system is rated for 1200V, the supervi-sor determined that 750V should be the voltage to be aimed for.
Roughly 300A is what the power electronics setup for this proto-type can handle.
The voltage thereby generated is given by (2.7):
Emf = −N∂(Bmax∗ Sf e)
Therefore, the number of turns should be the one given by (2.8):
N = Emf
BmaxSf e2π ∗ f
(2.8)
2.5
Winding construction method
When the transposition scheme was determined, the work on con-structing the prototype began. This was not a straightforward pro-cess: it required the improvisation of intermediate technical solutions to put it into practice. As new obstacles were encountered, new ne-cessities appeared, and new ways of overcoming them had to be put forward. A lot of careful thinking and precautions are natural when doing something for the first time, and these were the conditions the project was under.
• The winding needed to be constructed around a bobbin.
• Said bobbin needed to replicate the geometry of the magnetic core.
Standard procedure is to construct the winding around a portable bobbin, and then coating the whole in resin or glue, so that they re-main one solidary unit. This solidary bobbin is then used to carry the winding and slide it into the machine.
However, in this case, it was given as a specification that the wind-ing should be built in such a way that it could be incorporated into the machine without a bobbin to support it.
The motive for this instruction was a drive to include as much alu-minum into the space between the iron core structure as possible, in order to reduce electric losses, without concern for guaranteeing struc-tural support to the winding in the way bobbins usually do. It was es-timated that the metal structure of the motor would keep the windings in place well enough by itself.
Therefore, instead of building a solidary bobbin for each core wind-ing, there would be a assembly bobbin, around which each and every winding would be built, and then removed, to be stored until the time came to build the core.
Said assembly bobbin will hereafter be known as the core-replica bobbin, or CRB, as wooden replica of the core was deemed as the best option originally.
Design
The design is the same as shown in Fig. 3.1, minus the supplemen-tary augmentations to upgrade it to the motor core’s dimensions. The details are shown in the schematics in Fig. A.14.
Materials
The CRB was made out of wooden panels cut into rectangular shapes as seen in the technical drawings. This material was chosen because it was the most readily-available in the electrical department’s work-shops, as well as the easiest to ’work on’.
The thickness of the panels themselves didn’t matter much, so long as the external shape of the core was faithfully reproduced. Maintain-ing reasonably straight lines and surfaces along the sides was, how-ever, quite important for structural integrity. Therefore, the type of wooden panel chosen didn’t matter much, so long as it was stable.
The edges of the wood panels were not quite straight originally, and errors in tool manipulation could have perpetuated the problem. Therefore, it was important to proactively and parsimoniously deter-mine the lines along which the wood panel should be cut.
The accurate drawing of the perimeters on the timber was achieved through the combined usage of redundant drawing tools, similar to the kind used in paper technical drawing, but with characteristics spe-cific to wood- and metal-working. The tools were:
• an edge square (see Fig. A.1): it allows the drawing of lines per-pendicular to the edge against which the broad section is held. • a straightedge ruler (see Fig. A.3): allows the drawing or
con-firmation of straight segments on flat surfaces, the measurement thereof, and can be a support for the flat square.
• a flat square: allows the drawing or confirmation of straight an-gles, and, slid alongside the straight edge, can be used to draw parallel lines.
• a compass (see Fig. A.6): allows the drawing of arc circles and the confirmation of equal distances.
• a caliper (see Fig. A.5): allows the measurement of distance be-tween surfaces.
The method described in Fig. A.6a complements the straightedge, while the one in Fig. A.6b complements the usage arithmetically di-viding a length and then using a graded ruler to measure whenever segments need to be divided in equal lengths, such as when determin-ing where to place the drill-holes.
Then, using a table circular saw (Fig. A.12) to cut down the pre-existing, very large wooden panels to a manageable size, then a band-saw (see Fig. A.11 to further cut it down to roughly the exact desired dimensions. Any further irregularities would be sanded off using files or sandpaper.
The aforementioned geometric methods were also useful for the purpose of drawing upon the surface of the base of the bobbin the positions where the side panels should go, as well as where the holes for the wood screws should be pre-drilled. This decision is further discussed in 3.3.3 and 4.4.2
2.5.2
Winding the bobbin
The following subsections describe in detail the construction of the winding cable bundle and winding procedure of the winding-coils. The following procedures to perform the winding were chosen with the desire to avoid cutting the winding in the middle, due to the dif-ficulties surrounding Aluminum terminations. This was thought to make the process less complex, but it turned out to instead increase the complexity.
Roughly 600kg corresponding to 28 000m of magnet wire were al-ready bought and stocked prior to the start of this thesis work, Con-sequently, that was the material that had to be used. The magnet wire came divided in 12 wooden bobbins, each weighing around 50 kg. The magnet wire stocked was an rectangular 2x4 mm aluminum strand with and 0.1 mm polyester-imide/polyamide-imide coating rated 180◦C.
Figure 2.8: Magnet wire bobbins in wooden boxes ordered from Zheng Zhou LP Industry Co,.LTD.
Figure 2.9: Schematic view of the different section lengths of the wind-ing
The 20x2 edge wound configuration
The bundle was made of two layers of twenty strands and having the total width of 84 mm and a height of 4.4 mm. Both the bundle and strands will be wound on the edge side in a pancake manner(bending on the short 2 mm side of each strand and on the 4.4 mm side of the bundle). This was due to the transversal magnetic flux being estimated a factor ten larger than the axial magnetic flux in the space where the winding shall sit as explained in 2.3.3.
Each strand in the bundle was approx. 115 m long thus correspond-ing to the length of havcorrespond-ing it wound 76 turns around the CRB. The con-struction of the bundle and winding began by building forty bobbins, one for each of the 115 m strands.
The material for the 40 boobins:
• 8 pieces of 2.5 meter wooden 45mm x 45mm beams
• 10 pieces of 1220x2440x3 mm hard-board for the circular sides Because of the large amount of bobbins to be made they were made a CNC milling machine able to take 1220x2440 mm boards was used as aid.
Figure 2.10: 8 circular parts milled and pre-drilled holes made for the six 40 x 40 x 55 mm spacers
Figure 2.11: Bobbins made for holding around 120 m of strand
The result was a stand that was able to hold one bobbin in place while winding them with 115 m of magnet wire from the 50 kg man-ufacturer bobbin.
A weighing scale was used instead of measuring the actual length of the strand. When the weight was increased to a certain point the bobbin had the amount of winding co-responding to the weight.
[]
When all the 40 strands were wounded the bobbins were put into a bobbin rack, separated into two rows holding 20 bobbins each, as seen in Fig. 2.12.
The purpose of this contraption was to make it possible to feed each strand independently of one another. This was very important because of the way the bundle was to be wound, where the inner part of the bundle would unreel each turn less strand from its bobbin than the strands on the outer side of the bundle. Basically, the contraption was meant to permit this: if one strand is unreeled from the bobbin
Figure 2.12: Bobbin rack
Figure 2.13: Midway strand support
rack, all the other strands should stay still.
Because of the large width of the bobbin rack, it was necessary to be able to get the strands near each other, with the purpose of form-ing the 2x20 strand bundle for this a "node"/"funnel" contraption was designed as seen in Fig. 2.14
To further bring the strands together and keep them from criss-crossing without control, a device was improvised using zipties. Fur-thermore, colored zipties were added in sequence to help in keeping track of the cables, as seen in Fig. 2.15.
Figure 2.15: Ziptie device
The bundle was now ready to be wound around the CRB, and, for this to work, the CRB was standing on a table that stood on wheels2.16, which made it possible to translate and at a fixed height on the hori-zontal plane as needed, and rotate it around the vertical axis (see Fig. 2.17 and 2.18).
It was quickly seen that it was impossible to wind it because of the twisting of the strands each time a corner was turned around the CRB. The problem was so grave that there was a need to clamp the cables down on the bobbin using a wide beam in order to simply be able to turn the corners. The process was physically strenuous, as the bobbins needed to be turned around consistently. It was mentally stressful, as one had to constantly keep track of all cables’ positions; the ziptie device was very helpful in this regard, but, ultimately, utterly insuffi-cient. All of this together made the process extremely time-consuming. Despite all those efforts and costs, the result remained inaccurate, and the cables couldn’t remain organized (see Fig. 2.19). The winding was therefore aborted.
The conclusion reached was that what made the bending the most difficult was the fact that it was being done edge-side, that is to say, along and against the shortest side of the conductor. Any irregulari-ties in the deformation were amplified and, due to the plasticity of alu-minum, difficult to rectify. We therefore decided to rotate the strands 90° despite the fact that this would increase the eddy currents by a fac-tor of four (see 2.3.3), it decreased the difficulty in the construction so much that it was deemed the only way to move forward.
Figure 2.16: Core replica bobbin on table with wheels
Figure 2.17: What the winding around the core could have looked like
Figure 2.18: Top view of the 20x2 attempt
The 40x1 flat side bent configuration
The flat side bent configuration however, turned out to be catastrophic, as can be seen in 2.20, 2.21 and 2.22; bending on the broadside when the cables were coming from the bobbins oriented towards edge re-quired each of them to undergo a twist along the way. Despite stren-uous efforts, to perform such a transition while simultaneously main-taining a consistent column organization turned out to be completely
Figure 2.19: The clamp does not help much
unfeasible.
Figure 2.20: Top view of the 40x1 attempt
Figure 2.21: Side view of the 40x1 attempt
One conductor at a time
Finally, the only viable remaining solution was to build the winding one conductor at a time. This necessitated abandoning the idea of hav-ing continuous cablhav-ing between both bobbins in a phase across the gap between cores, as it was not possible to move on to a next conductor while remaining linked to the previously winded conductor’s bobbin
Figure 2.22: The ziptie device at the 40x1 attempt
without carrying said bobbin along with the CRB; it would be neither practical nor sensible to carry forty bobbins of winding under the ta-ble. The solution is explain in thorough detail below in the Results section.
2.5.3
Damage to the Insulation: Prevention and
Cor-rection
During the construction, the winding was damaged on several occa-sions. As this was in the middle of the winding, there was no possibil-ity of using common shrinking tube, and abandoning a whole wind-ing was deemed excessive. A solution was found in dielectric tape, as shown in 2.23; the data-sheet for it is in A.12. Rated 7.5kV, it was deemed sufficient.
Figure 2.23: Dielectric Tape
