Magnetically Levitated 2-Level Slice Motor for Application in High Purity Process Environments


Doctoral Thesis / Dissertation, 2010

194 Pages, Grade: 1


Excerpt

Contents

Acknowledgments

Abstract

Kurzfassung

Notation

1 Introduction
1.1 High Purity Process Environments
1.2 Motor Requirements
1.3 Motor Concept
1.3.1 Magnetic Bearing Unit
1.3.2 Drive Unit
1.3.3 Motor Frequency Converter
1.3.4 Magnetically Levitated 2-Level Motor
1.4 Overview of the Work

2 Design of the Magnetic Bearing Unit
2.1 Basic Considerations
2.1.1 Force Generation in Magnetic Circuits
2.1.2 Principle of Proposed Magnetic Bearing
2.1.3 Characterization of the Levitation Properties
2.1.4 Interference with Drive Unit
2.2 Selection of Geometrical Parameters
2.2.1 Influence of Rotor Permanent Magnet Depth
2.2.2 Influence of Stator Permanent Magnet Depth
2.2.3 Influence of Permanent Magnet Height
2.2.4 Summary of Geometrical Parameters
2.3 Scaling Laws of the Magnetic Bearing Unit
2.4 On the Feasibility of a Full Circumferential Drive Unit

3 Design of the Drive Unit
3.1 Basic Considerations
3.1.1 Drive Topology and Layout
3.1.2 Drive Segment Opening Angle
3.1.3 Drive Unit Height
3.1.4 Rotor Drive Iron Thickness
3.2 Drive Segment Tooth Shape
3.2.1 Need for Drive Tooth Shape Optimization
3.2.2 Drive Tooth Performance Investigation
3.2.3 Investigation of Saturation Effects
3.3 Optimization of Acceleration Capability
3.3.1 Contributing Mechanisms
3.3.2 Physical and Mathematical Background
3.3.3 Optimization Routine
3.4 Summary of Construction Parameters

4 2D vs. 3D FEM Simulation
4.1 Characteristics of 2D and 3D Simulations
4.2 Results of Investigative Comparison

5 Implementation and Verification
5.1 Experimental Setup
5.1.1 Laboratory Prototype
5.1.2 Frequency Converter
5.2 Experimental Verification
5.2.1 Magnetic Bearing Unit
5.2.2 Drive Unit

6 Concept Comparison
6.1 Motor Concepts
6.1.1 Magnetically Levitated Homopolar Motor
6.1.2 Bearingless Fractional Pole/Slot Motor
6.1.3 Bearingless Segment Motor
6.2 Comparison of the Motor Concepts

7 Conclusion and Outlook
7.1 Conclusion
7.2 Outlook

Bibliography

List of Figures

List of Tables

Curriculum Vitae

Acknowledgments

I would like to thank my supervisor, Professor Dr. Johann W. Kolar, for the opportunity to pursue my PhD thesis under his guidance at the PES laboratory. Due to this opportunity I learned how to conduct a higher level of quality research. I also have to thank him for the many opportunities he gave me during this work.

I am very grateful to Professor Dr. Jorma Luomi for agreeing to be a co-examiner for my PhD exam and for his very helpful feedback regarding this thesis.

Since this PhD thesis was carried out in close collaboration with the Levitronix GmbH, I would like to express my gratitude to all the em­ployees from Levitronix, especially to Dr. Reto Schöb and Dr. Natale Barletta for giving me the chance to work in such an interesting and challenging environment.

I would like to thank all my former colleagues at ABB Corporate Research for encouraging me to pursue a PhD degree, especially Didier Cottet and Wolfgang Knapp, with whom I shared an office and with whom I am still good friends.

Many of the results in my thesis are based on the productive conver­sations I had with Dr. Thomas Nussbaumer. Therefore, I would like to show my gratitude to him for always finding time to provide me useful input and for being a friend whom I could talk to outside the scope of my work.

Many thanks to all my ETH colleagues for the pleasant stay at the lab and for the support, especially the group from Technopark, including Klaus Raggl for being there during difficult times and Thomas Schnee- berger for always finding time to help me out. I would also like to thank Marcelo for showing me the enjoyment of digging deeper into the smallest problems and Andreas Müsing for sharing his flat with me.

My gratitude goes also to the PES staff, Peter Seitz for all the help with the prototypes, Peter Albrecht for always having the right compo­nent when I needed it and Roswitha and Isabelle for helping out with administrative problems.

My stay in Switzerland would not have been so much fun without all the friends I made there. I would like to thank them all, especially Markus Weiss and Alex Ilic for forcing me to the gym each morning, Daniel Aggeler for the Swiss German lessons and Uwe Badstübner for being a very good friend.

Special thanks to my friends Anthony Karloff and John Schönberger who helped me with proofreading this thesis.

Without the support of my family, the writing of this thesis would not have been possible. I would like to thank my mother Silke Karutz for her year-long support and for encouraging me in every step I took. Thanks to my sisters Juliane und Annette for serving me food during my studies and for being there to listen.

Last but not least I would like to thank my girlfriend Insa Riese for her love, her support, her smile and all the great moments we shared together. I hope there will be a lot more to come. Nie wieder ihle. Danke.

Cologne, 25th August 2010 Philipp Karutz

Abstract

In recent years, the demand for ultra-clean process environments for spin processes in high-purity industry branches, such as pharmaceutical, biotechnology and semiconductor industries has been growing. In these industries small particles generated through lubricants and wear in the bearings can damage the processed structures.

The implementation of magnetically levitated motors in these appli­cation fields offers the advantage of a contactless and wearless operation. Furthermore, due to the fully circumferential air gap of such motors, a process chamber can be inserted into the air gap that creates a com­pletely encapsulated space. In this space process dependent conditions, such as pressure, temperature, humidity can be provided locally and cost efficiently.

A high acceleration capability of the motor is crucial for these pro­cesses in order to keep the process times low and increase the equipment throughput. Additionally, the achievement of high rotation speeds in the order of several thousand revolutions per minute is demanded by the processes.

In this thesis, the conception, design and optimization of a magnet­ically levitated slice-shaped motor, that fulfills the industry’s demand for high acceleration capability and high achievable rotation speeds is presented. Additionally, a high purity environment is ensured through an air gap large enough to accommodate a mechanically stable process chamber wall.

The slice motor, which features a small motor height compared to its diameter, allows a very high level of compactness. The motor is implemented with a homopolar magnetic bearing and the permanent magnet synchronous drive on two circumferentially and axially shifted levels, giving the motor its name: “Magnetically Levitated 2-Level Motor (M2M)”. Through the resulting magnetic decoupling, the drive unit can be designed independent from the bearing unit, aiming for maximum acceleration capability and maximum achievable rotation speed.

Due to the two-level nature of the motor the bearing design is more challenging. Factors such as tilting issues and avoidance of couplings between bearing and drive unit must be considered. These issues are investigated in detail in this thesis.

A general classification and applicability of magnetic bearing types suitable for the application at hand is presented. The scaling laws con­cerning stability, stiffness and dynamics for the magnetic bearing are presented and are supported by analytical design guidelines addressing typical bearing parameters, such as permanent magnet and iron dimen­sions. The actual design of the magnetic bearing unit is then explained based on 3D finite element method (FEM) simulation results. The im­pact of different stator drive structures, which can be segmented or fully circumferential, on the bearing parameters is investigated in detail by means of 3D FEM simulations.

The drive unit is optimized for high acceleration capability and high rotation speeds in two steps. First, the optimal stator tooth shape is identified taking the high occurring ampere-turns values into considera­tion that are necessary to generate sufficient torque with the large im­plemented air gap. It is shown that the simplified straight tooth shape is more than adequate for the motor at hand. The findings can also be applied to other motor applications, where saturation effects rather than thermal issues limit the performance.

In a second step, an analytical optimization supported by 3D FEM simulation results is carried out. Here, the number of winding turns per drive phase and the tooth dimensions are varied in order to identify the optimal parameters that result in the smallest acceleration time for a given process speed span. The presented optimization method can be applied for any setup employing a permanent magnet synchronous machine.

In order to prove the necessity of 3D FEM simulations an investigative study is presented that compares the torque results of 2D and 3D solvers against each other. Here, a modeling error can be defined and general conditions, such as the air gap length, motor height and ampere-turns values, allowing 2D simulations with similar accuracy than for the proven 3D simulations are formulated. For the given setup it is shown that only 3D simulations achieve a good accuracy and that the ampere-turns value as an indicator of the degree of saturation is a crucial parameter when deciding for an appropriate simulation method.

The scaling laws, design guidelines and optimization results are veri­fied on a laboratory prototype. Additionally, the experimental setup and the applied control schemes are presented.

The prototypes performance parameters, which include acceleration time, maximum rotation speed, radial and axial displacement during ac­celeration, are then qualitatively and quantitatively compared to other existing magnetically levitated slice motor topologies. The major ad­vantage of the prototype system in terms of maximum rotation speed is highlighted.

Kurzfassung

Der anhaltende Trend zur Miniaturisierung und die steigenden Rein­heitsanforderungen in der Pharma- und Halbleiterindustrie sowie in der Biotechnologie verlangen nach immer reineren Prozessbedingungen, da bereits kleinste Partikel die zu prozessierenden Strukturen beschädigen können.

Bei zahlreichen Bearbeitungsprozessen ist es notwendig die Prozess­mittel durch Rotation gleichmässig zu verteilen oder abzuschleudern. Für diese Prozesse ist eine grosse Beschleunigungskapazität des Antriebs not­wendig um die Durchlaufzeiten der Prozesse und damit die Betriebs­kosten gering zu halten. Weiterhin werden für einige der Prozesse hohe Drehzahlen verlangt.

Die heute standardmässig eingesetzten Servomotoren verursachen mit ihren mechanischen Lagern und Dichtungen Abrieb und somit Kleinst- partikel, welche die Prozessreinheit beeinträchtigen könnten.

Die Verwendung von magnetisch gelagerten Scheibenläufermotoren für den beschriebenen Anwendungsbereich bietet die Möglichkeit eines langlebigen, verschleiss- und abriebfreien Betriebes, wobei der Prozess durch eine in den Luftspalt eingefügte Prozesskammer komplett her­metisch abgeschlossen werden kann. In dieser Prozesskammer können prozessabhängige Bedingungen (Druck, Temperatur, Reinheit) lokal be­grenzt und damit kosteneffizient erzeugt werden. Für die Konstruktion einer mechanisch stabilen und chemisch beständigen Prozesskammer be­darf es eines grossen Luftspalts, damit eine ausreichende Wandstärke garantiert werden kann.

Das Konzept, die Entwicklung und die Optimierung eines magnetisch gelagerten Scheibenläufermotors, der die Anforderungen der Industrie bezüglich Beschleunigungsvermögen und hoher erreichbarer Drehzahl bei gleichzeitig grossem Luftspalt erfüllt, wird in dieser Arbeit vorgestellt.

Die Verwendung einer Scheibenläufertopologie (geringe Motorhöhe im Vergleich zum Motordurchmesser) stellt hierbei ein hohes Mass an Kom­paktheit sicher. Der entwickelte Motor vereint ein homopolares Magnet­lager und eine permanenterregte Synchronmaschine, welche auf zwei am Umfang und axial verschobenen Ebenen angeordnet sind. Daher wird der Motor als “Magnetisch gelagerter 2-Ebenen Motor (M2M)” bezeichnet. Durch die resultierende vollständige magnetische Entkopplung können das Magnetlager und der Antrieb unabhängig von einander ausgelegt werden. Hierbei wird durch die Verwendung von zwei Ebenen die La­gerauslegung anspruchvoller (Verkippungsproblematik, Vermeidung von magnetischen Kopplungen zwischen Lager und Antrieb), weshalb sie im Detail in dieser Arbeit untersucht wird.

Die grundsätzliche Klassifizierung von verschiedenen Magnetlagerty­pen und deren Anwendbarkeit für die beschriebenen Industrieprozesse wird einleitend gezeigt. Die Skalierungsgesetze der Lagerstabilität, der Lagersteifigkeit und der Lagerdynamik werden präsentiert und mit Hil­fe von analytischen Auslegungsrichtlinien untermauert. Der eigentliche Entwurf des Magnetlagers wird dann an Hand von 3D FEM Simulatio­nen erklärt. Zusätzlich wird der Einfluss von verschiedenen Antriebssta­torstrukturen (segmentiert oder vollumfänglich) auf die Lagerparameter mit Hilfe von 3D FEM Simulationen untersucht.

Die Antriebseinheit wird in zwei Schritten auf hohe Beschleunigungs­fähigkeit und hohe erreichbare Drehzahlen optimiert. Als erstes wird die optimale Statorzahngeometrie (klassischer T-förmiger Zahn oder verein­fachter gerader Zahn) unter Berücksichtigung der hohen auftretenden Durchflutungswerte bestimmt. Die hohen Durchflutungswerte sind not­wendig, um trotz des grossen Luftspalts ein ausreichend hohes Antriebs­moment zu erzeugen. Es wird gezeigt, dass die gerade Zahnform für den untersuchten Motor geeigneter ist. Die Resultate der Untersuchung kön­nen auch auf andere Motoranwendungen, bei denen die Sättigungseffekte und nicht die thermischen Effekte limitierend wirken, übertragen werden.

In einem zweiten Schritt wird die analytische Optimierung des An­triebs gestützt auf 3D FEM Simulationen durchgeführt. Dabei werden die Windungszahl pro Antriebsphase und die geometrischen Dimensio­nen der Antriebszähne ermittelt, für welche die kleinste Beschleunigungs­zeit für einen vorgegebenen Drehzahlbereich erreicht werden kann. Die vorgestellte Optimierungmethode kann dabei auch auf andere permanen­terregte Synchronmaschinen angewendet werden.

Um die Notwendigkeit für 3D FEM Simulationen aufzuzeigen wird eine Untersuchung durchgeführt, welche die Resultate von 2D und 3D Drehmomentsimulationen vergleicht. Der Unterschied zwischen 2D und 3D Simulationen wird dabei mit dem Modellierungsfehler bemessen. Wei­terhin werden grundsätzliche Bedingungen formuliert, welche die Verwen­dung von 2D Simulationen erlauben. Für den vorgestellten Motor wird gezeigt, dass sich eine ausreichende Simulationsgenauigkeit nur unter Ver­wendung von 3D Simulationen erreichen lässt. Dabei ist der Durchflu­tungswert als Mass für die Sättigung ein entscheidender Parameter, der bei der Auswahl der Simulationsart berücksichtigt werden muss.

Die Skalierungsgesetze, Auslegungsrichtlinien und Optimierungser­gebnisse werden anschliessend anhand eines Laborprototyps verifiziert. Der experimentelle Aufbau und die verwendeten Regelverfahren werden dabei näher beschrieben.

Die Leistungsparameter wie Beschleunigungszeit, maximale Drehzahl und radiale und axiale Auslenkung während der Beschleunigung werden abschliessend sowohl qualitativ als auch quantitativ mit drei anderen bestehenden magnetisch gelagerten Motorkonzepten verglichen. Dabei wird der Hauptvorteil des M2M Konzepts, die hohe Maximaldrehzahl, bestätigt.

Notation

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Chapter 1 Introduction

The everlasting trend for miniaturization and the increasing cleanness specifications in chemical, pharmaceutical, biotechnology and semicon­ductor industry applications demand for high-purity process environ­ments. This is since already smallest particles can damage the processed structures. The standard motors for these kinds of applications are servo motors, whose mechanical bearings and fittings cause small particles that decrease the process purity.

The implementation of magnetically levitated slice motors in these application fields gives the advantage of an almost unlimited life time, frictionless and wearless operation and the possibility of inserting a pro­cess chamber into the air gap that creates a completely encapsulated miniature clean room.

This thesis demonstrates the development of a magnetically levitated slice motor to be applied in the purity sensitive industry. Therefore, in this chapter the demand for high purity process environments is ex­plained in detail and two exemplary spin processes are described. Then, the motor requirements are formulated based on the demands for the ap­plication field. Here, the term motor is understood as the overall system, thus the combination of a suitable bearing and drive unit. Subsequently, the available topologies for bearing unit, drive unit and frequency con­verter are briefly presented and their feasibility for the applications at hand is explained. The highly suitable concept of the “Magnetically Lev­itated 2-Level Motor (M2M)” is described in more detail. Finally, an overview of the work is presented with the description of the main tasks.

1.1 High Purity Process Environments

Nowadays, many industry spin processes must be operated in high purity process environments, especially in the purity sensitive industry branches (e.g. biotechnology, semiconductor, pharmaceutical and food industry). The feasibility of these processes is at the limit, so that even the smallest impurities greatly reduce the process quality and increase the scrap rate. Two examples are explained in order to illustrate the sensitivity of these processes.

Firstly, the current feature size of a static random-access memory cell is in the range of 32 nm [1]. A chip area of 1 μm2 can theoretically contain as much as 976 structures. A clean room operator although entirely covered in a protective suit looses about 1 billion dead skin cells with sizes in the range of up to 10 μm per day. If only one of these skin cells finds its way onto the processed object it can possibly damage or destroy thousands of structures.

Secondly, although the impurity sensitivity of processes is less dis­tinct in the pharmaceutical and food industry, the processes must still be operated under high purity conditions in order to avoid chemical re­actions (e.g. drug coating) and in order to maintain a high level of hygiene (e.g. pelletizing during food processing) [2]. The previous ex­amples demonstrate the demand for high purity process environments in modern industry processes.

In addition to a high purity environment many industry processes also demand process dependent conditions (e.g. pressure, humidity, in­ert gas). These conditions can only be applied cost efficiently in a locally limited and hermetically sealed space denominated as the process cham­ber. Such process dependent conditions include the nitrogen flooding during wafer polishing processes [3] or the vacuum condition needed dur­ing layer coating processes for pharmaceutical drugs [2].

Until now, the standard machines commonly used for these processes are servo motors with lubricated ball bearings and gas proof seals. Due to the apparent mechanical wear and the presence of lubricants, particles are generated. These particles increase the risk of pollution within the process chamber, consequently affecting the overall process quality. In the future, the feature size in semiconductor applications is expected to decrease even further [4]. Therefore, the future process quality can hardly be sustained in a cost efficient manner with the currently applied technology.

The implementation of magnetically levitated slice (large ratio of di­ameter to height) motors in the described application fields gives the advantage of the complete avoidance of all particle generating sources caused by wear and lubricants [5]. Furthermore, the magnetic bearing technology includes key features such as almost unlimited life time, built- in fault diagnostics [6], a full circumferential air gap and the possibility of active vibration damping [7]. The full circumferential air gap gives the possibility of inserting a process chamber that hermetically encapsulates the whole process.

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Figure 1.1: Schematic cut view of an industry spinning process applied in semiconductor industry (e.g. coating, cleaning and polishing) that is hermetically sealed within a process chamber, using magnetic bearing technology for the levitation of the rotor.

Two possible magnetically levitated motor arrangements for semicon-ductor and pharmaceutical processes are depicted in Fig. 1.1 and Fig. 1.2. Figure 1.1 depicts a semiconductor manufacturing process. Here, the process source applies a process liquid onto the process object. The process liquid is subsequently removed through the centrifugal forces gen­erated by the spinning of the rotor. The process is hermetically enclosed by a process chamber and the rotor is levitated and accelerated through the process chamber walls with the aid of electromagnetic bearings and drives, respectively. Fig. 1.1 demonstrates another advantage of the implementation of magnetically levitated slice motors, which is the pos­sibility of the parallel processing of both sides of the process object.

A granulation process applied in pharmaceutical and food industries is depicted schematically in Fig. 1.2. The contactless levitated rotor with the granulation wheel generates an upstream air flow, while process liquids are applied through the spray nozzle. The rotor is levitated and spun through the process chamber walls, which ensures the high purity process environment. For this process the process objects enter through the upper opening and continue through the lower opening after pro­cessing, therefore the chamber is depicted with openings. Assuming a hermetic encapsulation of the whole process installation, this setup still guarantees very high purity conditions.

Considering the general advantages of the magnetically levitated slice motor topology, the aim of this thesis is the analysis, optimization and development of a magnetically levitated motor that satisfies the require­ments for current and future high purity spin process environments.

1.2 Motor Requirements

The previous section presented the magnetically levitated slice motor technology as a possibility to satisfy the demand for future high purity environments in the processing industry. The motors applied in these application fields must fulfill several requirements in order to be appli­cable and economically viable. These requirements are explained here in more detail.

The outer diameter of the rotor must be selected such that the fea­sibility for a variety of applications can be shown. Since the rotor di­ameters differ between the different applications (from 200 mm [8] up to 600 mm [9]), the rotor diameter is set to a medium value of 370 mm.

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Figure 1.2: Schematic cut view of an industry spinning process applied in pharma­ceutical and food industry (e.g. granulation, pelletization and powder coating) that is hermetically sealed within a process chamber, using magnetic bearing technology for the levitation of the rotor.

Depending on the target process (spinning off of process liquids, gran­ulation, pelletization etc.) the motor must reach a certain rotation speed, which is commonly in the range of several thousand revolutions per minute (r/min). In order to demonstrate the feasibility of high rotation speeds and to cover the process requirements of multiple applications the target rotation speed is set to 3000 r/min.

The process chamber inserted into the full circumferential air gap must withstand pressure differences of at least 1 bar (vacuum condition). Therefore, its mechanical integrity (mainly defined by its thickness) must be guaranteed, resulting in a minimum value for the air gap length. The choice of any metal (usually high integrity even for small thicknesses) as the material for the process chamber is disadvantageous. These materi­als usually are electrically and/or magnetically conductive, which causes high motor losses and lower efficiency. The implementation of composite materials avoids these losses, but requires a larger thickness in order to guarantee the same mechanical integrity. Therefore, assuming a compos­ite process chamber wall thickness of 5 mm as sufficient for the mechanical integrity and considering a maximum allowable deflection of the rotor of 2 mm sums up to a minimal design air gap length of 7 mm. A motor with an air gap of 7 mm is considered as a large air gap motor, since for standard industrial motors the air gap length is usually kept as small as possible (range only 0.3 — 0.7 mm) in order to obtain minimal losses and to increase the motor efficiency.

Although the effort involved with the implementation of a magnetic bearing is usually higher compared to mechanical bearings, the overall motor setup should be as compact as possible in order to save valuable process equipment space. Here, the profile height is a major geometric parameter that must be kept as small as possible.

A stable levitation of the rotor, especially when driving through the rotors resonance frequencies, must be provided. This is very crucial in order to avoid particle generation through a touchdown of the rotor onto the process chamber wall at all costs.

Besides the technical requirements dictated by the process also eco­nomical drivers must be considered during the specification phase of the motor. In several applications the motors are operated in start-stop mode. Here, the resulting acceleration time dictates the capacity of the equipment and eventually the cost-benefit ratio. Therefore a minimiza­tion of the acceleration time is a crucial design parameter that must be considered for the drive design.

Summarizing the main motor requirements, the challenge of the mo­tor design is the maximization of the acceleration capability while per­mitting stable levitation over the whole operating range. This must be achieved while providing a large air gap that allows the insertion of the separating chamber wall. Here, the motor must be as compact as possible and must have a low profile.

1.3 Motor Concept

In this section the available topologies for the magnetic bearing unit, the drive unit and the frequency converter are presented. The advantages and disadvantages of each topology and the possible interaction between the units are briefly explained. Based on the motor requirements introduced in the previous section, a highly suitable combination of these topologies is then selected and the resulting “Magnetically Levitated 2-Level Motor” concept is presented.

1.3.1 Magnetic Bearing Unit

The magnetic bearing unit is used for the contactless levitation of the rotor. Generally, magnetic bearings can be classified into active and passive bearings (cf. Fig. 1.3). The class of superconducting magnetic bearings is not considered in this thesis, since the cooling effort to sustain the superconduction is cost intensive and the involved cooling apparatus volume contradicts the aim of a compact motor setup. However, for the sake of completeness it is mentioned here.

The stabilizing effect of the passive magnetic bearings is generated through reluctance forces between attracting and repelling permanent magnets (PM). The force of active magnetic bearings is generated with the aid of controlled electromagnets. Passive magnetic bearings are pre­ferred, since they are highly compact and have a low complexity. Though, not all degrees of freedom can be stabilized passively as was shown in [10]. For slice-shaped rotors, three of the six degrees of freedom can be stabi­lized passively. Therefore, passive and active magnetic bearings must be used in combination.

In [11] a multitude of possible permanent magnet arrangements for passive magnetic bearings are introduced and examples for a possible permanent magnet arrangement for each topology are presented in Ta­ble 1.1. The class of passive radial bearings is less suited for an applica­tion with a process chamber wall, since the radial displacement is only controlled passively. Consequently, the rotor can touch or damage the process chamber wall for higher rotation speeds and possibly occurring rotor resonances. Therefore, the group of axial bearings is preferred. Here, the concepts based on repellent forces seem disadvantageous, since rotor and stator level have to be arranged on top of each other. This would lead to an axially high and therefore less compact setup.

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Figure 1.3: Classification of passive magnetic bearings suitable for industry spinning processes using a process chamber.

The class of attractive axial magnetic bearings with iron is compact and allows the active control of the radial position. However, this type of bearing is usually implemented with a bearingless (bearing unit and drive unit share the same iron path) motor [12]. Therefore, the rotor magnets are inversely magnetized in order to generate an alternating flux density distribution in the air gap, which is demanded by the drive unit in order to spin the rotor. This alternating flux debsity distribution is proportional to the rotation speed and the number of pole pairs. The resulting high frequency bearing flux consequently limits the maximum rotation speed of the rotor, since the current rise time in the bearing windings and the processing speed of signal electronics are limited. This behavior contradicts the high rotation speed requirement explained in section 1.2.

Both the attractive axial bearing with radially magnetized permanent magnets and axially magnetized permanent magnets are suitable for the described application fields. However, a similar concept [13] with an axial magnetic bearing with axially magnetized permanent magnets (cf. section 6.1.1 and Fig. 6.1) has been successfully tested before the start of the design phase of this thesis. Therefore, this bearing concept was selected to be implemented into the motor. Due to the permanent magnet arrangement the bearing concept causes an almost homogeneous air gap flux density. Hence, the axial magnetic bearing with axially magnetized permanent magnets is denominated as homopolar magnetic bearing in the following.

Table 1.1: Force direction and possible permanent magnet arrangement for different passive magnetic bearing topologies (Permanent magnets are shown as grey boxes with the arrow pointing in the direction of magnetization).

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1.3.2 Drive Unit

The drive unit is used for the spinning of the rotor. Due to the choice of a homopolar magnetic bearing topology in the last section, the permanent magnets of the magnetic bearing unit cannot be used directly for the drive torque generation as this is usually done for bearingless motors.

A concept that applies gaps between the rotor bearing magnets in order to generate a alternating flux debsity distribution in the air gap was presented in [13]. However, since only the stray flux components can be used for the drive torque generation, this concept has a relatively low acceleration capability (cf. section 6.1.1), which contradicts the motor requirements formulated in section 1.2. Additionally, the high number of pole pairs might limit the maximum rotation speed.

As a consequence, in order to design the drive unit for maximum ac­celeration capability and high rotation speeds independent of the bearing unit, the drive unit must be implemented on a second axially shifted level.

A review of the suitable drive units for magnetically levitated motors was presented in [13] and is therefore only briefly repeated in this thesis for the sake of completeness. The standard industrial drive topologies that are more or less suitable for the application field at hand are: in­duction machines, synchronous machines, brushless DC machines and reluctance machines.

In induction machines the magnetizing current for a given magnetiz­ing field is proportional to the air gap length [14]. For large air gaps this results in a small air gap flux density and a consequently small drive torque. Besides the large copper losses resulting from a large air gap length and a low power factor, additional losses are generated through the relatively large end windings stray flux. This is the case for the small profile height of the slice motor topology. Regardless of the simple me­chanical motor construction, this concept is unfavorable for applications with large air gap motors.

Since contactless energy transfer to the rotor is demanded by the field of application, only the permanent magnet synchronous machine (PMSM) [15] can be considered from the group of synchronous machines. Here, the magnetizing field is generated through permanent magnets, which reduces the losses (no magnetizing current at rotor) and leads to high air gap flux densities (high torque). Despite the higher price for the permanent magnets this drive concept seems very favorable.

The construction of brushless DC machines (BLDC) [16] is very sim­ilar to a PMSM. Only the control of the BLDC is different, since the currents employ block rather than continuous commutation. This sim­plifies the structure of the power electronics. However, this is not a strong enough driver to choose this concept, since a power electronics capable of driving a PMSM was already available at the beginning of the design phase.

Reluctance machines offer a simple rotor construction, but have a very low power factor, low efficiency and a low drive torque [17]. Also the rotor construction with distinct iron teeth seems disadvantageous, since it must be closed through a back iron ring (rather than a star connection) for the ring shaped rotor, resulting in a higher rotor weight. Therefore, this machine is not considered as a possible drive concept for the magnetically levitated motor.

Summarizing the general conclusions for each machine type, the per­manent magnet synchronous machine is the most favorable drive unit concept and is therefore implemented into the magnetically levitated motor.

1.3.3 Motor Frequency Converter

Considering the motor frequency converter topology in general, the de­cision between two-phase or three-phase bearing and drive unit arises. In [18] it has been shown that the major advantage of a three-phase topology is the reduced component stress and the possibility to employ commercially available three-phase frequency converter modules. How­ever, the resulting acceleration time is slightly lower for a three-phase topology compared to a two-phase topology for the motor investigated in the publication.

The advantage of a two-phase topology is the possibility to choose the switches depending on the actual component stress level, which is usually lower for the bearing unit. Additionally, the arrangement of three-phase windings along the limited circumferential space is challenging as this is explained in more detail in chapter 3. Therefore, a two-phase approach is preferred for the design of the magnetically levitated motor.

Two possible converter structures being able to drive the two-phase magnetic bearing unit and the two-phase drive unit are presented in [19]. Their application for a magnetically levitated motor was already analyzed in detail in [13], therefore they are discussed here only briefly for the sake of completeness.

The classical arrangement presented in Fig. 1.4(a) applies a full-bridge for each of the four phases (two phases for the bearing unit and two phases for the drive unit). Due to this arrangement the phases can be controlled completely independent of each other. However, the resulting number of switches is rather high (sixteen), whereby the switches can be selected dependent on the occurring component stress, which is usually lower for the bearing phases.

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Figure 1.4: Converter topologies for driving the two-phase bearing unit (Bel, Be2) and the two-phase drive unit (Dr1, Dr2). (a) Classical arrangement with full bridge for each phase demanding sixteen switches. (b) Interleaved half-bridge topology as proposed in [19] demanding only twelve switches and giving the possibility to use standard integrated three-phase frequency converter modules.

In Fig. 1.4(b) the interleaved half-bridge topology extracted from [19] is presented. Since this concept only uses two times six switches, stan­dard integrated three-phase frequency converter modules can be imple­mented, reducing the costs and frequency converter volume. In order to have a similar thermal stress for both modules, one bearing and one drive phase are connected to each module. Since the drive and bearing phase are connected to a common middle point bridge leg, the resulting max­imum duty cycle for this topology is lower as compared to the classical arrangement.

Due to the possible higher acceleration capability, the classical ar­rangement was employed for the setup of the magnetically levitated mo­tor.

1.3.4 Magnetically Levitated 2-Level Motor

After the definition of the applicable magnetic bearing, drive and fre­quency converter topologies this section presents the overall concept of the magnetically levitated motor. The fundamental principle of the mo­tor is the generation of the bearing forces and the drive torque on two different axially shifted levels. Therefore, the motor is denominated as “Magnetically Levitated 2-Level Motor (M2M)”.

The separated structure allows significantly increased torque values and therefore a higher acceleration capability compared to [13], even though the rotor mass is increased with the additional permanent mag­nets. In comparison to motors with integrated drive and bearing func­tionality the two-level structure reduces the control efforts. Additionally, the concept allows for a separate optimization of the bearing and the drive unit, while assuming a sufficient distance between bearing and drive level in order to avoid interactions. Furthermore, the homopolar bearing of the M2M allows very high rotation speeds, while for concepts featuring a multipolar bearing [12] the maximum rotation speed is limited by the current rise time in the bearing windings and the time delays in the signal electronics.

A cross-sectional view of the motor depicting the arrangement of the bearing and the drive unit along the circumference is shown in Fig. 1.5. At the upper level, the magnetic bearing is located. It consists of rotor and stator permanent magnets and the bearing windings around the four stator bearing teeth.

The drive unit is based on the permanent magnet synchronous ma­chine principle and is positioned at an axially lower level. The rotor magnets are round-shaped and have an inverse diametrical magnetiza­tion. In order to obtain a low profile height and to avoid interactions between bearing and drive unit (influence of full circumferential drive stator - cf. section 2.4) the drive stator is implemented using four drive segments. These are fitted into the limited space between the bearing teeth.

illustration not visible in this excerpt

Figure 1.5: Schematic cut view of the “Magnetically Levitated 2-Level Motor (M2M)” including the bearing and the drive unit on stator and rotor. The arrows within the permanent magnets point into the direction of magnetization.

Position and angular sensors are distributed around the stator to detect the radial position [20] and rotation speed, additionally limiting the available space along the circumference.

1.4 Overview of the Work

The aim of this work is the creation of a magnetically levitated mo­tor that fulfills the requirements for applications in high purity process environments as presented in section 1.2. The “Magnetically Levitated 2-Level Motor” presented in the previous section is a highly favorable motor design that meets the requirements of high acceleration capabil­ity and high rotation speed, while having a large air gap and a small height. The necessary analysis, design and verification of this machine are presented in the course of this thesis.

In chapter 2 the principle and the design of the magnetic bearing
unit is described. First, the bearing performance parameters and general design considerations are described. Then, the scaling of the bearing performance parameters is analyzed through geometry variations imple­mented into 3D finite element (FEM) simulations. Subsequently, the influence of the drive on the bearing stability is described.

The drive principle and design is presented in chapter 3. General con­siderations concerning the selection of geometry parameter values and the choice of a segmented stator are presented, followed by the analysis of the best suitable stator tooth shape. Subsequently, an overall accelera­tion capability optimization considering the acceleration speed span, the sizing of the stator segment and the number of winding turns per drive phase is presented.

Since the design of the bearing and drive unit is mainly based on FEM simulations, chapter 4 investigates the influence of the simulation (2D vs. 3D) on the overall modeling error. General guidelines are presented to simplify the choice between the two methods.

The implementation of the M2M and the experimental verifications of the simulation and optimization results are presented in chapter 5.

The performance of the M2M is compared to three other magnetically levitated slice motors in chapter 6. First, the principle and construction of the other three concepts is briefly introduced. Then the major perfor­mance parameters are identified. Using these parameters a quantitative and qualitative comparison is carried out, which highlights the strengths and weaknesses of the different concepts.

In chapter 7 the thesis is concluded and an outlook to future devel­opments is presented.

Publications

The results achieved during the course of this doctoral work have been published at international conferences and in journals as listed below.

Journals

1. T. Nussbaumer, P. Karutz, F. Zürcher and J.W. Kolar, “Magnetically levitated slice motors - An overview,” IEEE Trans. Ind. App., Ac­cepted, Aug. 2010.
2. P. Karutz, T. Nussbaumer, W. Gruber, and J.W. Kolar, “Acceleration performance optimization for motors with large air gaps,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 52-60, Jan. 2010.
3. P. Karutz, T. Nussbaumer, W. Gruber, and J.W. Kolar, “Novel mag­netically levitated two-level motor,” IEEE Trans. Mechatron., vol. 13, no. 6, pp. 658-668, Dec. 2008.
4. S.D. Round, P. Karutz, M.L. Heldwein, and J.W. Kolar, “Towards a 30 kW/liter three-phase unity power factor rectifier,” IEE Japan Trans., vol. 128-D, no. 4, Apr. 2008.

Conferences

1. P. Karutz, T. Nussbaumer, and J.W. Kolar, “Magnetically levitated slice motors - An overview,” Proc. IEEE Energy Conversion Congress and Exposition (ECCE’09), San Jose, USA, pp. 1494-1501, 2009.
2. P. Karutz, T. Nussbaumer, and J.W. Kolar, “Magnetgelagerte Schei- benlaeufermotoren - Ein Ueberblick,” Tagungsband der 3. VDE/ VDI- Fachtagung - Elektrisch-mechanische Antriebssysteme, Boeblingen, Ger­many, pp. 23-28, 2008.
3. P. Karutz, T. Nussbaumer, W. Gruber, and J.W. Kolar, “Maximizing acceleration capability of magnetically levitated slice motors,” Proc. 18th Intern. Conf. on Electrical Machines (ICEM’08), Vilamoura, Portugal, pp. 1-6, 2008.
4. P. Karutz, T. Nussbaumer, W. Gruber, and J.W. Kolar, “Saturation effects in high acceleration bearingless motors,” Proc. IEEE Intern. Symp. on Industrial Electronics (ISIE’08), Cambridge, UK, pp. 472­477, 2008.
5. P. Karutz, T. Nussbaumer, W. Gruber, and J.W. Kolar, “The bearing­less 2-level motor,” Proc. 7th Intern. Conf. on Power Electronics and Drive Systems (PEDS’07), Bangkok, Thailand, pp. 365-371, 2007.
6. S.D. Round, P. Karutz, M.L. Heldwein, and J.W. Kolar, “Towards a 30 kW/liter three-phase unity power factor rectifier,” Proc. Power Conversion Conf. (PCC’07), Nagoya, Japan, pp. 1251-1259, 2007.
7. P. Karutz, S.D. Round, M.L. Heldwein, and J.W. Kolar, “Ultra com­pact three-phase PWM rectifier,” Proc. 22nd IEEE Applied Power Electronics Conf. (APEC’07), Anaheim, USA, pp. 816-822, 2007.

Supervised Master Theses and Seminar Papers

During the course of this doctoral work the following non-public master theses and seminar papers have been supervised.

1. T. Holenstein, “Auslegung und digitale Implementierung von Regelver­fahren für einen magnetisch gelagerten Motor,” Master Thesis, Nov. 2009.
2. S. Pfister, “Aufbau und Inbetriebnahme eines 2 kW PFC,” Master Thesis, Sep. 2009.
3. A. Steiner, “Hochbeschleunigender, magnetisch gelagerter Antrieb für 450 mm Wafer,” Master Thesis, Jun. 2009.
4. C. Wildmann, “Voruntersuchungen für den High Speed Motor,” Master Thesis, Feb. 2009.
5. R. Burkart, “Aufbau und Inbetriebnahme eines magnetisch gelagerten Plattenspielers,” Seminar Paper, Jan. 2009.
6. C. Wildmann, “Mechanical Design of the KULKO Fusion Snake Ro­bot,” Seminar Paper, Dec. 2008.
7. E. Ilguensatiroglu, “Aufbau und Optimierung der Wirbelstromsenso­ren für den Einsatz in einem magnetgelagerten Wafer-Bearbeitungs­werkzeug,” Seminar Paper, Jun. 2007.
8. M. Baldinger, “Design and Implementation of a Resonant Converter for High Voltage and High Power Application,” Master Thesis, Oct. 2006.

Chapter 2 Design of the Magnetic Bearing Unit

The steps that are necessary to design the M2Ms magnetic bearing unit are presented in this chapter. First, the principle of the attractive axial magnetic bearing with axially magnetized permanent magnets and the force generation mechanisms are explained. Then, the radial and axial stiffness and the force-current factor that are needed for the characteri­zation of the levitation properties are described. From these parameters, the general guidelines that must be satisfied for a proper operation of the magnetic bearing unit are formulated. Additionally, the influence of the drive unit on the tilting tendency of the rotor is defined by analytical equations.

In the following sections the selection of the geometry parameters for the magnetic bearing unit is carried out based on the before formulated bearing design requirements. Due to the non-linear flux density distri­bution in the air gap the design is based on 3D FEM simulations. The impact of different geometrical parameters, such as permanent magnet depth and height, is described in detail and the selection of the best suited parameter set is explained.

Subsequently, the scaling laws of the magnetic bearing unit are pre­sented by showing the influence of selected geometrical parameters on the levitation properties.

Finally, the chapter closes with an investigation of the feasibility of a full circumferential drive unit. The impact of such a drive unit on the levitation properties is shown with the aid of 3D FEM simulation results. It is shown that the M2M can not be implemented with a full circumferential drive unit while fulfilling the formulated bearing design requirements.

2.1 Basic Considerations

2.1.1 Force Generation in Magnetic Circuits

With the aid of the homopolar magnetic bearing, the rotor of the M2M is levitated in a contactless manner. In section 1.3.1 the attractive axial magnetic bearing with axially magnetized permanent magnets was iden­tified as a highly suitable bearing topology. It provides the advantages of active radial position control, applicability for high rotation speed op­eration and a compact construction.

In order to understand the magnetic bearing principles, the force on the pole faces shall be calculated based on the magnetic circuits depicted in Fig. 2.1. For the following considerations it is assumed that the cross section area Amag of the magnetic circuit is constant and that the air gap length is small compared to the dimensions of the yoke in order to guarantee a homogeneous flux density distribution in the air gap.

Assuming a linear demagnetization curve, a permanent magnet can be modeled by replacing the magnetization with a thin coil with constant current along the surface of the permanent magnet [21]. The permanent magnet then corresponds to a coil with the magnetomotive force Fm defined as

illustration not visible in this excerpt

where 1pm is the length of the permanent magnet (cf. Fig. 2.1(a)) in the direction of magnetization and Hc is the coercive field strength of the magnet material.

In case of an electromagnet (cf. Fig. 2.1(b)) the magnetomotive force

illustration not visible in this excerpt

Figure 2.1: Magnetic circuit (a) with permanent magnet excitation and (b) with current excitation.

The force in the direction x (cf. Fig. 2.1) is obtained by taking the derivative of Wc in that direction and keeping the magnetomotive force

illustration not visible in this excerpt

If no magnetic saturation is present, the coenergy can be expressed as

illustration not visible in this excerpt

for the setup decpicted in Fig. 2.1(a) and as

for the setup decpicted in Fig. 2.1(b).

In order to link the previous equations to the operation of a magnetic bearing the magnetic circuit depicted in Fig. 2.2 shall be considered in the following. Compared to Fig. 2.1 this circuit has two air gaps on each side of the free yoke, which can be moved by superposing a control current Ix to the bias current 10. Here, Δχ defines the deflection along

illustration not visible in this excerpt

Figure 2.2: Magnetic circuit with moveable yoke and two current excited coils.

illustration not visible in this excerpt

the x-axis from the center position. With the constant k0 defined as

illustration not visible in this excerpt

(2.10) the force on the yoke of each pole shoe can be written as

The resulting force Fx on the yoke in x-direction can be calculated

illustration not visible in this excerpt

Radial Deflection Ax [mm]·

Figure 2.3: Resulting radial force Fx/k0 on the rotor as the sum of the forces 2-Fxi/ko and —2 · Fx2/ko in the air gaps along the ж-axis. The curve Fx/k о shows a linear behavior around the center position of the yoke.

by

illustration not visible in this excerpt

The characteristic of these forces is depicted in Fig. 2.3 for Smech = 10 mm and Δχ = —5... 5 mm. Here, the force is mostly linear for small deviations around the center position and becomes non-linear for a larger deflection. This is also visible in (2.17) for Δχ C Smech. Furthermore, a positive deflection causes a positive force and leads to a further movement of the yoke away from the center point. This mechanism is similar to the radial destabilization of the magnetic bearing.

Although the passive axial stabilization of the proposed magnetic bearing is based on the same mechanisms it cannot be directly visual­ized by the previous equations. Here, the assumption that Amag and Imag stay constant is not fulfilled due to the inhomogeneous flux density distribution in the air gap. However, in order to visualize the effect of the axial stabilization the simple example in the x-z plane as depicted

illustration not visible in this excerpt

Figure 2.4: Flux lines and resulting force vectors for a simulation setup with two inversely magnetized permanent magnets (a) without and (b) an axial deflection.

in Fig. 2.4 is used. Here, two inversely magnetized permanent magnets are axially shifted along the z axis and the resulting forces are computed (cf. Fig. 2.5).

The magnitude of the force defined as

IF | = CFf+rf (2.18)

consists of two components. The first component is the force along the z-axis. The stabilizing characteristic is based on the fact that for a positive deflection along the z-axis, the force becomes negative. Hence,Fz counteracts the deflection and stabilizes the permanent magnet back in to its original position.

illustration not visible in this excerpt

Figure 2.5: Simulation results (cf. Fig. 2.4) of axial force Fz and magnitude of force |F| dependent on the axial deflection Δζ.

The second force component is the radial force Fx in x direction, which naturally comes along with the axial stabilizing force according to [10], [11] and [22].

The permanent magnets in Fig. 2.4(a) show no axial deflection. Therefore, the magnitude of the force is parallel to the x axis and no axial force Fz is present (cf. Fig. 2.5). This equilibrium position depends on the permanent magnet properties, such as magnet material and per­manent magnet dimensions. Since both permanent magnets in Fig. 2.4 have the same dimensions and the same material and the weight force is not included in this example, the equilibrium position is at z = 0 mm (cf. Fig. 2.5).

In Fig. 2.4(b) the right permanent magnet is shifted by Δζ resulting in the presence of an axial force component. This axial force component increases with increasing Δζ, hence the magnet is always pulled back into the equilibrium position. However, considering Fig. 2.4(b) it can be een, that the length of the magnetic circuit increases with increasing Δζ, hence the magnitude of the force gets reduced (cf. (2.10)). Due to this effect there exists an axial deflection for which the permanent magnet does not return into the equilibrium position and the magnetic bearing loses its axially stabilizing property (cf. Fig. 2.5). This axial deflection is reached, once ÔF*/ôz changes its sign.

illustration not visible in this excerpt

Figure 2.6: Schematic cut view of the M2Ms bearing unit. The arrows within the permanent magnets show the direction of the magnetization.

2.1.2 Principle of Proposed Magnetic Bearing

In the previous section the force generation in a magnetic circuit and the resulting stabilizing and destabilizing effects were explained. In this section these mechanisms are used for the explanation of the principle of the proposed magnetic bearing.

A schematic cut view of the magnetic bearing unit is depicted in Fig. 2.6. The bearing unit combines a passive axial magnetic bearing, which stabilizes the axial rotor position and the rotor tilting, with an active ra­dial magnetic bearing for the stabilization of the radial rotor position. In this section the explanations focus first on the passive magnetic bearing and are then extended for the active magnetic bearing.

The passive axial magnetic bearing consists of inversely axially mag-netized permanent magnets located on an iron ring on the stator and the rotor (cf. Fig. 2.6). The flux paths and the flux density distribu­tion generated through the permanent magnets of the passive magnetic bearing are depicted in Fig. 2.7. Here, the main flux component closes via the stator and rotor permanent magnets, the stator and rotor iron and the air gap. This flux component contributes to the generation of the stabilizing forces. Additionally, there are minor flux components that close only via the stator or the rotor permanent magnets and iron. These stray flux components are not contributing to the generation of the stabi­lizing force, but influence the flux density in the bearing iron. The force generation mechanisms for this radial destabilization were explained in section 2.1.1.

The flux paths and the resulting force magnitude for an axial de­flection of the rotor are depicted Fig. 2.8(a). For a tilted rotor, the stabilizing forces generate a stabilizing torque Ttut,stab (passive tilting stabilization) as depicted in Fig. 2.8(b). In the same way, the destabiliz-ing radial forces generate a destabilizing torque, which is investigated in more detail in section 2.1.4. With these mechanisms, three (axial posi­tion and tilting along the x- and y-axis) of six degrees of freedom of the M2Ms slice shaped rotor can be passively stabilized.

illustration not visible in this excerpt

Figure 2.8: Principle of the passive (a) axial and (b) tilting stabilization for the axially magnetized permanent magnet bearing of the M2M.

The radial destabilization must be actively compensated, which can be achieved with the aid of an active radial magnetic bearing. This active magnetic bearing is implemented into the bearing unit through the bearing winding, which allows the alteration of the air gap flux density through the appliance of an appropriate bearing current similarily to the example explained in section 2.1.1.

A bearing phase consists of two opposite bearing teeth including the bearing windings with inverse winding directions (cf. Fig. 2.9). The bearing current Ibe causes a flux density increase in front of one bearing tooth, while decreasing the flux density in front of the opposite bearing tooth. Consequently, the rotor is then moved into the direction of the larger flux density. Since the M2Ms bearing unit consists of two bear­ing phases that are arranged perpendicularly to each other, any radial deflection of the rotor from its reference position can be controlled by the superposition of the two radial force components. Additionally, due to the slice shape of the rotor and the passive tilting stabilization only one radial bearing level is necessary, unlike for motors with large motor heights as in [23].

Despite the passive stabilization of the rotor, the permanent magnets also increase the effective flux density in the air gap, which serves as a biasing flux for the active radial control. Due to the quadratic relation­ship between the flux density and the radial force, this magnetic biasing effectively reduces the necessary ampere-turns value that is needed to generate the forces for the radial stabilization of the rotor.

Typically, the permanent magnet dimensions are designed to have the bias flux density in the range of half of the saturation flux density of the iron Bsat,Fe. In this way, the bearing winding effort is greatly reduced for generating large forces and there is still a safety margin in order to avoid the saturation of the iron. However, for a stable levitation further design aspects must be considered. Therefore, in the following section crucial parameters that characterize the levitation properties are introduced and simply applicable guidelines that must be satisfied are given.

2.1.3 Characterization of the Levitation Properties

In this section, the parameters used for the characterization of the lev­itation properties of the magnetic bearing unit are explained. The pa­rameter definition is based on the coordinate system and force directions depicted Fig. 2.9.

The axial force Fz,stab shows a non-linear dependency of the axial deflection Δζ. However, for small deflections Δζ the force Fz,stab has a linear characteristic, which allows for a linearization around the operating point z = 0 mm. The same applies also for the radial forces Fx,dest and Fy,dest for a radial deflection Δχ and Δy, respectively. Considering the linearization around the operating point three parameters defining the levitation properties of the passive axial magnetic bearing unit can be defined.

illustration not visible in this excerpt

Firstly, the axial stiffness kz,be defined as describes the stabilizing axial force Fz,stab per unit movement length along the z-axis in the vicinity of z = 0 [24]. Here, z = 0 defines the axial equilibrium position of the rotor, which is influenced by the weight of the rotor. Since Fz,stab counteracts the movement of the rotor it is defined to be negative (see definitions of directions and axis in Fig. 2.9).

illustration not visible in this excerpt

Secondly, the radial stiffness kr,be defined as describes the destabilizing radial forces Fx,dest and Fy,dest per unit move­ment length along the x- and y-axis in the vicinity of x = 0 and y = 0, respectively. Here, x = 0 and y = 0 define the centered position of the rotor. The radial stiffness kr,be is positive, since the destabilizing radial force acts in the same direction as the deflection. Due to the symmetry of the M2Ms magnetic bearing unit the stiffnesses in x- and y-axis are identical, which allows the formulation of a general radial stiffness kr,be.

illustration not visible in this excerpt

And thirdly, the force-current factor ki,be defined as describes the stabilizing radial forces Fx,stab and Fy,stab per unit ampere- turns value Obe in the vicinity of Obe = 0. The ampere-turns value is defined as

illustration not visible in this excerpt

with the number of winding turns per bearing phase Nbe and the bearing current Ibe. Similar to the radial stiffness, the force-current factor is identical in both the x- and y- axis and can therefore be defined with the general stabilizing force-current factor kitbe.

With the aid of the three defined levitation parameters, the following general guidelines must be fulfilled in order to assure the levitation of the rotor. Generally, a high axial stiffness kz,be is desired to counteract the weight force of the rotor

illustration not visible in this excerpt

Here, it is assumed that Δζ is small enough in order to still have a linear characteristic of Fz,stab. From (2.23) the minimal required axial stiffness can be calculated with

illustration not visible in this excerpt

where Δζηο_χ is the maximum allowable displacement in the axial direc­tion, mro is the mass of the rotor and g is the gravitational constant.

A high stabilizing axial stiffness comes along with a destabilizing radial stiffness that must be overcome by the stabilizing active mag­netic force generated by the bearing currents. Therefore, for allowing a maximum radial deflection Δτηα,χ from the centered position, the force-
current factor ki¡be must be larger than a minimum value given by

illustration not visible in this excerpt

with the number of bearing turns Nbe and the bearing current Jbe. Again, it must be considered that kr,be is only linear in a limited operating range, which consequently applies also for (2.25). Considering the construction of the M2M, the destabilizing radial stiffness of the drive unit kr,dr must be additionally considered in (2.25).

In order to facilitate the fulfillment of (2.25), Nbe must be selected as high as possible. However, a high number of winding turns per bearing phase decreases the capability to dynamically change the current in the bearing winding inductance Lbe. The electrical response time tr,el of the bearing is given by

illustration not visible in this excerpt

where Ibe,max is the maximum bearing current, D the duty cycle given by the current controller and Udc the DC link voltage of an frequency converter in full bridge configuration driving the bearing windings. As­suming that the maximum duty cycle of D = 1 can be set by the current controller, only the constructive parameters of the bearing unit influence trel. Hence, since Lbe scales with N{¡e the electrical response time trei increases quadratically with Nbe.

illustration not visible in this excerpt

must be satisfied, thus a small number of bearing windings is desirable from this point of view. Therefore, the selection of Nbe will always be a trade-off between high dynamics (cf. (2.26) and (2.27)) and the maximum force condition (cf. (2.25)) [25].

The presented parameters and guidelines have a general validity for all axial magnetic bearings. They can also be adapted to radial mag­netic bearings by considering the different stabilizing and destabilizing stiffnesses.

2.1.4 Interference with Drive Unit

Generally, with the parameters and guidelines of the previous section a magnetic bearing can already be adequately described. However, for the M2M concept, possible interferences of the drive unit with the bearing unit must be additionally considered.

Due to the axial and circumferential separation of the drive and bear­ing unit the mutual coupling effects can be assumed to be low. However, in addition to the bearing stiffnesses, the diametrically magnetized per­manent magnets of the drive unit cause a magnetic force towards the stator. This leads to an additional stabilizing axial stiffness kz,dr and a destabilizing radial stiffness kr,dr. These stiffness parameters must be considered and added into the bearing design formulas presented in (2.23) — (2.25).

Furthermore, interactions between the bearing and the drive unit may cause tilting problems, which must be considered and are addressed briefly here. The tilting mechanisms are schematically depicted in Fig. 2.10 for a rotor that is tilted around the bearing axis. The destabilizing radial force Fr,dr of the drive causes a tilting torque Tr,dr around the bearing axis center with the distance between the bearing and the drive unit dbe,dr acting as a lever with the restoring passive tilting force Fa acting on the radius of the rotor Tro as the lever. The tilting force Fa can be calculated out of the axial bearing stiffness kz,be with ka being the tilting stiffness and fa being a weighting factor depend­ing on the bearing tooth opening angle φbe (cf. Fig. 2.9). This factor summarizes the different contributions of the four bearing teeth at the stator dependent on φbe for a tilting situation around a certain radial axis. For practical bearing teeth opening angles in the range of φbe = 25... 60°, this factor is approximately fa « 0.5 rad-1. This weighting factor can be interpreted such that in total, two of the four bearing teeth contribute to the restoring tilting force Fa.

illustration not visible in this excerpt

Figure 2.10: Schematic cut view of the tilted M2M rotor with radial stabilizing torque Tz be and destabilizing torque Tr ¿r indicated.

illustration not visible in this excerpt

In order to guarantee a stable operation the condition, £tilt C 1 must be ensured. This is usually the case for rotors with large diameter to height ratios including the M2M concept.

An additional destabilizing torque through the drive unit might be caused by the superimposed electromagnetic forces resulting from the currents in the drive windings. However, as will be shown in section 3.1.2, the drive opening angle ydr is selected equal to ydr — 180°/p. With this, there is always the same amount of attracting and repelling radial forces caused by the drive unit for any rotor position. Therefore, no resulting radial force acting on the rotor is caused by the drive current, which is why it is not considered in (2.34).

2.2 Selection of Geometrical Parameters

The selection of the geometrical parameters based on the aforementioned design guidelines is presented in this section. In order to allow the se­lection of the most suitable set of geometrical parameters, the motor requirements from section 1.2 must be considered. Therefore, the bear­ing unit must fulfill the following specifications:

- In section 1.2 the mechanical air gap is specified with Smech — 7 mm. With the process chamber wall thickness of 5 mm, this leaves a maximum radial deflection of the rotor of Δrmax — 2 mm. There­fore, the bearing unit must be designed, such that the rotor can be moved from touching the process chamber wall (non-operational state) to the center position (operational state).
- The bearing unit must be able to compensate the sum of the desta­
bilizing radial stiffnesses of the bearing unit kr,be and the drive unit kr,dr. The destabilizing radial stiffness of the drive unit is evaluated to kr,dr 4 N/mm in a separate investigation in section 2.4.
- The expected mass of the rotor is set to mro — 4.5 kg, including

[...]

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Details

Title
Magnetically Levitated 2-Level Slice Motor for Application in High Purity Process Environments
College
Swiss Federal Institute of Technology Zurich  (Power Electronic Systems Laboratory (PES))
Grade
1
Author
Year
2010
Pages
194
Catalog Number
V374110
ISBN (eBook)
9783668515789
File size
5538 KB
Language
English
Tags
Magnetic, Bearing, Levitation, Design, Permanent Magnet Drive, Motor, Saturation, 2D, 3D, Optimization
Quote paper
Philipp Karutz (Author), 2010, Magnetically Levitated 2-Level Slice Motor for Application in High Purity Process Environments, Munich, GRIN Verlag, https://www.grin.com/document/374110

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