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Levitating Bearings using Superconductor Technology
Martim de Lacerda Machado Vaz de Carvalho
Thesis to obtain the Master of Science Degree in
Mechanical Engineering
Supervisors: Prof. Carlos Baptista Cardeira Prof. Paulo José da Costa Branco
Examination Committee
Chairperson: Prof. João Rogério Caldas Pinto Supervisor: Prof. Paulo José da Costa Branco
Members of the Committee: Prof. João Carlos Prata dos Reis
November 2016
i
Acknowledgements
I would like to express my gratitude to everyone that contributed to the development of this thesis.
To Professor Carlos Cardeira, Professor Paulo Branco and Professor Rui Melício I would like to thank for their
amazing support and for being always available to discuss any aspect of the project. Their help and motivation
were crucial for the development of this work.
To António, who left an invaluable contribution by working with me on this project.
To Sr. Raposeiro, for all the time spent helping me with the 3D printing.
To Sr. Duarte, for his help with the set-up of the practical experiments.
To IDMEC/LAETA, Instituto Superior Técnico, for all the collaboration and finance support of the project.
To the CSI – Centro de Sistemas Inteligentes – Instituto Superior Técnico, for all the collaboration.
To Formula Student, specially to João Antunes, for providing some of the materials needed.
To Mitera and Fablab EDP for their help and availability to do the complex machinery involved in this work.
To my friend Eduardo Montenegro, for all the work regarding the photography and image processing.
A special thanks to my mother, my father, my siblings and all my family, who contributed so much and always
believed in me.
To all my friends, for their friendship and for always supporting me.
ii
Abstract
This dissertation focuses on the viability, conception and experimental evaluation of using the zero field cooling
technique to build a superconductor magnetic bearing based on NdFeB permanent magnets and YBCO
superconductor bulks, also referred to as high temperature superconductors.
Among many others, advanced works have been carried out where similar prototypes were developed, either
for the construction of large-scale flywheels as for the application in the textile industries. However, the
approaches made in these works use the field cooling technique, whereas the approach in this thesis uses zero
field cooling, which in fact have proved to be more efficient, presenting less Joule losses. In this work, the
geometric placement of the permanent magnets and high temperature superconductors is carefully performed
to keep symmetry along the main axis and to minimize the air gap of the prototype between the rotating part
(rotor) and the static part (stator). Moreover, studies made during the development of this work involve changes
in these geometric placements, either in the rotor as in the stator. Additionally, a finite element model is
designed for simulation and viability study of the bearing, calculating the estimated levitation and guidance
forces involved. Experimental validation is achieved by building a structure in conformity with the previously
simulated geometry and comparing the simulation results with the ones obtained by measuring the existing
forces in the real prototype. The results allow the conclusion that it is possible to build a superconductor
magnetic bearing using the zero field cooling technique, providing an important insight on how the system
behaves.
Keywords
Superconductor magnetic bearing
High temperature superconductors
Permanent magnets
Magnetic levitation
Zero field cooling
iii
Resumo
Rolamento de Levitação Magnética utilizando Tecnologia Supercondutora
Esta dissertação incide sobre a viabilidade, concepção e avaliação experimental da utilização da técnica de zero
field cooling para construir um rolamento magnético supercondutor baseado em ímanes permanentes de NdFeB
e peças supercondutoras de YBCO, também conhecidos como supercondutores de alta temperatura.
Entre muitos outros, trabalhos avançados foram realizados onde protótipos semelhantes foram desenvolvidos,
tanto para a construção de volantes de inércia de grandes dimensões, como para aplicação na indústria têxtil.
Contudo, as abordagens utilizadas nestes trabalhos usam a técnica de field cooling, enquanto a abordagem desta
tese usa supercondutores em zero field cooling, que de facto, provou ser mais eficiente, apresentando menos
perdas por efeito de Joule. Neste trabalho, o posicionamento geométrico dos ímanes permanentes e dos
supercondutores de alta temperatura é cuidadosamente efectuado de forma a manter a simetria ao longo do
eixo principal e minimizar o entreferro do protótipo entre a parte rotativa (rotor) e a parte estática (estator).
Além disso, estudos feitos no decurso do presente trabalho envolvem mudanças neste posicionamento
geométrico, tanto no rotor como no estator. Adicionalmente, um modelo de elementos finitos é projectado para
simulação e viabilidade do rolamento, calculando as estimativas das forças de levitação e guiamento envolvidas.
Validação experimental é efectuada construindo uma estrutura em conformidade com a geometria
anteriormente simulada e comparando os resultados da simulação com os obtidos quando se medem as forças
existentes no protótipo real. Os resultados permitem a conclusão de que é possivel construir um rolamento
magnético supercondutor usando a técnica de zero field cooling, fornecendo importantes informações de como
o sistema se comporta.
Palavras-chave
Rolamento magnético supercondutor
Supercondutores de alta temperatura
Ímanes permanentes
Levitação magnética
Zero field cooling
iv
Contents
Acknowledgements ....................................................................................................................... i
Abstract ....................................................................................................................................... ii
Resumo ....................................................................................................................................... iii
List of Figures ............................................................................................................................... vi
List of Tables .............................................................................................................................. viii
Nomenclature .............................................................................................................................. ix
1. Introduction ......................................................................................................................... 1
1.1. Historical background .............................................................................................................. 1
1.2. Advantages of magnetic bearings ........................................................................................... 1
1.3. Superconductor magnetic levitation ....................................................................................... 2
1.4. Motivation and contributions ................................................................................................. 3
1.5. Publications ............................................................................................................................. 4
1.5.1. International Conferences Proceedings .......................................................................... 4
1.6. Document structure ................................................................................................................ 5
2. State of the Art ..................................................................................................................... 6
2.1. Studies ..................................................................................................................................... 6
2.2. Recent products ...................................................................................................................... 8
3. Viability of the SMB .............................................................................................................. 9
3.1. Modeling ................................................................................................................................. 9
3.2. Simulation .............................................................................................................................. 11
3.3. Full structure model .............................................................................................................. 17
3.4. Studied model ....................................................................................................................... 18
3.5. Rotor geometry influence ..................................................................................................... 20
4. Prototype design and conception ........................................................................................ 22
4.1. Choice of materials ................................................................................................................ 22
4.2. Prototype design ................................................................................................................... 25
4.3. Prototype construction ......................................................................................................... 31
4.4. Improvements ....................................................................................................................... 35
4.4.1. Design improvements.................................................................................................... 35
4.4.2. Construction improvements .......................................................................................... 38
4.5. Final inventory ....................................................................................................................... 42
v
5. Experimental Methods ........................................................................................................ 43
5.1. Robustness to working conditions ........................................................................................ 43
5.2. Leak tests ............................................................................................................................... 44
5.2.1. Nitrogen pouring ........................................................................................................... 45
5.3. Nitrogen usage ...................................................................................................................... 46
5.4. Material wear ........................................................................................................................ 48
5.5. Polyethylene structure .......................................................................................................... 49
5.6. First rotor insertion experiment ............................................................................................ 50
5.7. Experimental method/set-up ................................................................................................ 51
5.8. Results ................................................................................................................................... 54
5.9. Free damping regime analysis ............................................................................................... 56
6. Conclusion and future works ............................................................................................... 58
6.1. Conclusion ............................................................................................................................. 58
6.1.1. Final remarks ................................................................................................................. 59
6.2. Future works.......................................................................................................................... 60
References ................................................................................................................................. 61
Appendix ................................................................................................................................... 63
vi
List of Figures
Figure 1.1 – Type I superconductors transition ....................................................................................... 2
Figure 1.2 – Type II superconductors transition ...................................................................................... 3
Figure 3.1 – Measurements in mm of the linear HTS magnetic levitation system ............................... 11
Figure 3.2 – Perspective view: spatial distribution of PMs and HTSs bulks .......................................... 12
Figure 3.3 – Projection view: spatial distribution of PMs and of HTSs bulks in mm ............................. 12
Figure 3.4 – Example of an used PM ..................................................................................................... 12
Figure 3.5 – Example of an used HTS .................................................................................................... 13
Figure 3.6 – ZFC distribution of magnetic flux at 12 mm vertical distance ........................................... 14
Figure 3.7 – ZFC and FC techniques: repulsion forces between a PM and a HTS [23] .......................... 14
Figure 3.8 – SMB:perspective view of magnetization directions and contours [23] ............................ 15
Figure 3.9 – SMB: transversal view of magnetization directions and contours [23] ............................ 15
Figure 3.10 – SMB: transversal view of magnetic flux contours [23] .................................................... 16
Figure 3.11 – Frictionless SMB: levitation forces [23] ........................................................................... 16
Figure 3.12 – Frictionless SMB: guidance forces [23]............................................................................ 16
Figure 3.13 – Forces applied in the SMB ............................................................................................... 17
Figure 3.14 – ZFC-SMB model with 6 HTSs ............................................................................................ 18
Figure 3.15 – Levitation forces vs. air gap ............................................................................................. 18
Figure 3.16 – Guidance forces vs. lateral displacement for the different air gap values ...................... 19
Figure 3.17 – First rotor and its PMs/HTSs relative positions ............................................................... 20
Figure 3.18 – New rotor and its PMs/HTSs relative positions ............................................................... 20
Figure 3.19 – Levitation forces vs. air gap for the new geometry ......................................................... 21
Figure 3.20 – Guidance forces vs. lateral displacement for the new geometry ................................... 21
Figure 4.1 – One stator slice with HTSs bulks [27] ................................................................................ 26
Figure 4.2 – Stator exploded view [27] ................................................................................................. 26
Figure 4.3 – Liquid nitrogen entrance and open channel details .......................................................... 27
Figure 4.4 – Detail of the inner wall of the stator ................................................................................. 27
Figure 4.5 – Exterior rotor slice with PMs [27] ...................................................................................... 28
Figure 4.6 – Exterior rotor slice with PMs [27] ...................................................................................... 28
Figure 4.7 – Rotor exploded view [27] .................................................................................................. 28
Figure 4.8 – SMB fasteners for final assembly [27] ............................................................................... 30
Figure 4.9 – Virtual SMB exploded view [27] ........................................................................................ 30
Figure 4.10 – Virtual SMB final assembly [27] ....................................................................................... 30
Figure 4.11 – Ouplan CNC milling machine .......................................................................................... 31
Figure 4.12 – One slice of the stator ..................................................................................................... 31
Figure 4.13 – Four stator slices in their orientation of assembly .......................................................... 32
Figure 4.14 – One rotor slice ................................................................................................................. 32
Figure 4.15 – Four rotor slices in their orientation of assembly ........................................................... 32
Figure 4.16 – MakerBot Replicator 3D printer ..................................................................................... 33
Figure 4.17 – Fasteners ......................................................................................................................... 33
Figure 4.18 – Stator assembly ............................................................................................................... 34
Figure 4.19 – Final assembly ................................................................................................................. 34
Figure 4.20 – Modifications in the stator part ...................................................................................... 36
Figure 4.21 – Improved rotor profile ..................................................................................................... 37
vii
Figure 4.22 – M6 rod with a length of 130 mm..................................................................................... 37
Figure 4.23 – Inner stator slice .............................................................................................................. 38
Figure 4.24 – Outer stator slice ............................................................................................................. 38
Figure 4.25 – Stator made of polyethylene ........................................................................................... 39
Figure 4.26 – Rotor D20 ........................................................................................................................ 40
Figure 4.27 – Rotor D5........................................................................................................................... 40
Figure 4.28 – Rods made of ertacetal ................................................................................................... 41
Figure 4.29 – Two types of film insulators used in the stator ............................................................... 41
Figure 4.30 – Final structure.................................................................................................................. 42
Figure 5.1 – Totally submerged stator with cables ............................................................................... 43
Figure 5.2 – Clamps with PVC plaques .................................................................................................. 44
Figure 5.3 – Jug with the volume of water read.................................................................................... 45
Figure 5.4 – Set-up used for the nitrogen usage information ............................................................... 46
Figure 5.5 – Nitrogen evaporation rate ................................................................................................. 46
Figure 5.6 – Crack insulated with silicone gel ....................................................................................... 48
Figure 5.7 – Cracked HTS ....................................................................................................................... 48
Figure 5.8 – Fully assembled polyethylene stator ................................................................................. 49
Figure 5.9 – SMB fully assembled structure .......................................................................................... 50
Figure 5.10 – Instruments used to measure the forces ........................................................................ 51
Figure 5.11 – Experimental set-up used to read the levitation forces .................................................. 52
Figure 5.12 – Guidance forces measuring structure ............................................................................. 53
Figure 5.13 – Guidance forces measurement ....................................................................................... 53
Figure 5.14 – Comparison between the real dynamics and the 2nd order model ............................... 56
Figure 6.1 – Levitation forces vs. eccentricity graph ............................................................................. 58
Figure 6.2 – Guidance forces vs. lateral displacement graph ............................................................... 59
viii
List of Tables
Table 2.1 – Rotating systems based on levitation forces [23] ................................................................. 6
Table 2.2 – evico superconductor magnetic bearing specifications [20] ................................................ 8
Table 3.1 – Air gap and eccentricity influence in the supported weight .............................................. 17
Table 4.1 – Thermal conductivity of several materials [25] .................................................................. 23
Table 4.2 – Inventory ............................................................................................................................. 42
Table 5.1 – Levitation forces results ...................................................................................................... 54
Table 5.2 – Guidance forces results ...................................................................................................... 55
ix
Nomenclature
Acronyms
FC Field Cooling
HTSs High Temperature Superconductor
NdFeB Neodymium magnet
PM Permanent Magnet
SMB Superconductor Magnetic Bearing
YBCO Yttrium-Barium-Copper-Oxide
ZFC Zero Field Cooling
Symbols
𝑴 Permanent magnetization
𝝁𝟎 Vacuum magnetic permeability
𝝁𝒓 Relative magnetic permeability
𝝁 Medium magnetic permeability
�� Volume force density
𝒇𝒎 Volume strength density
�� Current density
�� Magnetic flux density
�� Magnetic field
𝜹𝒎𝒏 Kronecker delta
𝑻𝒎𝒏 Maxwell stress tensor
𝑭𝑳𝒆𝒗 Levitation forces
𝝃 Damping constant
𝛚𝐧 Natural frequency
1
1. Introduction
In this chapter, an introduction is made in order to better orientate and provide the reader with the importance
of the present work. Particular historical aspects, advantages and knowledge have been written, to allow a clear
understanding regarding the topic. Moreover, aspects about the motivation and organization of the text are also
addressed, providing detailed information.
1.1. Historical background
The Oxford English Dictionary defines a bearing as “a part of a machine that allows one part to rotate or move in
contact with another part with as little friction as possible”. Additional functions include the transmission of loads
and enabling the accurate location of components. A bearing may have to sustain severe static as well as cyclic
loads while serving reliably in difficult environments [1]. Bearings are classified broadly according to the type of
operation, the motions allowed, or to the directions of the loads applied to the parts.
Magnetic bearings have been introduced into the industrial world as a very valuable machine element with quite
a number of novel features, and with a vast range of diverse applications [2].
1.2. Advantages of magnetic bearings
A magnetic bearing is a kind of bearing that supports a load using magnetic levitation. They exist in several
different types, all of them offering noncontact operation. Thus, they all have very long lifetime, are lubrication
free and therefore maintenance free. They have low stiffness and thus do not transmit vibrations to the housing.
Magnetic bearings are quiet and they have very low losses, even at very high speed [3]. Therefore, the efficiency
of any system using Superconductor Magnetic Bearings is likely to be higher, while saving in maintenance and
new material parts.
Energy saving is one of the most important technologies for our time. Fossil fuels will not be available forever.
Therefore, it is necessary to reduce the use of this kind of fuels and to increase the use of new energy sources
such as a solar and wind power [4]. With Superconductor Magnetic Bearings lower friction coefficients can be
achieved, therefore they present a viable solution to increase the efficiency within a wide variety of systems.
2
1.3. Superconductor magnetic levitation
Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and repelling the
magnetic fields when their temperature is lowered below the critical temperature. After cooled,
superconductors perform as Permanent Magnets (PMs), generating a magnetic field. Each superconducting
material has an absolute critical temperature above which it loses its superconducting properties [5].
In 1911, superconductivity was first observed by the Physicist Heike Kamerlingh Onnes [6]. It was found during
this observation that when mercury (Hg) is cooled to the boiling point of helium (He), which is 4.2 K, the electrical
resistivity of mercury is almost zero. In 1913, it was discovered that lead (Pb) has almost zero resistivity at
absolute temperatures below 7 K. Later, in 1933, the researchers Walther Meissner and Robert Ochsenfeld
noticed that superconductors expelled applied magnetic fields, a phenomenon that has come to be known as
the Meissner effect [7]. In 1935, the brothers Fritz London and Heinz London showed that the Meissner effect
was a consequence of minimization of the electromagnetic free energy carried by superconducting current. In
1950, Lev Landau and Vitaly Ginzburg postulated the Ginzburg-Landau theory of superconductivity basing on
which it was possible to first explain the behavior of type II superconductors [7]. The complete microscopic theory
of superconductivity, also known as the BCS theory, was finally proposed in 1957 by John Bardeen, Leon N.
Cooper, and Robert Schrieffer. This theory explains the superconducting current as a superfluid of Cooper pairs,
pairs of electrons interacting through the exchange of phonons. The main peak of discoveries took place between
1986 and 1987, when High Temperature Superconductors (HTSs) with critical absolute temperatures above 30 K
started to be discovered. In 1987, the Chu’s group and Kitazawa’s group jointly announced and published the
discovery of Yttrium-Barium-Copper-Oxide, i.e., 𝑌𝐵𝑎2𝐶𝑢3𝑂7 (YBCO) with critical temperature 92 K, as type II
superconductor. The discovery of the YBCO was an important achievement because liquid nitrogen could now
be used for cooling instead of the expensive liquid helium.
The transition of type I superconductors from normal state to superconducting state occurs instantly at the
critical temperature and they repel magnetic field lines fully, therefore lines cannot penetrate this
superconductor. This transition is shown in Fig. 1.1. In type II superconductors, the transition from a normal state
to a superconducting state occurs in a continuous way. The YBCO superconductor is the most common example
of type II superconductor. This transition is shown in Fig. 1.2.
Figure 1.1 – Type I superconductors transition
3
Figure 1.2 – Type II superconductors transition
Some magnetic field lines can penetrate through this type of superconductor allowing flux pinning, which is also
known as Quantum Locking. This property allows the Field Cooling technique (FC) to be used with the Type II
superconductors, in which they are cooled in the presence of a magnetic field, fixing their position and
orientation once the state of superconductor is achieved.
When type II superconductor bulks are cooled in the absence of any magnetic fields, known as the Zero Field
Cooling (ZFC) technique, flux pinning does not occur and the trapped flux density is almost null. In this case, the
superconductor is repelled to a position where the magnetic flux is nearly zero [8], [9]. Hence, levitation systems
can be FC [10] or ZFC [11].
1.4. Motivation and contributions
The motivation behind the execution of this work was due to the following facts:
Bearings that support a load using magnetic levitation are able to support higher speeds with very low
friction and no magnetic wear;
Passive magnetic bearings based only on permanent magnets do not require any power but are difficult
to design as proved by the Earnshaw's theorem;
Active magnetic bearings are used together with passive magnetic bearings to control and stabilize the
loads, but they require continuous power and control;
Earnshaw's theorem does not apply to diamagnetic materials and superconductors may be considered
perfectly diamagnetic because they completely expel magnetic fields due to the Meissner effect.
Therefore, the design of a Superconductor Magnetic Bearing is possible, without the requirement of
feeding continuous power.
ZFC outperforms FC technique contributing with less Joule losses [11]. With the right geometry, it is
possible to build a Superconductor Magnetic Bearing using the ZFC technique.
Due to the previous reasons, this work consists in the development of a SMB using Permanent Magnets (PMs)
and High Temperature Superconductors (HTSs) with the ZFC technique, to analyze its features, advantages and
drawbacks. The final experimental results are compared to the simulations and validated. Moreover, this bearing
could be implemented and tested to replace the usual bearings of a standard electric motor.
4
1.5. Publications
When working in an original investigation subject where the objective is not only to contribute for the scientific
and technological development, but also to obtain an academic degree, it is fundamental that the results are
periodically published to incentive the discussion and sharing of ideas in the scientific community, with the intuit
of achieving scientific and technological improvement.
Subsequently, a section with the scientific publications in international conferences including the
accomplishments and contribution of this thesis is hereby presented.
1.5.1. International Conferences Proceedings
- A.J. Arsenio, M.V. Carvalho, C. Cardeira, R. Melício, P.J. Costa Branco, "Experimental set-up and energy
efficiency evaluation of zero-field-cooled (ZFC) YBCO magnetic bearings", in: Proceedings of the Applied
Superconductivity Conference — ACS 2016, pp. 1–5, Denver, USA, 04–09 September 2016.
- A.J. Arsénio, M.V. Carvalho, C. Cardeira, P.J. Costa Branco, R. Melício, "Conception of a YBCO
superconducting ZFC-magnetic bearing virtual prototype", in: Proceedings of the IEEE 17th International
Conference on Power Electronics and Motion Control — PEMC 2016, pp. 1–6, Varna, Bulgaria, 25–30
September 2016.
- A.J. Arsénio, M.V. Carvalho, C. Cardeira, P.J. Costa Branco, R. Melício, "Viability of a frictionless bearing
with permanent and HTS magnets", in: Proceedings of the IEEE 17th International Conference on Power
Electronics and Motion Control — PEMC 2016, pp. 1–6, Varna, Bulgaria, 25–30 September 2016.
5
1.6. Document structure
While writing this dissertation, the intention of providing an easy and interesting understanding of the topic was
always taken into account. This reason led to its text organization that, besides this chapter, is divided in the
following:
Chapter 2, dedicated to the state of the art of SMB.
In this chapter, different types of levitation systems and their distinct techniques are explained. The
characterization of NdFeB Permanent Magnets (PMs) and Zero Field Cooled (ZFC) type II High Temperature
Superconductors (HTSs) is made, concerning the levitation forces. Previous work results and other magnetic
bearing projects are also mentioned.
Chapter 3, dedicated to the viability study of the SMB.
This chapter includes the technical viability of a frictionless rotating bearing model comprising one inner rotor
part, and one outer stator part, as well as the geometric distribution arrangement that guarantees enhanced
levitation and guidance forces using the ZFC technique. Additionally, extensive finite element model simulations
are carried out to estimate these forces depending on the air gap dimensions and the subsequent eccentricity
and axial displacement of the rotor are estimated.
Chapter 4, consisting in the design and conception of an original ZFC SMB prototype.
In this chapter, an important overview regarding the choice of materials for the prototype is made, since this
subject has a great influence in its properties and in the form that it can be built. Afterwards, the aspects of its
design and construction are discussed, especially how to provide an impermeable structure to put in place the
PMs and HTSs, according to the geometry presented in chapter 3. This section also contains a sub-chapter related
to the improvements that were made in a later phase of the project.
Chapter 5, involving the experimental methods and set-up used to measure the behavior of the real prototype.
In this chapter, different tests to the structure are carried out and the overall concerns regarding topics like
robustness, leakage and material wear are addressed. Furthermore, the set-up preparation for the results
extraction is explained and the obtained results are discussed.
Chapter 6, providing information about the conclusions of this work.
In this chapter, the comparison of the simulation values with the results taken from the real prototype is shown.
Additionally, publications regarding the development of the present work are mentioned and the direction for
the future development of the project is discussed.
6
2. State of the Art
In this chapter, some of the previously carried out studies regarding the SMB technology are presented, showing
the technological advances made prior to the present work. Additionally, recent products that use similar
technology are described.
2.1. Studies
In [12]-[15] recent studies confirm that some of the existing levitation systems use permanent magnets on one
part and type II superconductor bulks on the other part and can be used as frictionless rotating bearings. These
can be sub-divided onto horizontal axis rotating systems, in which the levitation forces are radial and vertical axis
rotating systems in which the levitation forces are axial to a vertical axis. The technical characteristics of some of
these systems are shown in Table 2.1 [23].
Table 2.1 – Rotating systems based on levitation forces [23]
Axis Application
Angular
velocity
(r.p.m.)
Bearing fixed part Bearing
rotating part
Load
capacity Refs
Horizontal Flywheel 40000 NdFeB PMs YBCO bulks 15 kg [12]
Vertical Flywheel 4000 YBCO Bulks NdFeB PMs 1.6 Ton [13]
Horizontal HTS Motor 400
kW 1500 YBCO
NdFeB
PMs 10.5 N/cm2 [14]
Horizontal Flywheel
10 kWh 15860 8 x 5 YBCO bulks 15 PM rings 550 kg [15]
In [16, 17] some other frictionless rotating bearing systems have been already designed to levitate using the FC
technique. This technique implies significant hysteresis losses due to magnetic flux trapping.
7
In [11], [18], further works have proposed a linear HTS magnetic levitation system based on the ZFC technique
with guidance, where this guidance is obtained by an adequate distribution of existing magnetic fields, generated
by a specific array configuration of multi-pole PMs.
In [11], it is proposed that when the cooling process takes place in the absence of a magnetic field, maximum
screening is generated in the superconductors. Such behavior causes only a small portion of flux lines to enter
the superconductor, resulting in the presence of more tangential field lines in the horizontal surface of the HTS,
hereafter responsible for the production of higher levitation forces. Concerning the guidance forces in an FC
vehicle, they depend on the height value where superconductors were cooled. The same does not occur for the
ZFC vehicle where guidance force values are preserved.
In [18], the Joule losses in this kind of systems were studied, proposing that in the ZFC-Maglev they are more
significant for higher speeds of the vehicle.
These proposals proved to be viable and feasible, showing that the ZFC technique presents higher levitation
power due to the Joule effect losses in the FC technique. For this reason, it is possible to say that the ZFC
technique over performs the commonly used FC technique.
In [19], another study proposed a linear electromagnetic launcher with propulsion forces using Meissner effect
based on the ZFC technique. In this work, it was proved that the values of levitation forces measured
experimentally using ZFC are similar to simulations considering a relative magnetic permeability of 𝜇𝑟 = 0.22 for
the YBCO bulk. Moreover, this approximation allows, at this level, to test the proposed SMB design not only
without excessive computational effort due the 3D representation, but also with enough reliable quantitative
results in the modeling and performed simulations. Therefore, the viability study in the present work relies in
this study, as it takes into account the same value for the magnetic permeability coefficient.
8
2.2. Recent products
A german enterprise named evico has recently revealed to be producing superconductor magnetic bearings in
both linear and rotating degrees of freedom [20]. It claims to have built a rotating superconductor bearing that
contains a permanent magnetic arrangement in the rotating part with a homogenous field along a circular line
and with strong magnetic gradients in axial and radial direction. The superconductor piece is situated in the
stationary part. The free air gap, bearing force and bearing-stiffness can be adjusted according to the appropriate
application by the bearing design. Several specifications of the product are shown in Table 2.2.
Table 2.2 – evico superconductor magnetic bearing specifications [20]
Axial Radial
Bearing force > 5000 N 1000 N
Bearing stiffness 2000 N/mm 1200 N/mm
Air gap 1,5 mm
SC-area 402 cm2
Dimensions 200 x 120 mm
Adelwitz Technologiezentrum GmbH (ATZ, foundation 1992) is a European technology Company with the
experience in the development and production of HTS materials and components. This company develops and
contributes to prototyping of magnetic bearings and magnetic systems, flywheel activities, power engineering,
conductor development, and cryostat periphery. They constructed a HTS bearing that presents maximum radial
forces of 4700 N, resulting in a magnetic pressure of 6 N/cm² (axial 13 N/cm²). The bearing consists of about 5 kg
melt textured YBCO which enables to levitate 1000 kg. The magnetic levitation efficiency approaches a surprising
1:200 value [21].
9
3. Viability of the SMB
In this chapter, the topics concerning the viability of the SMB are debated. The section is divided into several
sub-chapters that have the purpose of showing how the modeling and simulations were carried out. Insight is
provided regarding the full structure and the analysis of levitation and guidance forces is performed for the
studied model, with discontinuous rings of superconductors, based on the ZFC technique. Several rotors are also
tested in this analysis. Furthermore, the rotor geometry influence in the system is studied.
3.1. Modeling
The cylindrical geometry of the frictionless rotating bearing model studied is based on the linear HTS magnetic
levitation system using a ZFC technique as presented in [11],[18]. Repulsion of magnetic fields can be modeled
considering a relative permeability lower than the unit 𝜇𝑟 < 1 for HTS bulks. The NdFeB PMs used have a
permanent magnetization 𝑀 given by:
𝑀 =
𝐵𝑟
𝜇0
; 𝐵𝑟 = 1.2 𝑇 (3.1)
where 𝜇0 is the vacuum magnetic permeability [22].
In the case of ZFC, the type II superconductors create a diamagnetic field such that, the normal component of
the resultant magnetic field on the boundary of the superconductor surfaces should be almost zero [11]. This
diamagnetic field is created by a superficial peripheral current density on the superconductor that contributes
for the levitation forces. Hence, a specific volume crossed by a specific current density under the influence of a
magnetic field, suffers a volume force density 𝑓 [31] given by:
𝑓 = 𝐽×�� (3.2)
𝑓 = 𝜇(∇×��)×𝐻 = 𝜇(∇ ⋅ 𝐻) 𝐻 −𝜇
2∇(𝐻×𝐻) (3.3)
where 𝐽 is the current density in the superconductor, �� is the magnetic flux density, 𝜇 is the medium magnetic
permeability and 𝐻 is the magnetic field.
The volume force density can be decomposed in Cartesian coordinates system [31] given by:
𝑓𝑚 =
𝜕
𝜕𝑥𝑛
(𝜇𝐻𝑛𝐻𝑚 −𝜇
2𝛿𝑚𝑛|𝐻|2) ; 𝛿𝑚𝑛 = {
0 𝑚 ≠ 𝑛1 𝑚 = 𝑛
(3.4)
Where 𝑓𝑚 is the volume strength density component, 𝑚, 𝑛 = (𝑥, 𝑦, 𝑧) depending on the considered component,
𝐻𝑛 and 𝐻𝑚 are the magnetic field components and 𝛿𝑚𝑛 is a Kronecker delta.
10
The component 𝑓𝑚 of the volume force density is the gradient in 𝑛 direction of the Maxwell stress tensor
component 𝑇𝑚𝑛 depending on the magnetic field components 𝐻𝑛 and 𝐻𝑚 [31]. 𝑇𝑚𝑛 is given by:
𝑇𝑚𝑛 = 𝜇𝐻𝑛𝐻𝑚 −𝜇
2𝛿𝑚𝑛|𝐻|2 (3.5)
Considering a cube or a rectangular block with one of the six surfaces parallel to the 𝑥𝑦 plan, using the ZFC
technique, the value of the magnetic field normal component to this surface should be 𝐻𝑧 = 0 . The normal
component of the Maxwell stress tensor to this surface 𝑇𝑧𝑧 [31] is given by:
𝑇𝑧𝑧 = −𝜇
2(𝐻𝑥
2 + 𝐻𝑦2) (3.6)
Considering 𝑛 and 𝑡 as normal and tangential components of the Maxwell stress tensor, equation (3.6) can be
rewritten, as given by:
𝑇𝑛 = −𝜇
2 |𝐻𝑡|2 (3.7)
Where 𝑇𝑛 is the Maxwell stress tensor normal component and 𝐻𝑡 is the magnetic field tangential component to
the surface parallel to the 𝑥𝑦 plane.
The levitation forces 𝐹𝐿𝑒𝑣 along the 𝑧 axis [31] are given by:
|𝐹𝐿𝑒𝑣| =
𝐴
𝜇
|𝐵𝑡|2
2 (3.8)
where 𝐴 is the parallel surface to the 𝑥𝑦 plane and 𝐵𝑡 is the magnetic flux density tangential component.
11
3.2. Simulation
In order to validate the model and estimate the magnitude of the levitating and guidance forces present in the
system using the ZFC technique, a virtual simulation was executed using a finite element method (FEM) software.
A specified geometry was proposed and simulated, analyzing if a real prototype of a ZFC SMB could be foreseen.
This step also allowed the choice of an adequate geometry, in order to decide the distance between PMs and
HTSs (air gap).
The cylindrical geometry of the frictionless rotating bearing model studied is based on the linear HTS magnetic
levitation system using a ZFC technique presented in [11], [18]. The geometry of the linear HTS magnetic
levitation system is shown in Fig. 3.1.
Figure 3.1 – Measurements in mm of the linear HTS magnetic levitation system
Repulsion of magnetic fields can be modeled considering a relative permeability lower than the unit 𝜇𝑟 < 1 for
HTS bulks. As explained in chapter 2, previous works showed that a relative magnetic permeability of 𝜇𝑟 = 0.2
allows reliable quantitative results.
Considering that the ZFC SMB is composed by a static part (stator) and a rotating part (rotor), the part that should
levitate is the rotor. Hence, the proposed design of the frictionless rotating SMB model [23] has an inner rotor
part including the trails of PMs and an outer stator part including the discontinuous lines of HTS bulks. The outer
stator part contains two discontinuous rings of equally spaced of YBCO HTS bulks. An alternative approach using
PMs and HTS rings instead of bulks was discarded for economic reasons. Actual rings have to be made with
specific geometry and dimensions, whereas generic bulks are much cheaper and easier to obtain.
The inner rotor part contains three discontinuous rings with five equally spaced NdFeB permanent magnets. All
PMs belonging to the same discontinuous ring, are magnetized with concordant poles towards the axis. The three
inner discontinuous rings of PMs are magnetized in an alternate North-South-North way, such as the two border
rings of magnets have concordant polarizations and the middle ring of magnets opposite polarization. The rings
of magnets in this geometry present a distance of 20 mm between each other. The discontinuous rings of PMs
and HTS bulks are interposed in such a way to provide guidance forces [8]. The distances between the HTSs as
well as the distances between the PMs were kept, according to Fig. 3.1, closing the track in a circular shape to
obtain the cylindrical geometry of the SMB, show in Fig. 3.2.
12
Figure 3.2 – Perspective view: spatial distribution of PMs and HTSs bulks
Analyzing the referential, it is possible to observe that the levitation forces are measured in the 𝑥 axis, while the
guidance forces in the 𝑦 axis.
The projection views of the frictionless SMB geometry (and dimensions) are shown in Fig. 3.3.
Figure 3.3 – Projection view: spatial distribution of PMs and of HTSs bulks in mm
Several case studies were analyzed. For all the case studies, calculations were performed by simulations using a
finite element modeling (FEM) approach. The PMs considered in the simulations are neodymium magnets,
i.e. 𝑁𝑑2𝐹𝑒14𝐵. Each one has a rectangular form with dimensions 25x25x12 mm and a mass of 0.06 kg. An
example of one of the PMs used is shown in Fig. 3.4.
Figure 3.4 – Example of an used PM
32
32
1 0
32
25
12
14
R 43.5
2 0 2 0
13
The HTS bulks considered in the simulations are made of YBCO (Yttrium barium copper oxide) material. Each one
has a rectangular form with dimensions 32x32x14 mm and a mass of 0.09 kg. An example of one of the HTSs used
is shown in Fig. 3.5.
Figure 3.5 – Example of an used HTS
For the simulations that were carried out, both FC and ZFC techniques are analyzed. The assumed value of the
permanent magnet remainder magnetic flux density is 𝐵𝑟 = 1.2 𝑇 [14]. For the ZFC technique, the assumed
relative magnetic permeability for the HTS bulks is 𝜇𝑟 = 0.2 [8, 9, 22].
14
A. Case 1- levitation forces between one PM and one HTS
This case study simulates and evaluates the levitation forces, namely the repulsion forces between one PM and
one HTS. For the simulation, it is assumed that both the PM and the HTS are horizontally disposed with both
centers aligned at a given vertical distance. An example of the simulation showing the ZFC distribution of
magnetic flux between the PM and the HTS at 12 mm vertical distance is shown in Fig 3.6.
Figure 3.6 – ZFC distribution of magnetic flux at 12 mm vertical distance
Both ZFC and FC techniques were simulated and compared. Several distances between the upper surface of the
PM and the lower surface of the HTS were considered. For FC, the magnetization distances are also taken into
account. The ZFC and FC techniques repulsion forces between a PM and a HTS at several distances are shown in
Fig. 3.7.
Figure 3.7 – ZFC and FC techniques: repulsion forces between a PM and a HTS [23]
It clearly shows that the ZFC repulsion forces between the PM and the HTS at several vertical distances are always
higher than FC repulsion forces. Moreover, it shows that when the FC magnetization distances increase, the
repulsion forces get closer to ZFC, as expected. The results obtained for the repulsion forces between the PM
and the HTS shown in Fig. 3.7 are similar to the ones presented in [8], [24].
15
B. Case 2 - SMB levitation and guidance forces
This case study evaluates the levitation forces and the guidance forces between the PMs and the HTSs for the
proposed design of the frictionless rotating SMB. Several air gap distances were considered. The perspective
view of the magnetization directions and contours for the frictionless rotating SMB is shown in Fig 3.8.
Figure 3.8 – SMB:perspective view of magnetization directions and contours [23]
The transversal view of the magnetization directions and contours for the frictionless rotating SMB is shown in
Fig. 3.9.
Figure 3.9 – SMB: transversal view of magnetization directions and contours [23]
The longitudinal view of the magnetic flux density lines for the frictionless rotating SMB is shown in Fig. 3.10.
16
Figure 3.10 – SMB: transversal view of magnetic flux contours [23]
The red arrows shown in Fig. 3.8 to Fig. 3.10 represent the magnetic polarization direction of the PMs.
The levitation forces and the guidance forces vs. the air gap size for the frictionless rotating SMB in both ZFC and
FC modes are shown in Fig. 3.11 and Fig. 3.12. Results for FC are shown for 150% and 200% relation between the
cooling distance and operational distance [10]. In this case, the operational distance is equal to the air gap. These
figures show that levitation forces and guidance forces decrease when the air gap increases, as expected.
Moreover, these figures clearly show that the forces obtained using ZFC technique outperform those obtained
by the FC technique.
Figure 3.11 – Frictionless SMB: levitation forces [23]
Figure 3.12 – Frictionless SMB: guidance forces [23]
17
3.3. Full structure model
Regarding the full structure, with the 16 YBCO bulks, it is important to note that it is symmetric, and so are all
the forces applied, with exception of the gravity force. Hence, for a horizontal SMB, the rotor will never have an
equilibrium position that is concentric to the stator if the magnetic forces are symmetric. As the rotor part tends
to fall down due to the gravity force, the bottom air gap is reduced while the upper one grows, until the
equilibrium is reached. It is also possible to say that the distance from the center of the rotor to the center of the
stator (eccentricity) will be reduced, the stronger the magnetic levitation forces are. A free body diagram is
shown in Fig. 3.13, where the forces applied by the magnetic fields are represented in blue and the gravity force
of the rotor part is represented in orange.
Figure 3.13 – Forces applied in the SMB
This behavior consents the estimation of the allowed rotor weight using the graphic of Fig. 3.11 for the ZFC
technique, depending on the air gap measure. The outcome is shown in Table 3.1.
Table 3.1 – Air gap and eccentricity influence in the supported weight
Eccentricity Bottom air-gap Upper air-gap Allowed weight
mm mm N mm N N Kg
2.5 6 28 11 12 16 1.63
1.5 7 21 10 14 7 0.713
0.5 8 18 9 15 3 0.306
0 8.5 17 8.5 17 0 0
18
3.4. Studied model
Due to some budget limitations, it was not possible to cover the cost of the 16 YBCO bulks. Subsequently, it was
inconceivable to build a full SMB prototype to validate the simulations. Therefore, a different prototype version
was implemented to validate the simulations, as shown in the next chapters. The major difference is that only 6
superconductors were used on the bottom of the stator (3 YBCO bulks for each one of the 2 stator rings). The
projection view of the model with 6 HTSs is shown in Fig. 3.14-A.
A
B
Figure 3.14 – ZFC-SMB model with 6 HTSs
Using this new prototype design, 3D FEM simulations were carried out, where the balanced rotor shown in
Fig. 3.14-A and an unbalanced rotor condition shown in Fig. 3.14-B are considered to obtain the sustaining rotor
forces. This is the model studied throughout the development of this work and all the executed practical
experiments refer to this model.
The plot of the levitation forces vs. the air-gap for the final model is shown in Fig. 3.15. Results were obtained
using the previous 3D FEM model, while changing the rotor/stator air gap value from a realistic minimum value
of 4 mm to the maximum value of 12 mm.
Figure 3.15 – Levitation forces vs. air gap
In order to obtain the estimated levitation forces, only the bottom half ring of HTSs was considered in the FEM
simulation. This means that the radial equilibrium forces were calculated based on the integration between 0
and 𝜋. Otherwise, since the structure is symmetric, if it was integrated between 0 and 2𝜋 to obtain the levitation
forces, the result would be null.
X X
19
The guidance forces can be measured imposing a specific translation displacement in the 𝑦 axis direction from
the equilibrium position. The graph of the guidance forces is shown in Fig. 3.16, where the same air gap values
from the levitation forces simulations were used.
Figure 3.16 – Guidance forces vs. lateral displacement for the different air gap values
For the current geometric dimensions, the interval between ±10 mm is the stable range, from where the rotor
can return to its equilibrium position. It is important to note that 8.5 mm of air gap correspond to a value of zero
eccentricity of the rotor axis in relation to the stator axis of the SMB (centered rotor).
As expected, both levitation and guidance forces are higher for a smaller air gap of 4 mm. These forces were
measured considering the influence of the bottom half HTSs in the system. The resulting frictionless rotating SMB
geometry and air gap dimensions are adequate to create levitation and guidance forces showing that, regarding
the computed results, it is possible to state that the SMB is viable and feasible.
The total weight of the 15 PM in the rotor is about 8.83 N. Fig. 3.15 and Fig. 3.16 show that for ZFC the levitation
and guidance forces estimated are higher than the rotor weight. Hence, the SMB can also be self-sustainable in
a horizontal position.
20
3.5. Rotor geometry influence
During the performance of the first rotor insertion, detailed in section 5.6, the necessity of building a SMB
presenting higher levitation forces while being built with the same parts was important. Moreover, an alternative
was studied in order to maximize the levitation forces in the SMB without changing the air gap. It consisted in
changing the distance between the PM rings in the rotor, as shown in Fig. 3.17 and Fig. 3.18. These figures show
a transversal cut view of the inferior part of the system to demonstrate the changes in the geometry.
Figure 3.17 – First rotor and its PMs/HTSs relative positions
Figure 3.18 – New rotor and its PMs/HTSs relative positions
The simulations with the new geometry were carried out. The values obtained confirm that this method provides
an increase in the levitation forces as the PM rings come closer to each other. The counterpart is that in this case,
the stable range for the guidance forces will be smaller and subsequently the guidance forces will decrease
relatively to the first geometry results, seen in Fig. 3.16. It is not possible to build a SMB with too low guidance
forces, as these would not be enough to provide the rotor with lateral stability.
PMs
PMs
HTSs
HTSs
20 mm 20 mm
5 mm 5 mm
21
Moreover, the results of the simulations made with the new rotor model stated the previously explained
behavior. The plot of the levitation forces vs. the air-gap is shown in Fig. 3.19.
Figure 3.19 – Levitation forces vs. air gap for the new geometry
The graphic of how the guidance forces measured for the new geometry vary for an air gap of 10 mm is shown
in Fig. 3.20.
Figure 3.20 – Guidance forces vs. lateral displacement for the new geometry
As it can be observed, when comparing this graph with Fig. 3.16, the change in the geometry with the
approximation of the PM rings caused a decline in the guidance forces. It is also possible to see that the stable
range from where the rotor can return to its equilibrium position has diminished to ±8 mm. Only the air gap of
10 mm is shown in this graph, since it is enough to study the new geometry behavior.
The results above clearly show that the distance between the PM rings in the rotor directly affect the levitation
and guidance forces, creating a “levitation vs. guidance” trade-off that could be optimized in the future.
0
5
10
15
20
25
30
35
40
45
50
55
4 5 6 7 8 9 10 11 12
Sust
ain
ing
roto
r fo
rce
(N)
Air gap (mm)
-6
-4
-2
0
2
4
6
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Gu
idan
ce f
orc
e (N
)
Displacement (mm)
22
4. Prototype design and conception
In this chapter, the information regarding the development of the design and conception of the SMB is provided.
Firstly, a careful choice of materials to build each part of the SMB prototype is described. Afterwards, the design
is elaborated, based on the necessities explained on chapter 3 and on the materials chosen and the details about
the construction of the first model are presented. Furthermore, improvements made to the design and to the
construction of the prototype are also addressed. Finally, an inventory of all the parts that constitute one SMB
after every improvement is shown.
4.1. Choice of materials
The choice of materials plays an important role in this work. The main characteristics of the SMB model result
from this choice. It will affect the structure resistance and stiffness, as well as the ability to conceal the liquid
nitrogen inside the stator part while providing a good thermal insulation.
The most important aspect when choosing the materials for this prototype is that none of these interferes with
the magnetic forces produced by the HTSs and PMs. This means that all the materials in the SMB should have a
relative magnetic permeability of about 1 (𝜇𝑟 = 1). Therefore, all the types of materials that would interfere with
the magnetic field were not considered.
In this sub-chapter, the material choice is presented for each part that constitutes the SMB, providing detailed
information about this selection.
23
A. Stator
Due to the fact that the stator is directly in contact with the liquid nitrogen, it has to be made of a material that
can resist to temperatures in the order of 77 K without breaking. Besides, it also needs to be impermeable in
order to seal the liquid nitrogen inside the structure. It is very important that the material possesses a low
thermal conductivity coefficient in order to retain the cold temperature inside the structure, therefore using the
smallest amount of liquid nitrogen as possible to keep the HTSs below their critical temperature. Some
information about the thermal conductivity values for various materials is shown in Table 4.1 [25].
Table 4.1 – Thermal conductivity of several materials [25]
Material Thermal conductivity
(W/m K)
Diamond 1000
Gold 314
Aluminum 205.0
Iron 79.5
Steel 50.2
Water at 20° C 0.6
Polyethylene 0.4
Fiberglass 0.04
Polystyrene (Styrofoam) 0.033
Polyurethane 0.02
Wood 0.12-0.04
Air at 0° C 0.024
Silica aerogel 0.003
From several materials that exhibit these properties, rigid polyurethane was considered the most appropriate
choice since this type of material is affordable and can also be easily machined, acquiring the desired forms for
the final structure. At a later stage, an experience was also performed using a stator made of polyethylene.
Although this material has a higher thermal coefficient, it is very cheap, easy to acquire as well as to be machined
in a CNC.
24
B. Rotor
The main function of the rotor part is to provide the structure to hold the 15 PMs with the lightest weight
possible, in order to maximize the effect of the levitation forces and reduce the eccentricity. Since the rotor is
not in contact with the liquid nitrogen, its material does not need to present a low thermal conductivity
coefficient. However, with the purpose of simplicity on the acquisition of material and construction, the rotor
was made from the same material as the stator: high density polyurethane.
In a later phase of the present work, as shown in section 4.4.2, rotors of Polylactic acid plastic (PLA) were built,
as this material also possesses the necessary characteristics, with the advantage that in can be fabricated using
additive manufacturing with a 3D printer, saving much construction time and resources.
C. Other parts
Several other types of parts were designed to assemble the SMB parts together, namely bolts, nuts, corners and
washers. Special care was taken choosing the materials for these parts, for their main function is to be able to
resist the pressure to close the structure at very low temperatures. There are no other special requirements
besides being transparent to the magnetic field and exhibit low thermal conductivity to keep the stator cooled.
These parts are possible to manufacture using Acrylonitrile Butadiene Styrene (ABS), with the intention of
building them in a normal 3D printer.
25
4.2. Prototype design
The use of 3D CAD Design Software for concept design has been widely spread. Besides, CNC machines are
nowadays able to produce real prototypes based on the 3D CAD designed models. Lately, additive manufacturing
techniques like 3D printers became more and more used for rapid prototyping [26].
Hence, a SMB prototype was modeled in 3D CAD Design Software to meet the following requirements:
i) Provide a structure to keep the distances, relative positions and the air gap of the HTSs and PMs [23];
ii) Provide a sealed body (stator) to cool and maintain the HTSs immersed in liquid nitrogen;
iii) Develop a modular prototype;
iv) Design a prototype with easy assembly and disassembly features for practical PMs and HTSs
accessibility, maintenance and/or replacement.
Three main blocks were designed for the SMB [27]: the stator, which is the outer static part of the SMB; the
rotor, which is the inner rotating part of the SMB; some fasteners to keep the structure together. These blocks
are here described in detail.
26
A. Stator
The outer part of the SMB is the stator. This part does not move and supports 16 HTSs distributed in two rings.
It is composed by 4 identical slices. The model of one stator slice with 8 HTSs bulks is shown in Fig. 4.1.
Identical slices that can be assembled to produce the whole SMB stator, i.e., the stator exploded view is shown
in Fig. 4.2.
Figure 4.1 – One stator slice with HTSs bulks [27]
Figure 4.2 – Stator exploded view [27]
In Fig. 4.2, 2 symmetric profiles of 8 cavities each are shown, where the HTSs are to be positioned.
This model guarantees the distance and relative positions of the HTSs. All of these cavities are connected through
a channel, so that liquid nitrogen can flow and cool the HTSs.
27
The liquid nitrogen entrance and the channel details are shown in Fig. 4.3.
Figure 4.3 – Liquid nitrogen entrance and open channel details
The stator was designed so that each cavity is slightly bigger than the HTS bulks, because when subjected to very
low temperatures the bulks size is reduced. The subsequent expansion can lead to an increment in the size of
the HTSs after several uses. The prototype is modular, namely because of the construction built on slices, that
allows multiple configurations. This type of construction also eases the assembly and disassembly of the
prototype. With the purpose of joining the assemblies together, 4 holes of 6 mm diameter were designed in the
edge of each slice.
In order to keep the liquid nitrogen concealed inside the stator, a 4 mm thickness wall was kept on the closest
side to the rotor, as shown in detail in Fig. 4.4.
Figure 4.4 – Detail of the inner wall of the stator
With the proposed design for the stator, the working range of the rotor is limited by a diameter of 92 mm.
The stator technical drawing is shown in Fig. A 1 of the appendix section presented in the end of this document.
Open channelTwo halves
of a hole
4 mm thick wall
28
B. Rotor
The inner part of the SMB is the rotor. It is the rotating part of the SMB and supports 15 PMs distributed in three
rings. This part design proposes two types of pieces to be built: two exterior slices and two interior slices. The
exterior rotor slice with 5 PMs in place is shown in Fig. 4.6. The interior rotor slice with 5 PMs in place is shown
in Fig. 4.7. The complete rotor, i.e., the rotor exploded view is shown in Fig. 4.8.
Figure 4.5 – Exterior rotor slice with PMs [27]
Figure 4.6 – Exterior rotor slice with PMs [27]
Figure 4.7 – Rotor exploded view [27]
29
In Fig. 4.8, the rotor exploded view is composed by 2 interior and 2 exterior slices assembled to produce the final
part. This type of slice construction was used to make possible a manufacturing in a 3D printer.
The modeled stator guarantees the distance and relative positions of the PMs. There is no need of liquid nitrogen
channels because the rotor does not need to be cooled. Like the stator, the rotor prototype is modular, namely
because of the construction based on slices, that also allows multiple configurations. This prototype modular
type of construction eases its assembly and disassembly. With the intention of joining the assemblies together,
4 holes of 6 mm diameter were designed.
Since the rotor diameter is 87 mm and the stator diameter is 92 mm, the clearance range of the rotor will be
5 mm. Subsequently, when the rotor is at rest in contact with the bottom part of the stator, the air gap between
the bottom HTSs and PMs is 6 mm, while the air gap between the upper HTSs and PMs is 11mm.
C. Fasteners
Other parts were designed, namely bolts, nuts, corners and washers to assemble the SMB parts together. Special
care was taken in the modeling of these parts. As the polyurethane from the stator part has limited mechanical
resistance, the miscellaneous parts were modeled to carefully keep the parts assembled without hurting the
delicate material. These miscellaneous parts have no special requirements besides being transparent to the
magnetic field and exhibit low thermal conductivity to keep the stator cooled.
1. Bolts
To keep the rotor slices together, hexagonal head bolts with a diameter of 6 mm and a length of 150 mm were
designed. Alternatively, to keep the stator slices together, hexagonal head bolts with a diameter of 6 mm and a
length of 115 mm were designed.
2. Nuts
For all bolts, eight nuts were designed to assemble both stator and rotor together. The threads of the nuts and
bolts were not designed because it is assumed that these are printed on a 3D printer, which normally does not
have enough resolution to print the threads with an acceptable quality. Hence, it is assumed that the threads will
be made manually, using a lathe machine.
3. Stator Corners
As the stator material is expected to be soft and fragile, eight corners were modeled to increase the surface of
contact, reducing the pressure applied to the material by the bolts.
4. Rotor washers
The rotor material does not need to resist to such low temperatures, because the PMs do not need to be cooled.
Nevertheless, assuming that the rotor might also be constructed with the same materials of the stator, two
washers were modeled to increase the surface of contact.
30
5. Fasteners complete set
The set of the fasteners complete set used for the final assembly of the SMB is shown in Fig. 4.8.
Figure 4.8 – SMB fasteners for final assembly [27]
D. Virtual assembly of the prototype
With the components modeled before, the SMB was virtually assembled. The full assembly exploded view is
shown in Fig. 4.9.
Figure 4.9 – Virtual SMB exploded view [27]
The SMB virtual prototype final assembly view is shown in Fig. 4.10.
Figure 4.10 – Virtual SMB final assembly [27]
31
4.3. Prototype construction
In the prototype construction, certain constraints must be considered, namely the manufacture techniques that
are more suitable to the implementation of the parts, depending on their materials. In this subsection, each part
is specified along with its production method.
A. Stator
The stator was built using a 3 axes CNC milling machine with the technical drawings provided by the CAD
software. Four holes of 6mm diameter were drilled for the bolts. In order to execute this task, access to the CNC
milling machine of Fablab EDP was granted. The machine used was an Ouplan 2010 with a working area of
1900x900 mm. It can reach a speed over the material of up to 200 mm/s. The software used with the CNC
machine was CUT2D. A photo of this machine is shown in Fig. 4.11.
Figure 4.11 – Ouplan CNC milling machine 1
One final slice of the stator part is shown in Fig. 4.12 and the set of the 4 slices is shown in Fig. 4.13.
Figure 4.12 – One slice of the stator
1 Source: http://www.ouplan.net/pt/fresadoras-cnc.html [20th September 2016]
32
Figure 4.13 – Four stator slices in their orientation of assembly
B. Rotor
The rotor was built using the same CNC milling machine. Four holes of 6 mm diameter were drilled for the bolts.
The middle hole was drilled to add the possibility of attaching the rotor to a rotating shaft. One final slice is shown
in Fig. 4.24.
Figure 4.14 – One rotor slice
The set of the 4 slices is shown in Fig. 4.15.
Figure 4.15 – Four rotor slices in their orientation of assembly
33
C. Fasteners
Rapid prototyping is a fast production technique that is growing in the market in the past few years. It is a fast
and easy way to obtain custom parts using CAD data. For this reason, and based on the models previously drawn,
the fasteners parts including bolts, nuts, corners and washers were manufactured in a 3D printer. Access to the
3D printer of the mechatronics laboratory was provided. The model used is the MakerBot Replicator. It presents
a dual extruder offering a layer height resolution of 0.2 mm, a positioning precision of 2.5 µm on the Z axis and
11 µm on XY axis. A heated building plate with a capacity build envelope of 225 x 145 x 150 mm is also
incorporated. The machine used for this purpose is shown in Fig. 4.16.
Figure 4.16 – MakerBot Replicator 3D printer 2
The miscellaneous parts produced with the 3D printer are shown in Fig. 4.17.
Figure 4.17 – Fasteners
The bolts and the nuts were threaded using a lathe machine since the finishing is relatively good for their purpose,
using ABS material.
2 Source: www.zahncenternyc.wikidot.com/replicator-1 [20th September 2016]
34
D. Assembly
The rotor assembly starts without using the PMs. The four rotor slices are held together using the rotor washers
and bolts. After the rotor parts are assembled, the PMs are inserted in the rotor with special care because of the
magnetic forces involved. Since the strong magnetic fields of the PMs inside the rotor produce strong repealing
forces, duct tape is used around each ring of PM’s. The duct tape does not influence the magnetic fields and only
avoids the PMs from falling of the stator.
The stator assembly is made slice by slice, with the insulator film between each slice, as shown in Fig. 4.18. Inside
each stator ring, 3 HTSs are placed in the bottom zone in accordance with the studied model, presented on
chapter 3.4. To minimize the distance from the HTSs to the rotor part, thin rubber pieces are glued to the HTSs
supporting wall inside the stator, in order to make sure that the HTSs touch the inner wall of the stator.
Figure 4.18 – Stator assembly
The stator should then be closed using the respective corners and bolts.
The final assembly including every part is shown in Fig. 4.19.
Figure 4.19 – Final assembly
Rubber pieces
35
4.4. Improvements
As the practical experiments with the SMB were being elaborated, some minor issues in the prototype had to be
corrected. Most of these improvements were made only after performing several experiences with the first
constructed model of the SMB.
4.4.1. Design improvements
The minor issues appearing inspired some new ideas on how to change the design of the SMB.
A. Stator
After some practical experiments, the designed structure proved to have some minor problems:
i. In the first moments of pouring the liquid nitrogen through one of the holes in the stator, most of the
liquid nitrogen would gasify, as expected. This gasified nitrogen would be forced to come out through
the same channel where liquid nitrogen enters, making the constant pouring of the liquid a difficult task;
ii. Some of the bottom cavities for the HTSs in the stator were not being filled with liquid nitrogen, due to
the imprisonment of air in some parts of the structure;
iii. The four holes designed for clamping were not consistent and did not provide a uniform clamp.
Subsequently, some modifications to the stator were made. In each cavity of the HTSs in the middle slices of the
stator, a hole was opened for the communication of nitrogen between the two symmetrical rings. These channels
ease the task of transferring liquid nitrogen to the stator, since there is now an open hole to the exterior where
the gasified nitrogen can escape through. It also allows the assurance that the two rings in the stator are equally
filled with liquid nitrogen.
Another inner channel was opened for the circulation of nitrogen in order to avoid the air imprisonment.
Likewise, 8 new holes were designed for a uniform clamping, closer to the center of structure, between each
cavity of HTSs.
These changes made are shown in Fig. 4.20.
36
Figure 4.20 – Modifications in the stator part
Subsequently, the stator design was changed and this part is now composed by two different type of slices: stator
inner slices and stator outer slices.
The holes designed for the rods were changed to a diameter of 6.5 mm. This change was done to provide an
easier fitting of the rods when passing through the holes.
The technical drawings of each one of the stator slices after improvement are show in Fig. A 2 and Fig. A 3 of the
appendix section presented in the end of this document.
Outer liquid nitrogen channel Inner liquid nitrogen channel
37
B. Rotor
The rotor part had many changes while this study was being performed. As shown in chapter 3.5, the levitation
and guidance forces vary in an inversely proportional way when the distance between the rings of PMs is
changed. Subsequently, several rotors were constructed having always in mind the main objective of minimizing
its weight. A new model was designed with only three holes for the rods and removing the unnecessary material.
The new model is shown in Fig. 4.21.
Figure 4.21 – Improved rotor profile
C. Fasteners
Most of the stress concentrates in the bolts, because their function is to provide a consistent clamping. These
proved to last very few when constructed with Acrylonitrile Butadiene Styrene (ABS) in a 3D printer, and broke
after a couple of usages. Instead, threaded rods made of ertacetal® were designed in order to achieve better
resistance, since this material is stronger and resists well at low temperatures. To keep the stator slices together,
rods with a diameter of 6 mm and a length of 130 mm were designed. The rod is shown in Fig. 4.22.
Figure 4.22 – M6 rod with a length of 130 mm
For the rotor slices, several rods with different dimensions were designed, depending on the rotor size.
38
4.4.2. Construction improvements
Resulting from the design improvements, several new constructions had to be made or changed along the
execution of this work. The details are described in the next sections.
A. Stator
The same construction techniques were used to produce the two different newly designed slices of the stator in
polyurethane, described in the previous section. The final construction of the inner stator slice is shown in
Fig. 4.23.
Figure 4.23 – Inner stator slice
Likewise, the final construction of the outer stator slice is shown in Fig. 4.24.
Figure 4.24 – Outer stator slice
39
Additionally, with the purpose of testing how the thermal conductivity coefficient of the stator material affects
the thermal insulation of the liquid nitrogen, another stator part was built in polyethylene. This part already
presented the design changes made in section 4.4.1. All the construction methods used before were also
appropriate for this material. Though it presents a higher thermal conductivity coefficient and therefore more
liquid nitrogen should be used to cool the structure, the cost of the material is much cheaper. This stator
construction made of polyethylene is shown in Fig. 4.25.
Figure 4.25 – Stator made of polyethylene
B. Rotor
Addictive manufacturing is a growing utility nowadays because of its ability to produce parts with the desired
shapes in a simple and quick way without wasting any material. Because of the necessity of having several rotors
for the experiments, Polylactic acid plastic (PLA) proved to be a relatively good material choice when compared
to high density polyurethane, since it can also be easily built using additive manufacturing with the already used
3D printers, also presenting relatively low weight.
The experiment later described in section 5.6 led to the construction of a rotor that would present a smaller
distance between the PM rings. The hypothesis proposed is that as the distances between the PMs of the
previous built rotor decrease, the levitation forces provided by the interaction of the PMs and the HTSs will
increase. The simulations made in section 3.5 confirmed this behavior. Therefore, such a situation creates the
need of carefully studying the behavior provided by these changes in the SMB and the necessity of designing a
rotor that optimizes the levitation forces in relation to the guidance forces. This topic is hereby left for future
studying regarding this project.
40
For an easier understanding and identification of each rotor model, names were given to the rotors based on the
distance between each PM ring. Therefore, the rotor constructed with the original geometry shown in section
3.2 – distance of 20 mm between each PM rings – was named “rotor D20”. This rotor is shown in Fig. 4.26.
Figure 4.26 – Rotor D20
After being fully assembled, the rotor D20 presented a mass of 1.245 Kg.
The rotor constructed with the later designed geometry – 5 mm between each PM ring – was named “rotor D5”.
This rotor is shown in Fig. 4.27.
Figure 4.27 – Rotor D5
After being fully assembled, the rotor D5 presented a mass of 1.038 Kg.
Like already described in section 3.2, the PMs have to be assembled in the three rings of the rotor with an
orientation North-South-North, respectively. Subsequently, each PM exerts a repulsion force on the other PMs
of the same ring. In order to safely keep each PM in the rotor avoiding the risk of falling, duct tape was used
around each ring. The duct tape does not influence the magnetic field in the system.
41
C. Fasteners
The rods mentioned in the previous section were built in a material named ertacetal. Likewise, they were
threaded using a lathe machine. This material can also provide a relatively good finishing for their purpose when
machined by the lathe. The result of the final constructed rods is shown in figure 4.28.
Figure 4.28 – Rods made of ertacetal
D. Leakage insulator
In order to avoid the dropping of liquid nitrogen between the slices of the stator, a thin film made of flexible
rubber was used as an insulator. This film was applied in the parts where the stator slices make contact with each
other. This material acts as a soft and flexible insulator, adapting to the imperfections in the points of contact
between the slices to close the gaps and contain the liquid nitrogen inside the structure. The film insulators used
are shown in Fig. 4.29.
Figure 4.29 – Two types of film insulators used in the stator
42
4.5. Final inventory
The inventory of all the parts that constitute one SMB after every improvement is shown in Table 4.2:
Table 4.2 – Inventory
Part Quantity
stator inner slice 2
stator outer slice 2
rotor inner slice 2
rotor outer slice 2
flexible rubber film 3
YBCO superconductor bulks 6
permanent magnets 15
stator rods 8
rotor rods 3
stator nuts 16
rotor nuts 6
The final assembled structure of the SMB, without the rotors already represented above, is shown in Fig. 4.30.
Figure 4.30 – Final structure
43
5. Experimental Methods
In this chapter, every aspect concerning the preparation of the real prototype to provide reliable results is
detailed. Firstly, numerous tests regarding the fine robustness and sealing are carried out. Furthermore, several
features like nitrogen usage and material wear are addressed. Finally, the experimental set-up of each experience
and the computed results are presented and examined.
5.1. Robustness to working conditions
To confirm the choice of the right materials made in section 4.1, namely the stator and the fasteners parts, an
experience was developed to study the behavior of the structure constructed in section 4.3 at working
conditions. These conditions are characterized by working at low temperatures, in the order of 77 K (liquid
nitrogen temperature) and under clamping forces that close the stator slices together. With the intention of not
harming all the structure, only half of the stator part was used in these first tests. Hence, the half of the stator
part was totally submerged in liquid nitrogen, without any HTS bulks inside, until the system achieved a state of
stability. For this purpose, some cables were attached to the structure so that it could be pulled. An example of
this process is shown in Fig 5.1.
Figure 5.1 – Totally submerged stator with cables
In this first test, the used materials presented a good resistance within the working temperature range during
the first experiences, without breaking or exhibiting any type of weakness.
44
5.2. Leak tests
To ensure the structure, namely the stator, would enclose the liquid nitrogen in an efficient way, some leak tests
were elaborated. These tests were made in a first phase with water, until the stator was successfully insulated.
In the first attempt, the stator was clamped only by the four holes in each corner. After pouring some water into
the stator through the nitrogen entrance channel, it was observed that the water would come out through
breaches between the slices of the stator.
In order to correct this issue, a rubber based insulation tape was applied between each slice of the stator in order
to insulate the structure. This insulation tape was cut accordingly to the profile of the inner part of the stator
slices, so that it was applied only where the slices make contact, as already seen in chapter 4.4.2-D.
It was observed that some water still fell between the breaches, although in much less quantity.
Subsequently it was decided to provide a better distributed and more uniform clamping to the structure, closer
to the inner part of the stator. In a first stage, this was achieved by using clamps with PVC plaques to distribute
the load. An example of how the structure was clamped is shown in Fig. 5.2.
Figure 5.2 – Clamps with PVC plaques
As this solution proved to solve the tightness problem, it led to a change in the design of the structure explained
in section 4.4.1, where as a way to avoid the clamps, 8 holes of 6.5 mm were designed closer to the inner part of
the stator to distribute the loads uniformly.
45
In order to measure the volume of liquid that the stator holds, the water inside the stator was poured to a
measuring jug. The jug is shown in Fig. 5.3.
Figure 5.3 – Jug with the volume of water read
The volume measured was about 270 ml.
After these steps, the stator was dried and some leak tests were executed, this time with liquid nitrogen.
5.2.1. Nitrogen pouring
Liquid nitrogen is unstable when exposed to room temperature. Since its boiling point is at 77 K, it immediately
evaporates. For this reason, when it is poured into the stator it often starts to boil, spilling if not handled with
caution. Hence, the pouring of nitrogen is executed slowly in short movements, periodically switching channels
of nitrogen entrances. This process usually takes about 10 to 15 minutes, until the structure is full of stabilized
liquid nitrogen. At this point we know that the temperature within the stator bulks is 77 K.
To complete the leak test, liquid nitrogen was poured inside the stator and the results were satisfactory, as the
stator remained well insulated without any nitrogen spills.
46
5.3. Nitrogen usage
In order to estimate the rate at which the liquid nitrogen would evaporate from inside the stator, a graph of time
vs. weight was elaborated. This was achieved by pouring liquid nitrogen inside the stator until the structure was
full. To read the weight values a weighting scale was used. With the structure standing on the weighing-scale,
the time was measured until the weight stopped falling. A box of Styrofoam was used to protect the scale and
the proper tare of this box was made to allow the precise reading of the structure weight. The set-up established
to read the weigh values is shown in Fig. 5.4.
Figure 5.4 – Set-up used for the nitrogen usage information
The graph of weight vs. time is shown in Fig. 5.5.
Figure 5.5 – Nitrogen evaporation rate
It is easy to see that the rate at which the liquid nitrogen evaporates in the first 600 seconds can be considered
linear, and therefore possible to calculate.
650
670
690
710
730
750
770
790
810
830
850
0 300 600 900 1200 1500 1800 2100 2400
Wei
ght
(g)
Time (s)
weight vs. time
47
In the calculation of the nitrogen usage rate, the first value considered was the weight measured after one
minute, because after pouring the liquid nitrogen in the stator, it takes some seconds to stabilize. The
evaporation rate in g/min of the liquid nitrogen in the stator was calculated and is given by:
𝐿𝑁𝑒𝑟 =
814 − 727
600 − 60= 0.161 𝑔/𝑠 = 9.67 𝑔/𝑚𝑖𝑛 (5.1)
Knowing that the density of LN is 0.807 g/mL, the evaporation rate in mL/min is given by:
𝐿𝑁𝑒𝑟 =
0.161
0.807= 0.200 𝑚𝐿/𝑠 = 11.979 𝑚𝐿/𝑚𝑖𝑛 (5.2)
48
5.4. Material wear
Through the development of this study, the repeated process of having liquid nitrogen in contact with some parts
caused the structure to present signs of wear, mainly on the stator part. This is due to the stator being the part
most subjected to very low temperatures while it is also subjected to the stress from the clamping forces that
keep the structure closed. These signs of wear were mainly noticeable in the form of cracks that started
appearing in the edge of the stator, on the closest part to the hole where the rotor fits. In this zone of the
structure the polyurethane wall is relatively thin (4 mm). This part of the structure is purposely thin in order to
provide the shortest air-gap possible between the HTSs and the PMs, making it the weakest wall of the structure.
For this reason, the solution for this problem was to insulate these cracks with silicone gel. The silicone gel was
previously tested and proved to resist very well to the liquid nitrogen temperatures while maintaining its
insulating properties. A crack insulated with silicone gel is shown in Fig. 5.6.
Figure 5.6 – Crack insulated with silicone gel
Superconductor materials work at an extreme low temperature and therefore they are subjected to important
volume variations [28]. Due to these variations in the volume, the HTSs used in these experiments started
showing some signs of wear. After using them in several experiences, some cracks started appearing as the
material started deteriorating due to the exposure to the liquid nitrogen. A crack in a HTS bulk is shown in figure
5.7.
Figure 5.7 – Cracked HTS
49
5.5. Polyethylene structure
The polyethylene structure was carefully assembled with the same set-up proceedings as for the Polyurethane
stator. The assembled structure is shown in Fig. 5.8.
Figure 5.8 – Fully assembled polyethylene stator
In this experience, even though the structure was well insulated, without the presence of any leak, it was not
possible to make the HTSs achieve the desired working temperature. As shown before in section 4.1,
polyethylene presents a thermal conductivity coefficient of 0.4 W/m.K, which is about twenty times higher than
polyurethane (0.02 W/m.K). For this reason, the heat that penetrates through the stator material is too much for
it to contain liquid nitrogen inside. Subsequently, the nitrogen evaporates faster, not letting the HTSs achieve a
temperature of 77 K. For this reason, the idea of using polyethylene as a stator material was discarded.
50
5.6. First rotor insertion experiment
Before proceeding to any measurement of the results, an experiment was elaborated with the SMB at fully
working conditions in order to verify the proposed model and the magnetic forces involved. This step was
important and had a big contribution in deciding the experimental set-ups in order to extract the information
needed with the best possible precision.
The procedure started by assembling the stator as already seen in section 4.3-D, with the clamps, and assembling
the improved rotor D20, shown in section 4.4.2. Afterwards, the process of nitrogen pouring described in section
5.2.1 was carried out for about 10 minutes, until the HTSs were completely submerged in liquid nitrogen,
therefore at 77 K. The rotor was then inserted in the stator as shown in Fig. 5.9.
Figure 5.9 – SMB fully assembled structure
As the rotor was being introduced, it was possible to feel relatively strong guidance forces. This behavior shows
that the HTSs were at the desired temperature. It was also observed that the rotor did not levitate, remaining at
rest in the lower part of the stator.
This fact created the necessity of maximizing the levitation forces in the SMB using the same PMs and HTSs,
leading to a change in the rotor geometry and a new rotor construction in section 4.4.2. The outcome allowed
the conclusion that the distance between each PM ring directly affects the levitation and guidance forces.
Moreover, the rotor D5 was also inserted in the stator. As expected, the levitation forces were higher using this
geometry. Due to this, the rotor levitated, reaching the higher part of the structure. It was also possible to feel
that the guidance forces were much weaker with this rotor than with the previous one.
51
5.7. Experimental method/set-up
The set-up was carefully planned in order to compute and compare the values of how the real SMB prototype
behaves with the simulations previously elaborated. With the purpose of measuring the forces associated to the
system, a dynamometer with a resolution of 5 g was used (approximately 0.05 N). With the intention of
measuring the air gap distances in the system, a caliper with a resolution of 0.05 mm was used. This object was
purposely made of plastic, with the intention of not interfering with the magnetic fields of the system when
examining the distances. The instruments used are shown in Fig. 5.10.
Figure 5.10 – Instruments used to measure the forces
In the next subsections, an overview about the set-up details of each experience carried out in order to compute
the results is made.
52
A. Levitation forces set-up
Previously, it was shown in section 3.4, that the final model is composed by 6 HTSs in the bottom part of the
SMB. As it was seen afterwards, in section 5.6, it is expected that using rotor D5, the rotor part will be pushed
upwards by the influence of the magnetic forces. Hence, the experimental set-up must provide a way to measure
the force needed to pull the rotor to the center of the stator part.
Therefore, a structure was built to support the SMB. With this structure, it was possible to connect the rotor to
a string and pull it down by the two sides. This string was then connected to a dynamometer, which measured
the levitation forces. For better precision, the dynamometer was hooked to a screw that was attached to the
structure. Rotating the screw would vary the air gap distance between the rotor and the stator. The experimental
set-up to read the levitation forces is shown in Fig. 5.11.
Figure 5.11 – Experimental set-up used to read the levitation forces
After the usual process of nitrogen pouring described in section 5.2.1 was carried out, the rotor D5 was inserted
and the values were read from the dynamometer while the screw was used to vary the air gap. The caliper was
used to read the air gap distances between the rotor and the stator.
The values computed for the levitation forces are shown in section 5.8.
53
B. Guidance forces set-up
In order to compute the guidance forces in the real prototype of the SMB using rotor D5, a simple set-up was
prepared. The structure consists in a fixed shaft to confine the rotor movement while measuring the guidance
forces by pulling the stator. To avoid friction, the stator is fixed to a cart that allows movement through the rotor
axis direction. The forces reacting to this movement are read with a dynamometer that is connected to the kart
with a string, in order to estimate the guidance forces. The structure with the rotor and stator in position is shown
in Fig. 5.12.
Figure 5.12 – Guidance forces measuring structure
After the usual process of nitrogen pouring described in section 5.2.1 was carried out, the rotor D5 was inserted
along with its shaft into the stator. While reading the values from the dynamometer, an axial rotor misalignment
was forced to measure the guidance forces that push or pull the rotor to its axial equilibrium position. The caliper
was also used to read the lateral displacement of the rotor in relation to the stator. The process of measuring
the guidance forces is shown in Fig. 5.13.
Figure 5.13 – Guidance forces measurement
The values computed for the guidance forces are shown in section 5.8.
54
5.8. Results
The results provided by each of the previous experiments are shown below.
A. Levitation forces results
In order to estimate the levitation forces results in the system, the weight of the rotor had to be added to the
values read on the dynamometer. The levitation forces results are shown in Table 5.1.
Table 5.1 – Levitation forces results
Eccentricity (mm) Measured forces (kg) Measured forces (N) Levitation forces (N)
-1,75 2,096 20,5408 30,7132
-1,1 1,184 11,6032 21,7756
-1 1,076 10,5448 20,7172
-0,3 1,036 10,1528 20,3252
-0,25 0,898 8,8004 18,9728
As already presented in section 4.4.2, the fully assembled rotor D5 has a mass of 1.038 Kg (10.18 N).
55
B. Guidance forces results
The guidance forces results are shown in Table 5.2.
Table 5.2 – Guidance forces results
Displacement (mm) Force (g) Force (N)
-16 0 0
-14 -120 -1,176
-12 -150 -1,47
-10 -190 -1,862
-8 -180 -1,764
-6 -155 -1,519
-4 -145 -1,421
-2 -120 -1,176
0 0 0
2 25 0,245
4 75 0,735
6 85 0,833
8 110 1,078
10 85 0,833
12 145 1,421
14 125 1,225
16 101 0,9898
18 0 0
56
5.9. Free damping regime analysis
Understanding the characteristics of the dynamic response of the ZFC SMB to an unbalanced rotor condition is
critical. For this reason, using the SMB prototype, the PM rotor was initially pulled to a lateral displacement
position of 17 mm away from its equilibrium. The rotor was then released from this initial position until it reached
its stable equilibrium, where the resulting guidance force becomes null. The graphic with the computed real
dynamics is shown in Fig. 5.14.
Figure 5.14 – Comparison between the real dynamics and the 2nd order model
On a preliminary analysis, it is possible to observe that the dynamics behave like a second order system.
Therefore, in order to make a first approach to determine the characteristic equation for the dynamic behavior,
it is necessary to find the parameters for a second order system.
�� + 2𝜉𝜔𝑛�� + 𝜔𝑛2𝑥 = 0, 𝑥(0) = 𝑥0 , ��(0) = 0 (5.3)
The solution of the differential equation is a decaying sinusoidal wave and is given by:
𝑥(𝑡) = 𝑒−𝜉𝜔𝑛𝑡 (𝑥0 cos(𝜔𝑑𝑡) +
𝜉
√1 − 𝜉2sin(𝜔𝑑𝑡)) (5.4)
Knowing that ωd = ωn√1 − ξ2 the parameters ξ and ωn need to be estimated.
To determine the damping constant ξ, an exponential data fitting model was used with the upper points of the
curve. Doing this step, it is possible to determine the coefficient of the exponential c = ξωn and with visual
inspection, the oscillations’ angular frequency ωd to be around 2Hz. With those two constants, ωn is given by:
𝜔𝑛 = √𝑐2 + 𝜔𝑑
2 (5.5)
57
With the determined constants, a new model was developed using a state-space representation and a simulation
plotted in Figure 1 using the same initial condition as the experiment made.
[𝑥1
𝑥2]
= [
0 1−𝜔𝑛
2 −2𝜉𝜔𝑛] [
𝑥1
𝑥2] (5.6)
Analyzing the two curves, it is possible to observe that there is a change in the frequency over time in the “real
dynamics” curve. Subsequently, it is viable to conclude that the damping factor changes over time and the system
cannot be represented by a second order linear system. The time change in the damping factor is a characteristic
of a system presenting energy dissipation, source of a non-linear damping [30]. In this case, it comes from the
fact that the ZFC superconductor has joule losses that are dependent of the oscillating frequency, which means
that the damping factor rises and the oscillation frequency rises. For simplicity, it should be assumed in further
studies that the nonlinear damping force depends on the n-power of the velocity as suggested in [30].
58
6. Conclusion and future works
In this section, the results obtained from the previously made experiences with the real SMB model are compared
with the simulation results computed in chapter 3.5. Furthermore, the conclusions regarding the project are
discussed and several ideas of possible future work are written.
6.1. Conclusion
The conclusion subchapter starts with the comparison of the results obtained by the real SMB model and the
simulations divided onto two sections, followed by a section regarding important final remarks of this project.
A. Levitation forces comparison
The levitation forces vs. eccentricity graph was computed and is shown in Fig. 6.1.
Figure 6.1 – Levitation forces vs. eccentricity graph
After comparing the plotted values, it is possible to observe that the approximation is reasonably good, with the
experimental values presenting the same behavior as the simulation results. However, one possible issue causing
the minor discrepancy between the results might be the simple linear approximation of the relative magnetic
permeability 𝜇𝑟 = 0.2 used in the simulations in order to characterize the model.
0
5
10
15
20
25
30
35
40
45
50
0 0,25 0,5 0,75 1 1,25 1,5 1,75 2
Forc
e (N
)
Eccentricity (mm)
Levitation forces vs. Eccentricity
Experimental
Simulation
59
B. Guidance forces comparison
The guidance forces vs. lateral displacement graph was computed and it is shown in Fig. 6.2.
Figure 6.2 – Guidance forces vs. lateral displacement graph
After comparing the plotted values, it is possible to observe a slight discrepancy between the experimental
results and the outcome of the simulation results. Such behavior can be justified again by the simple linear
approximation of the relative magnetic permeability modeled. Nevertheless, it can be seen that one more time
the experimental values present the same behavior as the simulation results.
6.1.1. Final remarks
Despite of the minor issues stated above, both results can be considered rather similar, allowing the conclusion
that the levitation and guidance forces previewed by our FEM model were successfully verified experimentally,
yielding accurate results with good agreement. Therefore, this work permits the conclusion that it is technically
viable to produce a frictionless SMB based on the studied geometry, using the ZFC technique.
Analyzing the overall outcome, it is possible to conclude that the methods chosen in the implementation of the
real SMB prototype such as the design, the choice of materials, the manufacturing techniques as well as the
carried out tests to the structure were successfully executed.
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18
Forc
e (N
)
Lateral displacement (mm)
Guidance forces vs. Lateral displacement
Experimental
Simulation
60
6.2. Future works
Regarding future works concerning this project, several aspects can be taken into account in order to improve
the SMB:
The most important feature that could provide a more precise study of the SMB would be the possibility of
building the whole system with the 16 HTSs. As explained in section 3.4, the studied model in this work was
composed by 6 HTSs in the bottom part of the stator. The availability of HTSs to build the full structure would
contribute for an improvement on the accuracy of the outcome.
Since the designed SMB is a rotating bearing, in order to produce an increase in both levitation and guidance
forces of the system, continuous rings of HTSs and PMs could be used instead. These rings would cause the
magnetic forces to be higher by occupying the spaces that are not currently being used by the discontinuous
rings of HTSs and PMs.
An improved design of the SMB could be also carried out with the objective of achieving smaller air gap distances
and produce an improved isolation structure for the system. Smaller air gap distances would express higher
magnetic forces while the improved isolation would result in a reduced nitrogen usage rate.
Moreover, as stated in section 3.5, the results on the rotor geometry influence clearly show that the distances
between the PM rings directly affect the levitation and guidance forces, creating a “levitation vs. guidance”
trade-off that could be more deeply studied in the future.
61
References
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[2] Schweitzer, Gerhard. "Active magnetic bearings-chances and limitations." IFToMM Sixth International
Conference on Rotor Dynamics, Sydney, Australia. Vol. 1. 2002.
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Appendix
Figure A 1 – Stator slice
64
Figure A 2 – Technical drawing of the stator inner slice after improvement
65
Figure A 3 – Technical drawing of the stator outer slice after improvement
