H. May, R. Palka, E. Portabella and W‐R. Canders
To describe the wide range of possible applications of high temperature superconductors (HTSCs) (e.g. magnetic bearings, levitation systems or electrical machines) several…
Abstract
To describe the wide range of possible applications of high temperature superconductors (HTSCs) (e.g. magnetic bearings, levitation systems or electrical machines) several appropriate calculation algorithms have been developed. They determine the force interaction between a superconductor and any even multidimensional magnetic field excitation system. Especially good agreements between experiments and computed results have been obtained for the Vector‐Controlled Model, which seems to be the best approximation of the macroscopic superconductivity behaviour. The validation of this model by means of measurements makes it a powerful tool for the design and optimisation of any HTSC application in the field of force generation. It can be used not only for the designing of levitation applications, but also to help the understanding of the flux penetration, flux trapping and magnetisation of bulk superconductors in non‐uniform magnetic fields. By means of this model, the force interaction between superconductors and external magnetic fields for practical multi‐polar configurations, e.g. superconducting levitation systems or inherently stable superconducting bearings has been determined. Furthermore, the time dependency of the forces taking flux flow and flux creep into account, can be considered.
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Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields…
Abstract
Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.
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W.‐R. Canders, H. May and R. Palka
The paper presents different topologies of inherent stable magnetic support systems consisting of monolithic high temperature superconductors (HTSC) and permanent magnets (PM)…
Abstract
The paper presents different topologies of inherent stable magnetic support systems consisting of monolithic high temperature superconductors (HTSC) and permanent magnets (PM). They may be used as contactless magnetic bearings for high speed rotating machines. Depending on the application, cylindric, conic or disk shaped HTSC‐PM arrangements with increased both radial and/or axial forces and stiffnesses are proposed. The dependencies of optimal pole pitch on the air gap are given including the effects of limited current densities associated with the behaviour of real monolithic superconductors. Furthermore, the effect of zero field and maximum field frozen HTSCs on the performance of magnetic HTSC bearings are represented. To compute the magnetic HTSC‐PM interaction a new extended finite element (EFEM) program is applied.
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Cornelius Bode, Wolf-Rüdiger Canders and Markus Henke
The purpose of this paper is to calculate slotting-based eddy currents in permanent magnet excited synchronous machine (PMSM) taking into account axial and circumferential…
Abstract
Purpose
The purpose of this paper is to calculate slotting-based eddy currents in permanent magnet excited synchronous machine (PMSM) taking into account axial and circumferential segmentation of magnets.
Design/methodology/approach
An analytical approach to calculate eddy current losses in PM caused by slotting harmonics of PMSM is presented. The eddy current reaction field is taken into account as well as axial and circumferential segmentation of the magnets.
Findings
The analytical model provides results comparable to 3D-FEM calculations even at high frequencies at reduced computation costs. To generalize the results the magnetic Reynold’s number is introduced.
Originality/value
Taking into account the axial and circumferential segmentation in the PDE; the approach is much more accurate compared to known approaches; accuracy is comparable to 3D-FEA.
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Hardo May, Jan Hoffmann, Wolf‐Ruediger Canders and Ryszard Palka
The purpose of this paper is to focus on superconducting magnetic bearings (SMB). SMB for high‐speed rotors are contact free and offer inherently stable operations thus they are…
Abstract
Purpose
The purpose of this paper is to focus on superconducting magnetic bearings (SMB). SMB for high‐speed rotors are contact free and offer inherently stable operations thus they are best qualified for the support of horizontally aligned rotors of turbo machines for gas‐compressors and expanders, e.g. special attentions have to be concentrated on the force activation of the SMB without dislocating the rotor from the aligned position.
Design/methodology/approach
For the activation of cylindrically shaped SMB‐designs, appropriate units with movable superconductor parts have been developed. They permit the maintenance of the rotor together with the field excitation unit in the aligned un‐displaced position. The eddy currents in the conducting cylinder of an EDD are induced by spatial fluctuations of the field and thus have been determined by transient calculations. The mechanical oscillation of the rotor was considered by a step‐wise displacement of the damper‐plate.
Findings
As the rotors of both the machine and the SMB operate best with reduced clearance to the stators, the shaft cannot be displaced to activate the force of horizontally aligned superconducting bearing assemblies. Thus, for cylindrical, co‐axial SMB‐designs the stator is shaped as two half shells embracing the SMB‐rotor. For the force activation the following procedure has to be carried out within the Dewar without displacing the shaft: at first the half shells are retreated from the rotor (warm HTSC) and after the cooling they are moved against the inner part of the warm bore thus generating the forces to compensate the weight and disturbances of the rotor. In case of planar‐cylindrical SMB‐designs, which are specially suited for extreme high speed applications, the bearing stators consist of a planar cylinder plate of HTSC‐bulks. The force activation is realised by lifting and descending the Dewar with the HTSC parts as a whole independently from the position of the rotor. The radial forces of the EDD and their partitioning in components which contribute to the damping‐ and to the spring‐force have been determined for different frequencies up to 160 Hz. To achieve accuracies in the percent range, the values of the time steps have to be well adapted to the electro dynamic conditions as oscillation frequency and conductivity.
Originality/value
Only the presented activation devices with movable HTSC stator parts enable the application of SMB even for horizontally aligned high‐speed rotors with reduced radial clearance. The recently developed fully integrated EDD secure a safe run of the rotor even during the speed up – passing the eigenfrequency in particular.
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E. Costamagna, P. Di Barba and R. Palka
The purpose of this paper is to describe a twofold methodology for evaluating the force between field excitation system and bulk in a magnetic‐levitation device based on…
Abstract
Purpose
The purpose of this paper is to describe a twofold methodology for evaluating the force between field excitation system and bulk in a magnetic‐levitation device based on high‐temperature‐superconductors (HTS). The paper focuses on two‐dimensional field models for HTS bulks. As far as field analysis is concerned, the finite‐element method in two or three dimensions is used. Alternatively, the conformal mapping approach provides a flexible and accurate calculation tool, useful for the optimization of superconducting bearings.
Design/methodology/approach
Powerful mapping algorithms, developed recently for Schwarz‐Christoffel‐like transformations, have proven successful in analyzing the fields, both in the activation and in the operation condition of superconductor devices.
Findings
Assuming small displacements of the superconductor sample with respect to the excitation magnets, the force‐displacement curve was obtained for operational field cooling via Schwarz‐Christoffel maps.
Originality/value
The specific theory used is the substitution theorem for magnetic fields, along with its capability to take complex geometries into account, making it possible to model devices for real‐life applications. Using only a scalar potential, the procedure proposed for computing fields proves, in the conformally‐mapped plane, the superposition method already introduced in FEM‐based models.
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Piotr Putek, Piotr Paplicki and Ryszard Pałka
In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose…
Abstract
Purpose
In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose the modified multi-level set method (MLSM) was proposed and applied to capture the shape of rotor poles on the fixed mesh using FE analysis. The paper aims to discuss these issues.
Design/methodology/approach
This framework is based on theories of topological and shape derivative for the magnetostatic system. During the iterative optimization process, the shape of rotor poles and its evolution is represented by the level sets of a continuous level set function f. The shape optimization of the iron and the magnet rotor poles is provided by the combining continuum design sensitivity analysis with level set method.
Findings
To obtain an innovative design of the rotor poles composed of different materials, the modified MLSM is proposed. An essential advantage of the proposed method is its ability to handle a topology change on a fixed mesh by the nucleating a small hole in design domain that leads to more efficient computational scheme then standard level set method.
Research limitations/implications
The proposed numerical approach to the topology design of the 3D model of a PM machine is based on the simplified 2D model under assumption that the eddy currents in both the magnet and iron parts are neglected.
Originality/value
The novel aspect of the proposed method is the incorporation of the Total Variation regularization in the MLSM, which distribution is additionally modified by the gradient derivative information, in order to stabilize the optimization process and penalize oscillations without smoothing edges.
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Ryszard Palka, Stanislaw Gratkowski, Krzysztof Stawicki and Piotr Baniukiewicz
The purpose of this paper is to develop a magnetic induction tomography (MIT) system as well as the conductivity reconstruction algorithms (inverse problem).
Abstract
Purpose
The purpose of this paper is to develop a magnetic induction tomography (MIT) system as well as the conductivity reconstruction algorithms (inverse problem).
Design/methodology/approach
In order to define and verify the solution of the inverse problem, the forward problem is formulated using mathematical model of the system. The forward problem is solved using the finite element method. The optimization of the excitation unit is based on the numerical solutions of the direct problem. All the dimensions and shape of the excitation system are optimized in order to focus the main part of the magnetic field in the vicinity of the receiver. Finally, two formulations of the inverse problem are discussed: based on the inversion of the Biot‐Savart law; and based on the artificial neural networks.
Findings
The formulation of the forward problem of the considered MIT system is given. The construction of the exciter unit that focuses the main part of the magnetic field in the vicinity of the receiver is proposed. Two formulations of the inverse problem are discussed. First using the inversion of the Biot‐Savart law and second using the artificial neural network. The neural networks seem to be promising tools for reconstructing the MIT images.
Originality/value
This paper demonstrates a real‐life MIT system whose performance is satisfactorily predicted by mathematical models. The original design of the exciter is shown. The new approach to the inverse problem in MIT – the use of the artificial neural network – is presented.
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The purpose of this paper is to introduce an aid for teaching transverse flux permanent magnet machines (TFPMs) with emphasis on their torque production.
Abstract
Purpose
The purpose of this paper is to introduce an aid for teaching transverse flux permanent magnet machines (TFPMs) with emphasis on their torque production.
Design/methodology/approach
The Lorentz force law is applied to fictitious current loops emulating the permanent magnets (PMs) mounted on the rotor according to different arrangements; the air gap flux density is created by the armature current.
Findings
Implemented in a master lecture on special AC machines, the proposed approach has revealed a renewed interest in electromagnetic fundamentals for pedagogical purposes. It makes simple the explanation of the principle of operation of a class of AC machines reputed by the complexity of their magnetic circuits. The latter incorporates axially stacked decoupled sub-circuits, one per phase generating alternating magnetic fields. More specifically, there is common air gap, shared by the machine phases, in which a rotating magnetic field is created by the superposition of the PM contribution and the armature one.
Research limitations/implications
Accounting for the complexity of the magnetic circuits and the three-dimensional (3D) flux paths characterizing TFPMs, a 3D finite element analysis (FEA) is required for the validation of the analytical predictions. Nevertheless, such a 3D FEA validation is far from being obvious to be carried on within a master lecture.
Originality/value
While the basis of Lorentz forces resulting from fictitious current loops emulating PMs has been considered in some referenced papers, its simple and pedagogical application to assess the torque production of several TFPM concepts represents the added value of the present paper.
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Amina Ibala, Ahmed Masmoudi, Glynn Atkinson and Alan G. Jack
This paper aims at the derivation of an accurate reluctance model of a transverse flux permanent magnet machine (TFPM) and its validation by finite element analysis (FEA).
Abstract
Purpose
This paper aims at the derivation of an accurate reluctance model of a transverse flux permanent magnet machine (TFPM) and its validation by finite element analysis (FEA).
Design/methodology/approach
Analytical prediction of the different reluctances in the core, the permanent magnets, and the air. These reluctances characterize the paths of both main and leakage fluxes. Then, a validation of the proposed reluctance model is carried out using FEA. An interesting application of the proposed reluctance consists in the assessment of the TFPM torque production capability.
Findings
The torque yielded by the reluctance model of the TFPM and the one computed using 3D‐FEA are in good agreement. This result is of great importance in so far as the CPU time required for 3D‐FEA computation is much more higher than the one consumed in the resolution of the reluctance model.
Research limitations/implications
Further validation of the results yielded by the proposed reluctance model through their comparison with experimental measurements shall be treated in the future.
Practical implications
The proposed reluctance model is of great interest for the TFPM sizing. It could be useful in the pre‐design procedure of the machine.
Originality/value
The paper proposes a new reluctance model where the leakage fluxes are accurately predicted.