Torque and torque components in high-speed permanent-magnet synchronous machines with a shielding cylinder

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Study of the effect of a shielding cylinder on the torque in a permanent-magnet synchronous machine considering two torque-producing mechanisms

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A general framework for the analysis and design of tubular linear permanent magnet machines

A general framework for the analysis and design of a class of tubular linear permanent magnet machines is described. The open-circuit and armature reaction magnetic field distributions are established analytically in terms of a magnetic vector potential and cylindrical coordinate formulation, and the results are validated extensively by comparison with finite element analyses. The analytical field solutions allow the prediction of the thrust force, the winding emf, and the self- and mutual-winding inductances in closed forms. These facilitate the characterization of tubular machine topologies and provide a basis for comparative studies, design optimization, and machine dynamic modeling. Some practical issues, such as the effects of slotting and fringing, have also been accounted for and validated by measurement

Fourier-based modeling of permanent-magnet synchronous machines operating at high speed

Two trends dominate the design of modern electric machines; a commitment to higher energy-efficiencies on the one hand and a tendency towards more dedicated drives on the other. As a result, the importance of rigorous optimizations during the design process of electric machines is at an all-time high. This, in turn, has sparked the interest for modeling tools that combine accuracy and a low computational time. The latter is especially important during the earliest phases of the machine's design, when the design space is still very large. Another result of the above-described trends is the emerging of new electric machine types. Especially high-speed electric machines have gained a lot of attention over the past decade. Indeed, the dedicated design of such machines enables a direct-drive configuration of high-speed systems. This doesn't only allow to omit the gearbox, resulting in a higher efficiency and reliability, it also reduces the system's weight and size. In addition to the importance of optimization procedures, the need to gain more insight in emerging machine types is another incentive to develop comprehensible models for these machines. The aforementioned needs for fast and accurate modeling tools and a better insight in emerging machine types form the motivation for this work. Because of their relative importance in the segment of high-speed machine, the focus is on surface-mounted permanent-magnet synchronous machines with a shielding cylinder. In the first place, the aim of this work is to study and improve the existing modeling techniques for high-speed synchronous machines with permanent magnets. Secondly, this work wants to provide the foundation for a better understanding of these machines. Especially regarding the physical processes through which the shielding cylinder affects the machine's performance. The first part of this work discusses the modeling of permanent-magnet synchronous machines, with a focus on machines that operate at high speeds. That discussion starts with an evaluation of the existing modeling techniques. Based on that evaluation, it was chosen to concentrate on the so-called Fourier-based modeling technique. This type of models combines the subdomain technique, i.e. dividing the studied machine topology in a number of subdomains, with the separation of variables technique to calculate the machine's magnetic field. Next, the physical background and implementation of Fourier-based models is described. The term Fourier-based modeling actually covers a wide range of different techniques. There are, for example, different possibilities to account for slotting and even the initial physical formulation of the problem can be based on two different magnetic potentials. Therefore, the next step is to use the previous discussion on Fourier-based modeling as a basis to evaluate the different techniques within Fourier-based modeling. By coupling that evaluation to an overview of the existing literature, this work presents a comprehensible selection guide that can be used by anyone who wants to build a Fourier-based model. The second part of this work concentrates on how the existing Fourier-based models can be improved. The first improvement has been to further reduce the computational times of Fourier-based models, even though they are already inherently low. It was found that this can be done by simplifying the studied geometry and by performing a preliminary analysis of the machine's harmonic content. Especially the latter results in spectacular computational-time reductions up to 99\% without affecting the model's accuracy. Another contribution of this work to the Fourier-based modeling technique has been to account for voltage sources, as opposed to the current-density sources that are traditionally used. Although this does add to the model's complexity, it may greatly improve its value, especially when the modeled machine is to be powered with a voltage source. Whereas the first two parts of this work focus on the calculation of the machine's magnetic field, the third part focuses on the electromagnetic quantities that can be obtained from that magnetic field. Firstly the postprocessing itself, i.e. the actual calculation of the electromagnetic quantities is discussed. Four quantities in particular are considered; the magnetic flux density, the back electromotive force, the torque and the eddy-current losses. This work contributed to the existing literature by introducing a division of the torque in two components, one that is related to the shielding cylinder and one that is related to the magnets. Secondly, the test setup that has been built in the scope of this PhD is introduced and used to validate the calculation of the back electromotive force and the currents that are obtained when imposing a voltage. Note that all other calculations have been validated with a finite-element model. Finally, a number of parameter studies are performed to investigate the shielding cylinder's effect on the torque and the eddy-current losses. By evaluating the effect of the shielding cylinder's conductivity and its thickness while applying various current and voltage sources, a number of interesting observations have been made. It was for example noted that the torque related to the shielding cylinder behaves similarly to the torque that is produced in an induction machine. Another observation is that, unlike expected, the synchronous harmonic content of the machine is affected by the shielding cylinder's conductivity. Although it is difficult to extrapolate the results to other machine topologies, the observations from these parameter studies clearly add to the understanding of high-speed permanent-magnet synchronous machines. Combined, the three individual parts of this work meet the initial goals of this PhD. The first part provides an elaborate study of the existing Fourier-based modeling techniques. The second part makes these models even more attractive for research and optimization purposes by reducing the computational time and accounting for voltage sources. The last part applies Fourier-based modeling to gain a better understanding of high-speed permanent-magnet synchronous machines.Een streven naar betere efficiënties enerzijds en een tendens naar meer gespecialiseerde elektrische aandrijvingen anderzijds, domineren momenteel de evolutie van elektrische machines. Het gevolg daarvan is dat het belang van doorgedreven optimalisaties tijdens het ontwerp van elektrische machines sterk stijgt, wat op zijn beurt weer zorgt voor een toegenomen interesse in wiskundige modellen die zowel nauwkeurig als snel zijn. Dat laatste is bijzonder belangrijk tijdens de eerste fases van het ontwerpproces, als de ontwerpruimte nog zeer groot is. Een ander gevolg van het streven naar efficiëntere en meer gespecialiseerde machines is dat er nieuwe types elektrische machines ontworpen worden. In het licht daarvan zijn hogesnelheidsmachines erg populair geworden tijdens de afgelopen tien jaar. Inderdaad, indien dergelijke machines specifiek ontworpen worden voor één bepaalde hogesnelheidstoepassing, is het mogelijk die toepassing aan te drijven zonder tussenkomst van een tandwielkast. Dit zorgt er niet enkel voor dat de efficiëntie en duurzaamheid verbeteren, het resulteert ook in een lichter en compacter systeem. Om een nieuwe machine te ontwerpen is er echter een goed inzicht in die machine nodig. In dit doctoraat bijvoorbeeld, ligt de focus op hogesnelheidsmachines met permanente magneten. Dergelijke machines worden vaak uitgerust met een beschermende cilinder rond de magneten. Het doel van die cilinder is de magneten op hun plaats te houden en/of de rotorverliezen te verminderen. Een goed inzicht in de fysische processen die zo'n beschermende cilinder teweegbrengt is belangrijk. Als aanvulling op het belang van optimalisatie procedures, is de behoefte naar meer inzicht in nieuwe types machines een extra reden om wiskundige modellen voor dergelijke machines te ontwerpen. De behoefte naar zowel snelle en nauwkeurige wiskundige modellen én een beter inzicht in nieuwe types elektrische machines vormen de motivatie voor dit doctoraat. In de eerste plaats is het doel de bestaande wiskundige modellen voor permanentmagneetbekrachtigde synchrone machines te bestuderen en te verbeteren. Ten tweede wilt dit werk de basis leggen voor een beter inzicht in dergelijke machines. In het eerste deel van dit werk wordt de wiskundige modellering van permanentmagneetbekrachtigde synchrone machines besproken, met een focus op machines die ontworpen zijn voor grote omwentelingssnelheden. In een eerste stap worden de bestaande modelingstechnieken vergeleken. Op basis van die vergelijking werd er gekozen voor de Fourier-gebaseerde modelleringstechniek. Deze techniek combineert de zogenaamde deelgebiedenmethode, die het bestudeerde probleem in kleinere delen opdeelt, met scheiding der veranderlijken om het magnetisch veld in de machine te berekenen. In een tweede stap wordt de fysische achtergrond en de implementatie van Fourier-gebaseerde modellen besproken. De term Fourier-gebaseerd modelleren dekt eigenlijk een brede waaier aan verschillende technieken. Er zijn bijvoorbeeld meerdere methodes om het gleufeffect in rekening te brengen. Zelfs de fysische formulering van het probleem kan gebaseerd zijn op verschillende magnetisch potentialen. Daarom is de volgende stap om, op basis van de voorgaande discussie, de verschillende technieken binnen Fourier-gebaseerd modelleren te evalueren. Door die evaluatie te koppelen aan een overzicht van de bestaande literatuur, slaagt dit werk erin een keuzehulp aan te bieden voor toekomstige onderzoekers die een dergelijk model willen maken. Het tweede deel van dit werk tracht de bestaande Fourier-gebaseerde modellen te verbeteren. Een eerste verbetering werd gerealiseerd door de rekentijd van Fourier-gebaseerde modellen te verlagen. Dit werd enerzijds gedaan door de bestudeerde geometrie te vereenvoudigen en anderzijds door een kwalitatieve studie van de harmonsiche inhoud van het magnetisch veld in de machine te gebruiken. Vooral die laatste methode levert een spectaculaire rekentijdreductie tot wel 99\% op, zonder de nauwkeurigheid van het model te verminderen. Een tweede bijdrage van dit werk is het in rekening brengen van spanningsbronnen, dit in tegenstelling tot het opdringen van stroomdichtheden. Ondanks het feit dat dit de complexiteit van het model vergroot, kan het een grote meerwaarde zijn. Zeker indien de te modelleren machine aangedreven wordt met een spanningsbron. Waar de eerste twee delen van dit werk focussen op de berekening van het magnetisch veld, ligt de focus van het derde deel op de elektromagnetische grootheden. In een eerste stap word de berekening van vier elektromagnetische grootheden besproken; de magnetische flux dichtheid, de tegen elektromotorische kracht, het koppel en de wervelstroomverliezen. Dit doctoraat draagt bij aan de bestaande literatuur door de opdeling van het koppel in twee componenten te introduceren; een component gerelateerd aan de beschermende cilinder en een component gerelateerd aan de magneten. In een tweede stap wordt de testopstelling, die gebouwd werd in het kader van dit doctoraat, kort voorgesteld. Vervolgens wordt ze gebruikt om de berekening van de tegen elektromotorische kracht en de stromen in de machine te onderzoeken. Merk op dat alle andere berekeningen eerder al gevalideerd werden met een eindige-elementen model. Ten slotte werden er verschillende parameterstudies uitgevoerd om het effect van de beschermende cilinder op het koppel en de wervelstroomverliezen te valideren. Door het effect van de geleidbaarheid en de dikte van de cilinder te bestuderen bij verschillende stroom- en spanningsbronnen, kunnen een aantal interessante observaties gedaan worden. Zo werd er bijvoorbeeld vastgesteld dat de koppelcomponent die gerelateerd is aan de beschermende cilinder dezelfde eigenschappen vertoond als het koppel in een inductiemachine. Verder werd er ook vastgesteld dat, tegen de verwachtingen in, de synchrone harmonische inhoud van de machine beïnvloed wordt door de geleidbaarheid van de beschermende cilinder. Ondanks het feit dat het moeilijk is de resultaten te extrapoleren naar andere machines, dragen de inzichten die voortkomen uit deze parameter studies zeker bij aan een beter begrip van permanentmagneetbekrachtigde hogesnelheidsmachines. Samen komen bovenstaande delen van het werk tegemoet aan de initële doelstellingen van dit doctoraat. Het eerste deel bevat een uitgebreide studie van de technieken binnen Fourier-gebaseerd modelleren. In het tweede deel worden twee verbeteringen van de bestaande techniek voorgesteld die Fourier-gebaseerd modeleren nog aantrekkelijker maakt voor onderzoeks- en optimalisatiedoeleinden. Het laatste deel van dit werk gebruikt Fourier-gebaseerd modeleren om een beter inzicht te krijgen in permanentmagneetbekrachtigde hogesnelheidsmachines

Electromagnetic and Mechanical Analysis of High Speed SPM Rotor with Copper Shield

For high-speed applications, the surface-mounted permanent magnet (SPM) machine is preferred due to its high torque density and efficiency. However, induced eddy currents in the rotor conductive parts result in a loss of efficiency and rotor heating. Therefore, several methods to reduce such losses have been proposed in the literature including copper shielding. In this paper, a high-speed SPM machine rotor with a copper shield is designed and investigated both electromagnetically and mechanically. Several quantitative investigations including placing the copper sheet around the retaining sleeve or magnets, different copper sheet and airgap thicknesses, different retaining sleeve materials, different harmonic contents in the current waveform, i.e. pulse amplitude modulation (PAM) and pulse width modulation (PWM) generated waveforms, and different frequencies and current levels are reported. Additionally, a mechanical analysis investigating possible failure modes of the rotor with the copper sheet is reported

Design and Multi-physical Fields Analysis of High Speed Permanent Magnet Machines

Due to the advantages of high power density, high efficiency and compact size, high speed permanent magnet machines (HSPMMs) have found wide application in industrial areas. Compared with a conventional speed permanent magnet machine, a HSPMM rotor can reach speeds of more than 10,000 rpm, which brings challenges with regard to electromagnetic, thermal and mechanical aspects of machine design. The higher power density also results in larger power loss per unit volume; due to the small machine size, machine thermal dissipation becomes difficult. Moreover, air frictional loss rises dramatically when the rotor is in high speed operation and this may also further increase rotor temperature. Therefore, research into HSPMM power losses and improving machine thermal dissipation capability is of significant interest. HSPMM mechanical issues also need to be considered to ensure safe and reliable machine operation. As rotor speeds rise, rotor strength becomes prominent and critical as the permanent magnets are vulnerable to the large centrifugal force. In addition, the machine rotor should also have enough rigidity and avoid operating at critical speeds. As such, this dissertation focuses on HSPMM design and research. Multi-physical fields analysis of a HSPMM is carried out to calculate machine power losses and temperature distribution, with factors influencing machine performance considered; HSPMM rotor mechanical research and analysis are also carried out and presented in this study. Firstly, the HSPMM design methodology and process are illustrated with machine rotor parameters, PM material, pole numbers and rotor sleeve considered for a 150 kW, 17000 rpm HSPMM. Then, HSPMM performance for different machine stator structures and PM pole arc pole pitches is investigated using the Finite Element Method (FEM) for the machine operating at both no load and full load conditions; HSPMM electromagnetic performance and how it is impacted by machine parameters is also studied. HSPMM power losses are comprehensively investigated in the following chapter. As machine core loss can be significantly increased with increasing machine frequency, it is critical to accurately estimate HSPMM iron loss. Based on the machine iron core magnetic field variation that is obtained by FEM analysis, machine steel iron core loss estimation for HSPMM is performed using an improved method with the influences of alternating and rotating magnetic fields, as well as harmonics effects, considered for high precision. Then the HSPMM air gap magnetic flux density distribution considering machine stator slotting effect is also analytically calculated with its effectiveness verified by FEM results. Then rotor eddy current loss is studied by time-stepping FEM, while the effects of rotor sleeve dimensions and properties, copper shielding composite rotor structure, air gap length, as well as slot opening width are further researched in depth. A PM bevelling method is also proposed and investigated to reduce HSPMM rotor eddy current loss while having little effect on machine output torque. Then a fluid field analysis is carried out to study HSPMM rotor air frictional loss when the rotor is in high speed operation. According to the characteristics of a machine axial forced air cooling system, the HSPMM temperature distribution is investigated by 3-D fluid–thermal coupling CFD modelling with the calculated power losses results. The machine thermal analysis theory and modelling method are also detailed and further explained. HSPMM thermal performance variation due to impacting factors of cooling air velocity, rotor eddy current loss and sleeve thermal conductivity are also comprehensively investigated and studied in this dissertation. The designed HSPMM is prototyped, and temperature experimental tests are also carried out to verify the effectiveness of the research and analysis for HSPMM. Then, thick-walled cylinder theory is introduced to study rotor mechanical strength analytically, while it also verifies the FEM calculation results. Then based on FEM analysis, HSPMM rotor stress distribution is investigated with sleeve material effects on rotor strength discussed. In order to alleviate the rotor sleeve stress, three pole filler materials are comparatively studied, while the temperature impacts on rotor mechanical stress is further considered; sleeve thickness and the interference between PM and sleeve are investigated in an integrated fashion for HSPMM rotor strength analysis, with some conclusions also drawn for HSPMM rotor mechanical design. HSPMM rotor critical speeds are also calculated by the established 3D rotor dynamic analysis FEM model to ensure the rotor is operating in a desirable condition

Comparison of three analytical methods for the precise calculation of cogging torque and torque ripple in axial flux PM machines

A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model

A high-speed permanent-magnet machine for fault-tolerant drivetrains

This paper details the design considerations of a permanent magnet (PM), three phase, high speed, synchronous machine for fault tolerant operation. A multidisciplinary approach to the optimal design of the machine is adopted targeted at minimising the additional losses resulting from faulty operating conditions and accounting for the remedial control strategy implemented. The design of a closed slot, 6 slots, 4 pole machine is presented. The machine is prototyped and tested to validate the analytical-computational performances predicted in the design and analysis stage under healthy and faulty condition