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Synchronous reluctance machines: eccentricity analysis and design criteria
Full text linkNowadays, the interest in the synchronous reluctance machines is growing up due to their several merits in comparison
to other machine types. These machines offer high torque density with respect to the induction machines. Their torque density is slightly lower than permanent magnet synchronous machines even though the lower performance is compensated by a much cheaper rotor. Since synchronous reluctance machines do not induce voltage when the stator is not supplied, there are not short circuit currents and braking torques due to the electrical faults, e.g. they have high fault tolerant capability. In addition, synchronous reluctance machine has a robust structure, and a wide constant power speed range.
For these aforementioned reasons, these machines are employed in several applications. However, there is a prominent defect of this kind of machines which is the low power factor. This defect is addressed by assisting the motor by permanent magnets within the flux barriers of the rotor leading to the permanent magnet assisted synchronous reluctance motor.
In addition, these kinds of machines has high torque ripple. This is due to the high harmonic content in the magneto motive force which interacts with the rotor anisotropy. Several approaches are proposed to reduce the torque ripple, such as: (a) using skewed rotor, (b) adopting two different flux-barrier geometries in the same lamination, i.e., asymmetric rotor, (c) using equally spaced the flux-barrier ends along the rotor periphery, and (d) optimization approaches were applied to smooth the torque.
The synchronous reluctance machine is becoming of great interest in the last years, due to two key reasons: (i) the increase of rare earth permanent magnet cost and (ii) the increasing request of high-efficiency machines. Therefore, the reluctance motor and the ferrite permanent assisted reluctance motor are becoming competitors of both surface-mounted permanent magnet machines and induction machines in many applications. Such motors are also becoming
particularly interesting when the control is based on the sensor-less rotor position detection.
Even if there is a great interest in this kind of machines, there is a few work about the analytical design of their rotor, e.g. about how to select the end barrier angles, designing the iron ribs, and designing the permanent magnet robust towards the demagnetization. In the majority of the cases the reluctance machine is analyzed by using finite element analysis. The results are precise and useful for achieving a specific geometry to
be prototyped, but they refer to that particular solution and they lose generality.
In other words, it is difficult to find general rules to design reluctance machines, since the analysis approach is focused on a single objective.
During the manufacturing process, there are some manufacturing imprecision, such as mass unbalance, bearing tolerance, shaft bow, and etc., cause eccentricity fault. Eccentricity may cause magnetic and dynamic problems with additional vibrations, noises, and torque pulsations. Although the eccentricity faults in induction and permanent magnet motors are extensively investigated, there are a few publications on synchronous reluctance machines with eccentricity. It is important to study the effect of rotor eccentricity on these machines because of their high anisotropy and critical iron parts in the rotor (iron ribs). For the aim of designing the iron ribs thicknesses, the unbalanced magnetic force acting on theses ribs should be accurately estimated.
Main contribution of the thesis
This thesis aims to give an useful analytical approach for reaching a preliminary geometry of both synchronous reluctance and permanent magnet assisted synchronous reluctance motors, as starting point for a successive optimization. For more accurate design of the rotor iron ribs, the electro-magnetic force acting on the rotor, in different rotor eccentricity cases, are analytically computed. In addition, a comparative studies (analytically and FE) between the synchronous reluctance, permanent magnet assisted, and surface mounted permanent magnet machines, in different eccentricity cases, is carried out. Therefore, this thesis is divided into four main parts.
At the first part, an analytical model based on the magnetic equivalent lumped network of the reluctance motor is discussed. This model studies the magnetic performance of the concentric synchronous reluctance motor. Then, this analytical model is adopted in order to study the impact of different eccentricity scenarios (static and dynamic eccentricity) on the reluctance motor. Different stator windings configurations (distributed and concentrated windings) and different rotor geometries (symmetric and asymmetric rotor) are considered.
After that, the eccentric synchronous reluctance machine is compared with the eccentric permanent magnet assisted synchronous reluctance machine. The impact of the barrier dimensions, the rotor geometry, and the permanent magnet type is highlighted in this comparison. Furthermore, an analytical comparison between the reluctance motor and the surface mounted permanent magnet motor is carried out in different cases of eccentricity. The axial non uniform displacement of the rotor axis from the stator axis, at one end and both ends of the axis, are involved in this analytical comparison.
The second part aims to achieve more realistic estimation of the electromagnetic forces acting on the rotor by considering the effect of stator slots and the magnetic voltage drop due to the actual B-H curve of the motor iron. The analytical model is developed for both eccentric and concentric synchronous reluctance motor. Then, an experimental validation of the analytical and FE analysis is carried out.
At the third part, an analytical approach for designing the permanent magnet of the permanent magnet assisted reluctance motor is proposed. The width and the thickness are selected so as to achieve the desired no-load air-gap flux density and resist the demagnetization under the desired loading conditions, respectively. Both complete and simplified analytical analyses are discussed. In addition, the analytical approach is presented in both cases of neglecting and considering the rotor iron ribs. Then, from the previously mentioned three parts of this thesis, a rapid multi-objectives analytical approach is proposed to achieve the initial design of the synchronous reluctance and permanent magnet assisted synchronous reluctance motors.
Finally, at the fourth part, a graphical user interface application for concentric and eccentric synchronous reluctance motor is developed. This application estimates stator and rotor scalar magnetic potential, air-gap flux density, electromagnetic torque, magnetic force acting on the rotor. The input parameters of this application are
- the geometrical data of the stator and rotor,
- the electric loading (kA/m), the electric load angle in (electric degree),
- the rotor geometry type, e.g., symmetric or asymmetric rotor geometry,
- number of flux-barriers per rotor pole,
- eccentricity type or no eccentricity, e.g., healthy case,
- the eccentricity value.
Then, the user can run the application to estimate the magnetic performance of both concentric and eccentric synchronous reluctance motor.Negli ultimi vent'anni l'interesse per le macchine sincrone a riluttanza è notevolmente cresciuto. Lo sviluppo e la ricerca dedicata a questi motori, supportata dai diversi vantaggi che presentano rispetto ad altri tipi di macchine, ha permesso a questa tipologia di macchina di guadagnarsi uno quota di mercato in diverse applicazioni industriali. I motori a riluttanza offrono una piu alta densità di coppia rispetto ai motori asincroni. Tuttavia, se confrontati con i motori sincroni a magneti permanenti, essi presentano una densità di coppia ed una efficenza minori. Tale decremento delle prestazioni rispetto alle macchine a magneti permanenti è tuttavia compensato dalla complessiva riduzione del costo di costruzione del rotore.
In aggiunta, essi presentano una struttura rotorica piu robusta delle macchine sincrone a magneti superficiali e consentono di ottenere un piu ampio range di funzionamento a potenza costante. I principali svantaggi delle macchine sincrone a riluttanza sono il basso fattore di potenza e le elevate oscillazioni di coppia. Il primo svantaggio, correlato alla assenza di alcun sistema di eccitazione sul rotore, viene normalmente mitigato attraverso l'introduzione di magneti permanenti all'interno delle barriere di flusso. Questo tipo di configurazione prende il nome di motore a riluttanza assistita da magnete permanente. Il secondo svantaggio, ossia l'eccessivo torque ripple, è dovuto all'elevato contenuto armonico della forza magnetomotrice che interagisce con l'anisotropia rotorica. Diversi approcci sono stati proposti in letteratura allo scopo di ridurre tali oscillazioni, tra i quali: (a) lo skewing del rotore, (b) barriere rotoriche geometricamente asimmetriche rispetto all'asse interpolare, (c) barriere rotoriche asimmetriche rispetto all'asse polare, (d) equa distribuzione delle barriere lungo la periferia del rotore, e (e) l'ottimizzazione della intera geometria delle barriere.
Il grande interesse suscitato negli ultimi anni è dovuto principalmente a due motivi: (i) l'aumento di costo delle terre rare, utilizzate in magneti ad elevato contenuto energetico (NdFeB e SmCo); (ii) la crescente richiesta di macchine ad alta efficienza. Pertanto, il motore a riluttanza e il motore a riluttanza assistito da magneti permanenti stanno diventando concorrenti di entrambe le macchine a magneti permanenti e macchine a asincrone in molte applicazioni. Un altro vantaggio intrinseco delle macchine sincrone a riluttanza è che non inducono tensione a vuoto, quando il rotore è fermo, conseguentemente le correnti di corto circuito e coppie frenanti che si possono creare a causa dei guasti elettrici, sono trascurabili. Per quanto concerne l'aspetto controllistico è doveroso sottolineare il crescente interesse verso le le macchine sicrone a riluttanza. Tale interesse è sostanzialmente giustificato dalla naturale propensione della stessa macchina ad essere controllata senza alcun sensore di velocità.
Sebbene vi sia un grande interesse per questo tipo di macchine, ci sono pochi lavori sulla progettazione analitica del loro rotore, ad esempio su come selezionare gli angoli di fine barriera, il dimensionamento dei ponticelli di ferro ed dettagli sulla progettazione robusta nei confronti della smagnetizzazione dei magneti permanenti. Nella maggior parte dei casi la macchina riluttanza viene analizzata mediante analisi agli elementi finiti. I risultati sono precisi e utili per realizzare una geometria specifica, ma si riferiscono ad una particolare soluzione perdendo generalità. In altre parole, è difficile trovare regole generali per progettare macchine a riluttanza. Per colmare questa lacuna, questa tesi si propone di fornire un approccio analitico utile alla determinazione di una geometria preliminare del motore, come punto di partenza per un'ottimizzazione successiva. La progettazione accurata dei ponticelli di ferro del rotore e gli effetti sulla forza elettromagnetica che agisce sul rotore con diversi gradi di eccentricità sono considerati. Questo lavoro di tesi è suddiviso in quattro parti principali.
Un modello analitico basato sul circuito magnetico equivalente a parametri concentrati del motore a riluttanza viene presentato e discusso nella prima parte. Questo modello studia il rendimento magnetico del motore sincrono a riluttanza concentrica. Lo stesso modello analitico è utilizzato per lo studio di differenti casi di eccentricità ed il loro impatto sulle prestazioni del motore a riluttanza. Motori a riluttanza con diversi tipi di avvolgimenti statici e diverse geometrie di rotore, simmetriche ed asimmetriche, vengono considerate. Lo stesso metodo viene applicato a motori a riluttanza con magneti permanenti e confrontata con il motore a riluttanza eccentrico. I risultati prodotti dai modelli utilizzati vensono confrontati tramie simulazioni agli elementi finiti. Inoltre, un confronto analitico tra il motore a riluttanza e motore a magneti permanenti superficiali viene condotta in diversi casi di eccentricità.
La seconda parte si propone di stimare in modo più accurato le forze elettromagnetiche agenti sul rotore, considerando l'effetto delle cave di statore e la caduta di tensione magnetica dovuta alla effettiva curva B-H del lamierino ferromagnetico. Il modello analitico è indicato per macchine con e senza presenza di eccentricità. Infine, misure sperimentali vengono condotte per validare la bonta' dei modelli analitici ed agli elementi finiti.
Nella terza parte, si propone un approccio analitico per la progettazione del motore a riluttanza assistito da magneti permanenti. La larghezza e lo spessore dei magneti sono scelti in modo da realizzare la densità di flusso a vuoto al trafetto desiderata e resistere alla smagnetizzazione che si possono presentare in condizioni di sovraccarico. Infine, un rapido approccio analitico e multi-obiettivo è proposto per la progettazione preliminare di motori a riluttanza e motori a riluttanza assistiti.
Nella quarta parte è stata sviluppata un'interfaccia utente grafica per l'analisi del motore a riluttanza. Questa applicazione stima i potenziali scalari magnetici di statore e rotore, la densità di flusso al traferro, la coppia elettromagnetica, la forza magnetica che agisce sul rotore. I parametri di ingresso di questa applicazione sono:
- dati geometrici dello statore e del rotore,
- carico elettrico (kA / m), e la sua fase (grado elettrico),
- il tipo di geometria del rotore, ad esempio, simmetrico o asimmetrico (Macaone),
- Numero di barriere di flusso per polo del rotore,
- il tipo di eccentricità o nessuna eccentricità, per esempio, il caso con rotore concentrico,
- il valore di eccentricità.
Perciò, l'utente può usare l'applicazione per stimare le prestazioni della macchina
Nonlinear Analytical Computation of the Magnetic Field in Reluctance Synchronous Machines
No full textThis paper deals with an analytical model of reluctance synchronous motor, able to consider both stator slotting effect and magnetic saturation in the stator and rotor iron paths. It joints the field distribution at the air gap to a lumped-parameter magnetic network. Local saturation factors are defined so as to adjust the flux-density distribution. The analytical approach exhibits great potentiality, since it is a formulation based on an harmonic study, and it is easily adaptable to any motor geometries. As an example, 36-slot 4-pole machine is analyzed, considering three flux barriers per pole. Finite element analysis confirms the results achieved by means of the analytical model
Fast synthesis of permanent magnet assisted synchronous reluctance motors
Full text linkThis paper describes a procedure for a practical synthesis of both a synchronous reluctance motor and a permanent magnet assisted synchronous reluctance motor. The procedure is completely analytical, yielding a rapid drawing of the motor geometry, taking into account both magnetic and mechanical considerations. From the application requirements, the external volume of the motor is computed. The further practical needs, such as maximum outer space, maximum available length, existing stator lamination, and so on are considered. Then, the design of the rotor geometry is carried out. The PM size is determined considering the demagnetisation limit according to the maximum current loading
A Nonlinear Analytical Model for the Rapid Prediction of the Torque of Synchronous Reluctance Machines
Full text linkThe synchronous reluctance motor works under heavy saturation. This paper presents a nonlinear analytical model of the reluctance machine, which is used to derive both average and torque harmonics as a function of the rotor geometry. Maps showing the torque harmonics as a function of the rotor barrier angles are derived. These maps are useful tools for the machine designer to get a proper rotor geometry. The torque maps are compared with those obtained from both linear analytical and finite element models. The maps computed analytically show good agreement with those derived by means of finite element analysis, and they are obtained in a much smaller computing time
Synchronous reluctance motor iron losses: considering machine non-linearity at MTPA, FW, and MTPV operating conditions
Full text linkSynchronous reluctance machine has high flux density fluctuations in the iron due to the high harmonics results from the rotor anisotropy. Thus, an accurate computation of the iron losses is of paramount importance, especially during the design stage. In this paper, a non-linear analytical model considering the magnetic iron saturation and the slotting effect is proposed. The model estimates accurately the iron losses at a wide range of operating speed. In addition, the accuracy of the non-linear model when the machine is highly saturated, i.e. when it works along the MTPA trajectory, is presented and verified. The model presented is general and can be applied to other configurations. A 36-slot four-pole machine, with three flux-barriers per pole is considered as a case study. Finite element analysis is used to validate the results achieved by means of the non-linear analytical model. Furthermore, an experimental setup is built to validate the simulation results
Advantages of a Double Three-Phase Winding Layout for a Dual Rotor E-Bike Motor Considering Third Current Harmonic Injection Technique
No full textThe transportation electrification process is rapidly demanding for drivers with enhanced performance. Modern systems are moving from fossil fuel technologies toward hybrid and fully electric solutions. Consequently, in automotive and motorcycle sectors the complete electrification process requires significant power and energy capabilities, and high efficiency. Also, to minimize the mechanical power loss and save the battery energy, the weight and volume of the vehicle have to be minimized. These features are significantly stressed in race applications, where the power density of the drive and its efficiency has to push the limits of state of the art. In this work, a multiphase machine with dual rotor architecture is employed, aiming at maximizing the performance of a full electric motorcycle (E-Bike). In particular, it is already known that in multi-phase machines it is possible to inject high frequency current component to increase the power density of the drive. Therefore, the analytical model for the injection of a third harmonic in the currents waveforms is presented for a case study of E-Bike featuring a dual rotor with Halback permanent magnet array. The third current harmonic is injected keeping the same peak current, when compared with the control technique without injection. The three-phase and multiphase winding layout of the machine are compared with and without current injection control by means of analytical equations. Finally, finite element results are shown in order to validate the model, the advantage of the multiphase winding and the current injection technique
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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