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The electromagnetic noise generated by the Maxwell radial pressure is a well-known consequence. In this paper, we present an analytical tool that allows air gap spatio-temporal pressures to be obtained from the radial flux density created by surface permanent magnet synchronous machines with concentrated winding (SPMSM). This tool based on winding function, a global air-gap permeance analytical model and total magnetomotive force product, determines the analytical air-gap spatio temporal and spectral radial pressure. We will see step-by-step their impacts in generating noise process. Also two predictive methods will be presented to determine the origin of the lows radial pressure orders noise sources. The interest lies in keeping results very quickly and appropriate in order to identify the low order electromagnetic noise origin. Then through an inverse approach using an iterative loop a new winding function is proposed in order to minimize radial force low order previously identified and chosen.

Abstract— This paper presents an analysis of low the space order of the air-gap radial Maxwell pressures in Surface Permanent Magnet Synchronous Machines (SPMSM) with fractional slot concentrated windings. The air-gap Maxwell pressures result from the multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, the armature, and the stator slots and their interactions. One low space order is selected and different approaches are compared to determine the origin of this pressure. First, an analytical prediction tool ACHFO (Analytical Calculation of Harmonic Force Orders) is issues to calculate the space and time orders of these magnetic pressure harmonics while identifying their origin in terms of interactions between magnet, armature and teeth effects. Additionally, the analytical prediction of ACHFO is compared with the flux density convolution and finite element approaches. The main advantage of our tool is the speed of computation. Finally, an experimental Operational Deflection Shape measurement (ODS) is performed to show the deflection shape of the low space order selected. Keywords— air-gap radial Maxwell pressures; lowest space order; analytical tool; convolution analysis; operational deflection shape.

Line start permanent magnet synchronous motor (LSPMSM) is a super-premium efficiency class motor with features of squirrel cage induction motor (SCIM) and permanent magnet synchronous motor (PMSM). This paper presents a reluctance network (RN) based analytical approach to determine the starting and steady-state performance of LSPMSM. The design parameters such as back electromotive force (EMF) and d-q axis inductance are calculated using the linear RN with a saturated flux bridge. Then the parameters are used in the analytical dynamic model to observe the machine performance. The objective of this study is to have a fast parameterized model to observe the effect of design variables such as rotor magnet and rotor bar dimensions on the motor performance. To validate the proposed technique, studied LSPMSM is also analyzed using the 2D finite element method (FEM).

The electromagnetic noise behaviour of a three phase Permanent Magnet Synchronous Machine (PMSM) is studies in this paper. A comparison between several electrical machines with Fractional Slot Concentrated Winding (FSCW) is produced. Firstly, through a well-known machine, an analytical model will be used and will allow the analysis of electromagnetic forces. In a second step, a vibro-acoustic and deflection shape study will be conducted to identify sources of electromagnetic noise in order to determine the configuration, number of stator slots (Zs) / poles (2p), most appropriate in terms of magnetic noise reduction. The objective is to minimize the low spatial order 2 considering a new stator topology or a new stator form.

The magneto motive force is an important physical quantity for electrical machines. Indeed its harmonic content leads to that of the air gap flux density. This paper presents an optimisation of the winding distribution for three phase fractional slot concentrated winding (FSCW) and distributed winding (DW) in order to reduce the magneto motive force harmonic content. This have an important effect on torque ripples, vibration and then noise. The optimization will be done on continue and discrete variables linked to the winding distribution.

The electromagnetic noise generated by the Maxwell radial force is a well-known consequence. In this paper, we present an analytical tool which allows obtaining the air gap spatio-temporal forces from the radial flux density created by surface permanents magnets synchronous machines concentrated winding. This tool based on winding function, global air-gap permeance analytical model and total magnetomotive force product, determines the spatio temporal and spectral radial force. We will see step by step their impacts in generating noise process. Also two predictive methods will be presented to determine the origin of the lows radial pressure orders noise sources. The interest lies in keeping results very quickly and appropriate in order to identify the low order electromagnetic noise origin. Then through an inverse approach using an iterative loop a new winding function is proposed in order to minimize radial force low order previously identified and chosen.

This paper presents an analysis of the air gap radial Maxwell forces in some three-phase, inner rotor Concentrated Winding surface Permanent Magnet Synchronous Machine (CW-PMSM). Two modular winding machines and one asymmetric, winding machine are considered and simulated by a Finite Element method (FE). The air gap Maxwell pressure results from multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, to the armature, to the stator slots and their interactions. An analytical prediction tool, (Analytical Calculation of Harmonic Force Orders -ACHFO) calculates the space and time orders of theses magnetic force harmonics while identifying their origin in terms of, interactions between magnet, armature and teeth effects. Additionally, an experimental Operational Deflection Shape measurement (ODS) is realised, for one modular machine prototype, to validate the electromagnetic model results. Finally the analytical prediction of ACHFO is compared with another method to obtain the origin of low orders radial pressure based on radial flux density convolution combination approach.

This paper presents an analysis of the radial Maxwell forces in the air gap of a concentrated winding for three-phase Permanent Magnet Synchronous Machine (PMSM). Many configurations are available with different windings or different topologies of stator-rotor. Radial forces versus time and spatial domains are the result of harmonics specific to the magnets, to the armature, to the teeth and their interactions too. A prediction tool (Analytical Calculation of Harmonic Force Orders - ACHFO) uses an analytical formulation; it gives the previous interactions, their own frequencies. Then a comparison will be made with finite element (FE) results.

Cette étude présente une analyse fréquentielle de la force radiale de Maxwell appliquée sur la surface interne du stator d’une machine synchrone à aimants permanents surfaciques (MSAP) à bobinage dentaire. Cette force radiale est le siège d’harmoniques spatio-temporels liés aux effets de la denture, de la saturation, de l’armature, des aimants inducteurs, et de leurs interactions. L’outil prédictif ACHFO (Analytical Calculation of Harmonics Force Orders) permet une détermination analytique de ces harmoniques spatio-temporels et plus particulièrement, l’ordre d’espace et la fréquence porteuse associée. De plus, un point important, il permet d’identifier les effets « sources » de ces harmoniques de forces à l’origine du « bruit magnétique ». Une comparaison à des simulations comportementales numériques par éléments finis (EF) mais aussi à des tests expérimentaux valideront les résultats.

Cette thèse porte sur la conception silencieuse par démarches inverses de machines synchrones à aimants permanents dotées de bobinages dentaires. Notre travail se focalise sur l’analyse des raies de forces radiales à l’origine du bruit magnétique. En premier lieu, un modèle direct électromagnétique, nous a permis de déterminer le spectre spatio-temporel de la force radiale dans l’entrefer. Ce dernier nous offre la possibilité d’obtenir pas à pas et de manière analytique l’induction radiale dans l’entrefer, résultat du produit de la force magnétomotrice totale et de la perméance d’entrefer globale. Plusieurs machines dotées d’un bobinage dentaire et distribué ont été évaluées, comparées à des simulations par éléments finis et corroborés par une analyse modale opérationnelle sur un prototype existant au laboratoire. Puis la démarche inverse de conception est abordée par le biais de deux outils «analytiques prédictifs» donnant les origines des ordres faibles spatio-temporels de la force radiale dans l’entrefer. Enfin, la résolution du problème inverse est conduite au moyen d’une boucle itérative d’optimisation donnant parmi un échantillon de solutions, une fonction de bobinage, visant à atténuer ou supprimer une raie potentiellement risquée en termes de nuisances acoustiques.