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This paper presents a comparison of several methods to compute the magnetic forces experienced by the stator teeth of electrical machines. In particular, the comparison focuses on the virtual work principle (VWP)-based nodal forces and the Maxwell tensor (MT) applied on different surfaces. The VWP is set as the reference. The magnetic field is computed either with finite element analysis or with the semi-analytical subdomain method (SDM). First, the magnetic saturation in iron cores is neglected (linear B-H curve). Then, the saturation effect is discussed in a second part. Homogeneous media are considered and all simulations are performed in 2-D. The link between the slot's magnetic flux and the tangential force harmonics is also highlighted. The comparison is performed on the stator of a surface-mounted permanent-magnet synchronous machine. While the different methods disagree on the local distribution of the magnetic forces at the stator surface, they give similar results concerning the integrated forces per tooth, referred as lumped forces. This conclusion is mitigated for saturated cases: the time harmonics are correctly computed with any of the presented lumped force methods but the amplitude of each harmonic is different between methods. Nonetheless, the use of the SDM remains accurate with MT in the air gap even with saturation for design and diagnostic of electromagnetic noise in electrical machines. However, for more accurate studies based on the local magnetic pressure, the VWP is strongly recommended.

The vibro-acoustic analysis of electrical machines under electromagnetic excitations (e-NVH) partly relies on the analysis of the stator response under Maxwell stress harmonic waves. In particular, the notion of unit-wave Frequency Response Function (FRF) is often used to diagnose magnetic noise issues during numerical simulations. However, such an FRF cannot be experimentally measured. This communication demonstrates the use of the stator tooth tip FRF which is compatible with both numerical and experimental approaches, and makes the link between tooth-excitation and wave-excitation based FRF. The two methods are compared in terms of physical insights and numerical aspects.

In an electrical machine, the Maxwell Tensor is widely used to compute global forces or local pressure along a surface in the air. This communication proposes to highlight the limits of the method with an academic case of slotless stator and rotor. In particular an analytic demonstration shows the existence of coefficients depending on the geometry and the wavenumber between the application of the Maxwell Tensor in the air-gap and the stator magnetic pressure.

This paper presents the first open-source development project for the electromagnetic design optimization of electrical machines and drives named Pyleecan – PYthon Library for Electrical Engineering Computational ANalysis. This paper first details the objectives of Pyleecan open-source development project, and the object-oriented architecture of the software that has been developed and released. Then it reviews and compares the available free and open-source software used during the multiphysic design of electrical machines including electromagnetics, heat transfer and vibro-acoustic analysis.

This article presents an experimental setup ded- icated to the analysis of magnetic noise and vibrations in radial flux electrical machines. Both electromagnetic excitation and structural response of the electrical machine are simpli- fied to provide the first benchmark of the phenomenon of electromagnetically-excited noise and vibrations. The test bench properties as well as the magnetic, vibration and acoustic upcoming extensive measurements are shared to the scientific community, providing a clear reference case to compare differ- ent

In this paper, a new hybrid method is developed for the fast and accurate computation of air gap flux density in the open-circuit Interior Permanent Magnet Synchronous Machines (IPMSM). The rotor magnetomotive force is estimated using a single non-linear FEA simulation. Then, rotor motion and stator slotting effect are included without loss of calculation performance using the semi-analytical subdomain method initially developed for Surface Permanent Magnet Machines. This hybrid method calculates the time and spatial distribution of radial and tangential airgap flux in a few seconds. It can be used to quickly estimate electromagnetic quantities (cogging torque, back emf) as well as magnetic forces for the electromagnetic and vibroacoustic design optimization of electric motors. The method is applied to the vibroacoustic analysis of the IPM machine of the Toyota Prius 2004 at open-circuit state and variable speed. Results show that the maximum sound power level occurs when the air gap magnetic pressure harmonics excite the breathing mode of the stator structure.

This paper reviews the recent developments of semi-analytical subdomains modeling techniques to compute the flux density distribution in electrical machines by the exact solving of Maxwell equations. It is shown that with an appropriate development methodology and numerical implementation, these harmonic models break the traditional compromise between accuracy and computation time that must be done using finite element or other analytical methods. Besides that, subdomains model development techniques have improved to overcome its topological limitations. This fact is demonstrated on three different subdomains models in comparison with finite element methods in terms of accuracy and processing time. The first one is a subdomains model of a surface permanent-magnet synchronous machine, the second one is for an inset permanent-magnet synchronous machine, and the third one is for a squirrel-cage induction machine. Thanks to an efficient implementation method, a very low computation time is obtained. The robustness of the subdomains on the geometrical assumptions is also demonstrated.

This paper studies the effect of magnetic forces on acoustic noise and vibrations of electrical machines designed for transport applications, and more especially induction machine used for traction application. The sources of electrical noise in electrical transportation systems are first briefly reviewed. Then, the main physical phenomena responsible for acoustic noise and vibration induced by Maxwell forces in a traction induction machine are reviewed, namely slotting, winding, saturation, eccentricity, asymmetries of the magnetic circuit, and Pulse Width Modulation Effect. In this example the main resonance is due to slotting effect and a detailed analysis of the harmonics (magnetomotive force and permeance waves) is provided based on convolution properties. All the numerical results and noise reconstitutions presented in this paper has been obtained thanks to MANATEE® software. MANATEE is a multi-physics environment dedicated to the fast design of electrical machines, including the computation of acoustic noise and vibrations due to magnetic forces, along with acoustic power level at variable speed.

L’objectif de cet article concerne la comparaison de différentes approches analytiques permettant d’estimer le contenu spatio-temporel des forces radiales dans l’entrefer d’une machine asynchrone. En effet, lors d’une phase de conception intégrant la problématique du bruit des machines électriques, il est intéressant de prédire les harmoniques de force d’origine magnétique qui pourraient solliciter la structure. Deux approches sont proposées, la première exploite un modèle analytique simple reposant sur le calcul de la force magnétomotrice et de la perméance d’entrefer globale ; et la seconde repose sur la théorie des sous-domaines. Ces deux approches sont comparées avec la méthode des éléments finis et des mesures de vibration valident qualitativement le contenu spatio-temporel des forces radiales dans l’entrefer obtenu par les deux approches.

Cet article étudie l’effet de l’angle de charge sur les efforts harmoniques de Maxwell (tangentiels et radiaux) dans deux machines synchrones à aimants permanents (MSAP) surfaciques d’architectures très différentes : une machine à 6 dents et 2 paires de pôles, à faible couple et très haute vitesse, et une autre à 120 dents et 58 paires de pôles, à fort couple et faible vitesse. Les efforts magnétiques en présence sont d’abord analysés de manière théorique. Des simulations numériques électromagnétiques sont ensuite réalisées à l’aide du logiciel MANATEE. On montre la difficulté d’établir a priori des règles générales pour déterminer l’angle de charge qui permet de minimiser un certain effort harmonique. Dans les deux cas étudiés, on constate cependant que l’angle de charge maximisant le couple ne minimise ni ne maximise aucun des efforts harmoniques parasites, radiaux ou tangentiels. En cas de présence d’un couple pulsatoire, il n’est pas possible de le minimiser tout en minimisant les efforts tournants de dentures. Cette étude sert de base à l’établissement d’un compromis entre performances électromagnétiques et vibro-acoustiques.

La présence d’harmoniques de forces électromagnétiques dans les machines électriques est généralement source de bruit acoustique et de vibrations (B&V). Ce phénomène doit être considéré dès les premières phases de conception pour respecter les normes en matière de B&V, en particulier dans le secteur automobile. Le niveau de B&V s’obtient à partir d’une simulation multi-physique basée sur des modèles électromagnétiques, mécaniques et acoustiques, de préférence rapides et précis de manière à l’inclure le plus tôt possible dans la phase de conception. Cette thèse CIFRE est partie intégrante du programme de recherche interne de la société EOMYS ENGINEERING, qui développe et commercialise son logiciel MANATEE dédié à la simulation électromagnétique et vibroacoustique des machines électriques. Dans ce contexte de modélisation, cette thèse porte sur la méthode électromagnétique semi-analytique des sous-domaines pour le calcul des harmoniques de forces 2D dans l’entrefer d’une large variété de machines électriques, et se concentre particulièrement sur la Machine Synchrone à Aimant Permanents en Surface (MSAPS) et la machine asynchrone à cage d’écureuil. La thèse s’intéresse également à deux verrous scientifiques concernant la contribution des forces tangentielles au niveau de vibration global, et l’effet de modulation des dents qui apparaît dans les machines avec un nombre proche d’encoches et de pôles. A cet effet, un banc d’essai comprenant une machine bruyante particulière (une MSAPS avec 12 encoches et 10 pôles) et l’instrumentation nécessaire a été conçu et réalisé. Le banc d’essai vise enfin à comparer les différents modèles utilisés couramment dans les simulations B&V