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The performance and energy efficiency of electro-mechanical converters are strongly bound to the properties of their magnetic cores. The latter are mostly made from stacked laminations of soft magnetic materials, such as Fe3%Si, which limits the core geometry design. However, when complex geometries are required, usually forging processes may be employed but with very low silicon steels (<0.5%) to be able to forge the steel. In that case, the low silicon content yields to higher electrical conductivity and then to higher eddy current loss. In this work, an additive manufacturing technique allowing to build complex geometries is studied with Fe3%Si magnetic materials. The fabrication process allows to obtain green parts which are then densified through debinding and sintering steps. The magnetic characterization is performed on toroidal cores and allows to observe a high level of magnetic induction and relative permeability. Finally, the impact of the printing strategy on the magnetic performances is investigated.

Nowadays, additive manufacturing of metallic materials is most often carried out using expensive and complex tools that leave the user with limited control and no possibility of modification. In order to make the printing of metal parts more accessible to small structures but also better suited for academic research, the use of a mixture of thermoplastic polymer and metal powder is a good solution as many granular feedstocks already exist for Metal Injection Molding applications. To perform the shaping process, the Fused Granular Fabrication 3D printing technology is set up by diverting the use of a feedstock in the form of pellets that are directly inserted into the print head. This solution, which is less costly, is implemented here by modifying a mid-range printer, the Tool Changer from E3D, and by making the hardware and software adaptations to mount a compact granulates extruder on it, which is also available on the market. The polymer portion present in the green part can then be removed in order to perform the heat treatments that will densify the powder by sintering and give a fully metallic dense object.

This paper shows the influence of the shift phase angle ψ between phase currents and back-electromotive forces on magnetic radial forces and torque ripple for a specific low power permanent magnet synchronous machine. This influence is firstly demonstrated through analytical development considering only the first harmonic values. Then, magnetic pressure harmonics versus space and frequency as well as torque ripple are evaluated on the studied motor for different angles using finite element approach. The aim is to establish a good compromise between consumed current, torque and radial force harmonics at the origin of the electromagnetic noise. Experimental measurements with a sensorless field-oriented control are detailed.

Purpose This paper deals with the study of the influence of the phase shift between currents and back-electromotive forces (back-EMF) on torque ripple and radial magnetic forces for a low power synchronous machine supplied with 120 degrees square-wave currents. This paper aims to establish a good compromise between efficiency, harmonics of torque and harmonics of radial forces at the origin of the electromagnetic noise. Design/methodology/approach Based on a finite element approach, torque and magnetic pressure harmonics versus space and frequency are evaluated for different angle values. The evolutions of the different harmonics against the load angle are analyzed and compared to those of experimental measurements. Findings Depending on the load torque, field-weakening or field-boosting can be used to reduce current harmonics contributing the most to the radial magnetic forces responsible for the noise. Besides, a compromise can be found to avoid deteriorating too much the performances of the machine, thus being suitable with an industrial application. Research limitations/implications This study concerns low power permanent magnet synchronous machines with concentrated windings and driven with a trapezoidal control, while having sinusoidal back-EMF. Originality/value The use of a simple mean and suitable with a large-scale manufacturing industry to reduce the identified electromagnetic-borne noise of a specific electric drive makes the originality.

This paper studies the electromagnetic noise behaviour of a 5 phase Interior Permanent Magnet Machine with fractional slot concentrated winding designed. A numerical model is used for analysing the torque characteristics and electromagnetic forces. The vibro-acoustics and mechanical resonance of the model are then investigated analytically. The purpose of both analyses is to identify the source of electromagnetic noise within the machine. A sonogram is also carried out on the existing prototype to correlate it with the numerical results. Finally, the choice of the appropriate method to attenuate noise for this case study is elaborated.

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 -- The aim of this paper is to simulate a large power brushless synchronous generator (BLSG) used for large turbo-alternator brushless excitation systems, under conditions of saturation and rotating rectifier diode failures. A reluctance network coupled with electric circuits and power electronic components integrating the movement and nonlinearities of materials has been developed. The approach achieves good compromise between accuracy and computing time for the complete analysis of a 39 phase machine with 117 teeth and 22 poles, and 78 diodes in the associated rectifier bridge. Our model is validated by comparison with experimental measurements and numerical simulation by a finite element package. For the simulations presented, a gain in computation time of 800 can be obtained compared with a finite element model. Different results are calculated for healthy and faulty states to study the impact of open diode block failure. Simulation results show that open diode failures have little effect on the rectified output voltage but the current through diodes and protection fuses increases. The currents in armature phase coil are very affected due to failures. A flux sensor coil can be placed on the stator pole to capture the impact of failures. The harmonic content of the pole flux can be used to monitor and detect diode failures. Index Terms-- Reluctance network, rotating rectifier, diodes, saturation, fault analysis, fault detection.

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.

Acoustic comfort is an increasingly important factor at the design stage of industrial inductors associated to converters. In addition, power converters in railway domain are more and more compact and powerful. In this paper, inductors with different air-gap materials are used in order to reduce vibration and noise of inductors. Finite element calculations are performed and the detail of the origin of electromagnetic noise is studied. Electric and vibratory measurements (modal and operational analysis) are compared with the numerical calculations.

Nowadays, developing electric motorization for land vehicles is essential due to the crucial need to save energy. This paper presents the development of a tool used for optimal acoustic and electromechanical modeling whose highly accurate calculations and speed of resolution make it stand out from standard analytical and Finite Element models. By coupling an analytical model with static FE simulations, our ’hybrid’ model calculates a complex global air-gap permeance per area unit, to take into account magnetic wedge permeability, pre-slot height, and rotor shape. An unparalleled level of precision and speed of resolution is obtained for the computation of air-gap magnetic pressures. Several results of comparisons between acoustic measurements and simulations on a concentrated winding motor for different speeds are presented.

This paper describes the modeling of a permanent magnet synchronous machine by using lumped models. Designing electrical machines necessarily involves several fields of physics, such as electromagnetics, thermics, mechanics and acoustics. Magnetic, electrical, electronic and thermal parts are represented by lumped models, whereas vibro-acoustic and mechanical parts are represented by analytical models. The aim of this study is to build a design model of a permanent magnet synchronous machine for traction applications. Each model is parameterized in order to optimize the machine. The method of taking into account saturation and movement is described. These fast, lumped models make it possible to couple the software used with optimization tools. Simulation results are presented and compared with the finite element method and the experiments performed.

In order to optimize the design of an enclosed induction machine of railway traction, a multiphysical model is developed taking into account electromagnetic, mechanical and thermal flow phenomena. The electromagnetic model is based on analytical formulations and allows calculating the losses. The thermal flow modeling is based on an equivalent thermal circuit which has the feature to consider the flow structure inside the machine. In this way, a numerical study has been carried out to evaluate this internal flow structure depending on the rotational speed. The results of the multi-physical model are confronted with experimental results.

This paper presents a method to characterize the main magnetic force waves occurring in a sinusoidally-fed induction machine. Three main force types are identified: slotting force waves, winding force waves and saturation force waves. Slotting force waves are characterized in terms of number of nodes, velocity, propagation direction and magnitude. On the ground of the expression of these forces magnitude, a method to cancel a given magnetic force wave by properly choosing the rotor slot or stator slot opening width is presented. This new method is validated with both simulations and experiments. Contrary to the common design rule that advices to decrease rotor and stator slot openings width in order to reduce magnetic noise, it is shown that a wider slot opening can lower the global noise level when properly chosen.

This paper first presents the analytical models of an ALSTOM simulation software, DIVA, which computes the vibratory and acoustic behavior of a variable-speed induction machine due to Maxwell forces. This radial magnetic pressure in the air-gap makes the stator vibrate in the audible range, creating the so-called magnetic noise characterized by a high tonality. On the ground on these analytical models, the main magnetic vibrations due to slotting, pulse-width modulation (PWM) harmonics and their interaction are then analytically characterized. Their number of nodes, velocity and propagation direction are experimentally validated by visualizing the stator deflection shapes. Finally, some experimental validations of the simulation tool are presented. On the ground of both analytical results and simulations, it is shown that some quieter motors can be designed acting on the motor geometry (especially slot numbers) and PWM strategy.

Numerous empirical rules have been established in order to rightly choose the number of stator and rotor slots and limit the audible magnetic noise level radiated by induction machines. However, these rules never take into account the stator natural frequencies neither the fact that the motor is run at variable speed. In this article, a fast simulation tool of the variable-speed magnetic noise emitted by induction machines, based on fully analytical models, is presented. On the ground of these models, the analytical expression of main magnetic vibrations due to slotting reluctance harmonics are derived and experimentally validated, confirming the prime importance of slot combination in magnetic noise radiation. Some simulations are then run on a 700 W squirrel-cage motor in order to quantify the noise emitted by all possible combination of slot numbers in two and three pole pairs cases, including odd slot numbers. The obtained database efficiently replaces the old empirical rules on slot combination numbers and helps designing quiet induction motors. Similar database can be built for other power ranges.

This paper derives the analytical characterization of Maxwell radial vibrations due to Pulse-Width Modulation (PWM) supply in induction machines, and especially in traction motors supplied with an asynchronous switching frequency. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the switching frequency, these forces can be responsible for high magnetic noise levels during starting and braking. A simple rule to avoid PWM noise is then proposed, and applied to an industrial traction motor. Experimental results show that the choice of the switching frequency can have a 15 dB impact on the sound power level emitted by the motor during starting, and that a lower switching frequency can sometimes lead to lower magnetic noise. In agreement with analytical predictions, the new proposed switching frequency that avoids resonances between PWM exciting forces and corresponding stator modes reduces magnetic noise of 5 dB during starting.

This paper presents the full analysis of the vibration behaviour responsible for audible magnetic noise in a PWM-fed fractional-slot induction machine, including theoretical predictions, numerical simulations, and experimental validations (stator modal analysis and deflection shapes visualisation). Magnetic force waves due to slotting harmonics, pulse-width modulation (PWM) harmonics and their interactions are characterised in terms of nodes number, rotation speed, and propagation direction. It is shown in particular that some odd spatial order vibration waves appear due to fractional slotting, and that some combinations between slotting lines and PWM lines can be very noisy due to an elliptical mode natural frequency close from the switching frequency.

This paper derives the analytical characterization of Maxwell radial vibrations due to saturation effects in induction machines, and especially in traction motors. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the stator and rotor slot numbers, and stator natural frequencies, these forces can be responsible for high magnetic noise levels during electrical starting and braking. A simple rule to avoid saturation magnetic noise is then proposed, and applied to an industrial motor. A fully analytical model of the motor vibro-acoustic behavior, including saturation effects, is finally presented. Simulation results show that the new proposed motor improves magnetic noise level up to 20 dB, whereas experiments give a 15 dB improvement.

The purpose of this paper is to present a fast analytical model of the acoustic behaviour of pulse-width modulation (PWM) controlled induction machines and clarify the interaction between space harmonics and time harmonics in audible electromagnetic noise spectrum. A multilayer single-phase equivalent circuit calculates the stator and rotor currents. Air-gap radial flux density, which is supposed to be the only source of acoustic noise, is then computed with winding functions formalism. Mechanical and acoustic models are based on a 2D ring stator model. A method to analytically derive the orders and frequencies of most important vibration lines is detailed. This method is totally independent of the supply strategy and winding type of the machine. Some variable-speed simulations are run on a 700 W fractional-slot induction machine in sinusoidal case as a first validation of theoretical results. he influence of both winding space harmonics and PWM time harmonics on noise spectrum is exposed. Most dangerous modes and frequencies expressions are demonstrated in sinusoidal and PWM cases. For traditional integral windings, it is shown that vibrations modes are necessarily even whereas when rotor and stator slot numbers are not both even, which is the case for fractional windings, electromagnetic power can dissipate as vibrations through all stator deformation modes, leading to a lower noise level at resonance. The analytical work of this paper does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation. The analytical model and theoretical results presented in this paper help designing low-noise induction machines, and diagnosing noise or vibration problems. This paper details a fully analytical acoustic and electromagnetic model of a PWM fed induction machine, and demonstrate the theoretical expression of main noise spectrum lines combining both time and space harmonics.

The purpose of this paper is to present the original study of an industrial device. Industrial inductors are used to decrease the current variations, resulting from the use of modern power converters. To reduce these variations, the magnetic energy stored in these components is automatically used when the receptor is unconnected to the principal sources. Such storage is generally obtained by using a magnetic circuit containing air-gaps. The rigidity of this circuit, associated to the magnetic stresses which appear in these areas leads the structure to produce mechanical vibration and to emit audible sounds. Design/methodology/approach – Experiments, simulations and test devices are used to determine the main physical phenomena that generate the undesirable audible noise. The resulting knowledge is used to design a quieter device.

Induction motors design requires making numerous trade-offs, especially when including electromagnetic noise criterion besides usual criteria like efficiency and cost. Moreover, adding the noise objective significantly increases computational time as it must be evaluated at variable speed in order to take into account resonance effects. In that case, the application of multi-objective optimization algorithms can be hard for their computational cost as for the difficulty to interpret multi-dimensional results in both design variables and objectives spaces. This paper first describes a fast analytical model of a variable-speed induction machine which calculates both motor performances and sound power level of electromagnetic origin. This model is then coupled to Non-dominating Sorting Genetic Algorithm (NSGA-II) in order to perform global constrained optimizations with respect to several objectives (e.g. noise level, efficiency and material cost). As induction machine design involves both continuous and discrete variables, a modified NSGA-II algorithm handling mixed variables is detailed. Finally, some optimization results are presented and analyzed by the aid of several visualization tools.

The concept of multidisciplinary optimization is applied to design an electric motor. It combines finite elements and analytical models to form together a multidisciplinary model. The models represent different machine phenomena as electromagnetic, thermal but also vibro-acoustic. These models are linked through a constrained optimization process, the whole forming an optimal design tool

Induction motors optimal design can involve many variables and objectives, and generally requires to make several trade-offs, especially when including the audible electromagnetic noise criterion beyond the usual performance criteria. Multiobjective optimization techniques based on Pareto optimality are useful to help us finding the most interesting solutions and decide which one(s) to adopt. However, it is not always easy to analyse the Pareto-optimal solutions obtained with such methods, especially when treating more than three objectives, and Pareto fronts may contain more data than we might think. This paper briefly describes an analytical model of the variable-speed squirrel-cage induction machine which computes both its performances and sound power level of electromagnetic origin. The model is then coupled to the Non-dominated Sorting Genetic Algorithm (NSGA-II) in order to perform global optimization with respect to several objectives (e.g. noise level, efficiency and material cost). Finally, an optimization problem is solved and analysed, and some useful visualization tools of the Pareto optimal solutions and their characteristics are presented.

The aim of this paper is to use an analytical multi-physical model - electromagnetic, mechanic and acoustic - in order to predict the electromagnetic noise of an asynchronous machine. This machine operating at variable speed generates vibrations that can be harmful for the machine itself and its environment. Thus, it is necessary for the manufacturer to take into account noise and vibration at the design stage. Acoustic measurements are performed in order to validate our multi-physical model. Afterwards, the experimental design method is used to build response surfaces of the noise with respect to the main factors.

The modelling of a turbo-alternator using permeance network is described. This approach allows implementing electrical and magnetic coupling as well as mechanical coupling. Such processes as saturation, movement, 3D effects are taken into account. The aim of this study is to set up a design model of 10 to 100 MW turbo-alternators. The method of taking into account of 3D effects is described. The first results of simulation were obtained. The experimental measurements validate the model. Key words – CAD application, reluctance network, magnetic circuit, magnetic field, air-gap permeance, automatic generation of the permeance network.

In the design process of any device, the computation of forces and torque is often a decisive step. Finite element solutions give accurate solution in term of magnetic field or flux density. But for local magnetic force computation, unfortunately, many formulations are available and give different results. Here, a new experiment is presented. It helps to discriminate such different formulations. Energy method proves to be the more accurate. Using this framework, another formulations or interpretations can be tested.

L’étude d’un système électrotechnique passe très souvent par la détermination des relations liant les grandeurs étudiées aux données d’entrée. Dans bien des cas, l’écriture explicite de ces fonctions de passage n’est pas aisée, voire même impossible en raison de la complexité des phénomènes physiques mis en jeu. La Méthode des Plans d’Expériences (MPE) peut alors se présenter comme un formalisme méthodologique simple répondant à cet objectif. Dans tous les cas, cette approche vise à construire un modèle – très simple de préférence – liant les entrées et les sorties, grâce aux résultats obtenus à l’issue d’une série d’expériences déterminées a priori : il s’agit du plan d’expériences. Après avoir introduit les principaux aspects de la MPE, plusieurs algorithmes d’optimisation basés sur cette méthode sont développés. Cet emploi particulier de la MPE comme base à des méthodes heuristiques, constitue une originalité. Deux applications sont présentées : un frein linéaire à courant de Foucault et l’étude d’une fonction analytique ayant 2 maxima d’amplitudes différentes.

A car alternator with claw poles is typically a 3D device because its shape is not axi-symmetrical nor XY-symmetrical. A 3D finite element model can be useful to simulate the thermic behavior of the machine but is rarely available. In this paper, it is shown that a 2D simulation can fit even if all the thermal phenomenon relating to the missing direction are neglected. The alternator have been modeled in two different sections to show their respective reliability. Moreover, thermal hybrid conductivities have been defined to take into account the succession of the different materials in the missing direction.

Nous présentons, dans cet article, une approche de modélisation et de simulation d’une machine tridimensionnelle par un réseau de perméances couplé à des circuits électriques. La saturation des matériaux, le mouvement du rotor et le couplage avec un pont de diodes sont pris en compte alors que les temps de simulations restent très faibles. Cette approche est appliquée à la modélisation d’un alternateur automobile qui est une machine à flux axial de type Lundell. Les résultats de simulations sont comparés aux relevés expérimentaux pour deux appareils différents, à vide et en charge. La qualité des résultats obtenus, montrent que la méthode proposée peut fournir des modèles dynamiques couplés magnétique-électrique de machines dont la géométrie est typiquement tridimensionnelle, avec un compromis temps de calcul-précision très satisfaisant.

Modélisation d’un turboalternateur par un réseau de perméances. Prise en compte des effets 3D, de la rotation, de la saturation... Outil dédié aux machines 2 poles et 4 poles de 10 à 100MW

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).

Fabrication of soft magnetic ceramic materials relies on time consuming conventional methods, such as molding and sintering, which restricts the possibilities of shapes the components can be given. Additive manufacturing of such materials can help reduce production lead time and unlock topological design limitations. In this work, the implementation of an indirect additive manufacturing methods for soft magnetic Mn-Zn ferrite, intended for high frequency applications, is presented. A blend of light sensitive polymer binder and fine powder is used for the shaping stage using Digital Light Processing (DLP) followed by a heat treatment that allows to remove the polymer part and to obtain a final dense part. Simple shapes were produced in order to characterize their magnetic performances and to validate this method for further fabrication of more complex magnetic core.

The performance and energy efficiency of electro-mechanical converters are strongly bound to the properties of their magnetic cores. The latter are mostly made from stacked laminations of soft magnetic materials such as Fe3%Si which limits the core geometry design. However, when complex geometries are required, usually forging processes may be employed but with very low silicon steels (<0.5%) to be able to forge the steel. In that case, the low silicon content yields to higher electrical conductivity and then to higher eddy current losses. In this work, an additive manufacturing technique allowing to build complex geometries is studied with Fe3%Si magnetic materials. The fabrication process allows to obtain green parts which are then densified through a final sintering step. The electromagnetic characterization of samples is performed. Finally, the results and possible improvement will be discussed in comparison with conventional Fe3%Si electrical steels and a forged magnetic steel that is commonly found in electromechanical applications.

In this work, we propose an FDM additive manufacturing process that uses a feedstock in the form of small pellets composed of a similar mix of 316L Stainless Steel powder bound by a thermoplastic polymer. The printing stage is performed using an affordable Archimedes screw system that is mounted on a classical 3-axis cinematic frame. The feedstock, provided by PolyMIM, is diverted from its original use, which is Metal Injection Moulding (MIM), and is intended to be debinded and sintered. This allows to consider a wide range of materials already available. The impact of the deposition strategy on the tensile properties will be investigated in relation with the microstructure.

To design and study an electrical machine, Finite Element Model (FEM) is nowadays the most accurate approach as it takes into account different phenomenon. However, it is also time-consuming which does not always make it suitable for an optimization process. Analytical model can then be used but it has to be as accurate as possible in order to obtain valid and relevant results. In case of squirrel cage induction machines, several analytical models have been proposed under different simplifying hypothesis [1]–[3] The well adapted one is the approach involving winding function to determine the armature Magneto Motive Forces (MMF) along with the air gap permeance. These two quantities can be expressed in a relatively accurate way [4]. The problem then remains in taking into account the rotor part in order to determine the currents which circulate in the bars of the squirrel cage. Indeed, in addition to the well estimate of the magnetic flux through the rotor surfaces, the determining of the elements of the equivalent electrical circuit which makes it possible to precisely calculate the currents of the bars in the most accurate way is required. In the present paper, an analytical model of the squirrel cage based on an equivalent electrical circuit along with the approach to accurately identify its parameters is proposed. This model that enables to determine the rotor bar currents can be generalized to any structure and thus be used either for design or optimization purposes. Results obtained in the case of an induction machine prototype are compared to the ones given by FEM.

Magneto Motive Force is an important quantity to analyze electrical machine performances. Indeed, the latter is directly linked to that of the air gap magnetic flux density and thus to the torque ripples, vibration and then noise. This paper proposes to reduce the MMF harmonic content by means of optimization process using mono-objective or multi-objective algorithms with discrete and continuous variables. For this aim, optimization algorithm is coupled with an analytical tool which enables calculating quickly the MMF harmonic content from winding parameters. A winding optimization of three different windings with the same number of pole pairs is proposed to show the suitability of this process.

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.

This paper deals with the study of the influence of the phase shift between currents and back-electromotive forces on torque ripple and radial magnetic forces for a low power synchronous machine supplied with 120 degrees square-wave currents. Based on a finite element approach, torque and magnetic pressure harmonics versus space and frequency are evaluated for different angle values. The aim is to establish a good compromise between efficiency, harmonics of torque and harmonics of radial forces at the origin of the electromagnetic noise. The evolutions of the different harmonics against the load angle are analyzed and compared to those of experimental measurements.

This paper studies the electromagnetic noise behaviour of a 5 phase Interior Permanent Magnet Machine with fractional slot concentrated winding designed. A numerical model is used for analysing the torque characteristics and electromagnetic forces. The vibro-acoustics and mechanical resonance of the model are then investigated analytically. The purpose of both analyses is to identify the source of electromagnetic noise within the machine. A sonogram is also carried out on the existing prototype to correlate it with the numerical results. Finally, the choice of the appropriate method to attenuate noise for this case study is elaborated.

Study of the impact of stator MMF from different winding distributions using FEM can be tedious when taking into account the stator slots as it introduces mesh constraint and reluctance variation of the air gap. To avoid this fact, a current sheet spread all around the inner stator surface is used. In the proposed approach, the MMF is modelled by the equivalent current sheet of the real stator MMF in the air gap. This current sheet is coupled with an analytical tool that allows obtaining the spatio-temporal stator MMF of any winding considered. Compared to an analytical model, the proposed approach enables taking into account the non linear behaviour of magnetic material in the yoke and thus testing different combinations of stator windings in more realistic conditions.

This paper shows the impact of the shift phase angle ψ between phase currents and back-electromotive forces (back-EMFs) on torque and radial forces for a low power synchronous machine (20 W). Pressure harmonics versus space and frequency on our motor and torque are evaluated with different angles with finite element approach. The aim is to establish a good compromise between consumed current, harmonics of torque and harmonics of radial forces linked to the electromagnetic noise for two strategies: maximum torque per ampere (MTPA) control and field weakening (FW) control. The evolution of each harmonic versus ψ are compared for both strategies. Experimental measurements in sinusoidal case are detailed.

Permanent magnet brushed DC motors are used in several applications such as home automation or automotive industry. This is mainly due to their lightweight, low cost and compact structure. Thus, the importance to study the sources of noise and vibration in these motors, which is often complicated and can be attributed to many factors. In this paper, the cogging torque and electromagnetic forces are studied in the case of a small permanent magnet brushed DC motor with 2 poles and 3 slots. Addition of dummy slots on the rotor side is described with its effect on the evolution of both aspects. The aim of this study is to give the quantitative effect about torque ripple and radial forces for each harmonic in relation with these dummy slots.

Magneto motive force is a key quantity of the energy conversion in the electrical machines. Its harmonic content is important as it leads to the one of the magnetic flux density in the air gap. To analyze it, a first step consists to study the winding function. Many tools already exist to tackle this point but generally they use some methods like Star of slots or matrix representation and the harmonic content is obtained by a Fast Fourier Transform of the total winding function. In the present paper, we propose to build up the winding function using elementary patterns whose harmonic contents are used to reach the one of the whole function using a geometrical construction. This approach is quite fast and allows easy analyzing in order to reduce or cancel a magnetic harmonic.

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 aim of this paper concerns the design with these targets for low power motors that offer a good compromise in terms of performance: speed, torque, current, and noise linked to the radial forces. Different low power machines and topologies are studied with the same constraints in term of volume for the same value of the torque. The study is carried out on a PMSM with surface permanent magnet ‘SPM’ and with insert permanent magnet ‘IPM’. In order to reduce the cost, a synchronous reluctance machine ‘SynRM’ is also designed and studied. 2D and 3D Finite Element modeling are used to compare the performance of the three different topologies. In addition, the best solutions are realized and tested.

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

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 studies different low power machines and topologies with the same constraints in term of volume for the same value of the torque. The aim of this paper concerns the design with these targets for low power motors that offer a good compromise in terms of performance: speed, torque, current, and noise linked to the radial forces. The study is carried out on a PMSM with surface permanent magnet ‘SPM’ and with insert permanent magnet ‘IPM’. In order to reduce the cost, a synchronous reluctance machine ‘SynRM’ is also designed and studied. 2D and 3D Finite Element modeling are used to compare the performance of the three different topologies.

Acoustics comfort is an increasingly important factor at the design stage of electrical machines associated to converters. The objective of this paper is to show the impact of the skew about the Maxwell pressures: radial and tangential components. Pressure harmonics versus space and frequency on induction motor are evaluated with no-skew and skew rotor with 3D finite element approach. The results are compared with analytical formulation in order to establish a fast and accurate analytical model to be used in an optimization tool. Experimental measurements with two induction motors with skew rotor and no-skew rotor validate our results.

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.

The aim of this paper is to simulate, with saturation and faults of rotating diodes rectifier, a large power brushless synchronous generator (BLSG) which is used for large turbo-generator brushless excitation systems. Reluctance network coupled with electric circuits and power electronic part integrating movement and nonlinearities of material has been developed. The approach realizes a good compromise between accuracy and computing time in order to completely analyze a 39 phases machine with 117 teeth and 22 poles and 78 diodes of the associated rectifier bridge. Experimental measurements validate our model and numerical simulations with finite element package.

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.

Acoustics comfort is an increasingly important factor at the design stage of electrical machines associated with converters. Skewing has a direct impact on pressure in the air-gap, which can be responsible for electromagnetic noise. This paper aims to compare different models to study the skewing. The impact of pressures is evaluated and analyzed for no-skew and skew rotors. Three numerical electromagnetic models are compared: 2D finite element method (FEM), 2D FEM multi-slice and 3D FEM. In addition, an experimental measurement validates our results.

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.

Vibration and acoustic noise can constitute a serious problem for Switched Reluctance Motors (SRMs). They are mainly caused by the deformation of the stator lamination stack due to its magnetic attraction to the rotor. This paper presents a 2D multi-physic methodology which permits to predict electromagnetic acoustic noise generated by SRMs, since the early design phase. In order to achieve the best compromise between accuracy and computational time, a hybrid methodology was adopted. It is based on a Finite Element (FE) magnetic model to take into account magnetic nonlinearities, especially for SRMs which are usually highly saturated. The vibration and acoustic models are based on analytic approaches and are integrated in an in-house tool we developed: GRIMM (Generic Ring Model for Magnetic Noise). This tool has been validated by a full FE approach for an 8/6 SRM at each step and good agreements are obtained. Its accuracy was improved by taking into account the stator teeth effect in terms of mass correction and by means of quasi-axisymmetry hypothesis.

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.

The main advantages of the Switched Reluctance Motor (SRM) are its robust construction and its low cost which makes this technology an attractive solution for traction applications. However, one of its major drawbacks is the high mechanical vibrations and acoustic noise. These vibrations and acoustic noise are mainly caused by the deformation of the stator lamination stack due to its magnetic attraction to the rotor. The aim of this study is to build a complete coupled multi-physic tool allowing the prediction of electromagnetic acoustic noise in an 8/6 SRM. The goal of such a tool is to be integrated in an optimization process. This tool is based on 2D electromagnetic, vibration and acoustic models which are calculated through analytical approaches. The vibro-acoustic analytical results are compared to those of a FE approach and good agreements are obtained.

Vibration and acoustic noise can constitute a serious problem in electric machines. They are mainly caused by the deformation of the stator lamination stack due to its magnetic attraction to the rotor. This paper presents a 2D multi-physic tool which permits to predict electromagnetic acoustic noise generated by electric motors, since the early design phase. This tool is based on 2D magnetic, vibration and acoustic models and the final goal is to find the best compromise between accuracy and calculation time. The magnetic model is based on the Finite Element (FE) method in order to take into account nonlinearities, especially for SRMs which are usually highly saturated. The vibration and acoustic models are calculated through analytic approaches. The analytical results are then compared to those of a full FE approach for an 8/6 SRM and good agreements are obtained.

This paper compares two rotor topologies of permanent magnet synchronous machines about the level and the origin ofelectromagnetic noise. The aim is to establish the origin of these radial forces: PM field, armature reaction or slotting harmonics. The first rotor has surface permanent magnet (SPM) and the second one has internal permanent magnet (IPM). The stator winding with concentrated winding, the yoke and frame will be the same for each machine. The magnetic noise generation requires modeling both the electromagnetic exciting force and the mechanical response of the excited structure: the magnetic force associated deflection shape and the structure vibration transfer. The finite element method is coupled to the analytical approach in order to estimate the electromagnetic noise.

At low speed, the acoustic power radiated by electrical transport systems can be dominated by a special source of noise called audible magnetic noise. This particular noise comes from magnetic vibrations due to magnetic forces, which are especially strong in traction motors. Some of them are called air-gap Maxwell forces and excite the stator structure, creating harmful resonances during starting or braking. Firstly, this paper presents the phenomenon of magnetic resonances due to Maxwell forces in traction induction motors, which are similar to tyre-road resonances. Two principal noise sources are analytically identified, namely slotting harmonics and Pulse-Width Modulation (PWM) harmonics. A fully analytical model of a traction motor and its PWM supply is then described. This model is validated at different stages (electrical, mechanical and acoustic) using several vibro-acoustic tools (experimental modal analysis, operational modal analysis, operational deflection shapes, spectrograms) and numerical methods (electromagnetic and mechanical finite element method, acoustic boundary element method). Finally, this model is coupled with a multi-objective optimization method in order to re-design an ALSTOM squirrel-cage induction motor by acting on the rotor geometry and the PWM strategy. Three objectives are considered: the improvement of average and maximum magnetic noise level during starting, and motor efficiency at nominal speed. Two designs are chosen to be manufactured. These ALSTOM motor prototypes are tested and successfully compared to simulations, and a reduction of 15 dB is observed when running the motors in real conditions. It is also shown that the choice of the switching strategy has a 15 dB influence on noise during starting.

This paper presents a fully analytical model of the electromagnetic and vibro-acoustic behavior of variable-speed squirrel-cage induction machines. This model is integrated in a fast simulation tool that can be used to design motors with low magnetic noise level on their whole speed range. Some simulation results at variable speed are favorably compared with experiments at both vibratory (spectrograms) and acoustic levels (sonagrams) on a 700 W laboratory motor and on an industrial 250 kW traction motor. These extensive tests show that the model correctly predicts the main exciting forces, motor natural frequencies and resonances during adjustable-speed drive. The simulation tool, called Diva, has been successfully applied to design a new low-noise ALSTOM motor.

The design of electrical machines involves several fields of physics, such as electromagnetism, thermics, mechanics but also acoustics. This paper describes the analytical multi-physics models of a computer-aided design (CAD) software which is applied to inverter-fed traction induction machines. The electromagnetic model computes rotor and stator currents, the induction machine traction characteristics, and the radial air-gap flux density. The mechanical and acoustic model computes the motor audible magnetic noise level due to Maxwell forces. The thermal model based on 3D nodal network, computes the transient temperature of different parts of the motor. These fast models make it possible to couple the software with some optimization tools. Finally, some simulations are presented on a self-ventilated closed motor, and an example of multi-objective optimization is exposed.

Traction motors optimal design involves minimizing or maximizing different objectives such as efficiency, temperature, audible electromagnetic noise, and weight. These characteristics are often conflicting, and require different types of models (electrical, mechanical, acoustic and thermal ones) containing both discrete (e.g. teeth numbers) and continuous variables. Moreover, the motor sound power level must be evaluated at variable-speed, which significantly increases computational time and prohibits the use of finite element methods (FEM) in an optimization process. In this paper, a fast multidisciplinary simulation tool of the induction machine is presented. It is based on analytical models validated with tests or FEM: an electrical model computes the air-gap Maxwell pressure responsible for noise, and all the traction characteristics of the motor; a mechanical and acoustic model determine the sound power level by modelling the stator structure as an equivalent ring; the electromagnetic model is coupled to a nodal-network thermal model which calculates motor temperatures and losses. Then, some constrained mixed-variable multi-objective optimizations based on Non-dominated Sorted Genetic Algorithm with a stochastic repair algorithm are exposed. They aim at designing a quiet, efficient and light motor fulfilling in particular the specified variable-speed output torque. Finally, the optimization results are discussed and some helpful visualization tools are presented.

Iron loss distribution in a railway traction induction motor is analyzed using time-stepping finite element for various operating modes. Tendencies are confirmed and validated by experimental results. Three zones concentrating the iron losses are identified: the stator teeth and yoke, and the top of the rotor teeth. These data are then used to establish a fast and accurate analytical model for iron loss in this type of motor.

A multi-physical parametric model of the induction machine and its pulse width modulation (PWM) supply was developed in order to predict its sound power level of electromagnetic origin at variable speed and load, and perform optimal design search including noise minimization. The electromagnetic model calculates the stator phase currents by the aid of a Simulink® PWM model and a multilayer single-phase equivalent circuit; it computes the air-gap radial flux density which is supposed to be the only source of acoustic noise. The mechanical and acoustic parts are based on a 2D cylindrical shell stator model. This paper presents some variable-speed simulations of a squirrel-cage traction machine, and demonstrates the ability of the simulation tool to investigate the role of harmonics in noise generation. Then, the possibility to use the Design of Experiments (DoE) method in order to find the leading variables on noise at variable speed is discussed. Finally, some PWM simulation results are presented and interpreted on the base of theoretical results.

The concept of multidisciplinary optimization is applied to design an electric motor. It combines finite elements and analytical models to form together a multidisciplinary model. The different models represent different machine phenomena as electromagnetic, thermal but also vibro-acoustic. These models are linked through a constrained optimization process the entire set forming an optimal design tool.

S. Dahel, M. Hecquet, P. Brochet

L’objectif de ce papier concerne la problématique de dimensionnement de machines synchrones de faible puissance sous contraintes de diamètre extérieur, de couple et vitesse, de courant et de bruit émis. Une machine synchrone à aimants en surface avec un bobinage sur dents est comparée à deux machines synchro-réluctantes avec ou sans assistance d’aimants avec le même type de bobinage. L’objectif visé est de réduire le cout en essayant de conserver les mêmes performances sous contraintes. Des simulations éléments finis 3D permettent d’évaluer et de comparer les différentes structures proposées ainsi que des résultats expérimentaux. Mots-clefs : machine synchrone à aimants, machine synchro-réluctante, harmoniques de couple, harmoniques de forces radiales.

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.

Le confort acoustique des machines électriques est à l’heure actuelle indispensable dès la phase de conception. De nombreuses références existent sur le sujet et proposent des formulations analytiques permettant d’identifier l’origine des raies acoustiques ou vibratoires comme l’effet de denture ou de la modulation de largeur d’impulsions (MLI). L’objectif de cet article est d’analyser ces forces spatio-temporelles dans le cas d’une machine asynchrone vrillée et de montrer l’impact du vrillage. Dans ce cas, peut-on exploiter ou non les formulations classiques et quel est l’impact du vrillage sur les harmoniques spatio-temporelles des forces radiales et tangentielles ? Ces forces seront estimées en exploitant une approche éléments finis (E.F.) tridimensionnelle sur machine asynchrone vrillée et non vrillée. Des résultats expérimentaux complètent cette analyse sur deux machines : l’une avec un rotor droit et l’autre avec un rotor vrillé.

A l’heure actuelle, les cahiers des charges deviennent de plus en plus drastiques et le confort acoustique est une des contraintes importantes dans le domaine du ferroviaire, chaque composant ayant une limite en décibel. Ce critère doit être intégré dès la phase de conception des composants de la chaine de traction comme les inductances de lissage associées à leurs convertisseurs. Dans ce papier, différentes structures d’inductances avec différents matériaux au niveau des entrefers et différentes topologies sont présentées et comparées en vue de réduire les vibrations et le bruit d’origine magnétique.

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.

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.

Cet article présente des résultats de simulations vibro-acoustique pour une machine à bobinage dentaire 10 pôles / 12 encoches équipée d’un rotor SPM (Surface Permanent Magnet). La machine répond à un cahier des charges type traction électrique. L’analyse du bruit d’origine électromagnétique, qui est pertinente pour des basses vitesses, devient une étape nécessaire dès la conception. Dans un premier temps, cet article justifie l’orientation vers l’usage des machines à bobinage dentaire. Ensuite, il détaille les méthodes d’analyse utilisées pour la détermination du bruit. La première méthode consiste à réaliser par éléments finis le calcul électromagnétique couplée à un module de calcul analytique mécano-acoustique, et la deuxième méthode réalise des calculs électromagnétiques via un Modèle à Constantes Localisées (MCL) couplé au même module mécano-acoustique. Une première validation est présentée dans le but d’évaluer la capacité du MCL à proposer un modèle comportemental satisfaisant, nécessaire à l’étude vibro-acoustique.

Cet article présente un modèle analytique permettant de calculer le bruit audible d’origine électromagnétique d’une machine asynchrone, en charge et en régime variable. Dans un premier temps, les courants rotor et stator sont calculés à partir de la tension d’alimentation à l’aide d’un schéma équivalent étendu aux harmoniques de temps générées par la MLI et aux harmoniques d’espace induites par le bobinage. Sa résolution sous forme matricielle est rapide malgré un grand nombre d’harmoniques prises en compte. Le formalisme des fonctions de bobinage est utilisé afin d’exprimer les forces magnétomotrices du stator et du rotor. Il est particulièrement adapté au bobinage fractionnaire, c’est-à-dire avec un nombre d’encoches par pôles et par phases non entier. L’induction radiale d’entrefer s’obtient alors comme le produit des forces magnétomotrices et de la perméance surfacique. Ce modèle électromagnétique a déjà fait l’objet de validations par des essais et des simulations éléments finis. Le bruit audible d’origine électromagnétique est supposé ne provenir que de la pression électromagnétique s’appliquant au stator, donnée par le carré de l’induction radiale. En réalisant une transformée de Fourier de cette force excitatrice, les déformations complexes statiques puis dynamiques du stator sont ensuite déterminées. La connaissance du comportement mécanique est obtenue en modélisant le stator comme un anneau d’épaisseur fine dont les fréquences naturelles sont également évaluées analytiquement. Enfin, on en déduit la vitesse de vibration de l’air à la surface du stator puis la pression acoustique émise par la machine. Une analyse permet de faire émerger les raies de forces prépondérantes dans le comportement vibro-acoustique par l’intermédiaire de développement en série de Fourier des grandeurs déterminant l’induction d’entrefer (fonctions de bobinage, courants, perméance). Les expressions des fréquences et des modes de déformation spatiale de l’ensemble de ces raies acoustiques sont dérivées en fonction des harmoniques d’espace et de temps induites par le bobinage et la MLI. Ensuite, ces expressions théoriques sont comparées à des simulations appliquées à une machine asynchrone à pas fractionnaire en régime sinusoïdal. Contrairement à une machine asynchrone à pas intégral et dont les nombres de dents seraient pairs, la conversion de l’énergie électromagnétique à l’énergie acoustique se fait dans ce cas à la fois par le biais des modes impairs et des modes pairs. L’énergie acoustique modale est ainsi répartie sur un plus grand nombre de modes, ce qui explique que les machines à pas fractionnaire soient réputées pour leurs faible bruit d’origine magnétique.

La conception d’un produit électrotechnique est une étape clé de son cycle de vie dont dépendent nombre de ses propriétés : valeur d’usage, coût, empreinte environnementale, fiabilité, etc.… La démarche de conception traditionnelle, « business as usual », est celle de l’approche progressive constituée d’essais et d’erreurs. . Celle-ci est devenue beaucoup trop coûteuse et hasardeuse. L’objectif principal de l’équipe Conception et Optimisation des Machines Electriques (C.O.M.E.), qui reste à l’heure actuelle utopique, est de substituer à ce processus long et coûteux une démarche entièrement virtuelle utilisant uniquement des procédés numériques. Pour l’atteindre, nous nous proposons dans un premier temps de dégager des méthodes de conception s’appuyant sur des outils logiciels adaptés, ce qui peut se résumer par « l’instrumentation de la démarche de conception ». Un de nos objectifs au cours de ces 10 dernières années de recherche a été de trouver des solutions de représentations des machines électriques de façon à éviter le coût d’un prototype. L’approche par réseaux de perméances, qui offre un bon compromis entre la précision des résultats et le temps de calcul, a été privilégiée. Ainsi, à chacun des systèmes réels étudiés s’est vu correspondre un équivalent virtuel infiniment plus avantageux. Celui-ci peut être modifié à volonté, au gré de l’expérimentateur. Cette démarche est typiquement appliquée lors d’optimisations pendant lesquelles les caractéristiques des modèles sont modifiées afin d’améliorer certaines performances. En ce qui concerne l’optimisation, la Méthode des Plans d’Expériences a été privilégiée. Dans ces développements, nous nous sommes efforcés d’assurer une bonne adéquation entre le modèle et la méthode d’optimisation choisie. Enfin, la confrontation avec l’expérience menée le plus souvent avec l’appui de nos partenaires industriels a permis de valider nos approches. Les différents exemples traités sont naturellement couplés et répondent à un besoin important en recherche technologique notamment dans le cadre du CNRT (Centre National de Recherche Technologique) Génie Electrique intitulé ‘Réseaux et Machines du Futur’. Le rapport est divisé en trois parties qui décrivent et situent mes travaux. La première partie constitue un résumé détaillé des activités pédagogique, administrative et recherche. La deuxième partie présente mes activités de recherche : du prototypage virtuel à l’optimisation par plans d’expériences et est illustrée par des exemples d’applications. Enfin, la dernière partie dresse un bilan ainsi qu’une présentation des perspectives à court et à long terme.

RESUME – Cet article a pour objectif de donner une réponse sur les origines du bruit des selfs. Ainsi, afin de définir une conception silencieuse d’une inductance alimentée par MLI, la mise en évidence des phénomènes générant le bruit électromagnétique est présentée. Différents matériaux au niveau des entrefers et différentes topologies sont détaillés et comparés en vue de réduire les vibrations et le bruit d’origine magnétique. Enfin, une comparaison des efforts de Maxwell et de magnétostriction est fournie. On montrera en ayant fixé le choix des matériaux qu’il est possible de trouver un bon compromis entre la hauteur du composant et l’épaisseur des entrefers. Mots-clés— Inductance de lissage, bruit magnétique, efforts de Maxwell et de magnétostriction, matériau, cales d’entrefer, mesures vibratoires.

Le bruit audible des machines électriques, qui participe à leur impact environnemental au même titre que leur consommation électrique ou leur recyclabilité, est devenu un critère de poids durant leur phase de conception, à la fois dans les applications industrielles, où l’exposition au bruit a un impact direct sur la santé, et dans les transports pour des raisons de confort acoustique. Le niveau de bruit global d’une machine électrique provient de trois sources principales : le bruit d’origine mécanique (roulements, engrènements, etc), le bruit d’origine aéraulique (ventilation), et le bruit d’origine magnétique. Dans les machines à courant alternatif, ce dernier peut dominer le niveau de bruit total à basse vitesse [1]. Il est produit par les courants présents dans la machine, et se caractérise souvent par une désagréable émergence de raies acoustiques. Cette tonalité est par ailleurs pénalisée par la norme de limite de bruit CEI 60034-9 : la compréhension du phénomène de bruit d’origine magnétique est donc primordiale en vue de concevoir des machines silencieuses, ou de diagnostiquer et résoudre des problèmes de bruit sur des machines existantes. La prédiction du bruit d’origine magnétique relève de la modélisation multi-physique : elle nécessite à la fois un modèle électromagnétique de l’excitation de la machine, et un modèle vibro-acoustique de la structure excitée. De plus, le bruit doit être simulé en régime variable afin de prendre en compte les phénomènes de résonance : l’utilisation d’outils éléments finis électro-vibro-acoustiques est alors inenvisageable, à la fois pour leur temps de calcul prohibitif et pour la difficulté d’en coupler les logiciels. Des modèles analytiques électromagnétique, vibratoire et acoustique ont donc été développés [2]. Leur rapidité permet également de les coupler à un algorithme d’optimisation multi-objectif en vue de concevoir des machines à faible niveau de bruit magnétique, à faibles pulsations de couple et à haut rendement [3,4]. Si les pulsations de couple peuvent en effet provoquer du bruit et des vibrations supplémentaires, que l’on peut limiter en agissant par exemple sur les harmoniques de courant [5], cet article n’en abordera pas les moyens de prédiction ni de réduction. Dans un premier temps, nous nous attacherons à caractériser l’ensemble des phénomènes susceptibles de produire du bruit audible d’origine magnétique dans les machines asynchrones de faible à forte puissance (quelques centaines de W à quelques centaines de kW). L’influence de l’alimentation par Modulation de Largeur d’Impulsion (MLI) [6,7,8] sera également traitée, et certains aspects psycho-acoustiques seront discutés. Dans un second temps, des outils de prédiction du bruit magnétique seront exposés (méthodes analytiques, graphiques et numériques). Des règles de conception permettant de réduire le bruit magnétique seront ensuite présentées. Enfin, nous verrons comment interpréter en pratique l’origine du bruit magnétique à l’aide de sonagrammes expérimentaux.