Gregory Bauw
email: gregory_bauw@ens.univ-artois.fr

Bertrand Cassoret

Olivier Ninet

Raphael Romary

Design of an induction machine with damper windings for noise and vibrations reduction

Keywords: Design, Induction machine, Damper, Noise and vibrations reduction, PWM. Paper type -Research paper

Purpose -

The paper presents a design method for induction machines including a three-phase damper winding for noise and vibrations reduction. Design/methodology/approach -In a first part, the principle of the damper winding is recalled. The second part presents the iterative design method which is applied on a 4kW PWM-fed induction machine in order to study the impact of the additional winding on the geometry. In a third part, the finite element method is used to validate the designed geometry and highlight the harmonic flux density reduction. Finally, some experimental results are given. Findings -The study shows that the impact of the additional three-phase winding on the geometry and weight of the machine is low. Moreover, the proposed noise reduction method allows one to reduce the total noise level of a PWM-fed induction machine up to 8.5dBA. Originality/value -The originality of the paper concerns the design and characterization of a three-phase damper winding for a noiseless induction machine. The principle of this proposed noise reduction method is new and has been patented.

I. INTRODUCTION

Induction machine design has been studied for decades as a field in its own right, and the construction rules are nowadays well known [START_REF] Boldea | The induction machines design handbook[END_REF][START_REF] Pyrhonen | Design of rotating electrical machines[END_REF][START_REF] Toliyat | Handbook of electric motors[END_REF]. The environmental context encourages manufacturers to design high efficiency electric motors in keeping with increasingly strong constraints. Thus, more recently, acoustic standards have added a new constraint on the design process. The main international acoustic standard (IEC 60034-9) (Rotating electrical machines -Part 9: Noise limits) specifies a total sound power level (SWL) limit depending on the speed of the machine.

When the machine is fed by sine voltage, magnetic noise can be predicted and anticipated in the design process by choosing an adequate number of stator/rotor slots or by skewing the rotor for example. If the machine is noisy despite the respect of the construction rules, it is possible to reduce noise and vibrations using active reduction methods [START_REF] Ojeda | Piezoelectric actuator design and placement for switched reluctance motors active damping[END_REF][START_REF] Pellerey | Active reduction of electrical machines magnetic noise by the control of low frequency current harmonics[END_REF]. When the machine is fed by a PWM inverter, noise is often corrected after the manufacturing by using an antiharmonic filter or by modifying the PWM strategy [START_REF] Brudny | Method for controlling the PWM switching: Application to magnetic noise reduction[END_REF][START_REF] Gabsi | Noise reduction of switched reluctance machine[END_REF][START_REF] Zhang | A new vibration reduction control strategy of switched reluctance machine[END_REF].

In this context, we propose a method to include a passive noise reduction solution for PWM supply in the design process. Numerical applications concern a 4kW induction machine which targeted characteristics are: 1500rpm -400V -8.8A -50Hz -3 phasespower factor: 0.79.

II. PRINCIPLE OF THE DAMPER WINDING

The proposed noise reduction method is a three-phase damper winding [START_REF] Cassoret | Moteur électrique à enroulement auxiliaire isolé[END_REF] wound into the stator slots and superimposed to the initial winding as shown in Figure 1. This additional winding, following the same path and having the same number of turn than the stator winding, is connected to three capacitors of suitable values in order to create a resonance around the switching frequency of the PWM inverter. At these frequencies, the voltage harmonics are important. They are responsible of flux density harmonics, and consequently at the origin of magnetic noise. The main principle is similar to that of a classical LC filter but in our case the inductance is integrated to the machine. Previous work [START_REF] Bauw | Damper winding for noise and vibration reduction of PWM-fed induction machines[END_REF] shows that the capacitors mainly resonate with the leakage inductances of the machine. Experimentations on a PWM-fed 4kW prototype including damper windings allowed to reduce the overall sound pressure level (SPL) by more than 8.5dBA in some cases. Vibrations were also considerably reduced.

III. DESIGN METHOD

A. Context

The proposed study is based on a classical iterative design method of induction machine [START_REF] Boldea | The induction machines design handbook[END_REF] which has to be adapted to take into account the space required by the damper winding in the stator slots. The difficulty is that this additional space is linked to the value of the current in the damper, itself linked to the impedance of the machine and the chosen capacitors.

The first step is to design a reference machine without damper windings to provide a comparison point. The computations using the characteristics defined in the introduction lead to a stator outside diameter 𝐷 𝑜𝑢𝑡 of 185.4mm and a stack length 𝐿 of 129mm. The stator has 36 trapezoidal slots and the squirrel-cage of the rotor has 28 bars. The current density in the stator winding is chosen at 4.5A/mm² as recommended by [START_REF] Boldea | The induction machines design handbook[END_REF]. Parameters of the classical single-phase equivalent diagram of the machine have been calculated analytically and are given in Table I. The goal of the design method is to minimize the increase of the diameter 𝐷 𝑜𝑢𝑡 of the machine with damper windings while keeping the same flux density in the yoke and the same performances. We assume that the damper does not impact the stator inner diameter and the rotor geometry.

B. Design of the machine with damper windings

Empirically, the maximum current value in the damper windings is first set to 20% of the rated stator current, which corresponds to 1.76A for the studied machine. Experience and experimentations on existing prototypes have shown that this value is coherent. The current density in the damper windings is the same to that of the stator. The design process has to be done again increasing the stator slot depth and so the outside diameter. The slot depth is increased while keeping the tooth width constant. Consequently, the outside diameter 𝐷 𝑜𝑢𝑡 is increased to 192mm.

C. Single-phase equivalent diagram

Since the geometry is now fully designed, analytical calculations of resistances and leakage inductances of the machine [START_REF] Lipo | Introduction to AC machine design[END_REF] allow one to establish the parameters of the equivalent diagram of Figure 2. 𝑙 𝑠 is the leakage inductance of the stator winding; 𝑙′ 𝑎𝑧 is a mutual inductance relative to the common flux between the stator and the auxiliary which does not link the rotor winding (Bauw et al., 2018a;[START_REF] Bauw | Equivalent circuit of PWM-fed induction machine with damper winding for noise and vibration reduction[END_REF]. 𝑙 𝑎𝑐 ′ corresponds to the leakage flux of the auxiliary which does not link any other winding, this flux is essentially composed of coil-end leakage. Analytical values of these parameters are given in Table II. One can notice that the sum of 𝑙 𝑠 and 𝑙′ 𝑎𝑧 gives a close approximation of the value of 𝑙 𝑠 given in Table I. Indeed, when the damper windings is not connected, the auxiliary branch of the equivalent diagram is open and the inductances 𝑙 𝑠 and 𝑙′ 𝑎𝑧 are then in series to give the classical induction machine diagram.

D. Capacitor value and auxiliary current

We assume that the machine is fed by a PWM inverter which minimum and maximum switching frequencies are respectively 3kHz and 8kHz. For each switching frequency, the harmonic voltage content can be experimentally measured. In our case, the main voltage harmonics are respectively 3100 and 8100Hz and their amplitudes are both 49V. Figure 3 shows the peak flux density 𝐵 ̂ in the air-gap at these frequencies as a function of the capacitor value, calculated from (1) where 𝐿 µ is the magnetizing inductance, 𝐼 µ the magnetizing current for the considered harmonic, 𝑝 the number of pole pairs, 𝑛 the number of turns per phase, 𝐷 𝑖𝑠 the stator inner diameter and 𝐿 the stack length. The value 𝐶 𝑎 ′ = 0 corresponds to the amplitude of the flux density harmonic when the damper has no influence. An optimal capacitor value for both operating point would be of 1µF, but taking into account the accuracy of leakage inductances estimation, there is a risk of amplification of the harmonic flux density. Therefore, we will choose the value of 2µF. For this particular capacitor value, considering every harmonic components of the 3kHz PWM voltage supply, the computed RMS current in the damper windings is 0.75A. The current value for higher switching frequency is lower because the nature of the damper winding's impedance is mainly inductive.

𝐵 ̂ = √2 𝐿 µ 𝐼 µ 𝑝 𝑛 𝐷 𝑖𝑠 𝐿 (1)

E. Optimization of the geometry

Since the calculated current value in the damper windings is lower than the estimated value of section III.B, the design can be optimized. By choosing a maximum current of 1A in the damper, the outside diameter of the machine can be reduce from 192 to 189mm. 𝐷 𝑜𝑢𝑡 is thus increased by less than 2% compared to the reference machine without damper windings as shown in Figure 4. The design process has been finally done again in order to verify that the current value in the damper and the optimum value of capacitor of the optimized machine are not changed.

F. Weight criterion

Let 𝐷 𝑜𝑢𝑡 and 𝐷 𝑜𝑢𝑡 ′ respectively be the outside diameters of the reference and optimized machine with damper windings, 𝐿 the stack length of both machines and 𝜌 𝑖𝑟𝑜𝑛 the density of the iron. The added iron weight due to the increase of the outside diameter can be easily calculated from:

𝑚 𝑖𝑟𝑜𝑛 = 𝜌 𝑖𝑟𝑜𝑛 𝜋𝐿 [( 𝐷 𝑜𝑢𝑡 ′ 2 ) 2 -( 𝐷 𝑜𝑢𝑡 2 ) 2 ]
(2)

Considering a density of the iron equal to 7860kg/m 3 , the weight of the magnetic core should be increased by only 1kg. The copper weight of the damper winding can be calculated considering 𝜌 𝑖𝑟𝑜𝑛 the density of the copper, 𝑙 𝑐 the coil-end length, 𝑆 the cross section of the wire, 𝑁 the number of turns per phase of the winding and 𝑞 the number of phases: 𝑚 𝑐𝑜𝑝𝑝𝑒𝑟 = 2 𝜌 𝑖𝑟𝑜𝑛 (𝐿 + 𝑙 𝑐 ) 𝑆 𝑁 𝑞

(3)

In our case, the damper winding represents a weight of 1.512kg. The total weight due to the addition of the damper winding is then 2.512kg, which is small as an induction machine of this size usually weighs about 40kg. This aspect can be particularly attractive for embedded applications giving the size and weight of a traditional anti-harmonic filter. The optimized geometry of the machine with damper windings obtained from the analytical design has been simulated on the FEM software Flux2D as shown in Figure 5. The coupling circuit in Figure 6 allows us to integrate the two three-phase windings, their resistances and coil-end inductances are calculated analytically. The stator winding is fed by a balanced system of voltage harmonics which amplitudes are frequency dependant. The damper windings are short-circuited via three 2µF capacitors. The rotor is a squirrel-cage rotor which ring impedances are calculated analytically.

IV. FINITE ELEMENT METHOD VALIDATION

A. Used geometry and coupling circuit

B. Current value in the capacitors

Table III compares the current value in the capacitors calculated analytically from the equivalent diagram of Figure 2 and by finite element method for different harmonics. The chosen voltage harmonics have been obtained experimentally and correspond to the most significant ones of a PWM inverter when the switching frequency is set to 3kHz. Results show a good correlation between analytical and numerical models, which confirms that the analytical computation of the leakage inductances has been done accurately. Moreover, one can notice that the RMS value of the capacitor current calculated by FEM with the four studied harmonics is 0.69A, which is close to the value of 0.75A obtained from the equivalent diagram in section III.D. We can therefore neglect the contribution of the fundamental and other harmonics on the current value.

C. Validation of the harmonic flux density reduction in the air-gap

Figure 7 shows the normal flux density in the air-gap without and with damper windings as a function of the position on a line plotted in the middle of the air-gap. The frequency is 3100Hz and corresponds, in our case, to the main voltage harmonic for a switching frequency of 3kHz. One can observe that the harmonic flux density at the origin of noise and vibrations is drastically reduced thanks to the damper windings. It also confirms that the capacitor value of 2µF is well chosen. A simulation has been done using three 4µF capacitors and give satisfactory results too but a slightly higher capacitor current value.

V. EXPERIMENTATIONS

In order to demonstrate the effectiveness of the proposed reduction method, experiments have been done on a 4kW prototype of induction machine with damper windings which characteristics are the same as the designed machine introduced previously. Nevertheless, the design method used by the manufacturer must be different than the one presented here so the geometry of the prototype is slightly different. Consequently, current value in the capacitors will not be compared to the theory. The machine is PWM-fed and the switching frequency is set to 4kHz. The noise level spectrum has been measured with a microphone at 1 meter of the machine in a semi-anechoic room. The A-weighting is used in order to take into account the sensibility of the human ear. Figure 8 shows the noise level spectrum of the machine without damper windings, the total noise level is 63.3dBA. With damper windings connected to three 4µF capacitors, the main lines around 8kHz are drastically reduced as shown in Figure 9. The total noise level of the machine with damper windings is 56.2dBA, so the reduction is about 7dBA in this case. Vibrations have been measured on the same machine using accelerometer and show significant reduction too.

CONCLUSION

In this paper, an iterative design method for induction machines including a passive noise reduction solution is proposed. It allows one to optimally design the geometry of a noiseless machine minimizing the impact of the damper windings in terms of size and weight of the magnetic core. Finite element method and experimental results validate the design process and the effectiveness of the proposed noise reduction method.

Fig. 1 .

 1 Fig.1. Induction machine with damper windings.

Fig. 2 .

 2 Fig.2. Single-phase equivalent diagram of the machine with damper windings.

Fig. 3 .

 3 Fig.3. Peak flux density in the air-gap with (solid line) and without (dashed line) damper windings as a function of the capacitor 𝐶 𝑎 ′ for 𝑓 = 3100Hz and 8100Hz.

Fig. 4 .

 4 Fig.4. Comparison of the geometries: reference machine (dashed line) / optimized machine with damper windings (solid line).

Fig. 5 .

 5 Fig.5. Used geometry of the 4kW induction machine with damper windings for FEM simulation (Flux2D).

Fig. 6 .

 6 Fig.6. Coupling circuit of the 4kW induction machine with damper windings for FEM simulation (Flux2D).

Fig. 7 .

 7 Fig.7. Normal flux density in the air-gap without (dashed line) and with (solid line) damper windings as a function of the position for 𝑓 = 3100Hz and 2µF capacitors.

Fig. 8 .

 8 Fig.8. Noise level spectrum without damper windings for 𝑓 𝑃𝑊𝑀 = 4kHz.

Fig. 9 .

 9 Fig.9. Noise level spectrum with damper windings for 𝑓 𝑃𝑊𝑀 = 4kHz and 4µF capacitors.

TABLE I PARAMETERS

 I OF THE SINGLE-PHASE EQUIVALENT DIAGRAM OF THE REFERENCE MACHINE

	𝑟 𝑠 (Ω)	0.56
	𝑙 𝑠 (mH)	9.3
	𝐿 µ (mH) ′ (Ω) 𝑟 𝑟 𝑙 𝑟 ′ (mH)	221.5 0.986 10.1

TABLE II PARAMETERS

 II OF THE SINGLE-PHASE EQUIVALENT DIAGRAM OF THE MACHINE WITH DAMPER (𝐼 𝑎 = 0.2 𝐼 𝑠 )

	𝑟 𝑠 (Ω)	0.56
	𝑙 𝑠 (mH)	4.9
	𝑙′ 𝑎𝑧 (mH)	5.7
	𝐿 µ (mH) ′ (Ω) 𝑟 𝑟 ′ (mH) 𝑙 𝑟 ′ (Ω) 𝑟 𝑎 𝑙 𝑎𝑐 ′ (mH)	215.4 0.986 10.1 5.61 2.6

ACKNOWLEDGEMENTS

This work has been achieved within the framework of CE2I project (Convertisseur d'Energie Intégré Intelligent). CE2I is cofinanced by European Union with the financial support of European Regional Development Fund (ERDF), French State and the French Region of Hauts-de-France.

The authors would like to thank SATT Nord-de-France (Société d'Accélération du Transfert de Technologie) that has patented this invention (Cassoret and Romary, 2016).


1. Sur quelles enquêtes se fonde votre livre ? Ce livre prend le parti du "statactivisme", néologisme proposé par Isabelle Bruno, Emmanuel Didier et Julien Prévieux (2014), "comme un slogan et comme un concept descriptif, utilisé pour qualifier des expériences visant à se réapproprier le pouvoir des statistiques". Pourquoi et pourquoi faire ? L'enjeu est à la fois scientifique et politique. Il s'agit d'abord et avant tout de valoriser certaines enquêtes de la statistique publique qui font partie de notre trésor commun. Trop de critiques de la production statistique, parmi les chercheurs comme parmi les militants, la réduisent au seul rôle d'outil de gouvernement sans considérer suffisamment sa place dans la production des savoirs scientifiques. On oublie ainsi souvent ce que les données des services statistiques ministériels doivent à la contribution des sciences sociales. Ainsi, Alain Darbel, puis Claude Seibel, coauteurs de Travail et travailleurs en Algérie (1963), ont joué un rôle décisif dans le développement des panels de suivi des élèves au ministère de l'éducation nationale. Pour notre part, nous avons beaucoup pratiqué le réemploi de ces enquêtes longitudinales, qui ont à la fois une large profondeur biographique (les scolarités des élèves y sont décrites de la 6 e jusqu'à la terminale, et au-delà, dans l'enseignement supérieur jusqu'à la fin des études) et beaucoup d'indicateurs variés et précis sur la socialisation familiale (propriétés sociales des parents, choix scolaires, implication dans le suivi de la scolarité… ) et sur la socialisation scolaire (enseignements suivis, déroulement des procédures d'orientation scolaire, acquis scolaires, notes… ). Dans le débat public, les données statistiques sont bien sûr utilisées pour justifier une politique ou au contraire la critiquer. Ainsi, dès l'été 2017, la ministre de l'enseignement supérieur prépare les esprits à la refonte de la plateforme de préinscription dans l'enseignement supérieur APB en prétendant que " 60 % des étudiants qui entrent dans le système de la licence générale échouent ". Pour notre part, avec Yaël Brinbaum [START_REF] Brinbaum | 50 % à la licence... mais comment ? Les jeunes de familles populaires à l'université en France[END_REF], nous montrons dans Économie et statistique au printemps 2018 que 61 % des étudiants inscrits au début des années 2000 en licence générale ont obtenu ce diplôme, que ce soit dans la filière de départ ou après réorientation dans une autre. Il est assez facile d'expliquer comment la ministre a dramatisé l'échec à l'université en se limitant à la première année de licence. En revanche, il est plus difficile de mesurer correctement les taux d'obtention de différents niveaux de diplôme au terme du parcours d'étude. Et pour montrer comment ils ont évolué depuis vingt ans, il nous a fallu compiler huit notes d'information des services statistiques du ministère de l'éducation nationale et du ministère de l'enseignement supérieur. Cette discrétion est regrettable. Est-ce parce que les données montrent une hausse de ce qu'il faut bien appeler des " ruptures universitaires " ? Parmi les bacheliers de 2014 entrés la même année en L1, 28 % quittent l'enseignement supérieur sans nouveau diplôme. Cette proportion était de 20 % parmi leurs homologues de 2002. En outre, 9 % des bacheliers de 2014 ont dû se contenter d'un diplôme de niveau bac+2, alors qu'ils visaient au moins un bac+3 pour la plupart. Qui souhaite sincèrement la réussite des étudiants à l'université ? Dans les " Bleus de Bercy " sont publiés les indicateurs de pilotage de la LOLF. La cible pour le taux de réussite en L1 est que 54 % des bacheliers de 2024 obtiennent le droit de passer en L2. On comprend dès lors que la ministre mette en avant " le droit de se tromper " quand on lui demande comment elle souhaite " ouvrir la façon de réussir ses études " (Le Monde, 16 septembre 2022).

2. En quoi peut-on parler d'un nouveau régime de sélection scolaire ? À l'été 2019, la revue Sociologie a publié le dossier Enseignement supérieur : l'art et les manières de sélectionner que Sévérine Chauvel et moi-même coordonnions [START_REF] Séverine | Enseignement supérieur l'art et les manières de sélectionner[END_REF]. Un peu plus d'un an après l'instauration de Parcoursup et la promulgation de loi relative à l'orientation et la réussite des étudiant•es (ORE), et quelques mois avant l'irruption de la crise sanitaire en France, nous faisions alors l'hypothèse que cette réforme symbolisait l'entrée de l'enseignement supérieur français dans « un nouvel âge de la sélection ». Le livre Héritocratie de Paul [START_REF] Pasquali | Héritocratie. Les élites, les grandes écoles et les mésaventures du mérite (1870-2020[END_REF] analyse lui aussi cette réforme comme une « véritable rupture » qui se combine avec « l'extension du domaine de l'ouverture sociale » au sein des grandes écoles et participe au renouvellement de la légitimité scolaire et symbolique des élites. Enfin, dans les deux derniers numéros de Formation Emploi (158 et 159) intitulés pour le premier Un nouvel âge de la sélection scolaire ? Formes et logiques de sélection dans un système éducatif massifié, et pour le second Les pratiques de la sélection : à la croisée de la formation et de l'emploi, Marianne Blanchard, Prisca Kergoat et Philippe Lemistre reprennent et confirment cette hypothèse d'un nouvel âge de la sélection scolaire et la relie à l'extension de la « logique compétence » tant dans le monde du travail que dans celui de l'école (2022). Notre livre va désormais un peu au-delà. Il défend l'idée qu'un nouveau régime de sélection scolaire a émergé au tournant des années 2000 en France et que Parcoursup l'a en quelque sorte codifié. Schématiquement, ce nouveau régime de sélection scolaire se caractérise par un niveau très élevé de diplomation des jeunes générations et des inégalités très importantes de transmission des savoirs scolaires entre les classes sociales. Nous vivons actuellement une réplique de la « seconde explosion scolaire » qui avait affecté les premiers cycles universitaires à la fin des années 1980 et pendant les années 1990. Après une relative stagnation, les proportions de diplômés repartent à la hausse depuis 15 ans sous le double effet des politiques scolaires (Loi Fillon, 2005 ; classes populaires. Pour les jeunes issus de ces milieux sociaux nés dans les années 1960, les CAP et BEP sont incontournables plus d'un membre de ces cohortes sur trois dispose de ce type de diplôme comme titre le plus élevé ; une proportion deux à trois fois supérieure à celle des détenteurs de bac + 2 et plus. Mais parmi les jeunes d'origine populaire nés à partir de 1970, la proportion de titulaires de CAP ou de BEP baisse. Et dans ces cohortes d'origine populaire, la proportion des diplômés de l'enseignement supérieur dépasse celle diplômés de l'enseignement professionnel. C'est encore plus net encore pour les filles qui ont été les premières actrices de cette petite conquête scolaire. Le livre documente alors les conditions sociales qui président, dans les classes populaires, à cette appropriation très inégale des diplômes. Et c'est tout d'abord dans le détail des configurations familiales que l'on observe des effets puissants sur le parcours des enfants de petites différences sociales, professionnelles et scolaires chez les parents. L'accès au diplôme des enfants fonctionne aujourd'hui comme un puissant révélateur d'une frontière interne entre une fraction stabilisée des classes populaires, désormais largement concernée par la scolarisation prolongée de ses enfants, et les fractions inférieures des classes populaires, o les pères sont distants de l'emploi quali é et les mères de l'activité professionnelle régulière. Il montre ensuite que les premiers cycles universitaires sont aujourd'hui le coeur des destinées des bacheliers et bachelières des milieux populaires. Beaucoup préparent des B S, mais plus encore des diplômes universitaires les S S ne rassemblent au total qu'un cinquième des étudiants d'origine populaire, ce qui s'avère nalement peu par rapport au poids des lières universitaires dans les destins scolaires de ces mêmes étudiants. En e et, 59 % des étudiants d'origine populaire sont inscrits en lettres, en sciences humaines et sociales, en économie, en droit, en sciences ainsi que dans les Inspé. A l'autre bout de l'échelle sociale, 54 % des étudiants des classes dominantes sont quant à eux inscrits dans des classes préparatoires, des écoles de commerce ou d'ingénieurs ou du secteur de la culture, des grands établissements et des études de santé. Ces institutions apparaissent au coeur de leurs nouvelles stratégies de reproduction quand les lières universitaires constituent à l'inverse le véritable centre de gravité des études supérieures des enfants des classes populaires. Enfin, grâce aux enquêtes présentées plus haut, nous combinons les variables d'origine sociale et de parcours scolaire pour montrer que quand les enfants des milieux populaires connaissent une entrée réussie dans les apprentissages élémentaires en français et en mathématiques, ils ont des parcours scolaires sans heurt majeur dans le secondaire et exactement les mêmes chances de décrocher une licence par la suite que les enfants des classes moyennes et dominantes avec les mêmes acquis scolaires. Les étudiants issus des classes moyennes et dominantes ont des parcours scolaires beaucoup plus homogènes que ceux des classes populaires. En schématisant, on peut dire que, pour les classes populaires, dans un système scolaire très diversifié et très hiérarchisé socialement et scolairement, le fait d'être une fille issue des fractions stables semble permettre -un peu plus qu'à d'autres -d'acquérir des connaissances et un capital scolaire qui se révèle très discriminant dans les études supérieures et particulièrement dans les études universitaires.

4. Mais alors, que faire? Votre livre donne-t-il des raisons d'agir pour la démocratisation scolaire ? Il suggère pour commencer de rediscuter de cette notion. Beaucoup pensent qu'elle a eu lieu, à travers la diffusion massive des diplômes entraînée par la politique scolaire. Et comment ne pas souligner en effet l'impact de la prolongation des études dans des catégories sociales longtemps tenues à distance de l'enseignement supérieur ! Mais si le diplôme reste un bon indicateur relatif du capital scolaire accumulé, il faut aussi réfléchir à des formes de hiatus qui se multiplient entre les « trois états du capital culturel ». « L'enseignement réellement démocratique », écrivaient Bourdieu et Passeron en 1964, « est celui qui se donne comme fin inconditionnelle de permettre au plus grand nombre […] de s'emparer […] des aptitudes qui font la culture scolaire ». Le plaidoyer pour une pédagogie rationnelle reste juste, mais pourrait fort bien être repris à son compte par l'injonction nouvelle à « l'innovation pédagogique » dans les universités, de plus en plus souvent dotées de services de pédagogie universitaire transversaux peu sensibles aux besoins didactiques de chaque discipline. Face à ce risque, il est heureux que les échanges sur les manières d'enseigner entre spécialistes d'une même discipline se développent : les enseignants-chercheurs eux aussi pourraient revendiquer de « reprendre la main sur le métier », comme le demande la FSU. De quoi ont besoin les étudiants ? Face aux malentendus sur les savoirs universitaires et leurs exigences, il faut leur « vendre la mèche », sans prendre appui sur des savoirs implicites acquis dans la sphère familiale. Mais en vérité, ces prérequis exigés sans être enseignés à l'université devraient s'accumuler tout au long de la trajectoire scolaire. Par quelque bout qu'on le prenne, on en revient toujours à ce problème. La remise à niveau n'est pas impossible à l'université, mais elle a un coût, comme le montre le diplôme d'accès aux études universitaires (DAEU) dont les programmes sur deux ans correspondent à ceux de la voie générale du lycée. Le problème est encore plus aigu depuis la réforme de cette voie. Il y a des prérequis disciplinaires. Comment débuter les mathématiques à l'université sans les avoir étudiées en première ni en terminale ? Quelles connaissances minimales sur l'histoire de la Cinquième république en France faut-il avoir acquises pour profiter pleinement d'un cours magistral de sociologie sur la société française contemporaine ? Peut-on redémarrer à zéro l'enseignement du fonctionnement du système immunitaire en licence de biologie au motif que certains bacheliers n'ont pas suivi cette spécialité au lycée ? Etc. Mais il y a aussi des prérequis plus généraux qui tiennent aux techniques intellectuelles de la culture écrite. Et les enseignantschercheurs ne sont pas spécialement qualifiés pour y remédier quand ils sont mal maîtrisés. Expliquer comment rédiger une dissertation, construire un exposé ou s'orienter dans une bibliographie, voilà des choses souvent prises en charges dans les cours d'introduction au travail universitaire. Mais imposer de réviser la grammaire ou les règles du calcul n'est pas chose aisée quand les lacunes remontent loin et n'ont pas empêché l'obtention du bac. L'université ne sortira pas toute seule de cet embarras. Si l'on souhaite maintenir le droit d'accès de tout bachelier à toute filière de son choix, nous ne pouvons pas seulement miser sur des aménagements des cursus en licence, sur des dispositifs de remédiation ou des techniques d'enseignement plus efficaces. L'augmentation des taux d'encadrement est sans doute nécessaire mais aussi insuffisante. La conclusion du livre invite à se demander quelle refondation du lycée il faudrait viser du point de vue de la réussite des étudiants, à l'université comme dans les autres segments de l'enseignement supérieur. Elle évoque, trop rapidement sans doute, la perspective d'un lycée unique débouchant sur un seul baccalauréat, de « haut niveau de culture commune » pour tous, à la fois littéraire, scientifique et technologique. Le bac technologique a été créé en 1965 pour « désencombrer » l'enseignement secondaire classique, à la demande expresse de De Gaulle soucieux de s'opposer aux « ambitions abusives » de « ceux qui n'ont rien à faire » à l'université. Le bac professionnel a été créé 20 ans plus tard pour prolonger la scolarité après un BEP. Ce nouveau diplôme a failli ne pas être un baccalauréat et il s'en est fallu de peu pour qu'il n'ouvre pas droit à la poursuite d'études. Le bilan de ces trois voies d'accès au bac est très ambivalent. D'un côté, elles ont permis une diversification qui est toujours défendue comme un levier de démocratisation. De l'autre, elles ont aussi été le moyen de la division scolaire reproduisant à l'intérieur des lycées les divisions sociales plus larges au sein de la société. Le nouveau régime de sélection scolaire s'accommode parfaitement de cette « démocratisation ségrégative » identifiée par P. Merle, mais au prix d'un gâchis et de frustrations considérables. Aujourd'hui, une très large majorité des familles espèrent un diplôme de l'enseignement supérieur pour leurs enfants et moins de la moitié des enfants d'employés ou d'ouvriers y parviennent. Les crises sanitaires, l'essoufflement des démocraties mais aussi la nécessité d'une bifurcation écologique exigent également des connaissances élaborées et largement partagées pour éviter le gouvernement des experts. Les structures scolaires héritées de la Cinquième république n'y suffiront pas.

  réforme du baccalauréat professionnel de 2007 ; Stratégie nationale de l'enseignement supérieur en 2015) et de l'appropriation de l'enjeu scolaire par les familles populaires. Quelques données aident à prendre la mesure de cette réplique : en 2006, 62 % d'une classe d'âge était titulaire d'un bac ; c'est 82 % en 2021 (+ 20 points en 15 ans). En 2006, 42 % des 25-34 ans sont titulaires d'un diplôme de l'enseignement supérieur ; c'est 50 % en 2021 (+ 8 points en 15 ans). En 2006, 23 % des 25-29 ans étaient titulaires au moins d'un bac+3 en 2006 ; ils et elles sont 38 % en 2021 (+15 points en 15 ans). Pourtant, notre système scolaire demeure profondément inégal. On connaît grâce notamment aux travaux d'Ugo Palheta (2012) les mécanismes d'éviction et de relégation des enfants des classes populaires dans les filières de la voie professionnelle. On connaît moins les travaux montrant comment les inégalités d'apprentissage se creusent au fil des scolarités, comme le montre l'article de Sylvain Broccolichi et Rémi Sinthon pour le collège et le lycée (2011). Mais surtout, les indices s'accumulent pour montrer que l'institution scolaire française transmet de moins en moins bien les savoirs scolaires. Le livre de Christian Baudelot et Roger Establet L'élitisme Républicain avait montré que l'école française était très tolérante aux inégalités.Elle semble l'être de plus en plus. Prenons deux illustrations parmi d'autres. À la même dictée de 85 mots, 26 % des élèves de CM2 faisaient plus de 15 erreurs en 1987 ; ils sont 46 % en 2007 (+20 points en 20 ans). En 1987, 74 % des élèves de CM2 réussissent les divisions en 1987 ; ils ne sont que 37 % en 2017 (-37 points en 30 ans). Dans cette configuration, Parcoursup représente certes une extension de la sélection : pour sa dernière année, APB comptait une centaine de licences qui recouraient à des tirages au sort illégaux pour départager leurs candidat•es. En 2021, pour la 3 e année de Parcoursup, 773 licences n'ont retenu au plus que la moitié des candidatures, soit un quart des licences proposées sur le portail i . Mais plus largement, Parcoursup permet d'atteindre l'objectif de diplômer 50 % d'une génération au niveau bac +3 tout en gérant les abyssales inégalités d'apprentissage entre les classes sociales par la hiérarchisation accrue des filières et établissements de l'enseignement supérieur. Il érige ainsi désormais les ratés du système éducatif français en principe d'organisation des études supérieures. C'est à ce titre que nous pensons qu'il s'agit là d'un nouveau régime de sélection scolaire et non plus seulement d'un nouvel âge de la sélection.

Les élèves des classes populaires peuvent-ils y réussir leurs scolarités ? Nous avions à coeur de documenter avec précision la profonde diversification actuelle des parcours scolaires des enfants issus des

i Données aimablement transmises par Julien Gossa, animateur de la Conférence des Praticiens de l'Enseignement Supérieur et de la Recherche.


Franc ¸ois Grégory Bauw

Bertrand Balavoine

Olivier Cassoret

Raphaël Ninet

Romary

Damper winding for noise and vibration reduction of PWM-fed induction machines

Keywords: Induction machine, noise, vibrations, harmonics, auxiliary winding, damper, PWM

The paper presents a system that allows the passive reduction of noise and vibration of a three-phase induction machine with a stator damper winding connected to capacitors. This is a simple and effective system for reducing the flux density harmonics of a machine. The theoretical study is based on the equivalent circuit of a machine equipped with the damper winding and the modeling is based on the analogy with a singlephase two-winding electrical machine. Analysis of the equivalent circuit allows to identify opportunities to reduce the flux density harmonics. Finally, an experimental validation is done.

I. INTRODUCTION

For user comfort reasons, the audible noise of electrical machines has become a fundamental aspect to be treated from conception [START_REF] Besnerais | Optimal slot opening width for magnetic noise reduction in induction motors[END_REF]. It is also a parameter to consider in many areas, such as the military one for example where the acoustic discretion is required [START_REF] Coat | Discrétion électromagnétique des machines électriques tournantes[END_REF], [START_REF] Borisov | Experimental investigation of a naval propulsion drive model with the pwm-based attenuation of the acoustic and electromagnetic noise[END_REF]. Moreover, vibration problems can cause disruption of the surrounding environment or premature mechanical wear. The overall noise level of an electrical machine results from three main sources: mechanical, aerodynamic and magnetic [START_REF] Timar | Noise and vibration of electrical machines[END_REF]. That paper will essentially focus on the magnetic one which can be predominant especially when the machine is powered by a Pulse Width Modulation (PWM) inverter [START_REF] Besnerais | Reduction of magnetic noise in PWM-supplied induction machines -low-noise design rules and multi-objective optimization[END_REF].

Actually, the magnetic noise is generated by the magnetic forces in the machine. Maxwell forces that attract the stator and the rotor cause deformations of the stator, and therefore noise and vibrations. They are related to the presence of flux density harmonics in the air gap. These harmonics may be generated by the slotting effect, saturation, eccentricity or by harmonics due to PWM power supply. These can lead to a significant specific noise.

Various methods are available to reduce the noise of an electric machine:

• When the machine is fed by the network, the design must respect the rules of construction of the machines [START_REF] Jordan | Geräuscharme elektromotoren[END_REF] by choosing an adequate number of stator and rotor slots. On the other hand, previous work suggested, for example, to reduce the noise by injecting a harmonic current system in the windings, thus creating opposing forces with those naturally generated by the machine [START_REF] Cassoret | Magnetic noise reduction of induction machines[END_REF]. These harmonic currents can also be injected into an auxiliary winding [START_REF] Lecointe | Analysis and active reduction of vibration and acoustic noise in the switched reluctance motor[END_REF]. Another method suggests to use piezoelectric actuators to reduce the vibration produced by the machine and therefore reduce the overall noise level [START_REF] Ojeda | Piezoelectric actuator design and placement for switched reluctance motors active damping[END_REF].

• When the machine is PWM-fed, the most common method is to increase the switching frequency beyond the audible range, but it affects the loss and heating of electronic components. Moreover, this is not possible for high power machines.

The method proposed in this paper is based on the generation of currents induced in auxiliary windings connected to passive elements. We will start with the description of a prototype including this technology and a theoretical analysis highlighting the resonances. Then we will conclude with experimental results demonstrating the validity and the effectiveness of the method.

II. TECHNICAL DESCRIPTION OF THE SYSTEM

A. General Description

The proposed system allows the passive reduction of air-gap flux density harmonics in an induction machine. The idea is to add into the slots a second three-phase winding superimposed to the stator winding, but electrically independent as shown in Fig. 1. This one will be named the damper or the auxiliary winding. The main principle is that the flux density harmonics create induced currents in the auxiliary windings, which in turn create flux density waves opposed to the cause that produce them.

At low supply frequency (typically 50 or 60 Hz, or less in variable speed), capacitors have a high impedance so that the induced currents in the auxiliary windings keep low values. Depending on the value of the capacitors and the number of turns of the auxiliary windings, these currents at supply frequency can, however, create a part of the reactive power required for the magnetization of the magnetic circuit and reduce the magnetizing current absorbed by the stator and the associated Joules losses (power factor improvement) [START_REF] Nicolae | Electric motor performance improvement using auxiliary windings and capacitance injection[END_REF]- [START_REF] Obe | Steady-state performance of a line-start synchronous reluctance motor with capacitive assistance[END_REF].

At high PWM frequency, unwanted flux density waves create high frequency induced currents in the auxiliary windings, for which the impedance is low. Therefore, the flux density in the air-gap becomes more sinusoidal.

B. Studied Prototype

The results presented in this paper are relative to a 4kW prototype of induction machine with damper windings. Its characteristics are: 230/400 V -15.3/8.8 A -1435 rpm -p=2 pole pairs.

The damper or auxiliary winding is clearly visible in Fig. 2, it is wound at the top of the slots, over the stator winding and near the air-gap. Arbitrarily, the number of turns and the pattern of the two three-phase windings are equivalent, each of them has 26 turns per slot; only the section is different. The section of the stator winding is about 1 mm 2 while the section of the auxiliary one is 0.159 mm 2 . This section was chosen in order to obtain a maximum fill factor. In this case, the damper winding takes up less than 15% of the total available space into the slots. One can also distinguish in Fig. 2 an exploring coil (in yellow) following the path of one turn of the stator winding. This coil allows us to visualize the image of the electromotive force of the machine, proportional to the derivative of the flux density in the air gap.

III. SINGLE-PHASE TWO-WINDING ELECTRICAL MACHINE MODELING

The single-phase equivalent circuit is given in Fig. 3. This is the classical single-phase equivalent circuit of the induction machine in which is added an auxiliary branch including the resistance and the leakage inductance of the winding as well as the capacitor connected in series therewith. All the physical variables and parameters are brought back to the stator.

The analogy of our system with the single-phase twowinding transformer allows one to create a simple analytical model and thus to understand the behavior of the various involved variables. For this, we consider the equivalent circuit presented in Fig. 4, where the influence of the rotor and the iron losses are neglected. Indeed, the damping effect of the rotor is less than that the auxiliary one which has a lower leakage inductance l a .

The supply voltage V s of the induction machine corresponds to one harmonic voltage of the PWM inverter at ω angular Let define:

• ω: angular frequency such as ω = 2πf with f the frequency; • r s , r a : stator and auxiliary winding resistances; • l s , l a : stator and auxiliary leakage inductances;

• n s , n a : numbers of turns of the stator and auxiliary windings;

• C a = C a ( n s n a
) 2 : capacitor in series with the auxiliary winding brought back to the stator; • L µ : magnetizing inductance;

• L s , L a : magnetizing inductances of the stator and auxiliary windings such as

-L s = L µ -L a = L µ ( n s n a ) 2
• M : mutual inductance between the two windings such as M = L s L a ; • Φ: common magnetic flux to the both windings and channeled by the magnetic circuit such as Vµ = jωn s Φ.

The equivalent complex impedance of the electrical machine taken from the stator is expressed by:

Zeq = 1 r a + j (L s + l a )ω - 1 C a ω × r s r a + L s ( 1 C a -l a ω 2 ) -l s (L s + l a )ω 2 - 1 C a + j(r s (L s + l a )ω - 1 C a ω + r a (L s + l a )ω) (1)
The study of this impedance shows the existence of two resonances:

• a series resonance f rs which can be expressed by:

f rs = 1 2π L s + l s C a (L s l s + l s l a + L s l a ) ≈ 1 2π 1 C a (l s + l a ) (2)
Neglecting the product of leakage inductances l s l a and assuming that L s +l s is about the same as L s we highlight the series nature of this resonance where C a resonates with l s in series with l a .

• a parallel resonance f rp done by [START_REF] Borisov | Experimental investigation of a naval propulsion drive model with the pwm-based attenuation of the acoustic and electromagnetic noise[END_REF], where C a mainly resonates with L s : The following numerical applications relate to the 4 kW machine previously described, whose main characteristics are given in Table I. One can notice that r a is higher than r s because the wire section of the auxiliary winding is smaller than that of the stator winding.

f rp = 1 2π 1 C a (L s + l a ) (3)
The frequency response of the currents shown in Fig. 5 illustrates these two resonances. The parallel resonance f rp at 217 Hz leads to a minimum current in the stator winding while the series resonance f rs at 620 Hz leads to the maximum.

The resulting magnetic flux Φ in the iron core can also be expressed by:

Φ = L s I s n s - M I a n s = M I s n a - L a I a n a = V µ n s ω (4)
Fig. 6. shows this flux (solid line) as a function of the frequency for C a = 4 µF. The magnetic flux that would naturally exist without the presence of the auxiliary winding (dashed line), is also presented. We can notice that for low frequencies, and particularly at 50 Hz, these two magnetic flux are similar and therefore the system does not disturb the normal running of the machine. However, there is a frequency range around 600 Hz for which the system amplifies the flux. It is therefore necessary to choose the value of C a with attention. For higher frequencies, here from 710 Hz, the flux Φ is less than the initial one, highlighting the fact that the auxiliary winding is opposed to the harmonic effects. Consequently, the system will be beneficial when the switching frequency of the PWM inverter

IV. COMPARISON OF THE DAMPER WINDING WITH AN ANTI-HARMONIC FILTER

Usually, unwanted frequencies due to PWM power supply at the origin of magnetic noise are mitigated using a passive filter, also called anti-harmonic filter. Depending on the used technology, this type of filter can also limit the premature aging of the conductors due to voltage front edge. The proposed damper winding operates in a similar manner. It requires to have enough space in the slots but the advantages of using a three-phase damper winding wound into the slots of the machine are real.

First of all, from a user point of view, the proposed solution offers an easy commissioning and maintenance. Its compact size is a non negligible advantage in comparison with a filter that often requires its own electrical cabinet. One can imagine that the capacitors could be included in the terminal box of the machine and thus become transparent to the user.

On the other hand, if the addition of copper can appear as a constraint, the economy is done on the volume of iron. Indeed, the auxiliary windings take advantage of the existing magnetic circuit. In the same time, the addition of an inductance which is likely to be noisy is avoided.

Finally, since the system is inside the machine, it also makes it possible to act on the frequencies due to internal phenomena such as slot harmonics in the case of a sinusoidal power supply. This is of course not possible with a filter placed upstream.

V. EXPERIMENTAL RESULTS

A. Test Bench Presentation

The machine used for the following experiments is presented in Fig. 8, its characteristics are detailed in section II-B. The latter is PWM-fed by an inverter whose possible switching frequencies are 3, 4, 6 and 8 kHz. One can notice the capacitor box whose size is similar to that of the terminal box of the machine. Three switches allow us to easily open or close the auxiliary circuit. The capacitors used have a value of 4 µF.

B. Sinusoidalization of the Flux Density in the Air-gap

The exploring coil wound into the slots of the studied machine and described previously in the paper gives us the opportunity to measure the electromotive force.

The machine is PWM-fed with a switching frequency of 8 kHz. In this way, it is shown in Fig. 9 and Fig. 10 that this physical quantity becomes more sinusoidal thanks to the damper windings and its three 4 µF capacitors. Since the electromotive force is proportional to the derivative of the flux density in the air-gap, the flux density harmonics are reduced, and therefore magnetic noise and vibrations.

C. Noise Spectra

Noise measurements have been performed in a semianechoic chamber on the 4 kW three-phase PWM-fed induction machine with a microphone at a distance of 1 m. The switching frequency is 8 kHz and the presented spectra use a weighting coefficient to take the sensitivity of the human ear into account (A weighting).

Fig. 11 and Fig. 12 clearly show that the lines around the switching frequency, which are predominant in the spectrum, are greatly mitigated thanks to the damper system. The line at 7850 Hz decreased from 68dB(A) to 52dB(A) and the overall sound pressure level is reduced by more than 8.5dB(A) in this case.

D. Influence of the Speed on Noise Reduction

In order to highlight the influence of the speed on the effectiveness of the system, the overall sound power level has been measured for several speed values. The machine operates at no-load but the PWM inverter, whose switching frequency is now set to 4 kHz, allows us to vary the speed. One can notice in Fig. 13 that the noise reduction is more important at 500 rpm. Actually, since the magnetic noise is predominant in the spectral content of the machine at low speed, the effectiveness of the system is optimal for this operating point.

Noise reduction can even be observed when the machine is stopped but fed by the PWM inverter.

E. Vibration spectra

Vibration measurements have been performed with an accelerometer fixed on the housing of the machine, under the same conditions as for noise measurements. Fig. 14 and Fig. 15 show the considerable decrease of the vibrations acceleration. In this case, the overall vibration level decreased from 52.6 m/s 2 to 13.7 m/s 2 .

VI. CONCLUSION

The proposed system can significantly reduce the magnetic noise passively, without using complex electronics and without any regulation. The obtained reduction is stable over time, even when the machine speed varies. A wide range of capacitor values is suitable. The system has the disadvantage of requiring space in the slots to add the auxiliary windings. Nevertheless, the latter are carrying low currents and require less space than the original windings.

The model presented in this paper provides an understanding of the parameters that affect the behavior of the system. It also allows to optimally size the windings and the capacitors for a given machine.

  Acknowledgment: SATT Nord de France (Société d'Accélération du Transfert de Technologie), CE2I (Convertisseur d'Energie Intégré Intelligent).

Fig. 1 .

 1 Fig. 1. Diagram of a machine with damper windings

Fig. 2 .

 2 Fig. 2. Auxiliary winding of the studied prototype

  Fig. 3. Single-phase equivalent circuit

Fig. 4 .

 4 Fig. 4. Single-phase two-winding equivalent circuit

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Is (dashed line) and I a (solid line) as a function of the frequency for C a = 4 µF

Fig. 8 .

 8 Fig. 8. Presentation of the test bench

Fig. 9 .Fig. 10 .

 910 Fig. 9. Electromotive force without damper windings for f P W M = 8 kHz

Fig. 13 .

 13 Fig. 13. Sound power level without and with damper circuit for different speeds

Fig. 14 .

 14 Fig. 14. Vibration spectrum without damper windings for f P W M = 8 kHz

ACKNOWLEDGMENT

The authors would like to thank SATT Nord de France (Société d'Accélération du Transfert de Technologie) that has patented this invention [14] and that allowed us to fund prototypes of modified machines and the necessary equipment for our experiments.

This work has been achieved within the framework of CE2I project (Convertisseur d'Energie Intégré Intelligent). CE2I is co-financed by European Union with the financial support of European Regional Development Fund (ERDF), French State and the French Region of Hauts-de-France.


Refurbishing an old machine or replacing it by a new one: comparative study of environmental impacts.

Bertrand CASSORET (1) , François BALAVOINE (1) , Raphael ROMARY (1) , Christophe DEBENDERE (2) (1) Univ. Artois, UR 4025, Laboratoire Systèmes Electrotechniques et Environnement (LSEE), Béthune, F-62400, France, (2) Flipo Richir Zone Industrielle A 13 rue de Lorival 59473 Seclin France

ABSTRACT

This article is based on the Life Cycle Assessment performed with Simapro software. It concerns a high-power asynchronous motor (1.9MW) dating from the 1950s and with poor efficiency compared to the performances of a new one. The aim is to compare the environmental impacts of the four possibilities:

-leaving the old machine in place despite relatively high losses.

-replace the machine by a new one with better efficiency and therefore lower losses. In this case, the manufacture and transport of the new machine generates environmental impacts that will have to be compensated by a less impacting running.

-renovate the old machine by replacing the winding with a new one with thinner insulation. This technique increases the copper cross-section and therefore reduces losses due to the Joule effect. By keeping the other parts of the machine, we minimize the impacts of material manufacturing.

-Renovate the old machine by replacing the winding as before, but also the stator laminations. Indeed, the new laminations have higher magnetic properties and allow less iron losses. In this case, the losses will be similar to those of a new machine, but the "material" impacts will be lower since the frame and the rotor are conserved.

Keywords : Refurbishment, Life Cycle Assessment, environmental effects, induction machine, magnetic circuit, electrical insulation

The study is based on an estimation of the efficiency gains associated with changes in insulation and laminations. It is necessary to estimate the masses of the main parts of the machine, the energy consumed in refurbishment and transport. It is also necessary to consider the machine's operating time, that determines the energy losses, as well as the type of electrical mix.

Several parts will be included in the final article:

-Background, machine description, differences between old and new materials,

-

  Photoche mical oxidAcidificatio n Eutrophica tion

For example, the graph below shows that the frame and the winding represent the major part of the impacts. Keeping the frame is therefore an important advantage in reducing the environmental footprint.

-Impacts of refurbishment compared to manufacturing, without taking into account the life cycle -Life cycle impacts based on service life and efficiency.

Here the lowest electricity consumption of a new or renovated machine comes into consideration. We can see that, over a long lifetime, the use phase is very important.

The graph below takes into account, for the 4 possibilities, the impacts related to manufacturing or refurbishment, and of the impacts related to electricity consumption.

-Influence of the origin of the electricity: depending on the country considered and the means of electricity production, the environmental impacts are not the same.

Conclusion:

The LCA allows us to affirm that the complete renovation of a machine, magnetic laminations and windings, is generally the technique that leads to the least environmental impact.