D.3 Résolution
D.3.2 Formulation discrétisée
ρ∂∂t2u2 = ∂σ∂xxx +∂σ∂yxy +fV x
ρ∂∂t2v2 = ∂σ∂yyy + ∂σ∂xxy +fV y (D.2.1) La loi de comportement (équation D.1.4), les relations cinématiques (équation D.1.5), et les conditions aux limites permettent de trouver une solution au problème posé.
D.3 Résolution
D.3.1 Formulation faible
En appliquant la méthode des résidus pondérés [Dhatt 05] aux équations (4.3.16), on aboutit à la relation intégrale suivante :
W(u, u∗) =
{u*} est le champ de déplacements virtuels qui induit un le champ de déforma-tions virtuelles {∗}. Ces grandeurs correspondent aux pondérations imposées par la méthodes des résidus pondérés.
D.3.2 Formulation discrétisée
Le volume V et la surface S sont maillés. En chacun des éléments e du maillage, l’outil éléments finis permet de calculer le vecteur de déplacement −→u sur chaque noeud. Pour un point M placé dans un élément, on y détermine le vecteur dépla-cement par interpolation. Par exemple, pour un élément de type T3 ; triangulaire à 3 noeuds pour un modèle 2D, on a :
oùuei est la valeur du déplacement suivant la direction x du noeud i de l’élément e et vei le déplacement suivant la direction y du même noeud du même élément.
138
D.3 Résolution
L’équation (D.3.2) peut se résumer à :
{u(M, t)}= [N(M)].{u(t)} (D.3.3) On constate que la matrice [N], qui regroupe les charges réparties sur chaque noeud, n’est constituée que de 3 termes non nuls dfférents (pour un élément de type T3), elle peut donc être entièrement déterminée à partir du vecteur {N0} :
{N0e}=
Etant donné la définition du vecteur de déformation {}, relative aux déplace-ments (equation D.1.5), on obtient :
{(M, t)}= On notera que cette matrice [B] ne contient que 6 termes non nuls différents issus de la matrice :
[B0] =
Compte-tenu des relations matricielles qui viennent d’être présentées, l’équation (D.3.1) devient :
W({U},{U∗}) ={U∗}T .[M].nU¨o+ [K].{U} − {F} (D.3.5) avec :
— {U} le vecteur des déplacements nodaux [m]
— nU¨ole vecteur des accélérations nodales [m.s-2]
— [M] la matrice de masse [kg]
— [K] la matrice de rigidité [N.m-1]
— {F} le vecteur force équivalent aux charges réparties [N]
L’équation (D.3.5) est unique pour le problème de mécanique des structures pour un solide donné. Elle tient en compte l’assemblage, c’est-à-dire la mise en commun de la contribution de tous les éléments du maillage du système étudié.
Bibliographie
[Amara 01] Yacine Amara. Contribution à la conception et à la commande des machines synchrones à double exci-tation : application au véhicule hybride. PhD thesis, Paris 11, 2001.
[Azar 13] Z Azar & ZQ Zhu. Comparative study of electroma-gnetic performance of switched reluctance machines under different excitation techniques. In Energy Conversion Congress and Exposition (ECCE), 2013 IEEE, pages 4334–4341. IEEE, 2013.
[Barcaro 12] Massimo Barcaro & Nicola Bianchi. Interior PM machines using Ferrite to substitute rare-earth sur-face PM machines. Proceedings - 2012 20th Inter-national Conference on Electrical Machines, ICEM 2012, vol. 50, no. 2, pages 1339–1345, 2012.
[Bertotti 88] Giorgio Bertotti. General properties of power losses in soft ferromagnetic materials. IEEE Transactions on magnetics, vol. 24, no. 1, pages 621–630, 1988.
[Bertotti 91] G Bertotti, Aldo Boglietti, Mario Chiampi, D Chia-rabaglio, F Fiorillo & M Lazzari. An improved esti-mation of iron losses in rotating electrical machines.
IEEE Transactions on Magnetics, vol. 27, no. 6, pages 5007–5009, 1991.
[Besharati 14] M. Besharati, G. Atkinson, J.D. Widmer, V. Pi-ckert & K.R. Pullen. Investigation of the Mechani-cal Constraints on the Design of a Super-high-speed Switched Reluctance Motor for Automotive Trac-tion. 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), vol. 2014, no. 628 CP, pages 2.5.04–2.5.04, 2014.
www
BIBLIOGRAPHIE
[Bianchi 05] Nicola Bianchi. Electrical machine analysis using finite elements. CRC press, 2005.
[Bianchi 09] Nicola Bianchi, Silverio Bolognani, Diego Bon &
Michele Dai Pre. Rotor Flux-Barrier Design for Torque Ripple Reduction in Synchronous Reluc-tance and PM-Assisted Synchronous RelucReluc-tance Motors. IEEE Transactions on Industry Applica-tions, vol. 45, no. 3, pages 921–928, 2009. www [Bianchi 15] Nicola Bianchi, Michele Degano & Emanuele
For-nasiero. Sensitivity analysis of torque ripple reduc-tion of synchronous reluctance and interior PM mo-tors. IEEE Transactions on Industry Applications, vol. 51, no. 1, pages 187–195, 2015.
[Boldea 10] I. Boldea, Z.X. Fu & S.A. Nasar. Performance eva-luation of axially-laminated anisotropic (ALA) ro-tor reluctance synchronous moro-tors. In Conference Record of the 1992 IEEE Industry Applications So-ciety Annual Meeting, volume 2, pages 212–218.
IEEE, 2010. www
[Bramerdorfer 16] Gerd Bramerdorfer, Alexandru-Ciprian Zăvoianu, Siegfried Silber, Edwin Lughofer & Wolfgang Am-rhein. Possibilities for Speeding Up the FE-Based Optimization of Electrical Machines—A Case Study. IEEE Transactions on Industry Ap-plications, vol. 52, no. 6, pages 4668–4677, 2016.
[Burnand 17] Guillaume Burnand, Douglas Martins Araujo &
Yves Perriard. Very-high-speed permanent magnet motors : Mechanical rotor stresses analytical mo-del. In Electric Machines and Drives Conference (IEMDC), 2017 IEEE International, pages 1–7.
IEEE, 2017.
[Caron 95] Jean-Pierre Caron & Jean-Paul Hautier. Modélisa-tion et commande de la machine asynchrone. Tech-nip, 1995.
[Cedrat 15a] Cedrat. Guide d’utilisation Flux 12 Volume 1 : Ou-tils généraux, Géométrie et maillage, 03 2015.
[Cedrat 15b] Cedrat. Guide d’utilisation Flux 12 Volume 3 : Les applications physiques, 01 2015.
[Cedrat 15c] Cedrat. Guide d’utilisation Got-It 2.0.1, 2015.
142
BIBLIOGRAPHIE
[Chai 16] Feng Chai, Yi Li, Peixin Liang & Yulong Pei. Calcu-lation of the maximum mechanical stress on the ro-tor of interior permanent-magnet synchronous mo-tors. IEEE Transactions on Industrial Electronics, vol. 63, no. 6, pages 3420–3432, 2016.
[Chatelain 89] Jean Chatelain. Machines électriques, volume 10.
PPUR Presses polytechniques, 1989.
[Chedot 04] Laurent Chedot. Contribution à l’étude des ma-chines synchrones à aimants permanents internes à large espace de fonctionnement. Application à l’alterno-démarreur. PhD thesis, PhD thesis, Uni-versité de technologie de Compiègne, 2004.
[Chiba 15] Akira Chiba, Kyohei Kiyota, Nobukazu Hoshi, Ma-satsugu Takemoto & Satoshi Ogasawara. Develop-ment of a Rare-Earth-Free SR Motor With High Torque Density for Hybrid Vehicles. IEEE Transac-tions on Energy Conversion, vol. 30, no. 99, pages 175–182, 2015. www
[Coey 95] JMD Coey.Rare-earth magnets. Endeavour, vol. 19, no. 4, pages 146–151, 1995.
[Collette 11] Yann Collette & Patrick Siarry. Optimisation mul-tiobjectif : Algorithmes. Editions Eyrolles, 2011.
[Courbon 88] Jean Courbon. Résistance des matériaux. Ed. Tech-niques Ingénieur, 1988.
[Cupertino 12] F. Cupertino, G.M. Pellegrino, E. Armando &
C. Gerada. A SyR and IPM machine design metho-dology assisted by optimization algorithms. In 2012 IEEE Energy Conversion Congress and Exposition (ECCE), pages 3686–3691. IEEE, sep 2012. www [Curnier 93] Alain Curnier. Méthodes numériques en mécanique
des solides. PPUR presses polytechniques, 1993.
[D.A.Staton, T.J.E.Miller 93] S.E.Wood D.A.Staton, T.J.E.Miller. Maximising the saliency ratio of the synchronous reluctance mo-tor .pdf. Electric power Applications, vol. 140, no. 4, pages 249–259, 1993.
[Dehlinger 07] Nicolas Dehlinger. Étude des performances d’une machine à flux transverse à noyaux ferromagné-tiques amorphes. PhD thesis, Université Laval, 2007.
BIBLIOGRAPHIE
[Dhatt 05] Gouri Dhatt, Gilbert Touzot & Emmanuel Lefran-çois. Méthode des éléments finis. Lavoisier, 2005.
[Di Nardo 16] Maura Di Nardo, G Lo Calzo, Michael Galea &
Chris Gerada. Structural design optimization of a high speed synchronous reluctance machine. In Elec-trical Machines (ICEM), 2016 XXII International Conference on, pages 2073–2079. IEEE, 2016.
[Duan 13] Yao Duan & Dan M Ionel. A review of recent deve-lopments in electrical machine design optimization methods with a permanent-magnet synchronous mo-tor benchmark study. IEEE Transactions on Indus-try Applications, vol. 49, no. 3, pages 1268–1275, 2013.
[El-Refaie 13] Ayman M El-Refaie. Motors/generators for trac-tion/propulsion applications : A review. IEEE Ve-hicular Technology Magazine, vol. 8, no. 1, pages 90–99, 2013.
[El-Refaie 14a] Ayman M El-Refaie, James P Alexander, Steven Galioto, Patel B Reddy, Kum-Kang Huh, Peter de Bock & Xiochun Shen. Advanced high-power-density interior permanent magnet motor for trac-tion applicatrac-tions. IEEE Transactrac-tions on Industry Applications, vol. 50, no. 5, pages 3235–3248, 2014.
[El-refaie 14b] Ayman Mohamed Fawzi El-refaie & Kum-Kang Huh. Induction machine with dual phase magne-tic material for sensorless control, April 15 2014.
US Patent App. 14/252,893.
[EL01 09] EL01. Phénomènes électromagnétiques tome2.
UTC, 2009.
[Ferrari 13] Marco Ferrari, Nicola Bianchi, Alberto Doria &
Emanuele Fornasiero. Design of synchronous reluc-tance motor for hybrid electric vehicles. In 2013 In-ternational Electric Machines & Drives Conference, numéro 1, pages 1058–1065. IEEE, may 2013. www [Ferrari 15] Marco Ferrari, Nicola Bianchi & Emanuele
Forna-siero. Analysis of Rotor Saturation in Synchro-nous Reluctance and PM-Assisted Reluctance Mo-tors. IEEE Transactions on Industry Applications, vol. 51, no. 1, pages 169–177, jan 2015. www
144
BIBLIOGRAPHIE
[Fiorillo 90] Fausto Fiorillo & Alexander Novikov. An improved approach to power losses in magnetic laminations under nonsinusoidal induction waveform. IEEE Transactions on Magnetics, vol. 26, no. 5, pages 2904–2910, 1990.
[Friedrich 02] G Friedrich, L Chédot & JM Biedinger. Compa-rison of two optimal machine design for integrated starter-generator applications. In Int. Conf. Electri-cal machines, 2002.
[Galioto 15a] Steven J Galioto, Patel B Reddy, Ayman M EL-Refaie & James P Alexander. Effect of magnet types on performance of high-speed spoke interior-permanent-magnet machines designed for traction applications. IEEE Transactions on Industry Ap-plications, vol. 51, no. 3, pages 2148–2160, 2015.
[Galioto 15b] Steven Joseph Galioto & Ayman Mohamed Fawzi El-refaie. Electric machine stator lamination with dual phase magnetic material, October 5 2015. US Patent App. 14/874,583.
[Gmür 00] Thomas Gmür. Méthode des éléments finis en méca-nique des structures. PPUR presses polytechméca-niques, 2000.
[Guy 00] G Guy & C Guy. Actionneurs électriques, principes modèles commande. édition Eyrolles, 2000.
[Haataja 03] Jorma Haatajaet al. A comparative performance study of four-pole induction motors and synchro-nous reluctance motors in variable speed drives.
Acta Universitatis Lappeenrantaensis, 2003.
[Hofmann 00] Heath Hofmann & Seth R Sanders. High-speed syn-chronous reluctance machine with minimized rotor losses. IEEE Transactions on Industry Applica-tions, vol. 36, no. 2, pages 531–539, 2000.
[Ibrahim 16] M. N. Ibrahim, P. Sergeant & E. M. Rashad. In-fluence of rotor flux-barrier geometry on torque and torque ripple of permanent-magnet-assisted syn-chronous reluctance motors. In 2016 XXII Interna-tional Conference on Electrical Machines (ICEM), pages 398–404. IEEE, sep 2016. www
BIBLIOGRAPHIE
[Ida 13] Nathan Ida & Joao PA Bastos. Electromagnetics and calculation of fields. Springer Science & Busi-ness Media, 2013.
[Imamura 13] Keigo Imamura, Masayuki Sanada, Shigeo Mori-moto & Yukinori Inoue. Improvement of charac-teristics by flux barrier shape and magnet thick-ness of IPMSM with Dy-free rare-earth magnet. In 2013 15th European Conference on Power Electro-nics and Applications (EPE), pages 1–10. IEEE, sep 2013. www
[Jannot 11] Xavier Jannot, Jean Claude Vannier, Claude Mar-chand, Mohamed Gabsi, Jacques Saint-Michel &
Daniel Sadarnac. Multiphysic modeling of a high-speed interior permanent-magnet synchronous ma-chine for a multiobjective optimal design. IEEE Transactions on Energy Conversion, vol. 26, no. 2, pages 457–467, 2011.
[Kato 14] Takashi Kato, Natee Limsuwan, Chen-Yen Yu, Kan Akatsu & Robert D Lorenz. Rare earth reduction using a novel variable magnetomotive force flux-intensified IPM machine. IEEE Transactions on Industry Applications, vol. 50, no. 3, pages 1748–
1756, 2014.
[Kedous-Lebouc 06] Afef Kedous-Lebouc. Matériaux magnétiques en gé-nie électrique 1. Hermès, 2006.
[Kimiabeigi 16] M. Kimiabeigi, J. D. Widmer, R. Long, Y. Gao, J. Goss, R. Martin, T. Lisle, J. M. Soler Vizan, A. Michaelides & B. Mecrow. High-performance low-cost electric motor for electric vehicles using ferrite magnets. IEEE Transactions on Industrial Electronics, vol. 63, no. 1, pages 113–122, 2016.
[Krebs 09] Benoit Krebs. Caractérisation et prévision des structures en bandes dans les aciers Dual-Phase : lien avec les propriétés d’endommagement. PhD thesis, Metz, 2009.
[Küttler 13] Sulivan Küttler. Dimensionnement optimal de ma-chines synchrones pour des applications de véhicules hybrides. PhD thesis, Université de Technologie de Compiègne, 2013.
146
BIBLIOGRAPHIE
[Langue 16a] Leila Nguimpi Langue, Guy Friedrich, Stephane Vi-vier & Khadija El Kadri Benkara. Dimensionne-ment optimal de machines synchro-réluctantes per-formantes : rotor assisté ou" Dual Phase mate-rials" ? In Symposium de Genie Electrique, 2016.
[Langue 16b] Leila Nguimpi Langue, Guy Friedrich, Stephane Vi-vier & Khadija El Kadri Benkara. Optimization of synchronous reluctance machines for high po-wer factor. In 2016 XXII International Conference on Electrical Machines (ICEM), pages 1976–1982.
IEEE, sep 2016. www
[Langue 17a] Leila Nguimpi Langue, Guy Friedrich, Stephane Vi-vier, Khadija El & Kadri Benkara. Comparative analysis of different approaches for an optimal de-sign of synchronous reluctance machines. IEEE, International Electric Machines and Drives Confe-rence, 2017.
[Langue 17b] Leila Nguimpi Langue, Guy Friedrich, Stephane Vi-vier, Khadija El & Kadri Benkara. Consideration of mechanical constraints for an optimal design of ferrite assisted flux-barriers synchronous reluctance machines. 5th International Electric Drives Pro-duction Conference (EDPC), Nuremberg, Germany, 15-16 Sept, 2015, 2017.
[Legranger 09] Jérôme Legranger. Contribution à l’étude des ma-chines brushless à haut rendement dans les applica-tions de moteurs-générateurs embarqués. PhD the-sis, Compiègne, 2009.
[Lei 14] Gang Lei, Tianshi Wang, Youguang Guo, Jianguo Zhu & Shuhong Wang. System-level design optimi-zation methods for electrical drive systems : Deter-ministic approach. IEEE Transactions on Industrial Electronics, vol. 61, no. 12, pages 6591–6602, 2014.
[Lei 15] Gang Lei, Tianshi Wang, Jianguo Zhu, Youguang Guo & Shuhong Wang. System-level design optimi-zation method for electrical drive systems—Robust approach. IEEE Transactions on Industrial Electro-nics, vol. 62, no. 8, pages 4702–4713, 2015.
BIBLIOGRAPHIE
[Leveque 05] Alain Leveque & Patrick Maestro. Terres rares. Ed.
Techniques Ingénieur, 2005.
[Lipo 04] TA Lipo, SM Madani, RJ White & W Ouyang.Soft Magnetic Composites for AC Machines–A Fresh Perspective. In 11th International Power Electro-nics and Motion Control Conference, EPE-PEMC, pages 2–4, 2004.
[Lu 98] Jian Lu & Henri-Paul Lieurade. Concentration de contraintes. Techniques de l’ingénieur. Génie méca-nique, no. BM5040, pages BM5040–1, 1998.
[Ly 03] Pascal Ly. Commande optimale de l’alterno démar-reur avec prise en compte de la saturation magné-tique. PhD thesis, Compiègne, 2003.
[MATLAB 12] MATLAB. The MathWorks, 2012.
[Mballa 13] Frederick Sorel Mballa Mballa. Modélisation du comportement magnéto-mécanique d’un acier Dual Phase à partir de sa description microstructurale.
PhD thesis, École normale supérieure de Cachan-ENS Cachan, 2013.
[Moghaddam 12] Reza-Rajabi Moghaddam, Freddy Magnussen &
Chandur Sadarangani. Novel rotor design optimi-zation of Synchronous Reluctance Machine for low torque ripple. In 2012 XXth International Confe-rence on Electrical Machines, pages 720–724. IEEE, sep 2012. www
[Moreau 05] L Moreau, M Machmoum & ME Zaim. Control and minimization of torque ripple in switched reluctance generator. In Power Electronics and Applications, 2005 European Conference on, pages 8–pp. IEEE, 2005.
[Morimoto 90] Shigeo Morimoto, Yoji Takeda, Takao Hirasa &
Katsunori Taniguchi. Expansion of operating li-mits for permanent magnet motor by current vector control considering inverter capacity. IEEE transac-tions on industry applicatransac-tions, vol. 26, no. 5, pages 866–871, 1990.
[Morimoto 01] Shigeo Morimoto, Masayuki Sanada & Yoji Takeda.
Performance of PM-assisted synchronous reluctance
148
BIBLIOGRAPHIE
motor for high-efficiency and wide constant-power operation. IEEE Transactions on Industry Applica-tions, vol. 37, no. 5, pages 1234–1240, 2001.
[Neuber 61] Heinz Neuber. Theory of stress concentration for shear-strained prismatical bodies with arbitrary non-linear stress-strain law. Journal of Applied Mecha-nics, vol. 28, no. 4, pages 544–550, 1961.
[NF04 06] NF04. Modélisation numérique des problèmes de l’ingénieur. UTC, 2006.
[Oh 01] Jae Yoon Ohet al. Flux barrier synchronous reluc-tance motor, May 29 2001. US Patent 6,239,526.
[Parviainen 05a] A. Parviainen, M. Niemela, J. Pyrhonen & J. Man-tere. Performance comparison between low-speed axial-flux and radial-flux permanent-magnet ma-chines including mechanical constraints. IEEE In-ternational Conference on Electric Machines and Drives, 2005., pages 1695–1702, 2005.
[Parviainen 05b] Asko Parviainenet al. Design of axial-flux permanent-magnet low-speed machines and perfor-mance comparison between radial-flux and axial-flux machines. Acta Universitatis Lappeenrantaensis, 2005.
[Pilkey 08] Walter D Pilkey & Deborah F Pilkey. Peterson’s stress concentration factors. John Wiley & Sons, 2008.
[Prieto 13] Dany Prieto, Benjamin Dagusé, Philippe Dessante
& Jean-Claude Vannier. Performance compari-son of the permanent magnet assisted synchronous reluctance motor and the double magnet synchro-nous motor. In Power Electronics and Applications (EPE), 2013 15th European Conference on, pages 1–7. IEEE, 2013.
[Prieto 14a] D Prieto, Ph Dessante, J.-C. Vannier, X Jannot
& J. Saint-Michel. Analytical model for a satura-ted Permanent Magnet Assissatura-ted Synchronous Re-luctance Motor. In 2014 International Conference on Electrical Machines (ICEM), pages 72–78. IEEE, sep 2014. www
BIBLIOGRAPHIE
[Prieto 14b] Dany Prieto, Alejandro Fernandez, Philippe Des-sante, Jean-Claude Vannier, Xavier Jannot &
Jacques Saint-Michel. Optimization methodology for synchronous reluctance motor by Finite Element Method. In 2014 16th European Conference on Po-wer Electronics and Applications, pages 1–9. IEEE, aug 2014. www
[Raminosoa 06] Tsaarafidy Raminosoa. Optimisation des perfor-mances des machines synchro-réluctantes par ré-seaux de perméances. PhD thesis, Institut National Polytechnique de Lorraine-INPL, 2006.
[Raminosoa 14] Tsarafidy Raminosoa, Ayman El-Refaie, Di Pan, Kum-kang Huh, James Alexander, Kevin Grace, Stefan Grubic, Steven Galioto, Patel Reddy &
Xiaochun Shen. Reduced rare-earth flux swit-ching machines for traction applications. In 2014 IEEE Energy Conversion Congress and Exposition (ECCE), volume 51, pages 318–327. IEEE, sep 2014. www
[Reddy 12] Patel B Reddy, Ayman M El-Refaie, Kum-Kang Huh, Jagadeesh K Tangudu & Thomas M Jahns.
Comparison of interior and surface PM machines equipped with fractional-slot concentrated windings for hybrid traction applications. IEEE Transactions on Energy Conversion, vol. 27, no. 3, pages 593–602, 2012.
[Reddy 15] Patel Bhageerath Reddy, Ayman El-Refaie, Ste-ven Galioto & James P Alexander. Design of synchronous reluctance motor utilizing dual-phase material for traction applications. In 2015 IEEE Energy Conversion Congress and Exposition (ECCE), pages 4812–4819. IEEE, sep 2015. www [Reddy 17] Patel B Reddy, Steven Galioto, Ayman El-Refaie &
James P Alexander. Design of synchronous reluc-tance motor utilizing dual-phase material for trac-tion applicatrac-tions. IEEE Transactrac-tions on Industry Applications, 2017.
[Schofield 95] John RG Schofield. Direct torque control-DTC [of induction motors]. In Vector Control and Direct
150
BIBLIOGRAPHIE
Torque Control of Induction Motors, IEE Collo-quium on, pages 1–1. IET, 1995.
[Séguier 99] Guy Séguier, Francis Labrique & Philippe Delarue.
Electronique de puissance. Edition DUNOD, année, 1999.
[Spargo 15] Christopher M Spargo, Barrie C Mecrow, James D Widmer, Christopher Morton & Nick J. Baker. De-sign and Validation of a Synchronous Reluctance Motor With Single Tooth Windings. IEEE Transac-tions on Energy Conversion, vol. 30, no. 2, pages 795–805, jun 2015. www
[Taghavi 14] Seyedmorteza Taghavi & Pragasen Pillay. A me-chanically robust rotor with transverse-laminations for a synchronous reluctance machine for traction applications. In 2014 IEEE Energy Conversion Congress and Exposition (ECCE), volume 51, pages 5131–5137. IEEE, sep 2014. www
[Vagati 12] A. Vagati, B. Boazzo, P. Guglielmi & G. Pelle-grino. Ferrite assisted synchronous reluctance ma-chines : A general approach. In 2012 XXth Inter-national Conference on Electrical Machines, pages 1315–1321. IEEE, sep 2012. www
[Vagati 14] Alfredo Vagati, Barbara Boazzo, Paolo Guglielmi
& Gianmario Pellegrino. Design of ferrite-assisted synchronous reluctance machines robust toward de-magnetization. IEEE Transactions on Industry Ap-plications, vol. 50, no. 3, pages 1768–1779, 2014.
[Widmer 14] J.D. Widmer, C.M. Spargo & B.C. Mecrow. Hi-gher Pole Number Synchronous Reluctance Ma-chines with Fractional Slot Concentrated Windings.
7th IET International Conference on Power Elec-tronics, Machines and Drives (PEMD 2014), pages 2.5.01–2.5.01, 2014. www
[Workbench 11] ANSYS Workbench. V13. 0 User’s manual. Ansys Inc, 2011.
[Yamazaki 14] Katsumi Yamazaki, Yusuke Kato, Takeshi Ikemi &
Shunji Ohki. Reduction of rotor losses in multi-layer interior permanent-magnet synchronous mo-tors by introducing novel topology of rotor flux
bar-BIBLIOGRAPHIE
riers. IEEE Transactions on Industry Applications, vol. 50, no. 5, pages 3185–3193, 2014.
[Yang 17] Yinye Yang, Sandra M Castano, Rong Yang, Mi-chael Kasprzak, Berker Bilgin, Anand Sathyan, Hossein Dadkhah & Ali Emadi. Design and Com-parison of Interior Permanent Magnet Motor To-pologies for Traction Applications. IEEE Transac-tions on Transportation Electrification, vol. 3, no. 1, pages 86–97, 2017.
[Youb 07] Lamia Youb & A Craciunescu. Etude comparative entre la commande vectorielle à flux orienté et la commande directe du couple de la machine asyn-chrone. UPB Sci. Bull., Series C, vol. 69, no. 2, pages 113–128, 2007.
[Zaim 09] Mohammed El Hadi Zaim. High-speed solid rotor synchronous reluctance machine design and optimi-zation. IEEE Transactions on Magnetics, vol. 45, no. 3, pages 1796–1799, 2009.
152