VIBRO-ACOUSTIC SIMULATION OF ELECTRICAL MACHINES · 2019-09-06 · [E1] M. Krishnamurthy, B....

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© EOMYS ENGINEERING 2019 – www.eomys.com 1 VIBRO-ACOUSTIC SIMULATION OF ELECTRICAL MACHINES Numerical challenges and application with MANATEE ® software Jean LE BESNERAIS 30 th August 2019 [email protected]

Transcript of VIBRO-ACOUSTIC SIMULATION OF ELECTRICAL MACHINES · 2019-09-06 · [E1] M. Krishnamurthy, B....

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VIBRO-ACOUSTIC SIMULATION OF ELECTRICAL MACHINES

Numerical challenges and application with MANATEE® software

Jean LE BESNERAIS

30th August 2019

[email protected]

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INTRODUCTION: EOMYS ENGINEERING & e-NVH

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*"Jeune Entreprise Innovante": the French government recognises that EOMYS runs significant R&D activities

• Young Innovative Company* created in 2013 in Lille, North of France

• Engineering consultancy specialized in electrical system NVH (e-NVH)

• 10 engineers (electrical engineering, vibro-acoustics, scientific computing)

• 90% of export turnover in transportation (automotive, railway, marine, aeronautics), energy (wind, hydro), home & medical appliances, industry

• More than 80 customers worldwide and up to 40 dB reduction

Who is EOMYS ENGINEERING?

© EOMYS ENGINEERING 2019 – www.eomys.com

ex: Nissan Leaf ex: Renaut Zoe

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1. variable current source

What do we call electromagnetic acoustic noise and vibration (e-NVH)?

noise and vibrations coming from variable electromagnetic forces

forces arising from the presence of a variable magnetic field : Maxwell & magnetostriction

3. rotating DC current source2. rotating permanent magnets

I=constant

Always present in e-motors Only present in magnet-based motors Only present in wound rotors

ex: Tesla S

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What do we call electromagnetic acoustic noise and vibration (e-NVH)?

(pole)

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= ++E-powertrain overall noise

Slot/pole interactionelectromagnetic noise

Pulse Width Modulationelectromagnetic noiseAerodynamic noise

~ball passing frequencies

~gear mesh frequencies

tyre/road noise

~slot/pole passing frequencies ~switching frequencies

e-NVH

What do we call electromagnetic acoustic noise and vibration (e-NVH)?

Strong harmonic/tonal nature of pole/slot effects + roughness of PWM effects

Mechanical noise +~blade passing frequencies

wind noise

Case of Renault Zoe e-powertrain - measurement by EOMYS- sound separation by GENESIS & EOMYS

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How electromagnetic noise is generated?

• Magnetic forces excite both stator and rotor, resulting in air-borne and structure-borne noise

• Resonance occurs when magnetic forces frequency + shapematch with a natural frequency + modal shape

+ RESONANCE=

magnetic excitation of wavenumber r=2 at fnat

modal shape (2,0) at fnat

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How electromagnetic noise is generated?

• It is therefore important to identify magnetic force wavenumbers r and frequency f as well as to identifymodal shapes, and vibro-acoustic transfer path

= + + +

+r=0

“tangential ripple”

“torque ripple”

pulsating+…

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What is so special about e-NVH?

• Depends on e-motor topology, load state, fault state and control strategy

• e-NVH problem solving requires skills in both electrical engineering & NVH

• e-NVH transfer path can be complex (structure-borne + air-borne, 3D excitations)

• e-NHV numerical simulation is very challenging (multiphysics + variable speed, high frequency effects)

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• A. Troubleshooting and solving of NVH issues on electrical systems

C. Technical trainings on vibroacoustics of electrical systems

B. NVH design optimization of electrical systems

EOMYS e-NVH services

D. MANATEE software leasing including e-NVH support

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e-NVH SIMULATION CHALLENGES

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• Mutiphysics + high frequency (PWM) + variable speed-> high CPU time

• Maxwell tensor approach is very sensitive to airgap mesh, numerical noise appears especially in 3D electromagnetic FEA (“remeshing ripple”)

• Spurious inter harmonics may appear in sound spectrum (continuous sound spectrum Vs discrete excitation) due to force spectrum leakage and acoustic solver interpolations

• Any parasitic force harmonic can be amplified by structural dynamics leading to unphysical results

e-NVH NUMERICAL CHALLENGES

[E41]

[E42]

[E42]

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• To avoid “mesh ripple”, some FEA software freeze the airgap discretization and synchronize rotor rotation with the mesh (“blocked step technique“ or “rotating mesh”)

• For a fixed number of timesteps the maximum frequency increases with speed -> mesh fineness tends to infinity to catch high frequency effects at low rotation speed fR

e-NVH NUMERICAL CHALLENGES

Flux, [E40] Ansys, [E67]

missing part of vibration and noise spectrum

• High frequency, low speed noise & vibration are wrongly estimated (e.g. resonances, or PWM)

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APPLICATION WITH MANATEE SOFTWARE

© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

MANATEE® SIMULATION SOFTWARE

Magnetic Acoustic Noise Analysis Tool for Electrical Engineering

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WHY ANOTHER SOFTWARE?

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• e-NVH numerical challenges are not solved by “multiphysics software suites” (Ansys Workbench, Comsol Multiphysics, Altair Program, Simulia etc)

• General purpose multiphysics software take a long time to be set-up for a particular problem

• Once the computation is finished, you don’t know much about why your motor is noisy, and you need to implement your own post processing, diagnosis tools and noise minimization methods

• Vibroacoustic level is highly determined in early design phase where fast models are needed -> no time to iterate on a multiphysic numerical model

Ex: effect of rotor slot number Zr in a SCIM

Max Sou

nd Pow

er Lev

el [d

B]

© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

MANATEE simulation software can be used for the electromagnetic design optimization of electrical machines including the analysis of magnetic vibrations and acoustic noise due to Maxwell forces (“e-NVH”).

MANATEE unique features include:

• - fast electromagnetic Noise Vibration Harshness (e-NVH) calculation in early electromagnetic design loops

• - optimized e-NVH calculation in detailed design phase (coupling with structural FEA) over full operating range

• - advanced post-processing for e-NVH root cause analysis

• - design optimization environments of e-motor noise mitigation technique

stator/rotor skewing pole/slot shaping current injection stator/rotor notching randomized PWM

OVERVIEW OF MANATEE SOFTWARE

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MANATEE is the central point for the integrated Noise, Vibration, Harshness design process of electric powertrains (e-NVH), from basic vibro-acoustic design at e-motor level to detailed vibro-acoustic design at system level:

Third-party sound quality tools

Third-party electromagnetic design tools

Third-party structural design tools

Third-party acoustic design tools

Third-party gearbox NVH design tools

Standalone e-motor NVH solution (electromagnetics

+vibro-acoustics)

© M

asta

© A

ctra

n

© O

ros

© Jmag

© A

nsy

s

Third-party NVH data acquisition tools

© O

ros

v1.08 coupling

v1.09 coupling

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OVERVIEW OF MANATEE SOFTWARE

© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

• MANATEE solver is currently under Matlab® (R2009b or later), but does not use any Matlab toolbox

• MANATEE GUI is in Python/Qt to define the machine and simulation parameters Python

• MANATEE v2.0 will be based on PYLEECAN open-source library under Python

• PYLEECAN currently include a unified object-oriented modelling of e-machines & drives coupled to FEMM

MANATEE programming environment

www.pyleecan.org

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Scripting environment (Matlab)

Command line post-processings

(Matlab)

GUI for simulation set-up (PyQt)

MANATEE graphical environment

GUI for machine set-up (PyQt from PYLEECAN)

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MANATEE demonstration: electrical machine definition

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© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

• MANATEE built-in fast electromagnetic models are based on geometrical layouts(cf. EOMYS website)

• The following radial flux electrical machine topologies are included in MANATEE v1.08:

MANATEE demonstration: electrical machine definition

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Magnet /

current

excitations

ELECTROMAGNETIC MODULE

ELECTRICAL MODULE

STRUCTURAL MODULE

ACOUSTIC MODULE

MANATEE software seamlessly integrates the following multiphysic modules:

Dynamic

vibrationsVariable

speed NVH

Geometry

and control

parameters

3D force

distribution

THERMAL MODULE

VARIABLE SPEED MODULEMULTI-SIMULATION MODULE

OPTIMIZATION MODULE

• Interface between physics (e.g. mesh to mesh projections) are automatically defined

• All module inputs can be user-defined / imported if necessary, resulting in a flexible simulation workflow

• Module interface are documented for possible integration in third-party scripts

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• Sinusoidal currents Id/Iq curves imposed as a function of speed

• Hybrid subdomain electromagnetic models [R1]

• Cylindrical shell vibroacoustic models

• All electrical, magnetic, structural and acoustic models can be changed for different accuracy / computing time tradeoffs

MANATEE demonstration 1: fast noise synthesis of an IPMSM (project AC_IPMSM_03)

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MANATEE demonstration 2: Toyota Prius 2004 case

• Objectives: quickly identify motor whine potential issues using MANATEE software

• Reference article: Z. Yang, et al., “Electromagnetic and vibrational characteristic of IPM over full torque-speed range”, IEMDC Proceedings, 2015 [R2]

• [R2] is based on Ansys workbench simulation, requiring several hours of simulation although acoustic noise is not calculated

• Conclusions of [R2]: potential resonances between H48 (48 times mechanical frequency) and H96 and breathing mode of the stack close to 3000 and 6000 rpm at open circuit; H24 appears at partial load but does not create significant resonance

H96H48

H24

From [R2]From [R2]

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MANATEE demonstration 2: open-circuit case (project tuto_IPMSM_01)

• Ansys-based results from [R2] are found within a few seconds of calculation

24fs (H96)12fs (H48)

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MANATEE demonstration 2: full load case (project tuto_IPMSM_03)

• Ansys-based results from [R2] are found within a few seconds of calculation

• The breathing mode of the stack is driving noise radiation as in most EV/HEV [R3]27

© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

Tangential and radial harmonic magnetic forces (magnitude,

wavenumber, frequency, phase)

3D airgap flux distribution

HARMONIC FORCE PROJECTION

r=2 r=3

ELECTROMAGNETIC MODEL

r=0

STRUCTURAL MODEL

Unit rotating loads identified with MANATEE

r=0, ±2, ±3 …

STRUCTURAL FREQUENCY RESPONSE FUNCTIONS

r=0 r=2

ELECTROMAGNETIC VIBRATION SYNTHESIS

Complex FRFs (radial & tangential) for each force

wavenumber r

Electromagnetic Vibration Synthesis (EVS): faster than a direct coupling, more physical insights

• 2D or 3D external FEA software (e.g. Flux, Jmag, Maxwell, Magnet)

• MANATEE 2,5D electromagnetic models (SDM, PMMF, FEMM)

• 3D external FEA software (e.g. Optistruct, Ansys, Nastran/Actran)

• MANATEE 2,5D structural models

Numerical Transfer Path Analysis (NTPA):Rotor Vs stator, radial Vs tangential, pulsating / UMP / rotating forces

Modal contribution to noise & vibrations

CALC

ULA

TION O

F

OPERATIONAL LO

ADS

STRUCTU

RAL

CHARACTE

RIZATION

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© 2013-2018 EOMYS ENGINEERING / 121 rue de Chanzy CS10128 59030 Lille Cedex FRANCE / www.eomys.com / [email protected]

Possibility to calculate FRF using an existing FEA model or building automatically a concept stator (orthotropic, winding mass, ideal boundary conditions):

Automatic set-up of Prius concept stator under Ansys

MANATEE demonstration 2: EVS refinement with Ansys Mechanical (project tuto_IPMSM_20)

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Conclusions

• Virtual prototyping of e-machine vibroacoustic behaviour in early and detailed design phases raises complex numerical challenges

• MANATEE is the only high-end e-NVH simulation software proposing solutions to thesechallenges

• MANATEE can be used at design stage or after manufacturing as an efficient e-NVH issue troubleshooting tool

• Leasing license includes a e-NVH support package and clustering options

• Regular e-NVH training sessions are organized EOMYS office in Lille (1 hour from Paris, France):

- e-NVH training: 10-12 Sept 2019 - MANATEE software training: 13 Sept 2019

• Training registration can be done at www.eomys-registration.com

© EOMYS ENGINEERING 2019 – www.eomys.com 31

Conclusions

• Any help is welcome on our open-source project for the electromagnetic simulation of electrical machines under Python, PYLEECAN -> see www.pyleecan.org

• EOMYS is looking for PhD Engineers in Electrical Engineering and Master’s students-> send us your spontaneous application at [email protected]

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REFERENCES[E1] M. Krishnamurthy, B. Fahimi, "Qualitative analysis of force distribution in a 3-phase Permanent Magnet Synchronous Machine," Electric Machines and Drives Conference (IEMDC) , 2009,[E2] J. Roivainen, “Unit-wave response-based modeling of electromechanical noise and vibration of electrical machines”, PhD Thesis, 2009.[E3] M. Van Der Giet, D. Franck, R. Rothe, and K. Hameyer, “Fast-and-easy acoustic optimization of PMSM by means of hybrid modeling and FEM-to-measurement transfer functions”, 2010.[E4] M. Boesing, T. Schoenen, K.A Kasper and R.W De Doncker, "Vibration Synthesis for Electrical Machines Based on Force Response Superposition", IEEE Trans. Mag, 2010,[E5] J. Le Besnerais, P. Pellerey, V. Lanfranchi and M. Hecquet, « Bruit acoustique d’origine magnétique dans les machines synchrones », Techniques de l’Ingénieur, 2014.[E6] A. Belahcen, “Methods of Calculating the Magnetic Forces for Vibration and Noise Analysis in Electrical Machines”, Acta Polytechnica Scandinavica, Electrical Engineering Series No 103. Finnish Academies of Technology Espoo, 2000.[E7] N. Jahyun, K. Chiho, S. Jeongyong and J. Gunhee, « Comparison of one-way and two-way coupled analyses of electromagnetic machines considering magnetic and structural interactions”, AIP Advances, 2017.[E8] M. Kirschneck, D.J. Rixen, H. Polinder and R.J. Van Ostayen, “Electromagnetomechanical Coupled Vibration Analysis of a Direct-Drive Off-Shore Wind Turbine Generator”, ASME, J. Comput. Nonlinear Dynam, 2015.[E9] M. Regniez, J. Le Besnerais, Q. Souron, P. Bonneel, “Numerical simulation of structural-borne vibrations due to electromagnetic forces in electric machines – coupling between Altair Optistruct and Manatee software”[E10] Gieras, Noise of Polyphase Electric Motors, CRC Press[E11] G. Verez and C. Espanet, “Natural Frequencies Analytical Modeling of Small Industrial Radial Flux Permanent Magnet Motors”, 18th International Conference on Electrical Machines and Systems (ICEMS), 2015. [E12] J.L. Coulomb, “A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness”, IEEE Transactions on Magnetics, 1983.[E13] F. Henrotte and K. Hameyer, “Computation of electromagnetic force densities: Maxwell stress tensor vs. virtual work principle”. JCAM, 2004,[E14] M. Boesing, « Noise and Vibration Synthesis based on Force Response Superposition », PhD Thesis, RWTH Aachen, 2013.[E15] F. Zidat, H. Ennassiri, «Webinar: Vibro‐acoustics Analysis for noise reduction of electric machines Example: Synchronous Machine – Flux 2D Coupling to ANSYS”, © FLUX CEDRAT, 2015.[E16] C. McCulloch, M. Tournour, and P. Guisset, « Modal Acoustic Transfer Vectors Make Acoustic Radiation Models Practical for Engines and Rotating Machinery », LMS International, 2002.[E17] M. Régniez, Q. Souron, P. Bonneel and J. Le Besnerais, “Numerical simulation of structural-borne vibrations due to electromagnetic forces in electric machines - coupling between Altair Optistruct and Manatee software”, 2016[E18] F. Marion, “Magneto-vibroacoustic analysis: a new dedicated context inside Flux ®11.2” , Cedrat News, 2013[E19] K. Vansant, “From Tesla to Pascal, a magneto-vibroacoustic analysis linking Flux® to LMS Virtual. Lab”, Cedrat News, 2014[E20] G. Kumar, “Noise prediction for electric motors by coupling electromagnetic and vibroacoustic simulation tools”, Proceedings of NAFEMS conference, 2014[E21] M. Solveson, C. Rathod, M. Hebbes, G. Verma, T. Sambharam, “Electromagnetic Force Coupling in Electric Machines”, ANSYS Inc, http://resource.ansys.com, 2011[E22] J. Hallal, “Études des vibrations d'origine électromagnétique d'une machine électrique : conception optimisée et variabilité du comportement vibratoire”, PhD thesis (in French), 2014[E23] P. Pellerey, V. Lanfranchi, G. Friedrich, "Coupled Numerical Simulation between Electromagnetic and Structural Models. Influence of the Supply Harmonics for Synchronous Machine Vibrations," in IEEE TMag, 2012,[E24] V. Wilow, “Electromagnetical model of an induction motor in COMSOL Multiphysics”, Master’s thesis, KTH University, Sweden, 2014[E25] M. K. Nguyen, “Predicting Electromagnetic Noise in Induction Motors”, Master’s thesis, KTH University, Sweden, 2014[E26] M. K. Nguyen, R. Haettel and A. Daneryd, “Prediction of Noise Generated by Electromagnetic Forces in Induction Motors” [E27] T. Hattori, “Starting With Vibration Noise Analyses” JMAG Newsletter January, 2014. [E28] F. Chauvicourt, C. Faria, A. Dziechciarz and C. Martis, "Infuence of rotor geometry on NVH behavior of synchronous reluctance machine," 2015 Tenth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte Carlo, 2015, pp. 1-6.[E29] H. Ennassiri, “Magneto-Vibro-Acoustic Analysis Linking Flux® to ANSYS® Mechanical”, 2016[E30] M. Senousy, P. Larsen, and P. Ding, "Electromagnetics, Structural Harmonics and Acoustics Coupled Simulation on the Stator of an Electric Motor," SAE Int. J. Passeng. Cars - Mech. Syst, 2014.

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REFERENCES[E31] X. Ge, “Simulation of Vibrations in Electrical Machines for Hybrid-electric Vehicles”, 2014[E32] P. Lombard, “Webinar: Summary of Vibro-acoustic Coupling”, © FLUX CEDRAT, 2017.[E33] D. Meeker, “Finite Element Method Magnetics” FEMM User Manual, 2015.[E34] D. Twyman, “Webinar: ANSYS Maxwell Coupling”, 2016. [E35] F. Lin, S. Zuo, W. Deng and S. Wu, "Modeling and Analysis of Electromagnetic Force, Vibration, and Noise in Permanent-Magnet Synchronous Motor Considering Current Harmonics," in IEEE Trans. Ind. Elec, 2016. [E37] Z.Q Zhu and D. Howe,“Electromagnetic noise radiated by brushless permanent magnet DC drives. 6th International Conference on Electrical Machines and Drives, 1993.[E38] J. Le Besnerais, “Fast Prediction of Variable-Speed Acoustic Noise and Vibrations due to Magnetic Forces in Electrical Machines”, ICEM 2016,[E39] S. Zuo, F. Lin and X. Wu, "Noise Analysis, Calculation, and Reduction of External Rotor Permanent-Magnet Synchronous Motor," in IEEE Trans. Indus. Elec, 2015.[E40] P. Pellerey, “Etude et Optimisation du Comportement Vibro-Acoustique des Machines Electriques, Application au Domaine Automobile”, PhD thesis, Univ. Tech. Compiègne, 2012[E41] J. Le Besnerais, "Fast prediction of variable-speed acoustic noise due to magnetic forces in electrical machines," ICEM, 2016.[E42] S. Peters and F. Hetemi, « Airborne Sound of Electrical Machines using Symmetric Matrices in ANSYS 14”, ANSYS Conference[E43] M. Van der Giet et al, “Comparison of acoustic single-value parameters for the design process of electrical machines”, Internoise 2010.[E44] G. Verez, “Contribution à l’étude des émissions vibro-acoustiques des machines électriques. Cas des machines synchrones à aimants dans un contexte automobile », PhD thesis, University of Le Havre, 2014.[E45] K. Balachandran, “Electric Motor Noise and Vibration simulation using Actran software”, MSC software, Nov 2016 [ppt][E46] D. Reeves, “From Electromagnetic Forces To Acoustics - Full Chain Analysis for Vibro-Acoustic Studies with Electromagnetic Excitations”, MSC software, 2015 [ppt][E47] J. Chen, Y. Ma, and R. HE, “SMFF Computation for Probe of Online Magnetic Flux Leakage Detection System with combination of ANSYS and Virtual Work Method”, In International Symposium on Mechanical Engineering and Material Science, 2016.[E48] L. Kostetzer, F. Hetemi, and D. Gerling, "Scalable system simulation for electric drives," in Electric Drives Production Conference (EDPC), 2011.[E49] P. Dular and C. Geuzaine, “GetDP reference manual: The documentation for GetDP, a general environment for the treatment of discrete problems”[E50] ME2D User Guide, Cobham Technical Services, Opera, Oxford, U.K. [Online] Available: https://operafea.com/[E51] FLUX3D User Guide, Version 10.3.3. [Online]. Available: https://altairhyperworks.com/product/flux[E52] J. Otto, “Simulation of Electric Machines with ANSYS”, © CADFEM (2017). [ppt][E53] M, Michon, “Workshop: Romax electrical machine NVH analysis”, © ROMAX Technology (Oct. 2016). [ppt][E54] K. Kouumdjieff and M. Popescu, “Webinar: Solving Electric Vehicle Powertrain problems using RomaxDESIGNER and Motor-CAD”, (2017). [ppt][E55] A. McCloskey, X. Arrasate, G. Almandoz, X. Hernandez, and O. Salgado, “Vibro-acoustic finite element analysis of a Permanent Magnet Synchronous Machine”. EURODYN, 2014.[E56] Owen Harris, April 2018 webinar, https://www.smartmt.com/video/webinar-nvh/[E57] A. Anderson “Electric Machine Control for Energy Efficient Electric Drive Systems”, PhD Thesis, Chalmers University, 2018[E58] R. Pile et al, “Application Limits of the Airgap Maxwell Tensor”, CEFC 2018[E59] Numerical Prediction of Motor Noise in a Continuous Speed Range, J. Wobbler, M. Hanke, TAE symposium Elektromagnetismus 2018, 8-9 March 2018*[E60] D. Torregrossa, B. Fahimi, F. Peyraut and A. Miraoui, "Fast Computation of Electromagnetic Vibrations in Electrical Machines via Field Reconstruction Method and Knowledge of Mechanical Impulse Response," in IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 839-847, Feb. 2012.[E61] Pile, R., Devillers, E., & Le Besnerais, J. (2018). Comparison of Main Magnetic Force Computation Methods for Noise and Vibration Assessment in Electrical Machines.IEEE Transactions on Magnetics, 54(7), 1–13. [E62] Parent, G., Dular, P., Ducreux, J.-P. P., & Piriou, F. (2008). Using a galerkin projection method for coupled problems. IEEE Transactions on Magnetics, 44(6), 830–833.[E63] Farrel, P. E. Galerkin projection of discrete fields via supermesh construction. 2009. Thèse de doctorat. Imperial College London.[E64] Liang, W. (2017). The investigation of electromagnetic radial force and associated vibration in permanent magnet synchronous machines. Cranfield University.[E65] P. Millithaler, “Dynamic behaviou of electric machine stators – modelling guidelines for efficient finite-element simulations and design specifications for noise reduction”, 2013, PhD thesis, UFC

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REFERENCES[E66] Michael Shwarzer, « Structural Dynamic Modeling and Simulation of Acoustic Sound Emissions of Electric Traction Motors”, PhD thesis, 2017[E67] https://www.youtube.com/watch?v=FlJ3thJ3I9Y

[R1] E. Devillers, J. Le Besnerais, “Fast calculation of the airgap flux density distribution based on subdomain and permeance magnetomotive force models of electrical machines”, ISEF 2019 [R2] Z. Yang, et al., “Electromagnetic and vibrational characteristic of IPM over full torque-speed range”, IEMDC Proceedings, 2015 [R3] A. Hofmann, F. Qi, T. Lange and R. W. De Doncker, "The breathing mode-shape 0: Is it the main acoustic issue in the PMSMs of today's electric vehicles?," 2014 17th International Conference on Electrical Machines and Systems (ICEMS), Hangzhou, 2014, pp. 3067-3073.