The webinar reviews the different noise and vibration sources in electric machines and then focus on the electromagnetic source. The magnetic noise and vibration generation process (interaction between Maxwell forces and structural modes) is briefly explained, and noise mitigation techniques are reviewed. Finally, available modeling strategies and simulation software are reviewed.

1. NOISE AND VIBRATIONS IN ELECTRIC MACHINES
Review of NVH sources & mitigation of electromagnetically-excited noise
LE BESNERAIS Jean
REGNIEZ Margaux
21th September 2017
www.eomys.com
contact@eomys.com
1

2. 2
EOMYS ENGINEERING
• Innovative Company created in may 2013 in Lille, North of France (1 hr from
Paris)
• Activity: engineering consultancy / applied research
• R&D Engineers in electrical engineering, vibro-acoustics, heat transfer,
scientific computing
• 80% of export turnover in transportation (railway, automotive, marine, aeronautics),
energy (wind, hydro), home appliances, industry

3. • Diagnosis and problem solving including simulation & measurements
• Multiphysic design optimization of electrical systems
• Technical trainings on vibroacoustics of electrical systems
• MANATEE simulation software for the integrated electromagnetic and vibro-
acoustic design optimization of electric machines
3
EOMYS can be involved both at design stage & after manufacturing of electric
machines
SERVICES & PRODUCTS

4. 4
WEBINAR SUMMARY
• INTRODUCTION
• REVIEW OF NOISE & VIBRATIONS IN ELECTRIC MACHINES
• FOCUS ON MAGNETIC NOISE AND VIBRATION MITIGATION
• MODELING & SIMULATION OF ELECTROMAGNETICALLY-EXCITED NOISE
• CONCLUSION

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Why vibro-acoustics are important when designing electrical machines
• Cost optimization leads to less stiff magnetic cores, increasing vibration & noise levels
• Skewing technique degrades torque and efficiency and can be avoided with a good NVH design
• New topologies with higher Noise, Vibration, Harshness (NVH) challenges: concentrated winding PMSM,
brushless DFIM
• Additionnal cost, weight, and delays may come when solving vibration and noise issues after
manufacturing
Importance of noise & vibration analysis

6. 6
Review of noise sources in electric machines
aerodynamic sources
(e.g. fans)
electromagnetic sources
(e.g. slot/magnet)
mechanical sources
(e.g. bearings, gearbox)
Noise of an electric traction machine during starting:

7. 7
• Bearings
• Shaft imbalance
• Shaft eccentricity
• Sliding contacts
- between rotor and bearings
- slip rings
- metal or carbon brushes
• Geared power transmission motor coupling
• Tightening fault
[Bertolini2012]
Contributors to mechanical noise
Mechanical noise and vibration sources

8. 8
Causes of mechanical noise and vibrations
Bearing noise and vibrations
• Journal bearings / Sleeve bearings
• Fluid bearings
- Floating bearings – oil film bearings
- Air bearings
• Ball bearings / Roller bearings
- “simple” ball bearings
- ball bearings with squeeze film dampers
⇒ Roughness of sliding surfaces
⇒ Lubrication fault
⇒ Manufacturing faults
⇒ Instability of oil film in bearing
⇒ Manufacturing faults (sphericity, waviness)
⇒ Presence of dirt / lubrication fault
⇒ Resonance of outer ring (natural frequencies)
⇒ Alignment fault (mounting) / shaft resonances
⇒ Noise depends on and can be modified by
- Running speed
- Load
- Temperature
- Alignment fault
[Momono1999]
[Sterling2009]
Rotor response orbit (oil whirl)
Rotor response orbit (inner & outer oil whirl)

9. 9
Frequency content
Bearing noise and vibrations
• Flow-induced vibrations due to instability of oil film in bearings
- Nonlinear characteristics of stiffness and damping coefficients of oil-film bearings
- Oil whirl (case of full-floating bearings) at subsynchronous frequency
[Sterling2009]
Excessive unbalance Rotor misalignment Contact rub between rotor and bearings

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Bearing noise and vibrations
Frequency content
• Ball bearings
- Balls frequency  rotational frequency (FT) 𝑓𝑓𝑇𝑇 =
1
2
𝑓𝑓𝑅𝑅 1 −
𝐷𝐷𝑏𝑏
𝐷𝐷𝑐𝑐
cos𝛽𝛽
- Balls passage frequency on outer raceway (FPE) 𝑓𝑓𝑃𝑃𝑃𝑃 =
𝑁𝑁𝑏𝑏
2
𝑓𝑓𝑅𝑅 1 −
𝐷𝐷𝑏𝑏
𝐷𝐷𝑐𝑐
cos𝛽𝛽
- Balls passage frequency on inner raceway (FPI) 𝑓𝑓𝑃𝑃𝑃𝑃 =
𝑁𝑁𝑏𝑏
2
𝑓𝑓𝑅𝑅 1 +
𝐷𝐷𝑏𝑏
𝐷𝐷𝑐𝑐
cos𝛽𝛽
- Balls rotational frequency (FRB) 𝑓𝑓𝑅𝑅𝑅𝑅 =
𝐷𝐷𝑐𝑐
𝐷𝐷𝑏𝑏
𝑓𝑓𝑅𝑅 1 −
𝐷𝐷𝑏𝑏
𝐷𝐷𝑐𝑐
2
cos2
𝛽𝛽
- Flaw noise
- Contamination noise (due to dirt)
[Vijayraghavan1999]
[Momono1999]
[Augeix]StructuralfaultHandling

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Mechanical noise mitigation
Bearing noise and vibrations
• Modification of damaged ball bearing
• Use of chemical additives
• Use of vibration absorption or vibration isolation device
• Modification of rotating speed
• Use of alignment tools when mounting the motor
• Application of axial pre-load by means of coil springs
• Addition of elastic damping elements in bearing housing
• Application of shield or seal to prevent dirt from entering the bearing
• Dynamic rotor balancing
[Vijayraghavan1999]
[Tillema2003]

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Causes of aerodynamic noise and vibrations
• Air flow in electrical machine (high speed)  centrifugal fan
• Cooling system
- air (fan)
-> fan rotating with electrical machine
-> fan rotating independently
- water
- oil
[Guédel]
[Parrang2016]
[Vijayraghavan1999]
Examples of water jackets, from
[Satrustegui2017]
-> external pump
-> fluid flow and interaction with obstacles
Acoustic radiation
Natural convection
Forced convection
Shaft-
mounted
fan
Aerodynamic noise and vibration sources

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Frequency content
Aerodynamic noise and vibrations
• Mechanisms of flow noise generation
- Monopolar noise  harmonic noise
=> due to quick variations of flow rate imposed by obstacles in flow
- Dipolar noise  harmonic or broadband noise (depending on periodicity of load)
=> due to load fluctuations imposed by the fluid on obstacles
- Quadripolar noise  broadband noise
=> directly generated inside the flow due to shear strains induced by turbulences in the fluid
• Fan noise at characteristic frequencies
- Vortex frequency: 𝑓𝑓𝑣𝑣 = 0,185
𝑣𝑣
𝐷𝐷𝑓𝑓
- Fan blades frequency: 𝑓𝑓𝑓𝑓 = 𝑁𝑁𝑏𝑏
𝑁𝑁
60
- Cooling air passing through rotor ducts frequency: 𝑓𝑓𝑟𝑟𝑟𝑟 = 𝑍𝑍𝑟𝑟
𝑁𝑁
60
[Guédel]
[Parrang2016]
[Vijayraghavan1999]
Rotation speed (RPM)
Number of blades Rotation speed (RPM)
Number of rotor slots
Air stream velocity (m/s)
Diameter of the fan (m)

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Aerodynamic noise mitigation
Aerodynamic noise and vibrations
• Blade geometry (circular to aerofoil cross-section) => no more vortex frequency
• Minimum distance between fan blades and stationary obstacle
• Reduction of number of rotor vents and lining air chambers with sound absorbent insulation
• Unevenly spaced fan blades (caution with unbalance)
• Reduction of fan diameter
• Texturing on blades
• Use of porous material for fan blades
• Use of axial fan rather than radial fan
[Vad2014]
[Wang2016]
[Vijayraghavan1999]
[Mizuno2013]
Example of texture, from [Wang2016]

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Causes of magnetic noise and vibrations
• Dynamic magnetic forces apply to active materials (laminations, magnets, windings)
• Magnetic forces include magnetostrictive & Maxwell forces
• Magnetostriction can be neglected
• Maxwell forces tend to bring stator closer to rotor (minimum reluctance / maximum flux)
Electromagnetic noise and vibration sources
Magnetostriction forces
Maxwell / reluctance forces
[Laftman 1995]
see video at https://eomys.com/ressources/article/videos?lang=en

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Causes of magnetic noise and vibrations
• Maxwell force harmonics include the effects of
- pole/slot harmonics
- time harmonics (Pulse Width Modulation)
- saturation harmonics
- winding harmonics
- eccentricities harmonics
• Resonance is due to frequency and spatial distribution match of exciting
forces with stator/rotor structural modes
Electromagnetic noise and vibration sources
Noise harmonic analysis of a PMSM
with MANATEE software
resonance

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Frequency content
𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑓𝑓𝑠𝑠
1−𝑠𝑠 𝑍𝑍𝑟𝑟
𝑝𝑝
+ 0, ±2
Electromagnetic noise and vibrations
• Complex spectrum due to 2D phenomenon
- wavenumber r: space frequency along the airgap
- frequency f: time frequency
• Lowest wavenumbers give highest vibrations due to lower yoke stiffness
• Slotting effect in induction machines mainly occur at
r=0 r=+/-1 r=+/2
𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑟𝑟 − 𝑍𝑍𝑠𝑠 + 0, ±2𝑝𝑝
𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 2𝑢𝑢0 𝑓𝑓𝑠𝑠
• Slotting effect in permanent magnet synchronous machines mainly occur at
𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝐺𝐺𝐺𝐺𝐺𝐺 𝑍𝑍𝑠𝑠, 2𝑝𝑝
s slip
fs fundamental electrical frequency
p pole pair number
𝐺𝐺𝐶𝐶𝐶𝐶 𝑍𝑍𝑠𝑠, 2𝑝𝑝 = |𝑢𝑢02𝑝𝑝 + 𝑣𝑣0 𝑍𝑍𝑠𝑠 |
u0 minimum positive integer
v0 relative integer
GCD=Greatest Common
Divider
Ex: Zs=12 p=5 GCD=2=|1*10-1*12| -> u0=1, first excitation with r=2 occurs at 2fs
but GCD=2=|7*10-6*12| -> u=7, another excitation with r=2 occurs at 14fs
Ex: Zs=36 Zr=28 p=3 -> an excitation of wavenumber r=-2=28-36+6 occurs at fs(Zr/p+2)

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Frequency f
Wavenumbers r
r=Mc
2u0fs
2(u0+Zs/Mc)fs
2(u0-Zs/Mc)fs
Frequency spacing=
LCM(Zs,2p)fR
r=2Mc
4u0fs
Wavenumber spacing
=GCD(Zs,2p)
2(u0+2Zs/Mc)fs
2(2u0+Zs/Mc)fs
Ncfs/p
2Ncfs/p
-Ncfs/p
n=2
n=1
n=0r=0
• General pattern of harmonic forces in PMSM open-circuit conditions
Frequency content
Electromagnetic noise and vibrations GCD=Greatest Common
Divider
LCM=Least Common Multiple
Mc=GCD(Zs,2p)
Nc=LCM(Zs,2p)
NcMc=Zs2p
r=0 cogging torque/pulsating radial force
other radial & tangential force harmonic

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Transfer path analysis
Electromagnetic noise and vibrations
Wave-
number
Force
direction
Transfer path Description
r>0 Radial,
tangential
Air borne Radial circumferential deflection of the outer stator yoke
and frame or outer rotor (rotating in forced regime,
pulsating at resonance)
r=0 Radial Air borne Radial pulsating circumferential deflection of the stator
yoke and frame or outer rotor
r=0 Tangential
(cogging torque
/ torque ripple)
Structural borne Propagation of rotor torsional vibration to rotor shaft line
and gearbox mount, or bearing sleeves and outer stator
frame
r=0 Tangential
(cogging torque
/ torque ripple)
Air borne Deflection of the outer stator yoke and frame or outer
rotor following a unbalanced torsional mode due to
particular boundary conditions
r=1 Radial
(unbalance
magnetic pull)
Air borne Bending / tilting deflection of the outer stator frame or
outer rotor, in particular in clamped-free conditions
r=1 Radial
(unbalance
magnetic pull)
Structural borne Propagation of rotor bending vibration to rotor shaft line
and gearbox mount, or bearing sleeves and outer stator
frame
Axial Air borne Axial deflection of the end-shields

20. 20
Magnetic noise mitigation (general)
• Avoid resonance between magnetic forces & structural modes
(simulation recommended)
• Reduce asymmetries so tolerances on
- eccentricities
- magnet position / magnetization
- lamination roundness
Electromagnetic noise and vibrations
Effect of stator roundness on variable speed sound level using MANATEE
software (left: circular stator, right: elliptical stator shape)
Effect of rotor slot number on maximum noise of an
induction motor using MANATEE software

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Magnetic noise mitigation (magnetics)
• Skewing
• Pole shaping
• Modulation of pole width / position
• Modulation of slot width / position
• Notches
• Flux barriers
• Airgap increase
Electromagnetic noise and vibrations
Effect of a PMSM rotor skew angle on acoustic noise
(MANATEE software)
Use of rotor notch to mitigate acoustic noise
(MANATEE software)
Example of stepped-skew PMSM
rotor

22. 22
Magnetic noise mitigation (control)
• Spread spectrum switching strategies
• Harmonic current injection
• Load angle
Electromagnetic noise and vibrations
Magnetic noise mitigation (structural)
• Lamination geometry (static + natural frequencies)
• Damping
• Coupling between housing & lamination
• Structural spacers
Effect of harmonic current injection on noise level
(MANATEE software)
0 10 20 30 40 50 60 70 80 90 100
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
Stator yoke [mm]
Frequency[Hz]
Frequency variation of m=0 mode
Effect of yoke height change on breathing mode
natural frequency (MANATEE software)
[Masoudi2013][Rasmussen2001]

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ELECTRICAL
MODEL
ELECTROMAGNETIC
MODEL
STRUCTURAL
MODEL
ACOUSTIC
MODEL
Analytical Analytical PWM
generation
Extended
equivalent circuits
Saturation
coefficient
Numerical Circuit simulation
(ODE)
Analytical Permeance / mmf
winding function
Semi-
analytical
Subdomain models
Complex permeance
Conformal mapping
Numerical Non linear
electromagnetic FEM
Analytical 2D equivalent shell
deflections
2D/3D natural
frequencies with tooth
correction factors
Semi-
analytical
Green’s function for the
vibration response
SEA
Numerical Structural FEM
Analytical Equivalent radiation
efficiency
Semi-
analytical
Dipole field expansion
SEA
Numerical Acoustic FEM/BEM
Fully analytical
Fully numerical
Hybrid (preferred)
Output: rotor & stator currents Output: time and space
distribution of radial &
tangential airgap flux density
Output: radial vibration of the
outer surface
Output: acoustic noise
spectrum
strong circuit coupling
Modelling and simulation of electromagnetic noise & vibrations
Overall simulation workflow (weak coupling)

24. 24
Available electromagnetic NVH simulation software
VWP Virtual Work Principle
MT Maxwell Tensor

25. 25
Available electromagnetic NVH simulation software

26. 26
Available electromagnetic NVH simulation software

27. 27
Conclusions on available software solutions
• All electromagnetic FEA software now propose a coupling with NVH tools
• Electromagnetic FEA software only offer a direct coupling approach with structural mechanics
• Multiphysic software like Comsol / Ansys Workbench do not give ready-to-use multiphysic simulation
workflow
• MANATEE is the only software with:
- indirect coupling approach (Electromagnetic Vibration Synthesis) to speed up simulation time
- semi-analytical models and model hybridation to be used in early design phase
- an integrated multiphysic simulation process

28. 28
Limitations of fully numerical approaches
• Variable-speed vibroacoustic simulation including switching effects up to 10 kHz can take several days of
simulation
• Numerical noise (remeshing ripple) can appear and sound power level may be wrong due to spurious
inter-harmonics (continuous sound spectrum Vs discrete excitations)
• Missing validation of magnetic force calculation & mesh to mesh projection techniques
[Pellery2012]
[LeBesnerais2016]
[Magnet website]
[Peters2011]

29. 29
Recommended simulation workflow
• Use of semi-analytical models (subdomain + equivalent cylinder) for the variable speed NVH
simulation of electric machines during early electromagnetic design loops
Airgap angle s
[rad]
0 2 4 6 8
B
r
[T]
-2
-1
0
1
2
radial airgap flux
MANATEE FEA (FEMM)
MANATEE permeance/mmf model
Wavenumber
0 20 40 60
Magnitude[T]
0
0.2
0.4
0.6
MANATEE permeance/mmf model
MANATEE FEA (FEMM)
Airgap angle s
[rad]
0 1 2 3 4 5 6 7
B
r
[T]
-1.5
-1
-0.5
0
0.5
1
1.5
radial airgap flux
MANATEE FEA (FEMM)
MANATEE subdomain model (exact, periodic)
Airgap angle s
[rad]
0 1 2 3 4 5 6 7
B[T]
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
tangential airgap flux
MANATEE FEA (FEMM)
MANATEE subdomain model (exact, periodic)
Wavenumber []
0 5 10 15 20
B
r
[T]
0
0.2
0.4
0.6
0.8
1
radial airgap flux FFT
MANATEE FEA (FEMM)
MANATEE subdomain model (exact, periodic)
Wavenumber []
0 5 10 15 20
B[T]
0
0.02
0.04
0.06
0.08
tangential airgap flux FFT
MANATEE FEA (FEMM)
MANATEE subdomain model (exact, periodic)
Comparison between FEA and subdomain electromagnetic
methods in MANATEE software (left: SPMSM, right: SCIM)
• Use of finite element models (electromagnetics + structural mechanics) combined with Electromagnetic
Vibration Synthesis algorithm in detailed mechanical design phase

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Electromagnetic Vibration Synthesis (from MANATEE software)
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 harmonic
loads for
wavenumbers r=0,
±2, ±4 …
STRUCTURAL FREQUENCY
RESPONSE FUNCTIONS
r=0 r=2
ELECTROMAGNETIC
VIBRATION SYNTHESIS
Complex FRFs (radial &
tangential) for each
wavenumber r
Vibration and noise spectrograms
Operational Deflection Shapes
Modal contribution
Radiating surface velocities
• 2D or 3D external FEA software (Flux,
Jmag, Maxwell, Magnet etc…)
• Manatee 2,5D analytic model
• Manatee 2,5D semi analytic model
• Manatee 2,5D numerical model (FEMM)
• 3D external FEA software (Optistruct,
Ansys)
• Manatee 2,5D analytic model
• Manatee numerical model (GetDP)
Torque/speed
curve (variable
speed control law)
SPECTROGRAM
SYNTHESIS

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Examples of experimental validation with obtained with MANATEE software
Sound level during a run-up
(experiments with gearbox+water-
cooling+converter harmonics)
Sound level during a run-up
(MANATEE simulation without
converter harmonics)
~10 seconds on a laptop
TESTS MANATEE
Motor A
Motor B
-40 dB
-> Semi-analytical models of MANATEE software can be successfully applied during
first electromagnetic design loops, even when neglecting saturation and housing effect

32. 32
• A good vibro-acoustic design can be carried without skewing, thus improving electric machine efficiency
• Magnetic noise & vibrations should be considered at the early electromagnetic design stage
• Numerical models can be accelerated using Electromagnetic Vibration Synthesis algorithm in detailed
design phase of electric motors
• Experiments should always be used to improve the simulation model accuracy (e.g. quantification of modal
damping)
Conclusions

33. 33
THANK YOU FOR YOUR ATTENTION
www.eomys.com
Q&A SESSION
For other EOMYS webinars, go to https://eomys.com/ressources/webinaires/?lang=en

34. 34
REFERENCES
[Vijayraghavan1999] P. Vijayraghavan, R. Krishnan, Noise in electric machines: a review, IEEE Transactions on Industry Applications
35(5), 1999. (Warning this reference is not reliable for electromagnetically-excited noise & vibrations)
[Guédel] A. Guédel, Bruit des ventilateurs, Techniques de l’ingénieur.
[Wang2016] Y. Wang et al., Numerical investigation of the passive control of cavity flow oscillations by a dimpled non-smooth
surface, Applied Acoustics 111, 2016.
[Vad2014] J. Vad et al., Aerodynamic and aero-acoustic improvement of electric motor cooling equipment, J. Power and Energy
228(3), 2014.
[Parrang2016] S. Parrang, Prédiction du niveau de bruit aéroacoustique d'une machine haute vitesse à reluctance variable, Thèse
ENS Cachan, 2016.
[Mizuno2013] S. Mizuno et al., Development of a totally enclosed fan-cooled traction motor, IEEE Trans. Indus. Appl. 49(4), 2013.

35. 35
REFERENCES
[Sterling2009] J. Sterling, Influence of induced unbalance on subsynchronous vibrations of an automotive turbocharger, 2009.
[Nguyen2015] H. Nguyen-Schäfer, Rotordynamics of automotive turbochargers, 2015.
[Kirk2011] R.G. Kirk et al., Turbocharger vibration show nonlinear jump, JVC 18(10), 2011.
[Kirk2010] R.G. Kirk et al., Turbocharger on-engine experimental vibration testing, JCV 16(3), 2010.
[Kirk2006] R.G. Kirk et al., Stability analysis of a high speed automotive turbocharger, IJTC 2006.
[Ishida2012] Y. Ishida and T. Yamamoto, Linear and nonlinear rotordynamics, Wiley 2012.
[Bekemans2006] M. Bekemans, Modélisation des machines électriques en vue du contrôle des efforts radiaux, PhD thesis, UCL, 2006.
[Tillema2003] H.G. Tillema, Noise reduction of rotating machinery by viscoelastic bearing supports, PhD thesis, Twente University,
2003.
[Vijayraghavan1999] P. Vijayraghavan, R. Krishnan, Noise in electric machines: a review, IEEE Transactions on Industry Applications
35(5), 1999.
[Momono1999] T. Momono and B. Noda, Sound and Vibration in Rolling bearings, Motion & Control 6, 1999.
[Augeix] D. Augeix, Analyse vibratoire des machines tournantes, Techniques de l’ingénieur.
[Bertolini2012] T. Bertolini and T. Fuchs, Vibrations and noises in small electric motors, Faulhaber, 2012.

36. 36
REFERENCES
[Laftman1995] L Laftman “The contribution to noise from magnetostriction and PWM inverter in an induction machine” PhD
dissertation, University of Lund, 1995
[Rasmussen2001] P. O. Rasmussen, J. Andreasen, and J. M. Pijanowski, “Structural Stator Spacers-the Key to Silent Electrical
Machines,” Thirty-Sixth IAS Annu. Meet. Conf. Rec. 2001 IEEE Ind. Appl. Conf., vol. 1, no. C, pp. 33–39, 2001.
[Masoudi2013] K. Masoudi, M. R. Feyzi, and A. Masoudi, “Reduction of Vibration and Acoustic Noise in the Switched Reluctance
Motor by Using New Improved Stator Yoke Shape,” in 2013 21st Iranian Conference on Electrical Engineering (ICEE), 2013, pp. 1–4.
[Pellery2012] Pellerey, P., “Etude et Optimisation du Comportement Vibro-Acoustique des Machines Electriques, Application au
Domaine Automobile”, PhD thesis, Université de Technologie de Compiègne, Compiègne, France, 2012
[LeBesnerais2016] J. Le Besnerais, "Fast prediction of variable-speed acoustic noise due to magnetic forces in electrical machines,"
2016 XXII International Conference on Electrical Machines (ICEM), Lausanne, 2016, pp. 2259-2265. doi:
10.1109/ICELMACH.2016.7732836
[Peters2011] S. Peters and F. Hetemi, « Airborne Sound of Electrical Machines using Symmetric Matrices in ANSYS 14”, ANSYS
Conference