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Fast Prediction of Variable-Speed Acoustic Noise and Vibrations due to Magnetic Forces in Electrical Machines

Authors:
Φ
Abstract -- This paper presents a new multiphysic model and
simulation environment for the fast calculation and analysis of
acoustic noise and vibration levels due to Maxwell forces in
variable-speed rotating electrical machines.
In the first part, some numerical methods for the prediction
of electromagnetic noise are analyzed and compared to
analytical or semi analytical techniques.
In the second part, a new coupling of electrical,
electromagnetic and vibro-acoustic models based on analytical
and semi-analytical modeling techniques is presented. This
model is validated by comparing simulation results to
experimental results on several electrical machines at variable
speed, including surface permanent magnet (SPMSM), interior
permanent magnet (IPMSM) and squirrel cage induction
machines (SCIM). The main resonances and noise levels are
correctly estimated by the models implemented in MANATEE
®
simulation software, and the calculation time at variable speed
varies from one second to a few minutes including harmonics up
to 20 kHz.
Index Terms—Acoustic noise, Vibration, Electromagnetic
forces, Numerical Simulation, Electrical machines
I. N
OMENCLATURE
Symbol Description
f frequency of an airgap permeance, mmf, flux or
magnetic pressure harmonic wave
f
R
mechanical frequency [Hz]
f
s
fundamental supply frequency [Hz]
mmf magnetomotive force [A]
p pole pair number (2p poles)
r wavenumber of an airgap permeance, mmf, flux or
magnetic pressure harmonic wave
Z
r
rotor slot number
Z
s
stator slot number
FEA Finite Element Analysis
GCD Greatest Common Divider
IPMSM Interior Permanent Magnet Synchronous Machine
LCM Least Common Multiple
SCIM Squirrel Cage Induction Machine
SPL Sound Pressure Level
SWL Sound Power Level
WRSM Wound Rotor Synchronous Machine
II. I
NTRODUCTION
A. Sources of noise and vibration in electrical machines
HE
vibro-acoustic design of electrical machines can be as
important as its electromagnetic or thermal design in an
increasing number of applications. This is the case of rotating
machines working close to human presence in industrial
applications (e.g. elevator, conveyor motors), household
Φ
J. Le Besnerais is with EOMYS ENGINEERING, 121 rue de Chanzy,
Lille-Hellemmes, France (website: www.eomys.com, e-mail:
contact@eomys.com).
appliances (e.g. HVAC, electric curtains), transportation (e.g.
ships, trains, electric cars, pedal-assist bicycles) and energy
(e.g. wind turbine generators). More generally, the vibration
and acoustic noise levels of electrical machines have to be
controlled and reduced as part of their global environmental
impact.
Noise and vibration sources of electrical machines are usually
classified in mechanical, aerodynamic and magnetic sources
[1]. Mechanical noise and vibrations can come from bearings,
gears and brush commutators, whereas aerodynamic noise is
due to air pressure periodic variations coming for instance
from mounted fans or air-gap vortices due to slotting effects ;
in high speed machines, these aerodynamic forces can also
excite the structural modes of the machine and give high pitch
noise [2].
Magnetic vibration and audible noise are due to the
deflections of the magnetic circuits of the electrical machines
under magnetic forces; magnetic forces are defined as forces
arising from the presence of a magnetic field, which can be
due to permanent sources as in permanent magnet
synchronous machines, or induced by some current sources as
in induction machines. Two types of magnetic forces occur in
electrical machines: magnetostrictive and Maxwell force [3].
Qualitatively, magnetrostrictive forces occur in magnetic
sheets and tend to shrink the material along the field lines,
whereas Maxwell forces are mainly located at the lamination
interface with air and globally tends to bring the stator closer
to the rotor (law of minimal reluctance); both phenomena are
quadratic function of the flux density and can result in radial
deflection of the yoke and acoustic noise. Although the
scientific debate is still not closed on the respective
contribution of these forces in the different electrical machine
topologies and power ranges [4][5][6][7], this paper only
focuses on Maxwell forces; experimental results presented in
this paper and author’s experience confirm that there is no
need to model magnetostrictive effects to account for main
electrical noise issues occurring in both asynchronous and
synchronous machines, even when considering power ranges
from W to MW.
A. Noise and vibration issues due to magnetic forces in
electrical machines
Electromagnetically-induced acoustic noise can be a key
contributor to the global sound power level of electrical
machines for several reasons. Firstly, due to the strong
harmonic nature of magnetic forces in both time and space
domains, magnetic noise is characterized by strong tonalities
(emergence of a given harmonic above the background noise)
T
Fast Prediction of Variable-Speed Acoustic
Noise and Vibrations due to Magnetic Forces in
Electrical Machines
J. Le Besnerais
and usually occur in the most sensitive frequencies of the
human ear (1 to 10 kHz). This makes it sound particularly
unpleasant, especially as some progress is made on the
reduction of the other broad-band noise sources (e.g. use of
water cooling technology instead of fans). Secondly, the
design optimization of electrical machines with respect to
cost, weight and efficiency tend to minimize materials,
leading to thinner yoke width and increased vibration levels.
The search for low-cost and high power density machines
requires to make a trade-off between electromagnetic and
NVH performances.
After manufacturing, the redesign of a noisy converter-fed
machine due to electromagnetic forces is generally expensive
and time-consuming. When electromagnetic noise is not due
to converter harmonics and is only related to fundamental
current, for squirrel-cage machines, a new rotor with a
different slot number is generally manufactured [8][9], or the
noisy rotor is skewed of one slot pitch, the stator
manufacturing being more expensive; for permanent magnet
synchronous machines (PMSM), a new magnet geometry, a
new stator slot number with a new winding architecture, or a
stepped-skew of the magnets are different techniques that can
be applied to reduce the noise and vibration levels. When
electromagnetic noise is coming from converter harmonics,
these design changes are useless and the main solution relies
on a change of the switching frequency or the switching
strategy [25]. Last-minute software modifications are not
possible for applications requiring high safety levels (e.g.
electrical traction); moreover, the change of the supply
strategy affect the loss distribution between the converter and
the machine, and can have side effects like the increase of
torque ripple harmonics and temperature rise.
Due to the lack of calculation models, these post-
manufacturing techniques are generally applied empirically,
without having enough time to identify the root cause of the
noise issue, and do not lead to expected improvements.
Besides that, they require to re-run the electromagnetic design
process and sometimes lead to a loss of electromagnetic
performances: as an example, the skewing technique lowers
the fundamental torque and the electromagnetic efficiency.
Some models must therefore be developed to estimate
acoustic noise and vibration levels at an early design stage.
Once the electrical machine is manufactured, some
specialized post-processing techniques must also be
developed to help understanding the noise and vibration
generation process, identify its sources and reduce them with
passive or active methods while keeping initial
electromagnetic performances.
These models must be multi-physics: an electrical model is
necessary to calculate converter current harmonics
responsible for high frequency magnetic forces and noise; an
electromagnetic model is necessary to calculate Maxwell
stress distribution in the machine; a structural model is
necessary to calculate the lamination dynamic deflection
under magnetic forces; an acoustic model is necessary to
calculate the sound power level and sound pressure level of
the machine.
This paper therefore reviews the different methods for
calculating noise and vibration due to magnetic forces,
especially numerical methods. A semi-analytical method is
then presented and validated, showing accuracy comparable
to FEA methods while achieving high calculation
performance.
II.
O
N THE USE OF
FEA
METHOD FOR VIBRO
-
ACOUSTICS OF
ELECTRICAL MACHINES
A. Analysis of some FEA-based vibroacoustic studies
A first method to estimate the noise and vibration levels due
to magnetic forces is to use a fully numerical model based on
Finite Element Analysis (FEA). To answer this need for
vibroacoustic virtual design of electric motors, most
commercial electromagnetic FEA software (e.g. Flux, Jmag,
Maxwell) already propose a coupling with some structural
FEA software; alternatively, some integrated multiphysics
environment (e.g. Ansys Workbench, Comsol Multiphysics)
can be used to carry integrated electromagnetic and
vibroacoustic numerical calculations. In this part, some
articles using these techniques are reviewed and their
conclusion are analyzed.
In [15] a Simulink model is coupled to 2D magnetodynamics
with Maxwell, and a 3D structural model is solved under
Nastran using a modal decomposition approach. Although
Simulink allows to obtain the full frequency spectrum of
stator and rotor currents, only 3 harmonics are then effectively
included in the FEA electromagnetic simulation. The solving
time of the 2D electromagnetic model made of 12,418 first
order triangular elements is not given (it is necessarily larger
than 45 min given in [14]), but the structural simulation time
is 45 min up to 3 kHz on a high performance workstation for
a single speed. The acoustic simulation under Actran is not
presented in the paper. This means that this type of simulation,
presented as a “fast numerical coupling method”, can easily
reach two days of calculation at variable speed (56 hrs in
[14]), without coupling with acoustics and assuming that the
coupling between Maxwell2D and Nastran has been
automated. The largest identified harmonics in the magnetic
forces and in the stator vibrations are {f=2f
s
, r=2p=4}
(clockwise direction), {f= ± 12f
s
, r=0}, and {f=-22f
s
, r=2p=4}
(anti-clockwise direction) (see Fig. 6).
Fig. 1: Stator and housing deflection under magnetic forces at 2f
s
(r=4)
,
12f
s
(r=0) and 22f
s
(r=4) [15]
The first vibration wave is due to the squared fundamental
flux density creating the largest harmonic force its
frequency is too low to excite the 2p lamination mode, but it
results in high magnitude forced vibrations. It is not linked to
slot / pole interaction. The second vibration wave is due to
stator current harmonics, the combination of stator flux waves
{f=-5f
s
, r=p} and {f=7f
s
, r=p} giving rise to a pulsating radial
and tangential Maxwell force wave {f=12fs, r=0}, which is
not linked to slot / pole interaction. The third vibration is
given by r=GCD(Zs,2p)=2p=4 and f=LCM(Zs,2p)f
R
-2f
s
=22f
s
and is linked to stator slot / rotor pole interactions. This
expression can be derived analytically as shown in [18][19].
The same type of harmonic force is present at the other
frequency LCM(Zs,2p)f
R
+2f
s
=26f
s
which is also mentioned in
[12].
[12] presents another FEA-based study on the same machine
at variable speed. The 2D electromagnetic FEA based on
Maxwell does not include any current harmonics, but includes
rotor eccentricity. The strong electrical circuit coupling is
ignored, although it may affect magnetic forces as noted in the
paper. The electromagnetic simulation time is not given, but
it is necessarily higher than the 45 min per speed of [14] due
to the eccentric model. The 3D structural simulation time is
45 min per speed as in [14].
A resonance at 4600 Hz is found with the 44
th
harmonic of the
rotation frequency (f=22f
s
) due to 4
th
circumferential mode of
the lamination, and a second resonance is found with the 48
th
harmonic (f=24f
s
) due to the 0
th
mode (breathing mode) of the
lamination at 5700 Hz.
Provided that the natural frequencies are calculated using
FEA or analytical methods, these two resonances could be
predicted analytically. The first force wave is the one
previously identified coming from a pole/slot interaction, the
second one is the pulsating (r=0) radial and tangential force
wave occurring at multiples of LCM(Zs,2p)f
R
=24f
s,
also due
to pole/slot interaction [13].
Due to high computation time in structural FEA, the speed
discretization step is only 1000 rpm, but it is not small enough
to correctly capture resonance effects. Indeed the minimum
speed steps ΔN
s
is given by (for a synchronous machine) [8]
( )
160
0
p
f
r
s
N
ξ
=
where f
r0
is the lowest natural frequency of the structure with
damping
ξ
. This is illustrated in Figure 2.
Figure 2 : Illustration of the impact of the speed discretization step on the
estimation of the maximum sound or vibration level
In this example where the lowest natural frequency is 400 Hz,
assuming a 1% damping the width of the peak at resonance is
4 Hz and the associated speed variation is 120 rpm. To capture
the maximum vibration level correctly, the speed step should
be chosen much smaller than 120 rpm.
More generally, the total number of simulation steps depends
also on the speed range of the machine:
N

=

− 

∆
=

− 



The larger is the electrical machine, the lower is the natural
frequency and the higher is the number of simulations to be
run. Similarly, the wider is the speed range of operation and
the larger is the number of simulations to run. Outer rotor of
PMSG have lower damping due to missing winding: to assess
their vibroacoustic behavior with 10 rpm variation and 0.15%
damping with a first mode at 50 Hz, one obtains Ntot= 200
simulations. For a high speed small BLDC machine going
from 0 to 100000 rpm with a lowest mode at 5 kHz and a 2%
damping due to stator damping one obtains Ntot=1000
simulations.
[14] is a similar FEA study on the same machine, still using
Maxwell2D and Nastran. The aim of the paper is to study the
effect of current induced harmonics on noise and vibration.
The 2D electromagnetic model has 3862 second order
triangular elements, and the quasi-static electromagnetic
solver takes 45 min for each speed. The coupling between
electromagnetic mesh and structural mesh takes 5min per
speed when optimized, due to large file (30000 nodes) writing
and reading processes. The Nastran 3D model, probably
similar to the one used in [15][12], has 497455 elements,
2305183 DOF, and 7056 nodes in which magnetic forces are
applied. The overall calculation time of a vibration
spectrogram with 100 rpm speed discretization, this time
meeting the criterion given by (1), is then 56 hours. It is shown
that a torsional mode at 800 Hz is excited by harmonics at
f=6f
s
, 12f
s
and 24f
s
; the stator mode r=4 is excited by
harmonics at f=20f
s
and 26f
s
. Simulation results show that the
effect of stator current harmonics due to slotting and winding
effects do not create new resonances and only shift the overall
vibration level of 17 dB independently of speed. The authors
do not provide any explanation for this large difference.
Flux [9] proposes a coupling with LMS Virtual Lab [11],
Nastran or Ansys. This coupling with Nastran has been
developed in the framework of AVELEC project [16][17] on
the same machine, a WRSM with p=2 and Zs=48.
[17] investigates the use of Flux to calculate the vibroacoustic
behaviour of this same WRSM. It is shown that a tradeoffs
must be done between calculation time (linked to rotor
angular step) and accuracy. It is advised to use regular mesh
of rotor and stator airgap bands, and make them coincident
using a rotor angular step proportional to the mesh angular
width. However, this means that the maximum frequency of
the force spectrum is proportional to the speed, giving only
results at 500 Hz at 1000 rpm (see Fig. 3).
Fig. 3: Calculated spectrogram from [17]
Even with this method, up to 4 dB of variations is obtained
below 10 kHz due to numerical errors. The choice of the
airgap radius to calculate the Maxwell stress is also discussed
and significant variations of airgap flux harmonic magnitude
are observed when the integration path is situated below the
middle of airgap; the path should be taken at the airgap middle
or closer to the stator. An experimental comparison between
calculation and tests is done, but no absolute comparison is
possible due to missing color legend. The same resonances as
previously identified based on analytical considerations are
found.
[30][31][32] investigates the use of COMSOL Multiphysics
to calculate the variable speed electromagnetic noise of an
induction machine. They report having to simplify the
problem in order to reduce the high computing time of the
electromagnetic fields (several hours for one operating
speed). Besides that, although COMSOL is supposed to be an
integrated multiphysic environment, a special tool had to be
developed by the authors in Matlab to make the harmonic
conversion of the Maxwell stress tensor, and be able to run
the structural and acoustic models in the frequency domain.
Finally, different structural models (with and without
housing) had to been defined due to the uncertainty on the
coupling between the stator lamination and frame. The
conclusion of the work presented in [32] is the ability of the
multiphysic numerical tool to account for a resonance at 1500
rpm.
The elliptic mode (m=2) natural frequency of the stator stack
can be estimated close to 1100 Hz using semi-analytical
models of [29]. The induction machine is a 4-pole (p=2) with
Zs=48 stator slots and Zr=38 slots. The largest magnitude
slotting harmonic magnetic force has then a wavenumber
r=Zr-Zs+4p=-2 due to saturation, which occurs at frequency
f=fs(Zr(1-s)/p+4)=1150 Hz at no-load based on analytical
considerations presented in [24]. A strong resonance therefore
occurs at nominal speed due to the excitation of the stator
stack ovalization mode with a saturated magnetic force
harmonic.
Jmag software also proposes a coupling with LMS Virtual
Lab for the calculation of magnetic vibration and noise.
In [36] Jmag is used in 2D for the magnetic force calculation
of a 18/6 SRM. The structural calculation is carried using
modal superposition with Nastran NX based on harmonic
loads. The acoustic model is solved up to 4000 Hz using AML
(Automatically Matched Layer) algorithm. The acoustic
impact of airgap length and winding layout is then studied.
The analysis is carried at fixed speed; no calculation time nor
comparison with experiments is given.
Following the same method, [36] presents a fully numerical
vibroacoustic analysis of a PMSM up to 4 kHz at a fixed
speed. It is demonstrated that the definition of the boundary
layer leads to 5 to 10 dB variation depending on the
frequency. No comparison with experiments is given.
Ansys [39] also proposes a methodology to calculate the
electromagnetically-induced vibration and noise levels in
electrical machines.
[33][34] presents a full electromagnetic and vibro-acoustic
calculation using Ansys environment for the calculation of
magnetic vibrations and Sysnoise for the calculation of
acoustic noise. The time varying magnetic forces are applied
to a 3D structural model, and the structural response is
calculated using modal superposition method. The acoustic
pressure is then calculated in the frequency domain using
BEM.
Some comparison are done between calculated and measured
vibration and acoustic spectra. The full numerical calculation
only contains 7 harmonics up to 6 kHz, whereas measured
spectra are very rich. The vibration and sound pressure level
magnitude matches with less than 5 dB on the calculated 6
harmonics. The paper concludes that the magnetic noise
excitations are proportional to the stator slot passing
frequencies, and that the highest peaks corresponds to the
excitation of some structural modes. The computing time is
not reported, but acoustic calculations are carried at a single
speed.
In [35] Ansys is also used to calculate the vibration response
of a stator using force wave decomposition. The modal
decomposition is stored and the vibration synthesis is
performed. The full process at variable speed takes a “couple
of hours” on a quad-core PC with 16 Gb RAM, but it depends
on the complexity of the magnetic loads and the calculation
time does not include magnetic force calculation with
Maxwell, nor acoustic calculations. Some comparison are
shown with experiments in terms of vibration, showing
excellent agreement with measurements, with up to 5 dB
difference in magnitude.
B. Conclusions on FEA advantages and drawbacks
Previous examples show that FEA calculation results are
sensitive to the meshing process of the electromagnetic,
structural and acoustic models, contrary to analytical or semi-
analytical techniques such as subdomain models [21]. The
high sensitivity of torque calculation [27] naturally applies to
radial magnetic forces as shown in [13], and therefore to the
resulting noise and vibrations. In acoustic FEA, the first order
elements (with linear shape functions) dimensions have to be
chosen such that the biggest one is at least six times smaller
than acoustic wavelength [38], which strongly limits the
maximum frequency that can be captured. At low speed,
assessing high frequency electromagnetic behavior requires
higher computation time.
Besides that, previous case studies show that the complexity
of the vibroacoustic behavior of studied machines is
sometimes limited, and that the use of FEA is not necessary
to identify the main harmonic forces and resulting resonances
with the main lamination modes.
To conclude, the advantages of numerical models are
A priori high accuracy compared to analytically based
techniques, although there is still a lack of valuable
comparisons between FEA and experiments in terms of
noise and vibration levels at variable speed
modeling of complex structural boundary conditions on
the motor frame and the effect of non-linear damping
viscoelastic materials
possibility to directly work on the “real” geometry based
on CAD files, and to model any type of topology contrary
to analytically-based techniques which necessarily
address a limited class of topologies (e.g. circular frames)
modeling of non-linear electromagnetic effects in electric
machines where saturation has a significant vibroacoustic
role
strong circuit coupling, allowing for instance to include
the vibroacoustic effect of eccentricity in equalizing
currents and induced current harmonics due to slotting.
The limitations of numerical models are
the prohibitive computation time of electromagnetic FEA
solver when either considering PWM effects up to 10
kHz, asymmetrical machines (e.g. eccentricities) or low
symmetry machine with a high number of poles and slots,
strong circuit coupling, or 3D effects (e.g. skewing)
the prohibitive computation time and representativity
limitation of structural FEA when considering vibrations
above 8 kHz and a speed discretization step small enough
to capture the maximum noise and vibration levels
the difficulty to estimate the high frequency vibroacoustic
levels at low speed, due to time-frequency limitations
(e.g. 500 Hz at 1000 rpm for [17])
the time consuming set-up of the coupling between the
physics (e.g. mesh interfaces, force projection, time to
harmonic conversions, load application), and the
resulting increase of calculation (5 min per speed to
couple Maxwell2D and NASTRAN in [14])
the time consuming set-up of the structural model (e.g.
homogenization techniques for the laminated core, resin
and copper mixture, coupling techniques for frame to
lamination interface)
the prohibitive computing time for use in an early design
stage as a relative comparison and not an absolute
evaluation (for instance, to help choosing the best slot
number or to optimize the magnet pole geometry),
the missing physical and mathematical validation of
electromagnetic force to mechanical mesh projection
(e.g. with energy conservation).
III. MANATEE
MULTIPHYSIC MODELS
A. Introduction
MANATEE [29] initially stands for Magnetic Acoustic
Analysis Tool for Electrical Engineering: it is a simulation
software dedicated to the fast electromagnetic design of
electrical machines including the evaluation of 3D
electromagnetic forces, vibrations and acoustic noise due to
Maxwell forces at variable speed. The topologies handled by
MANATEE include induction machine, surface, inset or
buried permanent magnet synchronous machines, with outer
or inner rotor.
It is an integrated multiphysic tool whose simulation process
is summarized in Fig. 4. Assuming a weak coupling between
structural mechanics and electromagnetics the electrical
currents are first calculated based on equivalent circuits.
Based on rotor and stator current waveforms, the
electromagnetic module calculates the airgap flux
distribution. The structural module consists in projecting the
Maxwell stress on the stator or rotor structure, and evaluating
the resulting dynamic deflections. The acoustic module
finally calculates the radiated sound power and pressure
levels.
Fig. 4: MANATEE simulation process
B. Electrical model
The equivalent circuits are based on similar analytical models
developed in [8][20] for the extension to time and space
harmonics. The difference is that the equivalent circuit
parameters (e.g. leakage inductance, magnetizing inductance,
back emf) can be either calculated using subdomain
electromagnetic models or with the freeware FEMM [26]. The
fast calculation time of subdomain models allow to strongly
couple the electrical circuit with electromagnetics [21].
C. Electromagnetic models
MANATEE offers the possibility to use three different
electromagnetic models: permeance / mmf models,
subdomain models [21] and finite element models with
FEMM [26]. These three models are compared in the
following table.
The permeance / mmf model allows to qualitatively account
for saturation [23], faults and asymmetries (eccentricities,
uneven airgap [22]), but also notches, and can easily include
the effect of PWM harmonics [25]. The accuracy of the
permeance / mmf model can be improved using an automated
coupling with FEMM; the rotor mmf of an interior PMSM can
be calculated accurately using FEMM, or the effect of
magnetic wedges on the permeance [23].
D. Structural model
The structural model includes a projection of magnetic forces
on the modal basis of the structure to calculate their effect on
the radial deflections of the outer yoke.
Similarly to the electromagnetic model, MANATEE offers
the possibility to work either with analytical models, or with
FEA. The software is indeed coupled to the open-source
software GetDP for structural calculations (modal analysis,
frequency response functions), but also to commercial FEA
software such as Altair Optistruct.
The analytical model is based on an equivalent cylinder,
where the effect of tangential forces on radial deflections of
the yoke are included using an equivalent bending moment as
in [28]. The natural frequencies are computed analytically
using similar models as in [8].
A. Acoustic model
The acoustic model uses an analytical model of radiation
efficiency as presented in [8]. [28] indeed demonstrates that
there is no need of higher accuracy radiation efficiency
models.
B. Numerical performances
A special care has been taken to optimize the numerical
implementation of MANATEE models. All the
electromagnetic domain calculations are done in the time and
angular domain with matrix computations.
A variable speed calculation can be done smoothly with a very
small speed step using synthetized spectrograms.
Spectrogram synthetization algorithm consists in evaluating
magnetic forces at a single speed, and identifying the rotation
direction and the speed of the harmonics and the evolution of
their magnitude with speed. This way the full noise and
vibration spectrogram can be synthetized using the modal
basis calculated at fixed speed. The variable speed noise level
of an induction machine up to 20 kHz can be calculated in less
than 1 second on a 2GHz single core laptop. The validation of
spectrogram synthetization is presented in Fig 5 where it is
favorably compared to several single speed simulations.
Fig. 5: Validation of the fast synthetization spectrogram algorithm
Besides that, time and space symmetries of the airgap field
are automatically identified to reduce matrix sizes. Some
field reconstruction techniques are also applied to avoid
calculating the full fields.
IV. E
XPERIMENTAL VALIDATION
In this part, some experimental validations of MANATEE
simulation environment are provided. It should be noted that
these experiments are done in “real conditions”: no semi-
anechoic chamber (sound pressure level may be affected by
reverberation field), background noise (load machine, cooling
units), real eccentricities and supply harmonics. However,
these conditions are more representative of the industrial
practice: very few electrical machine manufacturers have the
possibility to test their machines in “ideal conditions” using
anechoic chambers. A favorable comparison of simulation
results to in-field measurement, far from laboratory
conditions, can therefore be seen as a proof of robustness.
The first comparison is given in Fig. 6 on a IPMSM traction
machine with concentrated winding run at 50 % partial load
up 7000 rpm. Two main resonances are observed in both
simulation and tests. MANATEE simulation shows that the
first one is only linked to rotor magnetic field (rotor pole mmf
/ stator slot harmonic interaction), whereas the second one is
linked to a stator subharmonic field due to tooth winding.
Both resonances occur with the ovalization mode of the
lamination stack, leading to 125 dB. This two huge resonances
can be avoided based on a few seconds of calculations without
any call to finite element methods. The redesign of this
machine with MANATEE led to 40 dB reduction in sound
pressure level.
Fig. 6: Comparison between experiments (top) and MANATEE simulation
(bottom) on two different IPMSM (motor A and motor B). Experiments
include gearbox, cooling and converter noise while simulation only contain
magnetic noise under sinusoidal supply
The second comparison focuses on the frequency
characteristics of noise in Fig. 7 in a large induction machines
for pump application. A strong resonance occurs due to the
interaction between a slotting line and the 4
th
lamination mode
of the stator. In this case, a redesign of the rotor slot with
MANATEE gave 15 dB reduction in sound pressure level.
The calculation time of the full noise spectrum up to 12.4 kHz
at variable speed takes a few seconds.
Fig. 7: Comparison between experimental SPL spectrogram (top) and
MANATEE simulation (bottom) on a SCIM. Experiments include gearbox,
cooling and converter noise while simulation only contain magnetic noise
under sinusoidal supply
V. C
ONCLUSION
The advantages and drawbacks of numerical techniques for
the prediction of variable speed noise and vibration due to
magnetic forces in electrical machines are underlined.
It is shown that the vibroacoustic behavior of an electrical
machines can be quantified using analytical or semi-analytical
methods in a very short computing time with the same order
of magnitude of accuracy than fully numerical methods (~5
dB). This allows the machine designer to avoid main
resonance issues during the early design phase; one can also
easily sweep pole per slot combinations or run magnet shape
optimization in order to minimize both torque ripple and
acoustic noise. Besides that, the significant sensitivity to
meshing process of finite element techniques is avoided using
subdomain models for electromagnetics and analytical
models for acoustics.
VI. A
CKNOWLEDGMENT
The authors would like to thank Prof. M. Hecquet from
L2EP laboratory, Ecole Centrale de Lille, France, for his
support in validating some of the models of MANATEE
software.
VII. R
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VIII. B
IOGRAPHIES
J. Le Besnerais currently works in EOMYS ENGINEERING as an R&D
engineer on the analysis and reduction of acoustic noise and vibrations in
electrical systems.
Following a M.Sc. specialized in Applied Mathematics (Ecole Centrale Paris,
France) in 2005, he made an industrial PhD thesis in Electrical Engineering
at the L2EP laboratory of the Ecole Centrale de Lille, North of France, on the
reduction of electromagnetic noise and vibrations in traction induction
machines with ALSTOM Transport. He worked from 2008 to 2013 as an
engineer in the railway and wind industries (Alstom, Siemens Wind Power,
Nenuphar Wind) on some multiphysic design and optimization tasks at
system level (thermics, acoustic noise and vibrations, electromagnetics,
structural mechanics and aerodynamics). In 2013, he founded EOMYS
ENGINEERING, a company providing applied research and development
services including modeling and simulation, scientific software development
and experimental measurements.
... The magnetic forces are numerically computed using MANATEE® software [9][12] to validate the previous theoretical study and then show the impact of the current load angle on the magnetic forces and induced noise and vibrations level. ...
... The vibroacoustic model of MANATEE is based on semianalytical models. MANATEE results are validated thanks to finite elements analysis and experimental measurements (Figure 2) on a SPMSM with concentrated windings [12]. ...
... The magnetic forces are numerically computed using MANATEE® software [9][12] to validate the previous theoretical study and then show the impact of the current load angle on the magnetic forces and induced noise and vibrations level. ...
... The vibroacoustic model of MANATEE is based on semianalytical models. MANATEE results are validated thanks to finite elements analysis and experimental measurements (Figure 2) on a SPMSM with concentrated windings [12]. ...
... It means that there might be various flux density waves with the same pole pair number, but with different rotational speeds. A typical case in converter-fed synchronous machines is the production of a flux density wave with the same spatial order as the fundamental, but with a frequency around the switching frequency [24]. The main spatial harmonic itself (i.e., seventh for this hydrogenerator) has a frequency equal to the fundamental frequency (i.e., 50 Hz here). ...
Article
This paper investigates the effects of converter-fed operation on magnetic forces and vibration in a hydrogenerator. The variable-speed hydrogenerator (in a pumped-storage power plant) is a large synchronous machine with fractional-slot windings. In this study, the generator is connected to either resistive load or voltage source converter. Loading cases include two-level converter and three-level neutral-point-clamped converter and the carrier frequency is equal to 450 Hz and 1050 Hz. Using electromagnetic finite element (FE) analysis, airgap flux density harmonics are analyzed in different loading cases. In addition, electromagnetic torque and variations in the rotor field current are also studied. Using Maxwell stress tensor, radial force density distribution in the airgap is investigated and the effect of converter-fed operation on different radial force harmonics are studied. Moreover, structural analysis and electromagnetic vibration synthesis are presented to investigate the effect of converter harmonics on the stator vibration.
... As mentioned before, only the radial modes with "low" circumferential orders will generally have an influence of noise and vibrations [11], particularly the modes (0,0), (2,0) and (4,0), as the vibration level decreases as a function of 1 ⁄ . However, for this type of machine with relatively large diameter and relatively thin yoke, it may be necessary to consider circumferential orders up to = 14 (pole number), especially because the PWM introduces magnetic forces of order = 0 and = 2 ( is pole pair number). ...
... Each model can be either analytical or numerical (FEA) for a better compromise between computation time and accuracy. MANATEE's principles are explained more in details in [2]. ...
... MANATEE ® software [13] (Magnetic Acoustic Noise Analysis Tool for Electrical Engineering) is dedicated to the fast optimal electromagnetic design of electrical machines including acoustic noise and vibration due to Maxwell forces. The evaluation of the airgap flux density can be based on analytical models (permeance/magnetomotive force and winding function approaches [14], [16][18]). Some analytical models allow to calculate the radial vibration of the yoke, and the resulting acoustic noise following similar analytical models as presented in [19], [20]. ...
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