ACOUSTIC NOISE AND VIBRATIONS OF ELECTRIC POWERTRAINS …€¦ · ACOUSTIC NOISE AND VIBRATIONS OF...

© EOMYS ENGINEERING 2013- www.eomys.com

ACOUSTIC NOISE AND VIBRATIONS OF ELECTRIC POWERTRAINS

Focus on electromagnetically-excited NVH for automotive applications and EV/HEV

1

LE BESNERAIS Jean

[email protected]

Note: this presentation is based on extracts of EOMYS technical traininghttps://eomys.com/services/article/formations?lang=en

Part 2 Characterization of electromagnetic NVH in electric motors

© EOMYS ENGINEERING 2013- www.eomys.com 2

NVH RANKING OF ELECTRIC MOTOR TOPOLOGIES


Review of electric traction-related NVH issues

• Traction motor magnetic noise depend on torque density (full electric Vs hybrid) and topology

• Dominant NVH excitation frequencies depend on topology

• Some secondary NVH effects of electric traction:

- Air-cooled self-ventilated traction motors introduces additional aerodynamic noise

- Water-cooled traction motors can create hydrodynamic and magnetic noise due to pump motor

- Cooling system of the electric batteries can create additional noise

- Power Split Device of HEV introduce gear whine


0

222/, S

t

R

t

S

r

R

rr BBBBt

0/, S

t

R

t

S

r

R

rt BBBBt

• In linear case the Maxwell stress can be expressed as

S

tr

R

trtr BBB ,,,

• The space and time harmonic « content » (zero magnitude harmonics) of the radial and tangential stress are the same

• Three group of harmonics can be defined in both radial and tangential stress:

(HSS) stator flux harmonics interactions

(HRR) rotor flux harmonics interactions (null for induction machines at no-load)

(HSR) stator and rotor flux harmonics (null for induction machines at no-load)

• Depending on the topology and the operation point, the dominant harmonic groups differ:

For IM and most vibration/noise issues can be explained based on stator flux harmonics HSS only𝐵𝑟,𝑡𝑅 <<𝐵𝑟,𝑡

𝑆

Excitation harmonics in IM

R

trB ,

S

trB ,

rotor radial/tangential airgap field

stator radial/tangential airgap field


Load (generator or motor) No-load (null average torque) Rotor-driven

SCIMWRIM

HSS+HRR+HSR magnetic noiseMechanical noiseAerodynamic noise

HSS magnetic noiseMechanical noiseAerodynamic noise

Mechanical noiseAerodynamic noise

• Summary of harmonic fields (S=stator, R=rotor) depending on operating mode:


• The space and time harmonic « content » (zero magnitude harmonics) of the radial and tangential stress are the same

• Three group of harmonics can be defined in both radial and tangential stress:

(HSS) stator flux harmonics interactions (null in open circuit)

(HRR) rotor flux harmonics interactions (always present for PMSM)

(HSR) stator and rotor flux harmonics (null for PMSM at open circuit)

• Depending on the topology and the operation point, the dominant harmonic groups differ:

For SM but vibration/noise issues generally comes from HRS (open circuit NVH issue) and HSR (NVH issue due to concentrated winding)

𝐵𝑟,𝑡𝑅 >>𝐵𝑟,𝑡

𝑆

0

222/, S

t

R

t

S

r

R

rr BBBBt

0/, S

t

R

t

S

r

R

rt BBBBt

• In linear case the Maxwell stress can be expressed as

S

tr

R

trtr BBB ,,,

R

trB ,

S

trB ,

rotor radial/tangential airgap field

stator radial/tangential airgap field

Excitation harmonics in SM


Load (generator or motor) No-load (null average torque, Iq=0)

Open-circuit

PMSMWRSM



HRR magnetic noiseMechanical noiseAerodynamic noise

• Summary of harmonic fields (S=stator, R=rotor) depending on operating mode:

• For PMSM above maximum voltage there are therefore 3 different control strategies:

- connected to DC link with fixed V=Vmax, giving energy to DC link (corresponds to regenerative mode of in traction), involves switching of inverter

- connected to DC link with V=Vmax but keeping null torque with Iq=0, involves switching of inverter

- open-circuit with V>Vmax, no current sent to DC link, no inverter switching

• These three strategies will not give same acoustic noise


• In order to identify the frequency content of the different force harmonics groups, one method is to use Fourier series developement (infinite summation of progressive rotating waves) and decompose the flux in permeance / mmf product (equivalent of law for magnetics)

• Note : the theoretical background for the application of the same permeance function on rotor and stator mmfis weak, but this affects the harmonics magnitude and not the spectra content

• To simplify the process all the Fourier development are represented using the following wave notation in the airgap linked to stator steady frame

𝑎 𝑡, 𝛼𝑠 =

𝑛,𝑟

ො𝑎𝑛𝑟 cos 2𝜋𝑛𝑓𝑅𝑡 + 𝑟𝛼𝑠 + 𝜑𝑛𝑟 =

𝑛,𝑟

{𝑛 𝑓𝑅 , 𝑟} = {𝑓𝑖 , 𝑟𝑖}𝑖∈𝐼

• By convention, frequencies are always positive and the sign of the spatial frequency gives the rotation direction

• The elementary wave rotates in anti clock wise direction for ri>0

• Mechanical rotation frequency of the wave is fi/ri

• Magnitude and phase information in hidden to be able to simplify wave calculations using

{𝑓𝑖 , 𝑟𝑖}. {𝑓𝑗 , 𝑟𝑗} = {𝑓𝑖±𝑓𝑗 , 𝑟𝑖±𝑟𝑗} {𝑓𝑖 , 𝑟𝑖} = {−𝑓𝑖 , −𝑟𝑖}


• The space harmonic is not defined with respect to the electrical angle but to the mechanical angle

• Using this notation the fundamental flux density wave is {fs , p} (or {fs , -p} depending on rotation direction) travelling at fs/p

• r is preferably called wavenumber, the naming « space order » being reserved for the multiplication factor between r and p (for fundamental r=p wavenumber, space order is 1)

• Mechanical rotor frequency is fR =fs /p (SM) or fR =(1-s)fs /p (IM)

• Spectrum « content » of magnetic force = spectrum of vibration velocity = noise spectrum

• Considering a force wave {f, r} we therefore directly hear f


Permeance « slotting » harmonics:o r=ksZs, f=0 for stator slotting (Ps)o r=kr2p, f=kr2pfR for rotor inset magnets (Pr)o r=ksZs+kr2p, f=kr2pfR for rotor / stator slotting

interactions (Psr)

Armature winding mmf harmonics:o r=𝜍𝜏qshs+p, f=fs for fundamental (Fs)o higher time harmonics due to PWMo space subharmonics or harmonics due to

winding types

Magnet mmf harmonics:o r=(2hr+1)p, f=(2hr+1)fs (Fr)

• Radial and tangential flux density have same harmonic contents

• The combination of high wavenumber harmonics of flux density can create low order of radial force

• The largest noise and vibration come from « low wavenumber » forces

airgap widthstator slot geometrymagnet groove geometryeccentricitiesslot / pole combinationsaturation, magnetic wedge

magnet shapingmagnetization typepole shiftingdemagnetization

winding patternslot / pole combinationPWM strategyslot openingshort circuit

• Summary of main design parameters and harmonics (PMSM)


Permeance « slotting » harmonics:o r=ksZs, f=0 for stator slotting (Ps)o r=ksZs+krZr, f=krZrfR for rotor / stator slotting

interactions (Pr)

Armature winding mmf harmonics:o r=(2pqshs+1)p, f=fs for fundamental (Fs)o higher time harmonics due to PWM

Rotor mmf harmonics:o r=hrZr+p, f=νrfR +fr (Fr)

airgap widthslot geometryeccentricitiesslot and pole numberssaturation, magnetic wedge

rotor slot numberrotor slot openingbroken barslip / load state

winding patternslot / pole combinationPWM strategyslot openingflux levelshort circuit

• Summary of main design parameters and harmonics (IM)

• Radial and tangential flux density have same harmonic contents

• The combination of high wavenumber harmonics of flux density can create low order of radial force

• The largest noise and vibration come from « low wavenumber » forces


Most significant magnetic force harmonics stator reference frame (SM)

Name Case Wavenumber r Frequency f Comments

HrrA =PsF0rP0Fr s=0ν r=2phr+pνr=p

ksZs+ sRp+ 2 sR(2phr+p)=0

sRfs + 2 sR(2hr+1)fs

=nrLCM(Zs,2p) fR

Pole / slot interaction (nr in N*)ks and hr varies with nr

HrrB =PsF0rP0Fr s=0ν r=2phr+pνr=p

ksZs+ sRp+ 2 sR(2phr+p)=+/-mrGCD(Zs,2p)


=nrLCM(Zs,2p) fR +/-2mrfs

Pole / slot interaction (nr in N*)ks and hr varies with nr and mr

HrrC =PsF0rP0Fr s=0ν r=2phr

+pνr=p

ksZs+ sRp+ 2 sR(2phr+p)=2p(hr+1) -ksZs


=2(hr+1)fs

Rewriting without involving GCD / LCMhr>=1ks fixed to 1(|hr| generally>>1 if Zs>>p)

• Obtained combining permeance stator harmonics (Ps) with fundamental rotor mmf (F0r) and rotor mmfharmonics (Fr)

• All the force harmonics are proportional to 2fs

• 2fs vibration can include the effect of several different wavenumbers

• The force harmonics are all rotating force waves, except the 0 order ones at multiples of Nc=LCM(Zs,2p)

• « Pole slotting lines » (open circuit case) : PsF0rP0Fr


• Example of a 48s8p IPMSM (Prius type) in open circuit case [C35]

• Pulsating forces (r=0) at 12fs are created by the interactions of rotor mmf m1p and m2p such as m1+/-m2=12p

• In particular H48= 12fs involves 13p and 11p rotor mmf harmonics


f0+2u0fs

f0=Nc fR

=LCM(Zs,2p)fR

f0-2u0fs

2u0fs

pole slotting

other lines 2fc2fc -2fs 2fc +2fsPWM

slotting PWM

dynamic eccentricity

fR

static eccentricity

Frequency

2fs

r 0 ±

1

r 0+

±1

r 0-±

1

r 0 =

0

r 0+=

r 0+

Mc

r 0--

1

r 0-+

1

r 0+

1

r 0-1

r 0+-1

r 0++

1

r 0-=

r 0-

Mc

• each group has « replicates » around the multiples of NcfR and of the switching frequency• the magnitude of symmetical lines is symbolic, it depends on the wavenumber & control• for the PWM lines the symmetry of magnitude around the switching frequency holds• the same pattern holds for both tangential and radial forces

Force

2fs

r=2

pfundamental

r 1 =

0

r 1+=

r 1+

2p

r 1-=

r 1-2

p

f0

f0 f0

2fc - fs -f0

r 0 r 0

2fc + fs +f0

f0-4u0fs

r 0-

2M

c

f0+4u0fs

r 0+

2M

c

1D schematics of SM force/vibration/noise harmonics


• The frequency content is theoretical and doest not take into account destructive interferences

• Particular value of the slot openings and pole arc width can cancel some groups of harmonics in permeance or mmf

• The load angle can change the 0-th order radial force harmonics magnitude

• The lowest non-zero wavenumber in open circuit is given by GCD(Zs,2p) for both tangential and radial forces

• It is also the case for distributed winding at full load

• Both r=0 tangential (cogging, ripple torque) and radial (pulsating radial force) frequencies are proportional to LCM(Zs, 2p)

• For concentrated windings (alternate teeth or all tooth wound), the winding pattern generates r=1 unbalanced pull if and only if Zs=2p+/-1 (this gives GCD(Zs,2p)=1) [C1]

• Static eccentricity only introduces new force wavenumbers, while dynamic eccentricity introduces both new wavenumbers and new frequencies (can be seen on a spectrogram)

Note that GCD(Zs,2p) LCM(Zs,2p)=Zs2p

Conclusions on the NVH excitations of synchronous machines


Pole/slot open circuit interaction, example 3 (WRSM) [C6]

• Zs=48, p=2

• LCM(48,4)/2=24 ->{24fs,0} (HrrA)

• {24fs+2fs,2p}={26fs,4} (HrrB)

• {24fs-2fs,-2p}={22fs,-4} (HrrB)383.3 Hz

16.7 Hz

{24fs,0}

{48fs,0}

m=0m=2m=4 {22fs,4} {26fs,-4}


Pole/slot open circuit and load interaction, example 9 (BPMSM for traction) [C36]

• Zs=48, p=4

• GCD(48,8)=8

• LCM(48,8)/4=12


Claw pole synchronous machines: most significant magnetic force harmonics


0 nr2pqsfR Zs=2pqsms

+/-kp (nr2pqs+/-kp)fR

• Force harmonics are not proportional to 2fs

• Pulsating radial force as cogging torque is at multiples of stator slot number for integral winding

• The force harmonics are rotating force waves, except the 0 order ones at multiples of Nc=LCM(Zs,2p)

• Lowest force wavenumber is given by GCD(Zs,p) and not GCD(Zs,2p), it is therefore given by p for integral winding


p=6 Zs=36 qs=3 m=1

r=0 f=ZsfR

r=-p f=(Zs-p)fR

r=p f=(Zs+p)fR

r=0 f=ZsfR

r=-p f=(Zs-p)fR

r=p f=(Zs+p)fR

p=8 Zs=48 qs=3 m=1

p=6 Zs=72 qs=6 m=1

p=6 Zs=36 qs=3 m=1

[C42]


Induction machines: most significant magnetic force harmonics

• « Pure slotting lines » at no-load: PsF0sPrF0s

Ex: Zr=36, Zs=48, p=2-> kr=4 and ks=3 give a slotting line of order 4=4Zr-3Zs+2p of frequency fs(4Zr/p+2)

Zs Zr : stator and rotor slot numbersfs : supply frequencyp : number of pole pairskr, ks : strictly positive integers (rank of permeance harmonics)s: slip

-> sidebands around the rotor slot passing frequency


HssA =PsFsPrFs νs=νs krZr-ksZs -2pkrZr-ksZs

krZr-ksZs +2p

fs (krZr(1-s)/p-2)fs (krZr(1-s)/p)=krZrfR

fs (krZr(1-s)/p+2)

ks>=0kr>=0


Sound Power Level at variable speedCase of a squirrel cage induction machine Zr=96 Zs=84 p=4

Frequency fs(Zr/p+2)Order Zr-Zs+2p=-4

Frequency fs(Zr/p+4)Order Zr-Zs+4p=+4

WITHOUT SATURATION

WITH SATURATION


• « Pure PWM lines » at no-load: P0FsP0Fs

Ex: Zr=38, Zs=48, p=2-> main asynchronous PWM lines are 2fc

of order 0 and 2fc+/-2fs of order 4

Zs Zr : stator and rotor slot numbersfs : supply frequencyp : number of pole pairsfc : carrier frequency

r r rfff rf


[C19]

Voltage/current


f+= f0+2fs

f0=Zr fR

f-=f0-2fs

2fs

slotting

winding

saturation2fc2fc -2fs 2fc +2fs

PWM

slotting PWM

dynamic eccentricity

fR

static eccentricity

Frequency

2fs

2fs r 0 r +

r ++

2p

r --2

p r -

f0 +4fsf0 -4fs

• each group has « replicates » around the multiples of the rotor passing frequency and of the switching frequency• the magnitude of symmetical lines is symbolic, it depends on the wavenumber & control• for the PWM lines the symmetry of magnitude around the switching frequency holds• the same pattern holds for both tangential and radial forces

Force

2fs

r=2

pfundamental

r 0=

Zr-

k sZ

s

r 0+=

r 0+

2p

r 0-=

r 0-2

p

r 1 =

0

r 1+=

r 1+

2p

r 1-=

r 1-2

p

2fc - fs -f0

r 0 r 0

2fc + fs +f0

r 0 ±

1

r 0+

±1

r 0-±

1

r 0--

1

r 0-+

1

r 0+

1

r 0-1

r 0+-1

r 0++

1

f0

f0 f0

© EOMYS ENGINEERING 2013- www.eomys.com

Analysis of acoustic noise and vibrations due to PWM

• PWM strategy influence the frequency content and magnitude of PWM force harmonics (mainly 0 and 2p wavenumbers)

• Different PWM strategies:

- Intersective Symmetrical or asymmetrical ISPWM

- Space Vector Modulation (equivalent to intersective symmetrical in term of frequency content) SVMPWM

- Direct Torque Control DTC

- Randomization techniques RPWM

• For traction application the following strategies are often used during starting from 0 to max speed

- « asynchronous » ISPWM: carrier frequency fc fixed independently of speed fs

- « synchronous » ISPWM: fc = m fs with progressive reduction of the ratio to avoid high switching losses

- calculated PWM strategy (optimized switching angles for torque ripple and loss reduction), n CA per a quarter period gives an equivalent switching frequency fc = (2n+1) fs

- « full wave » ISPWM: the input voltage is a square pulse, inducing main exciting force at 6fs 12fs etc. of order 0


• The ISPWM current harmonics vary with speed due to increasing voltage / modulation ratio during the constant torque phase

[E16]

[E4]

• Main PWM exciting force frequencies therefore vary with speed

• Depending on the carrier shape (symmetrical, forward or backward asymmetrical) the frequency content of voltage and thereof current harmonic also change


• Same conclusions apply to SVM, equivalent to intersective PWM

• Main PWM forces have 0 wavenumber with sidebands of wavenumber 2p

• These lines are separated with 2fs , the frequency gap is increasing with speed

• This makes the roughness vary with speed, worst case is a 75 Hz gap


[C24]


Load (generator or motor)

No-load (null averagetorque)

Rotor driven by anothermachine (open circuit) / run-down

IM Stator AC winding field (Id) AC winding field (Id) None

Rotor AC winding field (Iq) None None

PMSM Stator AC winding field (Iq) AC winding field (Id) None

Rotor PM DC field PM DC field PM DC field

WRSM Stator AC winding field (Iq) AC winding field (Id) None

Rotor DC winding field DC winding field None

• Magnetic noise & vibrations are due to varying magnetic fields

• What magnetic fields are present in electrical machines ?

Effect of operating conditions on Maxwell forces in electrical machines


• For IM & WRSM magnetic forces are null if the machines is current-free (on both stator & rotor sides)

• For all electrical machines with permanent magnet (PMs), e.g. surface PM synchronous machines, somesources of magnetic fields are present even if the machine is current-free

• When there is no PM, the nature of noise & vibration (magnetic or non magnetic) can be easily determined

• PM machines can be noisy even in open circuit due to Maxwell forces


Main market electric motors topologies for EV / HEV

WRSM(Renault)

[R4]


Main market topologies

[R4]


• Concentrated winding gives higher efficiency and higher compacity but are more challenging for NVH due to higher space harmonic

[R4]

Winding topologies for SM


• The most challenging machine is the Switched Reluctance Machine (control strategy is very important)

• NVH behaviour of SynRM is still a reasearch topic

• NVH behaviour of WRSM and PMSM are equivalent, but the WRSM offers more control possibilities

• IM have lower torque ripple than SRM & PM so they are more robust to structural borne noise due to eccentricities

NVH comparison

• IM Vs PMSM: for PMSM magnetic noise starts at LCM(Zs,2p) (H48) whereas for IM noise it occurs at H44 -> magnetic force harmonics occur in similar frequency ranges for IM and SM with distributed windings

[R4]


SCIM

SPMSM

IPMSM

SRM

SyRM

WRSM

• Ranking by MACCON [R12]


Currentharmonics

Rotor permeanceharmonics

Stator permeanceharmonics

Stator mmf spaceharmonics

Rotor mmf spaceharmonics

Overall NVH (qualitative !)

SCIM + + (Zr can be chosen)

+ + + (negligible even at full-load)

-

IPMSM + ++ + + (distributed)- (concentrated)

++ (shaped poles)+ (V shape)

++

SPMSM + ++ + + (distributed)- (concentrated)

+ (shaped magnets)- (unshaped

magnets)

-

WRSM + -(fixed to 2p)

+ + (distributed)- (concentrated)

+ (shaped pole-shoe)

+

SRM -- --(fixed to 2p)

- -- NA --

SynRM + + (fixed to 2p)

+ + + (optimized flux bariiers)

+

• Ranking by EOMYS

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