Study of Radial Forces of Permanent Magnetic Synchronous Motor

8/9/2019 Study of Radial Forces of Permanent Magnetic Synchronous Motor

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Study of Radial Forces of Permanent Magnetic

Synchronous Motor

Claudia Martis Florin Pop Piglesan

Florin Jurca Claudiu Oprea

Universitatea Tehnica Cluj!apoca" Romania

claudia#martis$emd#utcluj#ro florin%&'(pop$yahoo#com

fjurca$mail#utcluj#ro Claudiu#Oprea$mae#utcluj#ro

Abstract The present work aims to show an comparative study of the radial forces behavior

analysis of a PMSM. For this work we used a single topology, an PMSM with ! slots and " pole pairs. To

analy#ed the radial forces, we have changed the airgap dimension, magnet shape and stator windings. The

radial forces delivered by the simulations with $%mag Studio and $%mag &esigner are e'ported in Math(ab

to process the results.

). )*T+&-T)*

Recent developments in rare earth permanent magnet )PM* materials and po+er electronics have created ne+

opportunities for design construction" and application of permanent magnet synchronous motors )PMSMs*# The

PMSMs are preferred over other motors used for ac servo drives due to their high efficiency" high tor,uetocurrent

and tor,ue -tovolume ratios" compact structure" and fast dynamic response# These motors are adopted in several

residential and industrial applications# .o+ever" many of such applications re,uire minimum tor,ue ripple" and

reduced vi/ration and acoustic noise#

Servo motor technology has moved in recent years from conventional 0C or t+ophase 1C motors drives to

ne+ maintenancefree /rushless three phase PMSM drives for motor applications +here ,uic2 response" light

+eight" and large continuous and pea2 to,ues are re,uired# The tor,ue produced /y these machines has a pulsating

component" +hich varies as a function of the rotor position" in addition to the dc component#

The tor,ue pulsation are 2no+n as tor,ue ripple# The shape of the tor,ue +aveform" thus" the fre,uency

content of the +aveform are influenced /y several factors related to motor design and construction# 1 conse,uence

of introducing PMs in the rotor is tor,ue pulsation even in the a/sence of any stator e3citation" this tor,ue is 2no+n

as cogging tor/ue#

The harmonics in the 45MF due to design imperfections also introduce tor,ue pulsations# The tor,ue ripple

content in PMSMs must /e improved through cogging tor,ue and 45MF harmonics reduction for smooth operation

of the motor#
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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Mechanical vi/ration and noise is mainly due to /earings" their defects" journal ovality" sliding contacts" /ent

shaft" rotor un/alance" shaft misalignment or rotor eccentricity" couplings etc# The rotor should /e precisely

/alanced as it can significantly reduce the vi/ration# The rotor un/alance causes rotor dynamic vi/ration and

eccentricity" +hich in turn results in noise emission from the stator" rotor" and rotor support structure# 1gain" the

rotor eccentricity causes un/alanced magnetic pull in the airgap that leads to+ard vi/ration#

)). +0&)0(F+1S)*PMSMS

The acoustic noise in PM machines is lo+er compared to s+itched reluctance and induction machines" yet

,uieter performance is desired in automotive and ro/otics applications# !oise and vi/ration of the electromagnetic

origin dominates in lo+ to medium po+er PM machines# The electromechanical energy conversion due to an

interaction /et+een the magnetic fields of PMs and armature conductors ta2es place in the airgap of these

machines# 1s a result of this interaction a strong electromagnetic force field e3ists /et+een the rotor magnets andthe stator teeth# This force field can /e decomposed into tangential and radial force components at any point in the

airgap#

The radial force density or pressure can /e +ritten as6

)%*

+here 47nand 47tare the normal and tangential components of the airgap magnetic field density# 1s the tangentialcomponent is much smaller than the normal component of the airgap magnetic field density" the magnetic pressure

results as6

)&*

The airgap magnetic flu3 density can /e +ritten as6

( ) ( ) ( )[ ] ( )t,Bt,Bt,B rsn += )'*

+ith 4s)8"t*94r)8"t* the stator9rotor magnetic field density for uniform airgap" as function of angle and time" and

:7)8* the relative permeance of the airgap#

The stator magnetic field density of a threephase symmetrical +inding fed +ith a /alanced current system

)considering only the fundamental of the supply source* can /e +ritten as6

( ) ( ) ( )[ ]tBtBtp tnrmp ""&

%"

&&

;

=

( ) ( )

0

2n

rmp2

tBtp

,

,

( ) ( )

=

=

1k6

ss ptcosBt,B


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))). 1(1T+M02*1T) 0*0(3S)S -S)*2 $%M02

The machine under study is a PMSM +ith & stator slots and B rotor poles t+olayer +inding" are analyGed for

/oth ;#@mm and %mm airgap length )Fig#%*#The main geometrical data of the machine are given in Ta/le H#

T14I5

M1H!5OM5TRHC1I01T1OFT.5STU0H50M1C.H!5S

a* /*Fig# %# & slots ' pole pairs field lines for6 a* % mm /* ;#@ mm

From fig#% it can /e deducted that the distri/ution is uniform in /oth cases#The flu3 density distri/ution is

comparatively analysed at tK;#;%B< s#

a* /*

Fig# & slots ' pole pairs9'


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The magnetic flu3 density for the motor +ith % mm airgap siGe has a ma3imum value of %#;@ T and for the

motor +ith ;#@ mm airgap siGe has a ma3imum value of %#& T#

Fig# ' Magnetic Flu3 0ensity

The airgap magnetic field density provides valua/le information on the electromagnetic machine /ehavior

)electromagnetic tor,ue" cogging tor,ue" /ac2emf" etc* /ut also on other aspects as thermal and vi/roacoustics#

The airgap magnetic field distri/ution for load regime" as +ell as the electromagnetic tor,ue developed /y the

motor is presented in Fig#


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The Space harmonic components of !odal Forces are given in Fig# @#

Fig# @# Space harmonics spectrum of the radial forces !oIoad regime

1 richer harmonic content can /e noticed for the ;#@ mm airgap length machine" +ith a higher value of the

amplitude and more harmonics" the % thand &Eth is missing from the % mm airgap length" in conclusion +ith a

smaller airgap length" +e have to,ue ripples and increased harmonics#

1nother regime of this study" that +e collect results is rated load# Hn this regime +e can notice that the

.armonic 1mplitude is smaller" than no load regime" and on the % mm airgap length is present the % thand &Eth

harmonic" +hich are missing from noload regime#

Fig# B# Space harmonics spectrum of the radial forces RatedIoad regime


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The time depending +aveform of the radial force for a virtual pro/e mounted on the stator tooth having the

coordinates )&@#@e'" ;* is given in Fig# " for /oth ;#@ and % mm airgap length#

Fig# # Time harmonic spectrum of the radial forces !oIoad regime

Hn Ta/le & is represented a comparative values of 1mplitude and Fre,uency /et+een the airgap length results#

Ne can notice that Time .armonics results has no impact and no major different values /et+een this part of

simulation +or2#

Ta/le & 1mplitude and Fre,uency results

H

Time 7armonics

0irgap lenght 8,9 mm 1irgap lenght % mm

Fre,uency 1mplitude Fre,uency 1mplitude

'


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0ifferent to space harmonics" the .armonic 1mplitude has different values for /oth regimes of +or2# For %

mm airgap length ratedload " the amplitude is smaller than the other regime /ut the same length and for ;#@ mm

airgap length ratedload " the amplitude is /igger than noload regim#

Fig# D# Time harmonic spectrum of the radial forces RatedIoad regime

1nother part of our +or2" represents the magnet shape# Hn our simulation +e change the edge of magnet to

study the influence of them on space and time harmonics# The simulation is made only for ;#@ airgap length no

load regime# Fig# E represents the shape of the magnets that +e used in our test simulation#

a* /*

Fig# E# Magnetic Shape a* rectangular /* Oval


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The Space harmonic components of !odal Forces are given in Fig# %;#

Fig# %;# Space harmonics spectrum of the radial forces !oIoad regime +ith Oval Magnets

From the spectrum +e can deduced that the harmonics have the same order li2e the other results"

+ith rectangular magnets /ut the amplitude on the % st" @thand %%th order is a little /it /igger comparative

+ith the others results#

The Time harmonic components of !odal Forces are given in Fig# %%#

Fig# %%# Time harmonic spectrum of the radial forces !oIoad regime +ith Oval Magnets


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@#

Study of Radial Forces of Permanent Magnetic Synchronous Motor

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