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Permanent Magnet Synchronous Motor (PMSM)
Design
Part 1 – General Considerations
Permanent Magnet (PM) Motor
Characterized by permanent magnets on rotor
Known for its simplicity and low maintenance
No copper loss on rotor High efficiency
Exploded View of a PM Motor
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines 2nd Edition, p. 44, Motor Design Books LLC, 2010.
Inner Rotor Possibilities (1)
surface radial magnet
surface parallel magnet
breadloafmagnet
ring magnet
Inner Rotor Possibilities (2)
(e) IPM in Toyota Prius
Toyota Prius Hybrid Electric Vehicle (HEV)
1. Four cylinder combustion engine;2. Generator/starter;3. Electric Motor;4. Power split device (PSD)
2
3
J. F. Gieras, Permanent Magnet Motor Technology -Design and Applications, 3rd Edition, p. 282, CRC Press, 2010.
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines 2nd Edition, p. 34, Motor Design Books LLC, 2010.
Segmented Magnets in Large PM Rotor
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines 2nd Edition, p. 94 & 602, Motor Design Books LLC, 2010.
Rotor Skew
stepped magnet
Magnetization Profile
parallel magnetization radial magnetization
radial sine magnetization sine angle or sine direction magnetization
most popular
Halbach Array (1)
R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives, p. 25-30, CRC press, 2010.
Halbach Array (2)
FEA
Halbach Array (3)Airgap Flux Density
Rotor is outside
Stator Volume and Size
0
2
VT
lD
The unit for D and L is inch.
30 4 ~ 5 in / (ft lb) for 10hp or more (water cooled)V
Typically3
0 8 ~ 9 in / (ft lb) for 10hp or less (air cooled)V
If we design D=L, we have the stator bore (inner) diameter estimated
31
0 )(TVDestimated
We can pick up D close to Destimated.
m
outPT
Stator Core Design
(1) ,,
iic
effpkg
iic
corepkcore lkPd
lDBlkd
B
(2) ,
iis
effpkgs
iis
toothtooth lkt
lBlkt
B
)( ,0 effspkgaeiaegefftooth lBdrBl
pkgeff
aeaepkgeff
P
aisageff
ole pitchper half pgapcore
BlPD
dBP
lD
drBl
,
2/
0 ,
/
0
,
)cos(22
)(
Take toothpkcoress BBt 8.0 ,5.0 ,
PDdc 6.1
Effect of Pole Number on Yoke Flux Density
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines 2nd Edition, p. 106, Motor Design Books LLC, 2010.
Finite Element Analysis
with the same dc
Number of Turns per Coil
pkgaepkgaerated NfNfV ,,,ˆ44.4ˆ2
PDlB pkg
pk,2
1.1/ˆawa NkN
sdpw kkkk
where
DlBqkfCV
Npkgwe
ratedc
,
,
221.1
Na is the number of series turns per phase of armature windingC is the number of parallel circuits of armature winding
CPqNN ca /
Consider leakage flux
Stator Slot Design
SD
s
3 7s s st d t
0.4 0.6s s st
0 (0.1 ~ 0.5)s sb b
General Consideration
sdst
s
0sb 0sd 1sd
Define s s sb t
0 (0.1 ~ 0.5)s sd b
1 (0.1 ~ 0.5)s sd b
Stator Conductor Size
Stator current density
a
ratedacoppers S
CIJ
/,,
where Sa is stator (armature) conductor cross section area and can be determined from the above formula together with:
2,
2 A/cm 800400A/cm :cooled-Air coppersJ
coppers
ratedaa J
CIS
,
, /
Permanent Magnets
Samarian Cobalt (SmCo) Operating temperature of up to 350ºC 2nd strongest rare earth magnet
Neodymium Iron Boron (NdFeB) Operating temperature of up to 150ºC Strongest rare earth magnet
From Yeadon – Handbook of Small Electric Motors
Permanent Magnet Properties
Rotor Peripheral Speed
The maximum allowable peripheral speed of the rotor is a central consideration in machine design. With present-day steel alloys, rotor peripheral speeds of 50,000 ft/min (or about 250 m/s) represent the design limit.
1 ft/min = 0.0051 m/s
Motor Losses (1)
Copper loss Typical
Stray losses Electrical phenomenon such as skin and proximity
effect
RIPCu2
Motor Losses (2)
Core (Iron) Loss Hysteresis loss Eddy Current loss
Mechanical loss Windage loss Friction loss
2/32 )()( BfBffBP ecn
hIron
Finite Element Analysis
Fundamental harmonic
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines 2nd Edition, p. 174-175, Motor Design Books LLC, 2010.
Part 2 – Surface Mount Round Rotor Multi-Pole PM Motor
Design
Magnetic Circuit Analysis
For a multi-pole surface mount rotor
md
Poles
aD
D
2 2 0g m mH g H d 0 0g m mgB H d
g
0
m m m
m g
d B Ag H A
m m g gB A B A
Working Point for Permanent Magnetics (1)
B
0H0 cH
rB
)( cc
r HHHBB HHH
HBBH c
c
r )(
max( )To get (BH) 0 ,
2 2r c
m mBH B HB HH
0 mRH
mRB
Maximum Energy Point
Working Point for Permanent Magnetics (2)
Load Line:
0
0
gmm m
m
c m
AdB Hg A
P H
1 1.2rm
Pc is called permeance coefficient
//
g g gm mc
m m m g m
A A gdPg A A d
RR
PP
Define: (1 )m m r m m cB B H H
0.5 0.9m Typically pick up:
0
rrm
c
BH
0 1m m
c rmm m
BPH
Airgap Magnetic Field from PM Rotor
/2 /2
/2 /2
2 cos( ) ( ) cos( )2
sin4 2
PM PM
PM PMrh m ae ae m ae ae
PM
m
B B h d B h d
hB
h
, 1,3,5...
cos( ) cos( )2
g rotor Rhh
Rh rh de rh d
B B
PB B h B h
sin2PM
phk h
pitch factor for the hth harmonic
, g rotorBmB
mB2
2P M
PM
2PM
22PM
de2
P M
2de dP
2PM
PM embrace: PM
electrical angle
Phasor Diagram
V
AE
ASjX I
full-load pull out
Typically, design cos 1 at full-load for PMSM.sin 1/3 ( =19.47 ) so that T (1 / 3)T
, , ,
, , ,
cos 0.94 sin 0.33
g pk r pk r pk
a pk r pk r pk
B B BB B B
netB
RB
SB
,4 sin
2PM
r pk mB B
Air Gap Size and PM Thickness
Initial total effective air gap size:
0, ,
ˆ4 1.5 2ˆ
aa pk A rated
total
NB Ig P
ˆ ' ' /ctotal total total m rmg k g g g d
0,
,
ˆ4ˆ 1.5 2atotal A rated
a pk
Ng IB P
From:
From: mc
d Pg
(1 ) ' '
m total
m m total rm
g gd g
( )g mA A
1m
c rmm
P
Carter’s coefficient
totalg
sdst
s
0sb 0sd 1sd
Effective Air Gap ˆ 'total c totalg k g
where the Carter’s coefficient
2
0 0 0
0
2 'atan ln 12 ' 2 '
sc
s s total ss
total s total
kb b g b
g b g
20
05 '
sc
ss
total s
kb
g b
approximately
Rotor Sizing
Total rotor diameter, including magnet
Rotor inner diameter
gDDr 2
2i r mD D d
Part 3 – Two Pole Super High Speed PM Motor with Magnet
Inserted in Rotor Shaft
Prototype
Rotor is assembled by heating and cooling.
Rotor is welded and well balanced after assembly.
Air Gap Size For a 2-pole PM rotor 2 0eff g m rg H H D
02 0e ff m m rg B H D
0
/ 2r mc
e ff m
D B Pg H
NS rDeffg
2 2rD Dg
( )g mA A
1 1 1( ) (1 )2 2 2
r rc c
c r m rm
D D Dk kP
Define: (1 )m m r m m cB B H H
0.5 0.8m Typically pick up: 0 1
m mc rm
m m
BPH
1 1c
rc
cc rm
kD DkkP
( )2 2
r reff c
rm rm
D Dg k g
2rD Dg
Carter’s coefficient
totalg
sdst
s
0sb 0sd 1sd
Effective Air Gap
ˆ 'total c totalg k gwhere the Carter’s coefficient
2
0 0 0
0
2 'atan ln 12 ' 2 '
sc
s s total ss
total s total
kb b g b
g b g
20
05 '
sc
ss
total s
kb
g b
approximately
ˆ , '2 2
r rtotal eff total
rm rm
D Dg g g g
Example - Specifications
Design a 2kW, 100krpm, NdFeB-38 PMSM, 2 pole36 V terminal voltage, Y connected, 90% efficiency.
Recommended