20 Permanent Magnet Motor Design

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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
breadloaf
magnet
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
V
T
lD 
The unit for D and L is inch.
3
0 4 ~ 5 in / (ft lb) for 10hp or more (water cooled)V  
Typically
3
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 
3
1
0 )(TVDestimated 
We can pick up D close to Destimated.
m
outPT 
Stator Core Design
 
(1) ,,
iic
effpkg
iic
core
pkcore lkPd
lDB
lkd
B 
(2) ,
iis
effpkgs
iis
tooth
tooth lkt
lB
lkt
B

 
)( ,0 effspkgaeiaegefftooth lBdrBl 
  
pkgeff
aeaepkgeff
P
aisageff
ole pitchper half pgapcore
Bl
P
D
dB
P
lD
drBl
,
2/
0 ,
/
0
 ,
 
)cos(2
2
 
)( 










Take toothpkcoress BBt 8.0 ,5.0 ,  
P
Ddc 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  
P
DlB pkg
pk
,2
1.1/ˆ awa NkN 
sdpw kkkk 
where
DlBqkf
CV
N
pkgwe
rated
c
,
,
22
1.1


Na is the number of series turns per phase of armature winding
C is the number of parallel circuits of armature winding
CPqNN ca /
Consider leakage flux
Stator Slot Design 
S
D
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 0s
d 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
rateda
coppers S
CI
J
/,
, 
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
rateda
a J
CI
S
,
, /
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
RIPCu
2
Motor Losses (2)
 Core (Iron) Loss
 Hysteresis loss
 Eddy Current loss
 Mechanical loss
 Windage loss
 Friction loss
2/32 )()( BfBffBP ec
n
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 A
g H A  
m m g gB A B A
Working Point for Permanent Magnetics (1) 
B
0H0 cH
rB
)( c
c
r HH
H
BB  HHH
H
BBH c
c
r )( 
max
( )To get (BH) 0 ,
2 2
r c
m m
BH B HB H
H
     
0 mRH
mRB
Maximum Energy Point
Working Point for Permanent Magnetics (2) 
Load Line:  
 
0
0 
gm
m m
m
c m
AdB H
g A
P H


 
 
1 1.2rm 
Pc is called permeance coefficient
/
/
g g gm m
c
m m m g m
A A gdP
g A A d
   R
R
P
P
Define: (1 )m m r m m cB B H H    
0.5 0.9m  Typically pick up: 
0
r
rm
c
B
H
 
0 1
m m
c rm
m m
BP
H
      
Airgap Magnetic Field from PM Rotor
/2 /2
/2 /2
2 cos( ) ( ) cos( )
2
sin
4 2 
PM PM
PM PM
rh m ae ae m ae ae
PM
m
B B h d B h d
h
B
h
  
     



 
      
   
 
, 
1,3,5...
cos( ) cos( )
2
g rotor Rh
h
Rh rh de rh d
B B
PB B h B h 


 

sin
2
PM
phk h
    
pitch factor for the 
hth harmonic
, g rotorB
mB
mB
2
2
PM
PM 
2
PM 
2
2
PM  de2
PM
2de d
P 
2
PM 
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 B
B B B


  
 
netB
RB
SB

,
4 sin
2
PM
r pk mB B


    
Air Gap Size and PM Thickness 
Initial total effective air gap size:
0
, ,
ˆ4 1.5 2
ˆ
a
a pk A rated
total
NB I
g P


ˆ ' ' /
ctotal total total m rm
g k g g g d   
0
,
,
ˆ4ˆ 1.5 2atotal A rated
a pk
Ng I
B P


From:
From: m c
d P
g

(1 ) '
 '
m total
m m total rm
g g
d g

 
  

( )g mA A
1
m
c rm
m
P   Carter’s coefficient
totalg
sdst
s
0sb 0s
d 1sd
Effective Air Gap 
ˆ 'total c totalg k g
where the Carter’s coefficient 
2
0 0 0
0
2 'atan ln 1
2 ' 2 '
s
c
s s total s
s
total s total
k
b b g b
g b g

 
               
2
0
05 '
s
c
s
s
total s
k
b
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 
Insertedin 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 m
c
e ff m
D B P
g H   NS
rD
effg
2 2
rD Dg  
( )g mA A
1 1 1( ) (1 )
2 2 2
r r
c c
c rm rm
D D Dk k
P      
Define: (1 )m m r m m cB B H H    
0.5 0.8m  Typically pick up: 
0 1
m m
c rm
m m
BP
H
      
1 1
c
r
c
c
c rm
kD Dkk
P 
   
( )
2 2
r r
eff c
rm rm
D Dg k g   
2
rD Dg 
Carter’s coefficient
totalg
sdst
s
0sb 0s
d 1sd
Effective Air Gap 
ˆ 'total c totalg k g
where the Carter’s coefficient 
2
0 0 0
0
2 'atan ln 1
2 ' 2 '
s
c
s s total s
s
total s total
k
b b g b
g b g

 
               
2
0
05 '
s
c
s
s
total s
k
b
g b



 
approximately
ˆ , '
2 2
r r
total eff total
rm rm
D Dg g g g    
Example - Specifications
Design a 2kW, 100krpm, NdFeB-38 PMSM, 2 pole
36 V terminal voltage, Y connected, 90% efficiency.