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)
3
1.
2.
3.
4.
Four cylinder combustion engine;
Generator/starter;
Electric Motor;
Power split device (PSD)
J. F. Gieras, Permanent Magnet Motor Technology Design and Applications, 3rd Edition, p. 282, CRC
Press, 2010.
2
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
most popular
radial sine magnetization
sine angle or sine direction
magnetization
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
2
Dl
 V0
T
T
Pout
m
Typically
V0  8 ~ 9 in / (ft  lb) for 10hp or less (air cooled)
3
V0  4 ~ 5 in / (ft  lb) for 10hp or more (water cooled)
3
The unit for D and L is inch.
If we design D=L, we have the stator bore (inner)
diameter estimated
Destimated  (TV0 )
1
3
We can pick up D close to Destimated.
Stator Core Design
 core   gap , per half pole pitch
 leff 
 /P
0
Bg ( a )ris d a
2  /2
D
leff  Bg , pk cos( ae )d ae
2
P 0
D
 leff Bg , pk
P

 core DB g , pk leff
Bcore , pk 

d c k i li
Pd c k i li
(1)

 tooth  l eff  B g ( ae ) ri d  ae  B g , pk  s l eff
0
 s B g , pk l eff
 tooth
B tooth 

t s k i li
t s k i li
(2)
Take t s  0.5 s , Bcore , pk  0.8 Btooth
 dc 
D
1 .6 P
Effect of Pole Number on Yoke Flux Density
Finite Element Analysis
with the same dc
J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines
2nd Edition, p. 106, Motor Design Books LLC, 2010.
Number of Turns per Coil
V , rated 
where
2 f e Nˆ a  g , pk  4 .44 f e Nˆ a  g , pk
 pk 
2Bg , pk Dl
P
Nˆ a  kw Na / 1.1
kw  k p kd ks
Na  PqNc / C
Na is the number of series turns per phase of armature winding
C is the number of parallel circuits of armature winding
Nc 
1 . 1V , rated C
2 2 f e qk w B g , pk Dl
Consider leakage flux
Stator Slot Design
General Consideration
s 
ts
bs0
s
d ds1
s0
ds
D
S
0.4 s  ts  0.6 s
3ts  d s  7ts
Define bs   s  ts
bs 0  (0.1 ~ 0.5)bs
d s 0  (0.1 ~ 0.5)bs
d s1  (0.1 ~ 0.5)bs
Stator Conductor Size
Stator current density
J s ,copper 
I a ,rated / C
Sa
where Sa is stator (armature) conductor cross section
area and can be determined from the above formula
together with:
Air - cooled : 400A/cm 2  J s ,copper  800 A/cm 2
Sa 
I a ,rated / C
J s ,copper
Permanent Magnets

Samarian Cobalt (SmCo)
Operating temperature of up to 350ºC
nd strongest rare earth magnet
 2


Neodymium Iron Boron (NdFeB)
Operating temperature of up to 150ºC
 Strongest rare earth magnet

Permanent Magnet Properties
From Yeadon – Handbook of Small Electric Motors
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
PCu  I 2 R

Stray losses

Electrical phenomenon such as skin and proximity
effect
Motor Losses (2)

Core (Iron) Loss
Hysteresis loss
 Eddy Current loss

PIron   h B f
n

Mechanical loss
Windage loss
 Friction loss


  c ( Bf )   e ( Bf )
2
3/ 2
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
dm
Da
D
g
Poles
2 H g g  2 H m d m  0  gBg  0 H m d m  0
dm
Bm Am


g
0 H m Ag
Bm Am  Bg Ag
Working Point for Permanent Magnetics (1)
Maximum Energy Point
B
Br
BmR
0 Hc
0 HmR
Br
B
(H  H c )
Hc
0 H
Br
 BH 
(H  H c )H
Hc
 ( BH )
Br
Hc
 0  Bm 
To get (BH) max 
,Hm  
H
2
2
Working Point for Permanent Magnetics (2)
 rm 
Br
0 H c
1   rm  1.2
Load Line:
Bm  
d m Ag
 0 H m 
g Am
  Pc   0 H m 
Define: Bm   m Br
H m  (1   m ) H c
Typically pick up:  m  0.5  0.9
Pc is called permeance coefficient
Ag / g
R m Pg
d m Ag



Pc 
g Am
Am / d m R g Pm
 Pc  
Bm
m

 rm
0H m
1 m
Airgap Magnetic Field from PM Rotor
PM embrace:
B g , rotor
  PM 
  PM
Bm
 Bm

 PM
 PM
2
2
B g , rotor 
 B
h 1,3,5...
2

PM

electrical angle

  PM
2

2  PM
2
2
 de
 de 
Rh
P
d
2
P
B Rh  Brh cos( h de )  Brh cos( h  d )
2
   PM /2
2   PM /2

B
h

d

cos(
)
(  Bm ) cos( h ae )d ae 
m
ae
ae



   PM /2
2    PM /2
  
pitch factor for the
sin  h PM 
4
th harmonic
 2 B
h

m

h
  
k ph  sin  h PM 
 2 
 Brh 
Phasor Diagram
V

jX S I A
Bnet

BS
BR
EA
Typically, design cos  1 at full-load for PMSM.
sin  1/3 ( =19.47 ) so that Tfull-load  (1 / 3)Tpull out

 B g , pk  cos  B r , pk  0.94 B r , pk
Ba , pk  sin  B r , pk  0.33 B r , pk
 PM 
Br, pk  sin 
 Bm
  2 
4
Air Gap Size and PM Thickness
From:
4 0 Nˆ a
1.5 2 I A,rated
Ba , pk 
 gˆ total P
Initial total effective air gap size:
4 0 Nˆ a
1.5 2 I A,rated
gˆ total 
 Ba , pk P
From:
gˆ total  k c g 'total
g 'total  g  d m / rm
dm
 Pc
g
Pc 
Carter’s coefficient
 g  (1   m ) g 'total
d m   m g 'total rm
( Ag  Am )
m
 rm
1 m
Effective Air Gap
gˆ total  kc g 'total
where the Carter’s coefficient
kc 
s
2

 b s 0   
2 b s 0 
bs 0
g ' total

ln 1  
s 
 atan
 
2 g ' total
2
'
 
bs 0
g

total   



approximately
kc 
s
bs20
s 
5 g ' total  bs 0
ts
g total
bs0
s
ds0ds1
ds
Rotor Sizing
Total rotor diameter, including magnet
Rotor inner diameter
Di  Dr  2d m
Dr  D  2 g
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
2 g eff H g  H m D r  0
For a 2-pole PM rotor
( Ag  Am )
 2 g e ff B m   0 H m D r  0
S
Dr

N geff
Dr / 2
Bm
 
 Pc
g e ff
0H m
Carter’s coefficient
g eff 
 (
g
Dr
D

2
2
1
1
D
D
1
D

 k c (1 
) r  kc
) r
 rm 2
 rm 2
Pc
2
 Dr 
Define: Bm   m Br
Dr
Dr
 kc ( g 
)
2  rm
2  rm
kc
1
1  kc
kc 

Pc
 rm
H m  (1   m ) H c
Typically pick up:  m  0.5  0.8
D
g
 Pc  
D  Dr
2
Bm
m

 rm
0H m
1 m
Effective Air Gap
gˆ total  kc g 'total
gˆ total  g eff 
Dr
,
2 rm
g 'total  g 
where the Carter’s coefficient
kc 
s
2


 


bs 0
g ' total
bs 0
2 bs 0 
ln 1  
s 

 atan
 
2 g ' total
2
'
 
bs 0
g

total   



approximately
kc 
s
bs20
s 
5 g ' total  bs 0
ts
bs0
s
g total
ds0ds1
ds
Dr
2 rm
Example - Specifications
Design a 2kW, 100krpm, NdFeB-38 PMSM, 2 pole
36 V terminal voltage, Y connected, 90% efficiency.