Permanent Magnet
Synchronous Motor (PMSM)
Introduction
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)
Toyota Prius
MS-TECH Japan
(e) IPM rotor with 2 magnets/pole in a
V-shaped flux concentrating arrangement
Rotor Flux Distribution of IPMs
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 (1)
parallel magnetization
radial magnetization
most popular
radial sine magnetization
sine angle or sine direction
magnetization
Magnetization Profile (2)
Flux of a 8 pole machine at no load
radial magnetization
45
90 135
180
d
d 

8
air gap flux density profile versus angle
Magnetization Profile (3)
Flux in 2 Pole Machine at no load
d
radial magnetization
d 
d

2
parallel magnetization
d 

2
Magnetization Profile (4)
PM embrace:  emb 
radial magnetization
Bg , rotor
   PM
Bm
 Bm

 PM
 PM
2
2


 PM

electrical angle
 PM
2
2 
 PM
2
2
 de
 PM
parallel magnetization
Bg , rotor
   PM
Bm

 PM
 PM
2
2


 PM
2
2 
 PM
2
2
 de
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
Permanent Magnet
Synchronous Motor (PMSM)
Design
Part 1 – General Considerations
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
 l
 /P
0
pole pitch
Bg ( a ) ris d a
D 2  /2
l  Bg , pk cos( ae )d ae
2 P 0
D
 lBg , pk
P

Bcore 
 core DBg , pk
=
d cl
Pd c
(1)

 tooth  l  Bg ( ae ) rd
i  ae  Bg , pk s l
0
Btooth 
Take
 tooth  s Bg , pk

ts l
ts
(2)
ts  0.5 s , Bcore  0.8Btooth
 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  2f e Nˆ a  g , pk  4.44 f e Nˆ a  g , pk
where
 pk 
2 Bg , pk Dl
P
Nˆ a  kw N a / 1.1
k w  k p kd k s
N a  PqN c / 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 ,ratedC
2 2f e qk w Bg , pk Dl
Consider leakage flux
Stator Slot Design
General Consideration
s 
ts
bs 0
s
d s 0d s1
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/cm2  J s ,copper  800 A/cm2
Sa 
I a ,rated / C
J s ,copper
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
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
 m  Bm Am
 g  Bg Ag
dm
Bm kl Am


g
0 H m Ag
 g  kl  m
kl : Leakage Coefficient
Working Point for Permanent Magnetics (1)
Maximum Energy Point
B
Br
BmR
 0 H c
0 H mR
Br
B
(H  Hc )
Hc
To get (BH) max
0 H
Br
 BH 
(H  H c )H
Hc
 ( BH )
Br
Hc

 0  Bm 
, 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 kl Am
  Pc  0 H m 
Define: Bm   m Br
Pc is called permeance coefficient
Ag / g
Bm
d m Ag
Rm Pg
Pc  




0 H m
g kl Am kl Am / d m Rg Pm
H m  (1   m ) H c
Typically pick up:  m  0.6
0.9
 Pc  
Bm
m


0 H m 1   m rm
Airgap Magnetic Field from PM Rotor
PM embrace:  emb 
Bg , rotor
   PM
Bm

 Bm
 PM
 PM
2
2
Bg , rotor 
BRh

h 1,3,5...

 PM  PM

2
2


2  PM
2
2
BRh
 PM

electrical angle
 de
 de 
P
d
2
P
 Brh cos( h de )  Brh cos( h  d )
2
   PM /2
2   PM /2
B
cos(
h

)
d


(  Bm ) cos( h ae )d ae 
m
ae
ae



   PM /2
2    PM /2
  
pitch factor for
sin  h PM 
4
th harmonic
 2 B
h

m

h
  
k ph  sin  h PM 
 2 
 Brh 
the
Phasor Diagram
V

B net
jX S I A

BS
BR
EA
Typically, design cos  1 at full-load for PMSM.
Need to specify torque angle, if sin  1/3 ( =19.47 ),
Tfull-load  (1 / 3)Tpull out .
 Bg , pk  cos  Br , pk  0.94 Br , pk
Ba , pk  sin  Br , pk  0.33Br , pk
Br , pk
4   PM
 sin 
  2

 Bm

Air Gap Size and PM Thickness
From:
Ba , pk
4 0 Nˆ a

1.5 2 I A,rated
 gˆ total P
Initial total effective air gap size:
gˆ total
From:
gˆ total  k c g 'total
4 0 Nˆ a

1.5 2 I A,rated
 Ba , pk P
g 'total  g  d m / rm
dm
k A
 Pc l m
g
Ag
Pc 
Carter’s coefficient
 can obtain g and d m
rmg
m
rm
1  m
Effective Air Gap
gˆ total  kc g 'total
where the Carter’s coefficient
kc 
s
2
 bs 0   
2bs 0 
bs 0
g 'total 


s 

ln 1  

atan
 
 
2 g 'total
bs 0
2
g
'

total   



approximately
kc 
s
bs20
s 
5 g 'total  bs 0
ts
g total
bs 0
s
d s 0d s1
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
For a 2-pole PM rotor
2 g eff H g  H m Dr  0
( Ag  Am )
 2 g eff Bm  0 H m Dr  0
N
Dr

Dr / 2
Bm

 Pc
g eff
0 H m
Carter’s coefficient
g eff
g eff 
S
(
g
Dr D

2
2
1
1 Dr
D
1 Dr

)
 kc
 k c (1 
)
Pc
rm 2
2
rm 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  0.6
0.9
D
g
 Pc  
D  Dr
2
Bm
m


0 H m 1   m rm
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





2bs 0 
bs 0
g 'total
bs 0

s 

ln 1  
atan
 
 
2 g 'total
bs 0

 2 g 'total   


approximately
kc 
s
bs20
s 
5 g 'total  bs 0
ts
bs 0
s
g total
d s 0d s1
ds
Dr
2 rm
Example - Specifications
Design a 2kW, 100krpm, NdFeB-38 PMSM, 2 pole
36 V terminal voltage, Y connected, 90% efficiency.