17 Permanent Magnet Motor Design

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.

Toyota Prius Power Train

J. F. Gieras, Permanent Magnet Motor Technology - Design and Applications, 3rd Edition, p. 22, CRC Press, 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 

Bcore , pk

 core DB g , pk leff   d c k i li Pd c k i li

 tooth  l eff

B tooth





0

(1)

B g ( ae ) ri d  ae  B g , pk  s l eff

 s B g , pk l eff  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

ds0ds1

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 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 Maximum Diameter

Dr max

v r (in length/s) v r (in length/min)   1.2 f m 1.2nm (in rev/min) 

Maximum rotor peripheral speed

v r  50000 ft/min

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

gH g  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

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 Am

  Pc   0 H m 

Define: Bm   m Br

H m  (1   m ) H c

Typically pick up:  m  0.5  0.8

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 Rh



h 1,3,5...

2





PM 

electrical angle

PM 2 2 

PM 2

B Rh

2

 de

 de 

P d 2

P  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 sin  h PM  4 th harmonic  2 B h  m  h    k ph  sin  h PM   2 

 Brh 

the

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

Br, pk

 PM   sin   Bm   2  4

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  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  bs 0 g ' total  atan ln s  1   2 g ' total   bs 0  

2  b s 0       2 ' 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

Example - Specifications         

Output power: 10 kW Terminal voltage: 270 V Mechanical speed: 10,000 rpm Input voltage configuration: Y-connected Number of poles: 4 Fractional stator pitch: 5/6 Number of slots in stator: 24 Permanent magnet: NdFeB-48 Efficiency: 95%

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   g e ff 0H

 Pc 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 s

kc 

s 

2 bs 0



bs 0 g ' total   ln 1    atan 2 ' g b  total s0 

2  b s 0       2 ' 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.