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.

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

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 Maximum Diameter

rev/min)in (2.1)length/minin (

2.1length/s)in (

maxm

r

m

rr n

vf

vD

ft/min 50000rvMaximum rotor peripheral speed

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

0g m mgH 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 0.8m 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

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 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.