2024年1月12日发(作者：小米10发布会视频)

DESIGN AND ANALYSIS

OF

HIGH-SPEED BRUSHLESS PERMANENT MAGNET MOTORS

Z.Q. Zhu,

K.

Ng, and

D.

Howe

University of Shefield,

UK

INTRODUCTION

High-speed brushless permanent magnet machines are

likely to be a key technology for electric drives and

motion control systems for many applications, since

they are conducive to high efficiency and a high power

density, small size and low weight

[I].

However, due to

the high fundamental operating frequency a more

detailed consideration of various operational issues,

such as stator iron losses and rotor parasitic eddy

current losses, and the influence of the winding

inductances on the dynamic system performance,

is

advisable at the design stage [2-51.

The paper reports

on

the design of a 20,00Orpm, 3-

phase brushless permanent magnet dc motor for use in

a friction welding unit,

in

which studs up to 3mm

diameter and welded by coordinating the rotational

speed of the motor with the force applied by a linear

permanent magnet servo-actuator. The motor consists

of a stator having

3

teeth, which carry non-overlapping

windings, and a 2-pole diametrically magnetised

sintered NdFeB magnet rotor, as shown in Fig.]. The

airgap flux density distribution

is

essentially sinusoidal.

The advantages and disadvantages of such a motor

topology for this and other high speed applications are

discussed, and an optimal airgap diameter is derived.

The effect of the stator tooth tip geometry on the

waveform of the induced emf

is

investigated by finite

element analysis, and validated by measurements,

whilst the merits of laminated silicon iron and

soft

magnetic composite materials for the stator core are

considered.

GENERAL DESIGN CONSIDERATIONS

The higher the operating speed

of

a motor the smaller

is

its physical size

for

a given output power. Hence, in the

case of a permanent magnet machine, the lower will be

the volume of magnet material. Therefore, high speed is

particularly appropriate when rare-earth permanent

magnets, such as SmCo and NdFeB, are used, since

they are still relatively expensive. The lower the pole

number of a motor the lower

is the hndamental

frequency. However, a low pole number necessitates

thicker back-iron on the stator and rotor in order to

limit magnetic saturation. Thus, the choice of pole

number

is

largely influenced by considerations

of

size

and iron losses. It

is

also influenced by a consideration

of switching losses in the power electronic converter,

which clearly favours a low pole number.

As

a result,

2-poles are often appropriate for high speed

applications, a diametrically magnetised rotor often

being preferred since

it

results in an essentially

sinusoidal airgap flux density distribution.

If the stator slot openings are neglected, the radial

component of the open-circuit magnetostatic field

in

the airgap can be derived as:

where

B,

and

p,

are the remanence and relative recoil

permeability of the magnet, and

R,, R,,

and

R,

are the

radii of the stator bore, the rotor magnet and the rotor

hub, respectively.

Fig.1 shows a prototype 2-pole, 3-slot, 20,00Orpm,

200Vdc, 1.3kW, brushless dc motor, for which

R,

=

18.5mm,

R,

=9mm,

R,

=

17mm,

B,

=

1.2T,

pr

=

1.05,

and the axial length

1,

=

26”. Fig.2 shows

instantaneous open-circuit

flux

distributions, whilst

Fig.3 compares the analytically calculated airgap field

with that predicted by finite element analysis when

stator slotting is neglected.

The stator winding inductances can have a significant

effect on the dynamic performance of high-speed

brushless drive systems [2-31. For example, they may

cause the torque-speed curve to depart significantly

from the ideal linear characteristic, which in

turn

may

necessitate advancing the commutation in order to

increase the high-speed torque capability. They also

influence the maximum ripple current in

PWM

controlled systems, which

in

turn

affects the motor

losses and torque ripple. For brushless dc operation, the

winding inductances can also cause the phase current to

depart significantly from the ideal rectangular

waveform, which can markedly reduce the torque

capability at high speed and limit the maximum

achievable speed [2]. However, the winding

inductances of the prototype motor are relatively low,

the values calculated using the analytical method

described in [3] being 0.775mH and -0.32mH and the

measured values being 0.872mH and -0.329mH, for the

self- and mutual-inductances respectively.

As

a

EMD97

1-3

September 1997 Conference Publication

No.

444

0

IEE

1997

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381

consequence, the torque-speed curves are essentially

linear, Fig.4,

and

the phase current waveform is

approximately rectangular, Fig.5.

the prototype motor.

Of

course, unbalanced magnetic

pull will exist if the rotor rotates eccentrically with

respect to the stator.

Stator

Diametrically

Non-overlapping

Concentrated

Winding

-1.5'

0

I

1

2 3

4

5

6

AnQular position (rad

)

Fig.3. Comparison

of

analytically and finite element

predicted airgap field distributions.

2mo

Vdc=200V

-

15000

Vdc=l5OV

Retaining Sleeve

Y

E

a

Fig.

1

Prototype 2-pole brushless dc motor.

U

8

lo000

cn

5000

0

0

100

200

300

400

500

600

Torque

(mNm)

Fig.4 Comparison of predicted and measured torque-

speed curves.

a

Fig.2 Instantaneous open-circuit field distributions in 2-

pole

3-slot

motor.

By employing non-overlapping windings, as in the

prototype motor, rather than overlapping windings, the

end-windings are shorter and therefore the copper

loss

is lower. Further, the axial length of the rotor is reduced

-

which

is

beneficial from mechanical considerations,

viz. critical speeds, stiffness etc.

Unbalanced magnetic pull is especially undesirable

in

high

speed

motors

since

it

may cause excessive rotor

and stator vibrations, and possibly induce resonances.

However, although the teeth in a 3-slot stator are

diametrically asymmetrical, if slot opening effects are

neglected and there is negligible magnetic saturation in

the tooth tips the airgap field distribution is

symmehical. Therefore,

no

unbalanced magnetic pull

will exist if the rotor and stator axes are coincident.

However, since, in practice, the tooth tips will be

saturated to some degree, some unbalanced magnetic

pull will exist, although it was found to be very small in

-4

.

"

0 0.001

0.002

Time

(second)

0.003

0.004

Fig.5 Comparison of predicted and measured phase

current waveforms at 19000rpm.

OPTIMAL SPLIT RATIO (RATIO OF STATOR

BORE DIAMETER

TO

OUTSIDE DIAMETER)

It is well

known

[6]

that for each type

of

machine there

exists an optimal split ratio, i.e. stator bore diameter to

outside diameter, for maximum torque. However,

382

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existing methods for determining this optimum are

either relatively complicated [6]

or

inappropriate for

motors having a diametrically magnetised magnet rotor

[7].

For

a brushless dc motor with 3 stator teeth and a

diametrically magnetised rotor, the fundamental airgap

flux density distribution at the stator bore is given by

equation

(l),

i.e.

Bgr

=

B,

K

sin

B

(2)

where

K

is a constant which depends only on

R,, R,,

and

R,.

Assuming

,ur

=

1

and

R,

=

0,

K

=

which generally gives a good approximation to the

open-circuit field calculation, and can significantly

simplify further analysis. For example, for the

prototype motor, when

R,

=

0

the resulting airgap flux

is: density at

r

=

Rs

nm

B

=

B,

-sin

8

=

1.2~sin

8

=

1.01

sin

8

gr

R,

18.5

which agrees well with the analytically and finite

element predicted results shown in Fig.3.

since the equivalent airgap (mechanical airgap plus

radial thickness of the non-magnetic sleeve) is 1.5mm.

--

02

03

04 05

06

07

OB

09

IO

11

Remanence

(T)

12

n2

*-I2

I/

Fig.6 Optimal ratio of stator bore to outside diameter.

OPTIMAL

TOOTH TIP

In the preceeding sections, the airgap

flux

density

distribution and the induced back-emf waveform in the

2-pole motor of Fig.1 have been shown to be

essentially sinusoidal. However, during design studies

it was found that the dimension of the stator tooth tips

in

relation to the width of the slot openings also

influences the back-emf waveform,

Fig.7.

This was

subsequently confirmed by measurements.

The induced emf in each phase winding, assuming 120”

coil span, is then obtained

as:

e

=

KR,~, ~,w,

sin

art

(3)

where

W,

is the number

of

turns

per phase and

U,

is the

angular velocity of the rotor.

J5w,

The electromagnetic torque is given by:

=I

4

where the electric loading Q is:

3WcI

Q=

K,-

2

rrR,

K,

=

2 13,

Dm

=

2R,,

and

I

is the phase current. The

optimal value

of

the stator bore diameter to outside

diameter ratio for maximum torque can be derived as:

T-<-,

ycc-llr,

(i) 0.5m tooth tip

where c, = 5.079

x

(7a)

and c2 =2.183~(2)~ +1.654~(2)-1 (7b)

where

B,,

is a prescribed value for the maximum flux

density in the stator. Equation 6 and Fig.6 show that the

optimal ratio

of

the stator bore to outside diameter

depends only on

B,

and

Bmm.

The optimal airgap

diameter reduces as the magnet remanence is increased.

Dr

1-.*L-,rr,

(ii) 0.8” tooth tip

,=

1.6T, and For the prototype motor,

B,

=

1.2T,

B,0,

the optimal value of

-

=

0365, while the optimal

Do

Dtn

1

rotor to stator diameter is obtained

as:

-

=

034

=

-

Do

3

Dr

PI

--m,

(iii)

2.0”

tooth tip

(a) measured

(3000rpm)

(b) predicted (3000rpm)

Fig.7 Effect

of

tooth tip height on back-emf waveform.

383

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For example, when the height of the tooth tips is only

0.5mm and significant magnetic saturation exists, the

emf waveform tends to a trapezoid, which is preferred

for brushless dc operation. However, when the tooth tip

the emf waveform is height

is

increased to 0.8"

almost purely sinusoidal, which is ideal for brushless ac

operation.

A

further increase

of

the tooth tip height to

2mm

causes the emf waveform to deteriorate, albeit

exhibiting a higher peak value.

stator core

[SI.

It will be seen that as the motor speed

is

increased the loss in the composite stator increases

essentially linearly, since it is now predominantly due

to hysteresis. The properties of such composites are

improving rapidly, with recently commercialised grades

having a permeability of

m500.

Thus, they have

considerable potential for use in high speed motors.

40

.-----e

v-----D

The prediction

of

stator iron losses

is

very important

for high speed motors. Under alternating flux

conditions, the total iron

loss

density

P,

can be

separated into a hysteresis component

Ph

and an eddy

current component

Pd.

When the flux density waveform

does not cause minor hysteresis loops, the hysteresis

loss

density can be expressed as:

ph

=

khfB:

(8)

where

B,

is

the peak induction, and

kh

and

a

are

experimentally determined hysteresis loss constants for

the particular grade of lamination material

[4].

The

eddy current loss density component can be expressed

as the

sum

of a classical eddy current loss component

and an excess

loss

component, i.e.

30

o-----o

Bm=l

IT

Bm=l

3T

Bm=l

2T

ia

C

0

100

200 300

400

Frequency (Hz)

(a) Transil300

A--&

Bm=llT

m---

-m

Bm=lZT

o-----*Bm=llT

v----v

Bm=

where

a,

d,

S

are the electrical conductivity, the

thickness, and

the

mass density of the lamination

material respectively, and

k,

is the eddy current loss

constant, which is again determined experimentally

[4].

40

0

100 200

300 400

Frequency

(HzJ

Yqn*I-l(U,

(a) Transi1300 (b)

soft

magnetic composite

Fig.8

B-H

characteristics of Transil300 and

soft

magnetic composite measured at

DC

and

500Hz.

Since the maxi" speed of the prototype motor

corresponded to a fundamental frequency of only

333Hz,

0.35"

Transil 300 silicon steel laminations

were

used. Measured hysteresis loops and iron loss

densities are shown in Figs.8 and 9, fiom which the

iron loss constants are obtained as:

k,

=

1.71

x

low2,

--**,

(b)

Soft

magnetic composite

Fig.9 Measured iron loss densities for Transil300 and

soft

magnetic composite materials.

(B

=

B,

sin

2jzft

)

750

.--.

A-A

@-e

rl- --P

o----o

-

Hyslerosis

loss of

TTB~SII

3CQ

€My

wren1

1055

01 Tran~il300

Tofa

loss

of Transit 300

Hy~lere~is loss

01 SMC

EddyarrmtlossofSMC

a

=

2.12,

k,

=

6.6

x

lo-'.

The variation

of

the iron

loss

in

the prototype motor as its operating speed

is

increased is shown in

Fig.

10,

from which it will

be

seen

that the

loss

at rated speed

is

relatively low, since the

flux

waveforms are essentially sinusoidal. However, for

comparison, Figs.8 to

10

also show characteristics and

losses for a

soft

magnetic composite (ABM100.32)

Motor speed (rpm)

Fig.10 Iron

loss

in

prototype motor with Transil300

and

soft

magnetic composite stator.

384

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PARASITIC ROTOR LOSSES

In high speed motors, the permanent magnets are often

contained within a retaining sleeve. However, the

sleeve and also the magnets are exposed to high order

flux harmonics which cause parasitic eddy current

losses [5][9]. On no-load these are due primarily to

stator sloking, whilst on-load they result from both

stator slotting permeance harmonics and mmf

harmonics which are not in synchronism with the rotor,

which

in a brushless dc motor are due to commutation

events.

In

order to calculate the losses, the accurate

prediction of the magnetic field distribution in the

airgap/magnet/sleeve regions is essential. A 2-d

analytical model, which accounts for slotting and the

induced eddy currents, has been developed

191

for

calculating the time-varying field distribution, from

which the losses can be deduced. By way of example,

Fig. 1 1 compares analytically and finite element

predicted open-circuit flux density distributions at the

interface of the sleeve/magnet, while Fig. 12 shows the

predicted eddy current

loss,

which varies approximately

with the square

of

the motor speed. However, for the

prototype motor the rotor

loss

at rated speed is

relatively small.

CONCLUSIONS

A 20,000rpm 3-phase brushless permanent magnet dc

motor has been developed for use

in

a friction welding

unit. It has a 3-slot stator which carries non-overlapping

windings, and a 2-pole diametrically magnetised

sintered NdFeB magnet rotor. The optimal airgap

diameter and stator tooth tip height have been

determined, and the open-circuit stator iron

loss

and the

rotor losses have been calculated. The calculation

methods are currently being extended to cater for load

conditions. Finally, the potential for the application

of

soft magnetic composite materials in high speed motors

has been highlighted.

REFERENCES

1. Pickup I.E.D., Tipping D., Hesmondhalgh D.E., AI

Zahawi B.A.T., 1996, “A 250,000rpm drilling

spindle using a permanent magnet motor”,

’96, Vigo, Spain, 337-342.

2. Zhu Z.Q., Howe D., and Ackermann B., 1992,

“Analytical prediction

of

dynamic characteristics

of

brushlessdc drives”, Electrical Machines and Power

Systems, 20,661-678.

3. Zhu Z.Q., and Howe D., 1997, “Winding

inductances

of

brushless machines with surface-

mounted magnets”, Proc. of International Electric

Machines and Drives Conference, Milwaukee,

Wiscosin, May 18-2

1,

1997.

4. Atalah

K.,

Zhu Z.Q., Howe D., 1992, “The

prediction of iron losses in brushless permanent

magnet dc motors”, Proc. ICEM’92, Manchester,

UK,

814-818.

5.

Mecrow B.C., Jack A.G., 1993, “Determination of

rotor eddy current losses in permanent magnet

machines”, Proc. 6th EMD, IEE, Oxford, 299-304.

6. Hesmondhalgh D.E., Tipping D., and Amrani M.,

1987, “Design and construction of a high-speed

high-performance direct-drive handpiece”,

Proc.

IEE-B 134 286-294.

7. Chabban F.B., 1994, “Determination of the

optimum rotor/stator diameter ratio of permanent

magnet machines”, Electrical Machines and Power

Systems, 22, 52 1-53

1.

8. Persson M., Jansson P., Jack A.G., Mecrow B.C.,

1995,

“Soft

magnetic composite materials

-

use for

electrical machines”, Proc.7th EMD, IEE, Durham,

UK, 242-246.

9. Ng

K.,

Zhu Z.Q., and Howe D., 1996, “Open-circuit

field distribution in a brushless motor with

diametrically magnetised PM rotor, accounting for

slotting and eddy current effects”, IEEE Trans.

Magnetics,

32,

5070-5072.

-9

-1

0

-

-

-15

0

-

15 30

45

00

75

Angular

position

(radian)

Fig. 1 1 Comparison

of

analytically and finite element

predicted open-circuit flux density distributions at

interface of sleevelmagnet.

300

0-

-7

-v

TcW(.1~praitiC~

z

L

s

- --c

E&ty

ann1

ba

h

nuen4

/

/!

200-

-

1

/

,

/I

3

f

W

2

100-

//

/‘

/r

-

/

or

----*--e

,*

-

__---

.

/‘

’

_---e

’

---_--*-

--

.A

385

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