the basics of permanent magnet motor operationselectrathonoftampabay.org/www/documents/motors... ·...

COURSE# - 1

The Basics of Permanent Magnet Motor Operations

By George Holling

COURSE# - 2

Introduction

• Introduction• The physics of permanent magnets• Basic PM motor operating principles• Basic motor parameters• Motor construction

COURSE# - 3

The Physics of Permament Magnets

COURSE# - 4


• a typical magnetization curve for a PM magnet is shown here

COURSE# - 5


• the outmost outline of the magnetization curve is for a single cycle of a fully magnetized magnet

• as the operating point of the magnetic circuit’s permeance PP line intersects with the demagnetization curve the magnet “weakens”

• the magnetization is not a single curve, but a family of curves

COURSE# - 6


• the permeance PP of the magnetic circuit determines the operating point of the permanent magnet

inches influx of direction theparallel thicknessgapair :1.5 - 1.1 typically-factor reluctance magnetic :

inches influx of direction theparallel cknessmagnet thi :leakageflux magnetic :

g

mF

gmFP

ℜ

⋅ℜ⋅

=

COURSE# - 7


• plotting the permeance into the magnetization curve yields the operating point of the magnetic circuit

– idealistic assumption• no saturated steel• µr>>1

– ignores the effects of demagnatization• internal field from windings• demagnetization curve• magnet temperature

– ignores the effect of the magnet’s temperature

COURSE# - 8


• the magnet’s flux changes with temperature– reversible– irreversible

COURSE# - 9


• the magnet’s linear, reversible flux change as a function of temperature is:

C)( peraturemagnet tem :ationdemagnetiz oft coefficienlinear :

tureat temperadensity flux gapair :)( tureat temperadensity flux gapair :)(

)](1)[()(

00

00

°

−−=

T

TTBTTB

TTTBTB

β

β

COURSE# - 10


• irreversible changes can occur in the magnet well below its Curie temperature

COURSE# - 11


• the motor’s conductors can cause irreversible damage to its magnet

• the flux generated by an inductor in the magnet is:

inches influx of direction theparallel thicknessgapair :inches influx of direction theparallel cknessmagnet thi :

circuit magnetic theof permeance the:Pcurrent winding the:i

conductors ofnumber total:

)(3

gm

Z

gmPiZH+⋅⋅

⋅=

COURSE# - 12


• each PM motor therefore has

– a thermal current rating due to wire constraints– an absolute peak current rating due to magnet constraints

COURSE# - 13


• most PM motors use one of the following PM magnet materials

– Alnico: Aluminum Nickel Cobalt– Fe3O4: Ceramic/Ferrite– SmCo: Samarium Cobalt– NeFeBo: Neodymium Iron Boron

• none is generally “better” or “worse”

COURSE# - 14


• a comparison of different magnet materials

COURSE# - 15

Basic PM motor operating principles

COURSE# - 16


• PM motors operate on the principle that a force is generated when current flows in an inductor that is placed in a magnetic field

COURSE# - 17


• force generated in a conductor in a magnetic field

rflux vecto magnetic :

flux) magnetic ular to(perpendicconductor theof length :

conductor thein flowingcurrent : vectorforce mechanical :

Β

l

iF

ΒliF

m

m ⊗⋅=

COURSE# - 18


• this force generates torque in a rotary motor

conductor thein flowingcurrent :conductors ofnumber :

length)(stack lengthconductor effective :radius windingaverage :

flux magnetic :uerotor torq :

iZlrBT

iZlrBT ⋅⋅⋅⋅=

COURSE# - 19


• a conductor that moves in a magnetic field generates a voltage

rflux vecto magnetic :

field magnetic thelar toperpendicuinductor ofy velocit:

voltageinduced :

0

x

y

l

xy

B

v

V

vlBdzBvV ⋅⋅−=⋅⊗= ∫

COURSE# - 20


• a rotary motor produces the back-EMF (Lenz’s Law)

locityangular ve :condutors ofnumber :

length)(stack lengthconductor effective :radius :

rflux vecto magnetic : voltageinduced :

ω

ω

ZlrBV

ZlrBV ⋅⋅⋅⋅−=

COURSE# - 21


• inductor loop in a magnetic field

COURSE# - 22


• adding a mechanical commutator yields a brush PMDC motor

• adding two or more mechanically offset windings yields a PM DLDC or PM BLAC motor

COURSE# - 23

Basic motor parameters

COURSE# - 24


• the torque constant Kt

A) / m(N

m)(N

⋅⋅⋅⋅=

⋅⋅=

ZlrBK

KT

t

t ω

COURSE# - 25


• the back-EMF (voltage) constant Ke

sec)(volt/rad/

(volt)

ZlrBK

KV

E

E

⋅⋅⋅=

⋅= ω

COURSE# - 26


• armature resistance Ra (Ohm)

• armature inductance La (Henry)

• electrical time constant τe (sec)

• rotor inertia Jr (Kg · m2)

• damping constant Dm (N · m / rad / sec)

• mechanical time constant τm (sec)

• thermal resistance RΘ (°C / Watt)

• thermal capacitance CΘ (Joules / °C)

• thermal time constant τtherm (sec)

COURSE# - 27


• example of a typical speed/torque curve of a PM motor

COURSE# - 28


• the “Safe Continuous Operating Area” SCOA– the motor can safely be operated continuously

anywhere in this region

• the “Safe Intermittent Operating Area” SIOA

– the motor may be operated in this region for short periods of time (typically < 1 min)

COURSE# - 29


• the electrical equation for the PM DC machine is:

ω⋅+⋅+⋅= Eaa KIRdtdILV

COURSE# - 30


• the electrical equation for a single phase of the PM BLDC/BLAC machine with sinusoidal phase current is:

( )dtdKIRLV Eaaϑϑππϑπϑππϑ ⋅

⋅⋅⋅

⋅⋅+

⋅⋅⋅⋅+

⋅⋅⋅

⋅⋅= )

3602sin(

3602)

3602sin()

3602cos(

3602

COURSE# - 31


• the power balance for the PM DC machine is:

ωωω

ω

⋅++⋅++⋅

+⋅+⋅

=

⋅⋅+⋅+⋅

=

)()()2

()2

(

)2

(

22

22

22

LmLM

E

TTDDJdtdIRIL

dtdP

IKIRILdtdP

COURSE# - 32


• the power analysis reveals that:

losses friction : )(

losses damping : )(

energy mechanical : )2

(

heat - windings thein lossescopper electrical :

energy ionmagnetizat : )2

(

2

2

2

2

ω

ω

ω

⋅+

⋅+

⋅

>⋅

⋅

Lm

LM

TT

DD

Jdtd

IR

ILdtd

COURSE# - 33


• the power supplied to the load is:

- 2 ωωω ⋅⋅−⋅⋅= mMEmech TDIKP

COURSE# - 34


• the maximum continuous torque allowed is:

(A) )(

25maxcont

Θ

°

⋅−

=RTR

TTIrise

Crise

• the maximum continuous current allowed is:

m)(N )(

)( 25maxcont

⋅⋅

−⋅=

Θ

°

RTRTTTKT

rise

Criseriset

COURSE# - 35

Motor construction

COURSE# - 36

Motor construction

• the field in the stator poles changes continuously, thus we must use laminated steel to reduce eddy current losses

• the backiron to support the PM flux is relatively constant and solid steel can be used

COURSE# - 37

Motor construction

COURSE# - 38

Motor construction

• the eddy current losses are:

)m / (ohmy resistivit electrical me volu: volumelamination :

(T)density flux ACpeak :(m) slamonation theof kness thic:

(Hz)motor theoffrequency electrical :

6

3

2222

eddy

ρ

τ

ρτπ

VΒ

f

VΒfP

P

P=

COURSE# - 39

Motor construction• motor steel choices

COURSE# - 40

Motor construction

• motor windings are generally copper wire with insulation (magnet wire)

• magnet wire comes in different grades– temperature

• B, F, H, C– insulation

• double, triple• voltage rating

COURSE# - 41

Motor construction

• the resistance of the magnet wire changes with (the wire’s) temperature

C0.0039/ is value theecopper wirfor t coefficien thermal :C)( re temperatu winding :

(ohm) C25 typicallyre, temperatureferenceat resistance :

]1[

0

00

°°

°

⋅+⋅=

α

α

T)R(T

)(T - T)R(TR(T)

the basics of permanent magnet motor operationselectrathonoftampabay.org/www/documents/motors... ·...

Documents