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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
The Physics of Permament Magnets
• a typical magnetization curve for a PM magnet is shown here
COURSE# - 5
The Physics of Permament Magnets
• 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 Physics of Permament Magnets
• 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
The Physics of Permament Magnets
• 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 Physics of Permament Magnets
• the magnet’s flux changes with temperature– reversible– irreversible
COURSE# - 9
The Physics of Permament Magnets
• 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
The Physics of Permament Magnets
• irreversible changes can occur in the magnet well below its Curie temperature
COURSE# - 11
The Physics of Permament Magnets
• 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
The Physics of Permament Magnets
• each PM motor therefore has
– a thermal current rating due to wire constraints– an absolute peak current rating due to magnet constraints
COURSE# - 13
The Physics of Permament Magnets
• 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
The Physics of Permament Magnets
• a comparison of different magnet materials
COURSE# - 15
Basic PM motor operating principles
COURSE# - 16
Basic PM motor operating principles
• PM motors operate on the principle that a force is generated when current flows in an inductor that is placed in a magnetic field
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Basic PM motor operating principles
• 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
Basic PM motor operating principles
• 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
Basic PM motor operating principles
• 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
Basic PM motor operating principles
• 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
Basic PM motor operating principles
• inductor loop in a magnetic field
COURSE# - 22
Basic PM motor operating principles
• 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
Basic motor parameters
• the torque constant Kt
A) / m(N
m)(N
⋅⋅⋅⋅=
⋅⋅=
ZlrBK
KT
t
t ω
COURSE# - 25
Basic motor parameters
• the back-EMF (voltage) constant Ke
sec)(volt/rad/
(volt)
ZlrBK
KV
E
E
⋅⋅⋅=
⋅= ω
COURSE# - 26
Basic motor parameters
• 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
Basic motor parameters
• example of a typical speed/torque curve of a PM motor
COURSE# - 28
Basic motor parameters
• 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
Basic motor parameters
• the electrical equation for the PM DC machine is:
ω⋅+⋅+⋅= Eaa KIRdtdILV
COURSE# - 30
Basic motor parameters
• 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
Basic motor parameters
• the power balance for the PM DC machine is:
ωωω
ω
⋅++⋅++⋅
+⋅+⋅
=
⋅⋅+⋅+⋅
=
)()()2
()2
(
)2
(
22
22
22
LmLM
E
TTDDJdtdIRIL
dtdP
IKIRILdtdP
COURSE# - 32
Basic motor parameters
• 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
Basic motor parameters
• the power supplied to the load is:
- 2 ωωω ⋅⋅−⋅⋅= mMEmech TDIKP
COURSE# - 34
Basic motor parameters
• 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)