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EE – 4420
Electric Machine Analysis
Fall 2005
ROTATING MAGNETIC FIELD
1.
Magnetic field in the machine with singlephase winding
Twopole machine with single coil (phase) is shown in Fig.1. If supplied by dc.
current the magnetic flux does not change in time. The mmf distribution along the
machine airgap (angle
Θ
) is described by rectangular wave as shown in Fig.2. Its first
harmonic is described by the function:
FF
m
11
Θ
a
f
a
f
=
sin
(1)
(a)
(b)
X
A
1
A
2
A
stator (armature)
rotor
coil (winding)
in the slot
1
2
4
3
magnetic flux
magnetic flux
represented by
vector
A
1
A
2
Coil
Fig.1. Twopole machine (a) with single coil (b)
F
Θ
τ
12
3
4
1
(Pole pitch)
(MMF)
F
1
Fig.2 MMF distribution in the airgap on the rotor circumference;
τ
– pole pitch
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If the coil is supplied with sinusoidal current the first harmonic of mmf is expressed
by the function:
()
( ) ( )
11
,s
i
n
c
o
s
m
Ft
F
t
ω
Θ=
Θ
(2)
The magnetic flux generated in the machine changes in time sinusoidally. Applying
the geometrical transformation to equation (2) we get:
1
i
n
s
i
n
22
mm
F
t
F
t
Θ
−
+
Θ
+
(3)
It means, the alternating magnetic flux can be represented by two magnetic fluxes
moving in opposite directions with the same speed and their amplitudes are half of
alternating flux. Fig.3 shows the vector of alternating flux as the sum of two rotating
fields drawn for two time instants t
1
and t
2
.
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This note was uploaded on 02/26/2012 for the course EE 4150 taught by Professor Wu during the Fall '10 term at LSU.
 Fall '10
 Wu
 Flux

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