Environmental Engineering Reference
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axis of rotation at a distance, r , from its axis of rotation. Torque on each conductor
is F r , so the total motoring action becomes
T
¼
2 Fr
¼
2BIL r
ð
5
:
4
Þ
U
¼
2BL v
¼
2BL r w
Equation (5.4) also includes the definition of the back electromotive force
(back-emf) induced in the same conductors as they rotate through the same
field, and according to Lenz's law, produce an opposition to the current being
injected.
In practical electric machines, the armature conductors reside within slots in an
iron core so that the reluctance to the permanent magnet flux across the gap is
minimized. Similarly, in order to provide a low reluctance magnet flux return path,
an iron sleeve is present around the magnet arcs. In ac electric machines, the
mechanical commutator is replaced by power electronics switches that regulate the
injection of currents into 'armature' windings, or more appropriately, into the fixed
stator windings. The windings are composed of a number of conductor turns per
coil, and multiple coils are present around the periphery of the stator according to
the number of magnetic pole pairs. Figure 5.8 illustrates a 'rolled-out' stator in
which the conductors are evenly distributed per unit length.
I
L
F
X
X
X
X
X
X
X
b
F
m = ∞
A x
I
ds = rdq
B z
Right hand rule
B z
Figure 5.8 Rolled-out stator showing electric loading, A x
The effect of conductors placed into slots in stator iron is an approximation to a
current sheet. The rotor magnets develop magnetic poles that interact with the
stator current sheet. The electromagnetic traction developed by the stator current
sheet, A x , and the magnet flux, B z , located at an angle b from the current sheet
vector is a surface traction, g s oriented in the y direction (tangential in a rotary
motor). The surface traction is the product of stator current sheet, A x , also referred
to as the electric loading, and B z , the magnetic loading. The Lorenz force is pro-
duced by the interaction of the electric and magnetic loading per unit surface area
of the rotor. A term ' Z ' is used to count conductor turns. It is evident from (5.4) that
the orientation angle b should be held as close to 90 as possible for maximum
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