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Lumped Electromechanical Elements
In the design of rotating machines, especially for operation on alternating currents, it is
desirable to have a system similar to that in Fig.
2.1.3
but to modify it in such a way that the
mutual inductance varies cosinusoidally with
O(L,
=
Mcos
0).
This is accomplished
by
putting additional slots and windings at different positions around the periphery of both
members.
By
using a proper distribution of slots and numbers of turns the dependence of
L,
can be made the cosinusoidal function shown
by
the dashed curve in Fig. 2.1.4. In many
later examples we assume that this design process has been followed.
When the two currents
i.
and i, and the angular position
0
are functions of time and the
mutual inductance is expressed as
Lm
=
M
cos
0,
we can write the terminal voltages as
dir
dil
di
di
V
1
=
=
L
1
"
+
M
cos
d

iM
sin
0
dt
dt
dt
dt
d)a,
di
di
de
v=
L,

+
M
cos
0


ilM
sin

.
dt
dt
dt
dt
Note that the first term in each expression is a derivative with a constant coefficient,
whereas the last two terms are derivatives with timevarying coefficients.
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 Fall '11
 Liu

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