HIGHER HARMONICS 157
and for a fractional-pitch winding of pitch deficiency, p, it thus is :
pnir
COSSr™
an = anQ------------ (19)
/?7T
COS2
93. By substituting the values: q = 4, 6, 3 and p = 0, %,
Ji, M, into equation (1?)7 we get the coefficients an of the
trigonometric series:
F = FQ {cos co + as cos 3 w + as cos 5 co + a7 cos 7 co + . . . },
(20)
which represents the current distribution per phase through the
air gap of the induction machine, shown by the diagrams F of
Fig. 58.
The corresponding flux distribution, <£, in Fig. 58, expressed by
a trignometric series:
<£ = <£o {sin co + &3 sin 3 to + &5 sin 5 co + 57 sin 7 co + . . . }
(21)
could be calculated in the same manner, from the constructive
characteristics of 3> in Fig. 58.
It can, however, be derived immediately from the consideration,
that $ is the summation, that is, the integral of F:
$ = J*Fdo> (22)
and herefrom follows:
bn = £ (23)
and this gives the coefficients, Z>n? of the series, $.
In the following tables are given the coefficients an and bn,
for the winding arrangements of Fig. 58, up to the twenty-first
harmonic.
As seen, some of the lower harmonics are very considerable
thus may exert an appreciable effect on the motor torque at low
speeds, especially in the quarter-phase motor. •