154

ELECTRICAL APPARATUS

In the same manner, the seventh space harmonic gives
£ _ _j^ the ninth space harmonic S = + %, etc.

91. As seen, the component torque curves of the harmonics
of the space distribution of magnetizing force and magnetic
flux in the motor air gap, have the same characteristics as the
component torque due to the time harmonics of the impressed
voltage wave, and thus are represented by the same torque
diagrams:

Fig. 55 for a quarter-phase motor,

Fig. 56 for a three-phase motor.

Here again, we see that the three-phase motor is less liable
to irregularities in the torque curve, caused by higher harmonics,
than the quarter-phase motor is.

Two classes of harmonics thus may occur in the induction
motor, and give component torques of lower synchronous speed:

Time harmonics, that is, harmonics of the voltage wave,
which are of higher frequency, but the same number of motor
poles, and

Space harmonics, that is, harmonics in the air-gap distribu-
tion, which are of fundamental frequency, but of a higher number
of motor poles.

Compound harmonics, that is, higher space harmonics of
higher time harmonics, theoretically exist, but their torque
necessarily is already so small, that they can be neglected, except
where they are intentionally produced in the design.

We thus get the two classes of harmonics, and their
characteristics:

Order of harmonic
1
3
5
7
9
11
13
15
17

Quarter-phase motor: Phase rotation ...............
-fl
P f P
4--fl
p f P
3/
P f
0
3/ (3p)
0
5/
P /
-M
5/ P / 5p
-H 7/ P /
7/ /
9/ P / 9p
0
(±^7)
9/ (3p)
0
-Mi il/ p f lip
-Mi ll / p f lip
-f-
13 / P f 13 p
-f 4-Ma 13 / P / 13 p
15/ P / 15 P
0 0
-f-
17/ P f 17 p
17 f P f 17 p

Synchronous speed

{ Frequency ..........

Time H i T. T . _ I No. of poles

_ __ f Frequency ........

Space H < ^AC^ueu^ ......... I No of poles

Three-phase motor: Phase rotation. .

Synchronous speed ..........

m. __ f Frequency.

Time H \ riet*ufnY .......... i JNo. oi poles. .....

Space H { XT 1 No. of poles ........