OPERATION OF SYNCHRONOUS MOTORS. HUNTING 121 



tarting. The two machines therefore fall readily into step, and if 

 ic resisting couple due to passive mechanical resistances (air-friction, 

 saring-friction, hysteresis, etc.) is not too high, the generator drags 

 e motor, in its progressive acceleration, the two always remaining 

 synchronism. 



Field Due to a Commutated Current. In this case, the effect 

 jroduced is altogether different. Two periods must again be dis- 

 tinguished, i.e., whether cu 2 is very different from a>i, or whether, on the 

 contrary, it is of the same order of magnitude. 



In the first case, i.e. at the beginning of the operation of starting, the 

 irrent is reversed a great number of times, both in the armature and 

 the fields, while the armature is moving an angular distance corre- 

 sponding to a period T 2 . The motor behaves like a commutator- 

 motor, and produces a torque which is always in the same direction 

 and which gradually increases the speed. 



In the neighborhood of the normal speed, the effect of the commutator 

 jn the excitation becomes apparent. The alternations of flux are 

 commutated in a dissymmetrical manner, with the consequence 

 that a very powerful field with slow oscillations is produced, on which 

 pulsatory undulations that are more feeble are superposed. This 

 effect may be expressed by the formula, 



= 0Q COS (tfto, 



in which IQ has a value which is variable as a function of the time. 



As soon as the two periods T\ and T 2 are near each other, the small 

 undulations disappear before the large undulation, namely, the undu- 

 lation of /o- The frequency, =r, of this great oscillation is evidently 



equal to the least common multiple of and . The period, T' y 



1\ 2 



therefore, lengthens indefinitely, when T 2 approaches Ti,at the same 

 time that the value of the field thus produced increases. 



Under these conditions, the power furnished by the motor varies 

 according to a complicated function. The oscillations of the field 

 can be taken into account on replacing ajto by at't and substituting the 

 value 



d 

 E 2 = -= -a/00 sin (a/t-Q, 



