128 



SYNCHRONOUS MOTORS 



neutralize this armature-flux. The result is that the armature-reaction, 

 or the apparent inductance in the armature, is reduced about one-half 

 and, at the same time, the noise of single-phase alternators disappears. 

 The loss of energy is much lower than might be supposed, because 

 it eliminates, incidentally, the hysteresis-effect in the fields. In any 

 case, the damping effect can be regulated easily to an amount that is 

 deemed sufficient, as can be seen in the following manner: 



Suppose the motor departs from synchronism; the period of 

 its induced E.M.F. is no longer the value T, but a slightly different 

 value, T'. The coefficient of mutual induction between the armature- 

 circuit and the damping-circuit, being a periodic function of the angle 

 described by the moving part, can be written in the following form: 



in which f is the phase-angle measured from the origin of time. 

 The current can be represented by the following expression: 



7=/o sin 27T +/ ' sin ( 27r^ 7 -/?Y 



The flux sent into the damping-circuit by the induced current, at 

 each instant will be 



$=MI= MQ!Q Sin 271 sin ( 271 -f\ 



+ A/o/o sin \2n-p\ sin ^2^ - 

 or, substantially, if we confine ourselves to the first term, 



(i) 



The corresponding E.M.F. will be 



M \ ^(7+^)^0 sin [(f+^)/- r ] 



