172 THE MAGNETIC CIRCUIT [ART. 54 



Prob. 10. Show how, in a compound-wound motor, the total 

 required field excitation must be divided between the shunt and series 

 windings in order to obtain a prescribed speed regulation between no- 

 load and full load. 



Prob. 11. Assume the curve OX in Fig. 43 to be given in the form 

 of an analytic equation, B=f(M). Show that the unknown excitation 

 Oa'=3/' is determined by the equation 2M 2 f(M) = F(M'+M 2 ) - 

 1-\M'-M Z ), where the function F is such that dF(M)/dM =f(M)] 

 -l/o = Oa is the excitation corresponding to the given value of e or B = ab. 



Prob. 12. Apply the formula of the preceding problem to the case 

 when the active layer characteristic can be represented by (a) the log- 

 arithmic curve y = a log (1 +bx) ; (6) the hyperbola y = gx/(h+x) ; (c) a 

 part of the parabola (y* 1/ 2 ) =2p(x )> continued as a tangent straight 

 Hue passing through the origin. 



54. Commutating Poles and Compensating Windings. The 

 two limiting factors in proportioning a direct-current machine are, 

 first, the sparking under the brushes, and secondly, the armature 

 reaction. In order to reverse a considerable armature current 

 in a coil during the short interval of time that the coil is under a 

 brush, an external field of a proper direction and magnitude is 

 necessary. In ordinary machines (Fig. 42) this field is obtained 

 by shifting the brushes so as to bring the short-circuited armature 

 conductors under a pole fringe. However, with this method the 

 specific electric loading and the armature ampere-turns must be 

 kept below a certain limit with reference to the ampere-turns on 

 the field ; otherwise the armature reaction would weaken the field 

 to such an extent as to reduce the flux density in the fringe below 

 the required value. Therefore, in many modern machines, instead 

 of moving the brushes to the poles, part of the poles, so to say, are 

 brought to the brushes (Fig. 44). These additional poles are 

 called commutating poles or interpoles. Their polarity is under- 

 stood with reference to Fig. 42 : Since the E brush had to be shifted 

 toward the north pole, now a north interpole is placed over each E 

 brush. 



The armature belts T e , T e , create a strong m.m.f. along the axis 

 of the commutating pole N c , in the wrong direction. Therefore, 

 the winding on each interpole must be provided first with a num- 

 ber of ampere-turns equal and opposite to that of the armature, 

 and secondly with enough additional ampere-turns to establish 

 the required commutating flux. These additional ampere-turns 

 are calculated only for the air-gap, armature teeth, and the pole 

 body itself. The m.m.f. required for the armature core and the 



