VIII. Armature Reaction 55. At no load, that is, with no current in the armature cir- cuit, the magnetic field of the commutating machine is sym- metrical with regard to the field poles. Thus the density at the armature surface is zero at the point or in the range midway between adjacent field poles. This point, or range, is called the "neutral" point or "neutral" range of the commutating machine. Under load the armature current represents a m.m.f. acting in the direction from commutator brush to commutator brush of opposite polarity, that is, in quadrature with the field m.m.f. if the brushes stand midway between the field poles; or shifted against the quadrature position by the same angle by which the commutator brushes are shifted, which angle is called the angle of lead. If n = turns in series between brushes per pole, and i = cur- rent per turn, the m.m.f. of the armature is Fa = ni per pole. Or, if r?o = total number of turns on the armature, nc = number of turns or circuits in multiple, 2np = number of poles, and t'0 = total armature current, the m.m.f. of the armature per pole is Fa = ^ — This m.m.f. is called the armature reaction of the 2npnc continuous-current machine. Since the armature turns are distributed over the total pitch of pole, that is, a space of the armature surface representing 180 deg., the resultant armature reaction is found by multiplying 194 ELEMENTS OF ELECTRICAL ENGINEERING C -j- go 2 Fa with the average cos = — , and is thus — yu ^" Fao 2 Fa 2 ni When comparing the armature reaction of commutating ma- chines with other types of machines, as synchronous machines 2 Fa etc., the resultant armature reaction Fao = - - has to be used. In discussing commutating machines proper, however, the value Fa = ni is usually considered as the armature reaction. 56. The armature reaction of the commutating machine has a distorting and a magnetizing or demagnetizing action upon the magnetic field. The armature ampere-turns beneath the field poles have a distorting action as discussed under " Magnetic Dis- tribution" in the preceding paragraphs. The armature ampere- turns between the field poles have no effect upon the resultant field if the brushes stand at the neutral; but if the brushes are shifted, the armature ampere-turns inclosed by twice the angle of lead of the brushes have a demagnetizing action. Thus, if r = pole arc as fraction of pole pitch, TI = shift of brushes as fraction of pole pitch, Fa the m.m.f. of armature reaction, and FQ the m.m.f. of field excitation per pole, the demag- netizing component of armature reaction is riFa, the distorting component of armature reaction is rFa, and the magnetic density at the strengthened pole corner thus corresponds to the m.m.f. rFa rFa FQ + -£- at the weakened field corner to the m.m.f. FQ g—