Figs. 1,601 to 1,604.—Synchronous motor principles VII. An essential condition for synchronous motor operation is that the mechanical lag be less than 90°. Figs. 1,601 and 1,602 represent the conditions which prevail when the lag of the motor armature A'B'C'D' is anything less than 90°. As shown, the lag is almost 90°. The direction of the current and induced poles are indicated by the arrows. The inclination of the motor coil is such that the repulsion of like poles produces a torque in the direction of rotation, thus tending to keep motor in operation. Now, in figs. 1,603 and 1,604, for the same position of the alternator coil ABCD, if the lag be greater than 90°, the inclination of the motor coil A'B'C'D' is such that at this instant the repulsion of like poles produces a torque in a direction opposite to that of the rotation, thus tending to stop the motor. In actual operation this quickly brings the motor to rest, having the same effect as a strong brake in overcoming the momentum of a revolving wheel.
Figs. 1,605 to 1,608.—Synchronous motor principles: VIII. If the torque and current through the motor armature be kept constant, strengthening the field will increase the mechanical lag, and the lead of the current with respect to the reverse pressure. In the figures, let A be an instantaneous position of the alternator coil, A°, synchronous position of motor coil, A', position corresponding to current phase, A", actual position or mechanical lag of motor coil behind alternator coil necessary to maintain equilibrium. In fig. 1,606, let A' and A" represent respectively the relation of current phase and mechanical lag corresponding to a certain load and field strength. For these conditions OG, O'G', O"G", etc., will represent the components of the induced lines of force in opposition to the motor field, that is, they indicate the intensity of the armature reaction at the instant depicted. Now, assume the field strength to be doubled, as in fig. 1,608, the motor load and current being maintained constant. Under these conditions, the armature reaction must be doubled to maintain equilibrium; that is, the components OG, O'G', etc., fig. 1,608, must be twice the length of OG, O'G', etc., fig. 1,605. Also since the current is maintained constant, the induced magnetic lines OF, O'F' are of same length in both figures. Hence, in fig. 1,608 the plane of these components is such that their extremities touch perpendiculars from G, G', etc., giving the other components FG, F'G', etc. The plane A', normal to OF, O'F', etc., gives the current phase. By construction, the phase difference between A° and A' is such that sin A°OA' (fig. 1,608) = 2 × sin A°OA' (fig. 1,606). That is, doubling the field strength causes an increase of current lag such that the sine of the angle of this lag is doubled. Since the intensity of the armature reaction depends on the lead of the current with respect to the reverse pressure, the mechanical lag of the coil must be increased to some position as A" (fig. 1,608), such as will give an armature reaction of an intensity indicated by the components OG, O'G', etc.
The following simple formula gives the speed relations between generators and motors connected to the same circuit and having different numbers of poles.
| P × S | ||
| s | = | |
| p |
in which