Torque Production - Rotor induced e.m.f., current and torque
Rotor Induced EMF, current and torque:
Fig: 1 Variation of rotor induced e.m.f and frequency with speed and slip
- The pattern of instantaneous voltages in the rotor is thus a replica of the flux density wave, and the rotor induced ‘voltage wave’ therefore moves relative to the rotor at slip speed, as shown in Figure 2.
- Since all the rotor bars are short-circuited by the end-rings, the induced voltages will drive currents along the rotor bars, the currents forming closed paths through the end-rings, as shown in the developed diagram In Figure 3 the variation of instantaneous e.m.f. in the rotor bars is shown in the upper sketch, while the corresponding instantaneous currents flowing in the rotor bars and end-rings are shown in the lower sketch.
- The lines representing the currents in the rotor bars have been drawn so that their width is proportional to the instantaneous currents in the bars. The axial currents in the rotor bars will interact with the radial flux wave to produce the driving torque of the motor, which will act in the same direction as the rotating field, the rotor being dragged along by the field.
Fig 2: Pattern of induced e.m.f.’s in rotor conductors. The rotor ‘voltage wave’ moves at a speed of sN with respect to the rotor surface
- We note that slip is essential to this mechanism, so that it is never possible for the rotor to catch up with the field, as there would then be no rotor e.m.f., no current and no torque. Finally, we can see that the cage rotor will automatically adapt to whatever pole number is impressed by the stator winding, so that the same rotor can be used for a range of different stator pole numbers.
- The rate at which the rotor conductors are cut by the flux – and hence their induced e.m.f. – is directly proportional to the slip, with no induced e.m.f. at synchronous speed (s = 0) and maximum induced e.m.f. when the rotor is stationary (s = 1).
- The frequency of rotor e.m.f. is also directly proportional to slip, since the rotor effectively slides with respect to the flux wave, and the higher the relative speed, the more times in a second each rotor conductor is cut by a N and a S pole.
Fig: 3 Instantaneous sinusoidal pattern of rotor currents in rotor bars and end-rings. Only one pole-pitch is shown, but the pattern is repeated
- At synchronous speed (slip = 0) the frequency is zero, while at standstill (slip ¼ 1), the rotor frequency is equal to the supply frequency. These relationships are shown in Figure 1.
- Although the e.m.f. induced in every rotor bar will have the same magnitude and frequency, they will not be in phase.
- At any particular instant, bars under the peak of the N poles of the Weld will have maximum positive voltage in them, those under the peak of the S poles will have maximum negative voltage (i.e. 1800 phase shift), and those in between will have varying degrees of phase shift.