To begin with, let us assume that the rotor circuit is open so that there is no current flowing in it, no electromagnetic forces are acting on the rotor, and it is at rest. Then the magnetic field in the machine will be solely due to the revolving magnetic field of the stator.
The winding of a squirrel-cage rotor consists of N bars. The phase difference between the emfs induced in two adjacent bars by the revolving magnetic field of the stator is 3600 p/N , It may be taken that the number of phases in a squirrel-cage rotor is equal to the number of bars. m2 = N, and that each phase has w2 = 1/2 turn.
Similarly, the circuit of a wound rotor is a three-phase system, m2 = 3, with w2 turns per phase. (Here and elsewhere the quantities related to a rotor phase will be labelled "2", and those related to a stator phase will be labelled "1".)
So long as the rotor is at rest, the frequency of the emf induced in the rotor winding is equal to the frequency f of the current in the stator circuit. When the rotor is rotating with the revolving stator field at the speed n, the frequency of the emf induced in the rotor winding goes down. This frequency can be deduced from Eq. (14.7) in which n1 should be replaced with the difference n1 - n because the revolving stator field can cut the rotor turns only when the rotor is lagging in speed behind the field
f2 = P (nl - n)/60
If we do not complete the rotor circuit, the currents in it will form a multiphase system (m2 = N) in the case of a squirrel-cage rotor, and a three-phase system (m2 = 3) in the case of a wound rotor. Acting similarly to the currents in the stator winding, they will produce a revolving magnetic field. The speed of this field relative to the rotor, nre1 can be found from the general expression, Eq. (14. 7), for the speed of a multipole field
nre1 = f 2 X 60/p
Since the rotor itself rotates in, the. same direction at the speed n rpm, the rotor field revolves at
nre1 + n = (nl - n) + n = n1
that is, the rotor field revolves at synchronous speed (at the same speed as the field), and faster than the rotor does.
Thus, the revolving fields of the stator and rotor are stationary with respect to each other, which is the decisive condition for a complete transfer of energy from the stator to the rotor. On being combined, the two revolving fields yield the working revolving magnetic field of an induction motor. This field also acts as a link between the stator and rotor windings, similarly to the alternating magnetic field transferring energy from the primary to the secondary in a transformer.
In our subsequent discussion we will call the working revolving field simply the revolving field of an induction machine. It is this field that is used when analysing the events taking place in the stator and rotor circuits.
An induction motor can operate in anyone of three characteristic modes: (1) the rated condition corresponding to the rated slip s = srtd , the rated supply voltage V1 = V1,rtd, and the rated supply current I1 = I1,rtd ; (2) the operating mode when the line voltage is close or equal to the rated value, V1 ≈ V1,rtd , and the load on the motor is determined by the braking torque applied to the shaft at the slip s ≤ srtd and at the supply current Il ≤ Il.rtd ; and (3) the starting condition which arises when the supply voltage is just turned on and the rotor is at rest, S = 1.
The conditions existing in anyone phase of the stator winding is the same as in the remaining two. This is also true of the rotor phases. That is why it is convenient to analyse the operation of only one phase of an induction motor.
Labels: Electricity and Magnetism