Electric machine 2 ioe notes

 pulchowk note for Electric machine 2 ioe em 2 note. ioe old question solution ioeallsubjectnotes

DOUBLE FIELD REVOLVING THEORY

Statement: According to this theory, any alternating quantity can be resolved into two  rotating components which rotate in opposite directions and each having  magnitude as half of the maximum magnitude of the alternating quantity.

In case of single phase induction motors, the stator winding produces an alternating magnetic field having maximum magnitude ofΦ 1m. According to double revolving field theory, consider the two components of  the stator flux, each having magnitude half of the maximum magnitude of  stator flux i.e.(Φ1m/2). Both these components are rotating in opposite direction at the synchronous speed Ns which is dependent on frequency and stator poles. LetΦ f is forward component rotating in anticlockwise direction whileΦ b is  the backward component rotating in clockwise direction. The resultant of these two components at any instant gives the instantaneous  value of the stator flux at that instant. So resultant of these two is the original stator flux.

Fig.1 stator flux and its two components

The fig.1 shows the stator flux and its two componentsΦ f andΦ b. At start both the components are shown opposite to each other in the fig.1.(a). thus  the resultantΦ R=0. This is nothing but the instantaneous value of the stator flux at  start. After 900 as shown in the fig.1(b), the two components are rotated in such a way that both are pointing in the same direction. Hence the resultantΦ is the

algebraic sum of the magnitudes of the two components. So

ΦR=(Φ1m/2)+(Φ1m/2)=Φ1m. This is nothing but the instantaneous value of the stator flux atθ=90 0 as shown in  the fig.1(c). Thus continuous rotation of the two components gives the original  alternating stator flux. Both the components are rotating and hence get cut by the motor

conductors. Due to cutting of flux, emf gets induced in rotor which circulates rotor current

The rotor current produces rotor flux. This flux interacts with forward componentΦ to produce a torque in one particular direction say anticlockwise direction. While rotor flux interacts with backward componentsΦ b to produce a torque in the clockwise direction. So if anticlockwise torque is positive then clockwise torque is

negative. At start these two torques are equal in magnitude but opposite in  direction. Each torque tries to rotate the rotor in its own direction.

Thus net torque experienced by the rotor is zero at start. And hence the  single phase induction motors are not self-starting.

TORQUE SPEED CHARACTERISTICS

The two oppositely directed torques and the resultant torque can be

shown effectively with the help of torque-speed characteristics.

Fig: 2 torque speed characteristics

It can be seen that at start N = 0 and at that point resultant torque is zero. So single phase motors are not self-starting. However if the rotor is given an initial rotation in any direction, the resultant average torque increase in the direction in which rotor initially  rotated. And motor starts rotating in that direction. But in practice it is not  possible to give initial torque to rotor externally hence some modifications are 9  done in the construction of single phase induction motors to make them self-  starting.

forward and backward slip

Rotor started by auxiliary means, it will develop torque & continue to run  in same direction as one of the fields. By definition, the direction in which  rotor is started initially will be called forward field.

Let ns=synchronous speed, n = rotor speed Slip of rotor with respect to forward rotating field is,

Since backward rotating flux rotates opposite to the stator, sign of n must be changed in equation (i) to obtain backward slip.