Problem 108-3    Source:   Problem prepared by the site authors.

Considering the motor data in the previous problem and assuming a slip of s = 0.045, find:

a) the air gap power;

b) the induced torque in the motor;

d) the load torque.

Solution of the Problem 108-3   

Item a

Since we know the value of the mechanical power (1,130 W) calculated in the previous problem, we will use eq. 108-27. Therefore, the power in the air gap is equal to:

Item b

Since the motor has 4 poles and the network 60 Hz, then the synchronous angular speed, ω_sync, is:

And the torque induced in the machine, τ_ind, is given by eq. 107-32, repeated below.

Replacing the variables with their respective numerical values and performing the calculation, we obtain:

Item c

To calculate the torque on the load, it is necessary to calculate the angular speed of the motor rotor. Thus, using eq. 108-22, we obtain:

Now, to calculate the torque on the load, we will use eq. 108-17, repeated below.

The value of P_n has already been calculated in problem 108-2 and is equal to P_n = 990 W. So, substituting these values into eq. 108-17, we obtain: