Problem 108-1    Source:   Problem prepared by the site authors.

Suppose a single-phase, 4-pole induction motor with a nominal power of 1 HP and slip of 3%. It is known that it has rotational losses of 120 W and is connected to a 60 Hz power supply. Find:

a) the synchronous speed of the motor in rpm;

b) the shaft speed of the motor in rpm;

c) the mechanical power of the motor;

d) the induced torque of the motor.

Solution of the Problem 108-1   

Item a

To calculate the synchronous speed of the motor we will use eq. 107-02, repeated below.

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

Item b

Knowing the slip and synchronous speed, the motor shaft rotation is:

Item c

Since we know the motor's nominal power of 1 HP = 746 W and its losses, it is possible to calculate the mechanical power using eq. 108-28. After an algebraic arrangement, we obtain:

Item d

In this case, we'll use eq. 108-23. First, we must find the value of ω_r. Since we know the value of n_r, calculated in item b), we just need to perform the transformation, or:

Therefore, the value of the induced torque is: