Problem 107-1    Source:   Adapted from example 6-1 - page 315 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

A three-phase induction motor of 208 V, 10 HP, 4 poles is connected to a network at 60 Hz na star setting. It has a full load slip of 5%. To determine:

a) the synchronous speed of the motor;

b) the speed of the rotor with rated load;

c) the rotor frequency at rated load;

d) the torque on the motor shaft, when at full load.

Solution of the Problem 107-1   

Item a

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

Replacing with numerical values ​​and carrying out the calculation, we obtain:

Item b

The rotor speed is given by eq. 107-05, repeated below.

Replacing with numerical values ​​and carrying out the calculation, we obtain:

Item c

The rotor frequency is given by eq. 107-07, repeated below.

Replacing with numerical values ​​and carrying out the calculation, we obtain:

Item d

To calculate the value of the torque at full load, τ_load, we must know the value of the angular velocity, ω_r, from the engine. We have already calculated n_r, so doing the transformation we obtain:

Now we can use eq. 107-33, as we know that P_n = 10 (HP) x 746 (W/HP) = 7,460 W. Soon: