Problem 108-7    Source:   Adapted from Example 9-1 - page 595 - CHAPMAN, Stephen J. -   Book: Fundamentals of Electrical Machines - 5th edition - Ed. McGrawHill - 2013.

Based on the data and results found in the previous problem "problesol108-6", find the following quantities:

a) the torque induced in the motor;

b) the nominal power of the motor;

c) the torque on the load;

d) the efficiency of the machine;

e) calculate the losses in the copper of the motor and verify if the law of conservation of energy is preserved.

Solution of the Problem 108-7   

Item a

To calculate the induced torque, we will first calculate the synchronous angular speed of the motor, given by eq. 108-14, shown below.

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

Then, the induced torque using eq. 107-32 will be:

Item b

The rated or output power of the motor is given by eq.108-28, shown below.

Note that rotational losses are given in the problem statement, encompassing friction, ventilation, and core losses. Therefore, substituting the variables with their respective numerical values and performing the calculation, we obtain:

Item c

To find the torque on the load, we need to calculate the motor shaft rotation, or ω_r. We will use the eq. 108-22, shown below.

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

Using eq. 108-17, we can calculate the torque on the load, or:

Item d

And to calculate the engine efficiency, we use eq. 108-31. So:

Item e

Let's check whether the powers involved in the problem are in accordance with energy conservation. The power dissipated in R₁, R_P, and R_R are:

Adding these three powers, we find the total losses in the motor's copper, P_cu = 72.09 W. To this value, we must add the losses stated in the problem statement. Therefore:

Let's use eq. 108-30 and check how much energy we need to power the motor. So:

Performing the calculation, we find:

Therefore, the difference of approximately 2 W in relation to the value calculated in item d in problem 108-6 is perfectly within the tolerance in the calculations. Therefore, it complies with the principle of conservation of energy.