Problem 107-7    Source:   Adapted from example 6-3 - page 326 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

Based on results from previous issue (Problem 107-6) get the following engine quantities:

a) the mechanical power, P_mec, and the nominal power, P_n ;

b) the induction torque, τ_ind, and the load torque, τ_load ;

c) the efficiency or yield, η, of the engine.

Solution of the Problem 107-7   

Item a

As we know the power factor PF = 0.831 we can calculate the input power of this motor using the eq. 107-22.

It is also possible to calculate stator losses, or:

Doing the math, we find:

Using the eq. 107-21 we can calculate the power in the air gap, P_gap. Remembering that iron losses are included in rotational losses. So, in eq. 107-21   we despise P_iron. Soon:

Knowing the value of P_gap we can calculate the mechanical power in the rotor, or:

Then the output or nominal power will be the difference between the mechanical power and the rotational losses. Soon:

Item b

The torque or induced torque of the machine is given by eq. 107-32.

Doing the math, we find:

And the nominal torque or output torque of the machine is given by eq. 107-33.

Doing the math, we find:

Item c

Under the conditions in which the engine is operating, the efficiency is: