Problem 102-1    Source:   Example 7-3 - page 447 - CHAPMAN, Sthephen J. -    Book: Fundamentals of Electric Machines - 5th Edition - Ed. McGraw-Hill - 2013.

A duplex armature with lap winding is used in a six-pole DC machine with six sets of brushes, each one spanning two segments of the switch. There are 72 coils on the armature, each with 12 turns. The flux per pole of the machine is 0.0039 Wb and it is turning at 400 rpm. Find:

a) how many current paths are there in this machine?

b) what is the induced voltage E_A?

Solution of the Problem 102-1   

Item a   

The number of current paths in this machine is given by eq. 102-08, repeated below.

So, replacing the variables by their respective values, knowing that for a duplex armature m = 2, we find

Item b   

To calculate the induced voltage in the armature it is necessary to calculate the number of conductors in the machine, Z, given by eq. 102-04 shown below.

Then, replacing the variables by their respective values, we find

We are now in a position to calculate the constant K_a using eq. 102-14, shown below.

Then, replacing the variables by their respective values, we find

With all these calculated values we are able to find the value of the induced voltage E_A, using eq. 102-13 shown below.