Why duplex lap winding has twice as many current paths as simplex lap winding?

Question

I found the statement of question on page 346 in the book "Electric Machinery Fundamentals, fifth edition" written by Stephen J. Chapman.

When I searched for how duplex lap winding looks like, I found the figure in this link: https://circuitglobe.com/lap-and-wave-winding.html#:~:text=The%20duplex%20lap%20winding%20is,number%20to%20the%20second%20winding, which is also cited in this thread: DC motor armature rewinding.

However, it seems to me the figure shows that the number of current path is the same as the simplex lap winding but with twice the length of current path. Why the number of current paths in a DC electric machine is m * P, where m means m-plex, P is the number of poles on the machine?

Answer 1

The diagram you found is pretty hard to understand, but seems to have proliferated.

A simplex lap winding has only a single coil. If you were to remove the brushes and put an ohm-meter on each commutator bar, you would see that they are all connected through the windings. Here is a picture from https://www.physicsforums.com/threads/some-basic-questions-about-a-dc-motor-and-a-dc-generator.982698/ that demonstrates this.

Trace the current paths from the red wires to the black ones, and you will see that the current flows in the direction of the arrows and each winding changes direction at each pole, as the arrows conveniently show. There are four poles and four current paths.

Here is another picture from https://holooly.com/solutions/design-and-draw-a-2-layer-progressive-duplex-lap-winding-for-a-6-pole-d-c-generator-with-24-slots-each-slot-having-2-coil-sides-indicate-the-direction-of-motion-position-of-poles-position-of-brush/ showing a duplex winding:

Not an ideal second picture, since the first was a four-pole and this one is a six-pole. But this time, if you were to remove the brushes, the odd-numbered commutator bars would not be connected to the even-numbered ones, so there are two distinct windings, and the brushes in this picture span two bars, so both coils are energized. So this would be a six-pole generator with 12 current paths.