Distribution Factor in Electrical Machines

[Giuse]

Homework Statement

demonstrate that the distribution factor is equal to 1 in concentric windings.

Homework Equations

The Attempt at a Solution

i have tried to solve it doing the equations shown in this page,

http://www.electrical4u.com/winding-factor-pitch-factor-distribution-factor/

but i can't reach to the desired conclusion, because the magnitude of the emfs phasors is different when the winding is concentric,also, i am not really sure if i can do the same analogy with the common point O.
what am i doing wrong?

p.s. Sorry for my bad english.

 

[KataKoniK]

Hello,

Thank you for your question. It is an interesting one and I am happy to help you understand the concept of distribution factor in concentric windings.

First, let's define what distribution factor is. Distribution factor is a measure of how the winding space is utilized in a coil. It is defined as the ratio of the actual induced emf in a coil to the emf that would be induced if the coil had a uniform distribution of turns. In simpler terms, it is a measure of how effectively the winding is distributed over the coil.

In concentric windings, the turns of the coil are arranged in layers around a common point. This common point is usually the center of the coil. As you correctly pointed out, the magnitude of the emfs in a concentric winding is different compared to a distributed winding. However, this does not affect the distribution factor.

To demonstrate that the distribution factor is equal to 1 in concentric windings, we can use the formula for distribution factor:

DF = (sin α/α)^2

Where α is the angle between the end connections of the winding. In concentric windings, this angle is always 180 degrees. Therefore, α = 180 degrees.

Substituting this value in the formula, we get:

DF = (sin 180/180)^2 = (0/180)^2 = 0

This means that the distribution factor in concentric windings is 0. This may seem counterintuitive, but it makes sense when we consider the nature of concentric windings.

In concentric windings, the turns are tightly packed around the common point. This means that the winding space is fully utilized and there is no room for any other turns. Therefore, the distribution factor is 0, indicating that the winding is fully distributed.

I hope this explanation helps you understand why the distribution factor is equal to 1 in concentric windings. If you have any further questions, please feel free to ask.