I vote LPS to both of the previous responders who are more knowledgeable about windings than me. I am just a student of windings – and I try to take the opportunity to learn when things like this come up on the board. (I’m doing that now)
After reading above responses and reviewing some references, I’d like to try to restate it from my perspective (open to comment).
Two pole motor coils tend to have very long span which causes lots of problems:
difficult to install, uses more copper in endwindings, increases leakage reactance due to long endwindings, makes cooling of endwindings more difficult, harder to accommodate clearances etc.
We can try to cut down on the coil pitch, but then we pay a price in pitch factor (low fundamanetal pitch factor and high harmonic pitch factor and harmonic leakage reactance). For example:
For your 2-pole motor with 54 slots.
Full pitch would be 1-28 (spans 27 teeth)
Here we have gotten all the 15 way down to a coil pitch of 1-16 (spans 15 teeth).
It is 15 / 27 = 56% of full pitch.
So we don’t have such long pitch or endwinding and those problems are gone.
If this pitch 15 was used on traditional winding, the pitch factor would be:
Kp(nu) = SIN(nu*Tau_coil*PI/(2*Tau_fullpitch))
Kp(nu) = SIN(nu*15*PI/(2*27))
Kp(1) =0.766
Kp(5) = -0.940
The pitch factor for fundamental (1) is very low and pitch factor for 5th harmonic is higher than for the fundamental! Not good at all.
So what do they do to make the harmonics lower? I don’t think traditional pitch factor can be used to describe this oddball configuration (interspersed). But I think we can understand the same thing by focusing on the smoothness of transition between phase belts instead of harmonics (because they represent the same thing, an abrupt transition in pattern is a square wave in mmf which is associated with harmonics).
In traditional lap winding, the center coils of pole phase group A will have top coils associated with phase A and bottom coils associated with phase A. The outer coils of that phase group of only top or bottom coils from A phase, while the other coil in the same slots are from phase B on one end of the group and from phase C on the other end. This provides a smooth blending in transition of the time angle of the mmf: it is completely aligned with phase A in the center of the A-phase pole phase group, and it shifts by roughly 60/2 = 30 degrees the outer coils where the A phase is combined with another phase that is 60 degrees away.
What would be the minimum span to implement that lap winding strategy in this motor. Let’s say the top coils of phase A occupy slots 1 through 9 and 28 through 37. We want the bottom half of the A phase coils whose top is at 9 to overlap the A phase coil at position 28 (minimum possible overlap is one slot). The coil span would be 9 to 28 (similar to 1 to 20), encompassing 19 teeth. It’s a longer span that the 16, and it doesn’t do a great job with harmonics because there is only one overlap in the middle. More overlap would be required to improve the harmonics which would cause even longer span.
Assume we don’t want the long span 19+ for reasons discussed above. Then we still have to create the smoothly changing angle as we transition from one phase to the next, but we can’t do it by making the clump of center slots A/A and the outer slots A/B or C/A. That leads to a strategy of interspersed windings where all (almost all*) slots of the pattern have only one coil from phase A, and to accomplish the smooth blend, we include some slots with NO phase A toward the outside of the pole phase group. Since the coils tend to average with their neighbors for all harmonics (except those that are too high order to worry about) , it gives a smoother blend.
Here, you have A phase winding top layer in slots
TopA1: 07, 09, 11, 12, 13, 14, 15, 17, 19
TopA2: 34, 36, 38, 39, 40, 41, 42, 44, 46
With coil pitch 1-15, the bottom coils of above slots will lie in
BottomA1: 22, 24, 26, 27, 28, 29, 30, 32, 34
BottomA2: 49, 51, 53, 54, 01, 02, 03, 04, 06
Combining like-polarity physically-adjacent groups Top2 and Bottom1:, we see the following pattern for this polarity of A phase:
TopA2: 34, 36, 38, 39, 40, 41,42, 44, 46
union..
BottomA1: 22, 24, 26, 27, 28, 29, 30, 32, 34
=…
22, 24, 26, 27, 28, 29, 30, 32, 34, 34, 36, 38, 39, 40, 41,42, 44, 46
Empty spots in the pattern (no A): 23, 25, 31, 33, 35,37, 43, 45
Double Spots in pattern (A top and bottom): 34 (exact middle)
The double spot in the center of the pattern and moreso the empty spots toward the outside of the pattern help to create a sinusoidal pattern with gradual change towards the edges of the pattern, which is what we want to avoid harmonics. The empty spots toward middle of pattern are not particularly helpful but also not particularly harmful considering two things;
1 – the top of a sine wave is relatively flat, so surpressing the peak in the center with these empty spots is not particularly harmful.
2 – the harmonic which is excited by depressing the peak of a sinusoid is the 3rd harmonic, which can be cancelled by wye connection.
Of course above only considered A phase and then we narrowed down to include only the coil sides of like polarity BottomA1 / Top A2. B and C are also present in any empty top/bottom/both positions in the above pattern and they will be 60 degrees different.
To fully analyse this winding, I’d say we cannot use the concept of pitch factor and distribution factors because those concepts have embedded assumptions about the standard winding which are not met. I think we would have to use a brute force spreadsheet which does vectorial sum of the contributions from all slots (including top and bottom), with each contribution’s angle adjusted based on
1 – position
2 – phase and polarity
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(2B)+(2B)' ?