# How to find the 120 degree phase angle in a single layered lap winding of a synchronous machine?

Ok, so I have a 4 pole synchronous machine with 24 slots meaning each slot has a phase difference of 30 degree with respect to each other.

1)That means pole pitch is 180 degree for a full pitched coil=6 slots. So, if 1 is the start then it's backside connection should be 1+6=7th slot.However, in this pic it's shown as the 6th slot 2)Let's assume Start(S) and End(E) for each coil then the connections are S-E-E-S-E-E-S (start to end to end to start .....) Is this correct ? What I think is happening... The motor produces forces from its poles, not its slots.

Now if you trace the U winding, you find it starts (0 degrees) in the first slot - i.e. after the first pole ... and returns (180 degrees) in the sixth slot i.e. just before the 7th pole.

But keep tracing it ... it starts again in the 12th slot and returns (180 degrees) in the 7th slot.

Thus the slots either side of the 7th pole are in phase, both 180 degrees.

Keep tracing the winding and you'll find slots 1 and 24 are both 0 degrees, as are slots 12 and 13, meaning poles 1 and 13 are 0 degrees. Likewise slots 6,7,18,19 are 180 degrees, thus poles 7 and 19.

Repeat for the V and W windings.

W1 starts in the 5th slot and returns eventually in the 4th slot, both 120 degrees (the 5th pole being 4 * 30 degrees after the first).

• Ok, so I'm understanding what you're saying is that the start of the 7th slot and the end of the 6th slot have nearly the same phase difference between them? – Nigel Goveas May 20 at 21:11
• Not nearly, precisely. They are the same winding.Slot 1 matches with Slot 7 (180 degrees apart) while Slot 6 matches with Slot 0 (24). – Brian Drummond May 20 at 21:24
• Now I understand why we didn't take the 7th slot because only it's start would be 180° phase shift from the start of the 1st slot. The remaining part of the 7th slot would be greater than 180° phase shift from the start of the 1st slot!! Thanks a lot – Nigel Goveas May 20 at 21:37