Hey guys. Time zones.
I'll throw my hat in to answer Lou's core question:
My understanding is that when you take two legs of a 208/120V wye source, and supply it to a customer, that is _defined_ as a 'single phase' service. There is some IEEE standards body that lists the recommended service types and voltages to use, and they decided to define it this way.
In practical use, this is a single phase system. You use single phase panelboards, with two ungrounded bus bars. All of your line-line loads are _single phase_. A Blondel Theorem compliant single phase meter would work (however a distinction is that most 120/240 services are served with meters that are not Blondel compliant), etc.
However the real physical reality is that you have multiple phases available. With the two ungrounded legs _and the neutral_, you essentially have severely unbalanced three phase service. With an appropriate set of transformers, you could synthesize the third leg of the wye. A graph of Van and Vbn would show two sine waves displaced by 120 degrees; the normal _three_ phase graph with one of the curves missing.
On to the motor examples: To do this justice, I would really need to have a real time conversation with pictures. I'll try to start with a few pieces, and then let questions guide other aspects.
First: distinguish between _poles_ and _windings_. The windings are the electrical structures that carry current through the motor. The _poles_ are a description of the shape of the magnetic field; describing the number of north and south magnetic poles created by the windings. A single phase winding of complex shape could develop many magnetic poles. A three (or more) phase winding with simple shape can produce as few as 2 poles.
The _simplest_ practical winding is a single coil of wire, stretched across the stator from one side to the other. This single coil of wire would develop a single north and a single south magnetic pole.
If you were to connect this single coil of wire to a single phase supply, then you would get an alternating magnetic field with no rotating component. Depending upon the specifics of the motor, this alternating magnetic field can probably power an already spinning rotor, but wouldn't develop any starting torque, and can't influence the _direction_ that the rotor spins. Such a simple single phase motor would sit and hum; give it a twist and it would then come up to speed in which ever direction you gave it the initial twist.
_Practical_ single phase windings actually have several coils of wire, spread out along the inner surface of the stator. Some of these motors have multiple terminals available on the coils that are part of this 'single phase', to permit operation at multiple voltages.
Various tricks are used to make single phase motors that actually have a direction sense. One of these tricks is to have a second set of coils arranged 90 'electrical degrees' away from the primary set. Current through this second set of coils is via a capacitor, which introduces a phase shift to the current flow. I'll get to this phase shift thing in a moment.
Definition: in a motor, 'electrical degrees' are used to describe the position of the coils, meaning a _mechanical displacement_ of the coils, but measured in terms of complete magnetic N-S cycles. In a 'two pole' motor (one with a single N-S cycle) the electrical degrees are equal to the mechanical degrees.
The _simplest_ three phase winding has 3 simple coils arranged on the same stator, but 120 'electrical degrees' apart. Each coil as _two_ sides, each coil half sitting in a slot. In a single phase machine, the two coil halves are 180 degrees apart. In this simplified three phase machine, you have 3 coils, each with two halves, each half 180 degrees apart, the net result is that you have a coil _half_ at every 60 degee position on the stator.
When properly energized with 3 phase alternating current, the _sum_ of alternating magnetic fields produced by each of the three coils will (hopefully) be a single _2 pole_ magnetic field that _rotates_. This single 2 pole rotating magnetic field will pull the rotor along. The unfortunate reality is that this magnetic field will have lots of 'harmonic components', all rotating at different speeds, and in actual manufactured motors each phase actually has lots of different windings all electrically connected together...but we don't need to go there for this discussion.
The key issue for getting the above rotating field is that the coils should be positioned with the same electrical displacement as the phase angle difference of the supply voltage.
If you had real 'two phase' service, then you would build motors with a 90 electrical degree difference between the windings. In single phase motors, you arrange coils with a 90 electrical degree difference, and then use reactive components to get a 90 degree phase difference in the current flow.
If you have a 17 phase motor, then you need to have lots of windings with suitable electrical angle difference. But if you arrange the windings, then the motor will run.
Going back to the 120/208V 'single phase' service. Clearly, between leg A and neutral, as compared to leg B and neutral, you have a 120 degree phase difference. A motor could be designed to operate on this phase difference, and would be 'self starting' and would develop a rotating field, just like a three phase machine or a 'true' two phase machine. There would need to be two phase bands, and they would need to be 120 electrical degrees apart for proper operation.
I believe that if you took a single phase motor, designed for dual voltage operation by reconnecting the single phase coils, and instead connected the 120V coil sections _separately_ to the 'two phases' of a 120/208V service, that you would _not_ get a rotating magnetic field, and that you would end up letting the magic smoke out in much the same fashion as if you connected those two 'out of phase' sources to the primary and secondary of a 120V:120V transformer. The reality would depend upon the specific details of the windings, but as far as I know, the two 'halves' of a dual voltage single phase winding are not positioned well for operation 120 degrees apart.
If, however, you connected the 'main' winding for 120 volt operation and supplied it from one leg to neutral, and then connected the auxiliary coil (the one normally supplied through a capacitor) to the other leg and neutral, the motor would probably function reasonably (if not perfectly).
-Jon
