The Topological Equivalence of Synchronous Machines and Core Type Transformers

I was reading a post yesterday from @Stephen Cary about how improvements to power transformers could be made by making them more along the lines of synchronous machines (or at least that's what I thought he might have been saying - I need a substantial increase in neural capacity to properly parse his posts, as I find them to be the educational equivalent of eating a 6 course dinner in 5 minutes). So with all due apologies to Stephen for completely missing his point and butchering his concept, here is my attempt at using synchronous machine construction techniques to build a better transformer.

Here is a badly drawn representation of a synchronous machine. We have a three phase stator (which in reality will have distributed windings, but I didn't have all night to draw this thing) which produces a rotating magnetic field due to the stator winding layout and the phase relationships of 3 phase networks. The rotor is fed with DC current from an exciter which then also produces a rotating magnetic field due to the fact that the rotor rotates (as you would expect from the name).

The first step in our transformation is to stop the rotor from spinning, as otherwise you can't put 60 Hz in the stator and get 60 Hz out of the rotor. Once we do this, we notice an immediate problem. In a synchronous machine the field from the rotor windings only aligns with one set of stator windings at a time. No problem. We're engineers, so we can fix this by making a three phase rotor.

Hey, we've accidentally reinvented the GE rotary transformer. If the rotor and stator are aligned as shown above, we have a transformer. If we shift the angle of the rotor and leave it stationary, we have a phase shifting transformer and if we let the rotor turn slowly, we can actually transfer power between two systems at different frequencies. Here's a diagram from the GE patent showing the three phase rotor inside a normal stator winding.

Having done this, if we aren't interested in the phase shifting or frequency matching capabilities of the rotary transformer, we can optimize the construction by throwing out the air gap and producing a "cylindrical transformer".

This should be a perfectly functional transformer, but at this point the representatives from the manufacturing department storm your office with torches and pitchforks and ask you if it's really necessary to have all these curved laminations. "No problem", you say. "I'll just slice it and unroll it!" Half the stator is on the top and the other half is on the bottom. We have stator windings on the top and bottom, and the rotor winding is in the middle. We might have to add a little bit more steel on the top and bottom to account for the fact that there is no longer a flux path from the right side of the stator to the left side, but that's easy.

The next visitors to your office are the representatives from the purchasing department who ask if it's really necessary to have those stubs sticking out from the top and bottom ends. "Cut them off. I don't care!" Finally, the old guy from the design department who has been shaking his head the whole time wanders up to you, says "If you stack the primary and secondary windings on top of each other, you'll get better performance." and walks away muttering to himself.

Gee, that looks familiar...