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motivation:
A guy I worked with years ago (~2015) who is an EE said that "an electric motor was just another form of a transformer". I'm not an EE, so I didn't do things with transformers. I think he meant that it turns energy from one form into another, but that he also meant there was a mathematical parallel in the modeling. Maybe something presuming steady-state, not accounting for spin-up of the armature?

Note: he loved 3-phase, for what that is worth.

Question:
Can you show the basic circuit and mathematical model of a simple electrical transformer, and then show a simple model for an equivalent electrical motor. Ideally there should be some python (numpy/scipy) with an ODE45 and a graph of current, voltage, accounting for windings, and somehow relating that to motor rotation or something.

Showing my homework:
I tried searching this forum and found no result that seemed to answer the question.

Links:

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    \$\begingroup\$ Thought experiment: how would you tell the difference, in circuit, of a changing flux vs. moving flux, cutting a winding? \$\endgroup\$ Aug 16, 2023 at 18:33

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You'd want to start with a reference book on electrical machines. It'll have the state equations to get you going.

The simplest form of a "motor transformer" is a two-phase stepper or BLDC motor. Apply a sine wave close to the electromechanical resonance frequency to phase 1 winding. Lock the rotor. Phase 2 winding will output "close to nothing". Now unlock the rotor. Phase 2 winding will output a phase-shifted version of the input to phase 1.

Compared to a regular transformer, there's additional phase shift due to rotor slip angle. The motor acts just like a 1:1 transformer would, less phase shift, with two additional transductions in series with energy flow: magnetic to mechanical on phase 1 ("primary"), and mechanical to magnetic on phase 2 ("secondary").

A BLDC/stepper with stator poles 180 electrical degrees apart will work very similarly to a 1:1 transformer.

A three-phase induction motor works similarly, except that the rotor magnetic field is due to current flow in the cage, induced by the stator.

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  • \$\begingroup\$ I have 4 or 5 texts but they must be the wrong ones. If you have one in mind then I would be grateful if you could share. \$\endgroup\$ Aug 17, 2023 at 2:48

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