electromagnetism - Is it valid to consider back-EMF in a DC motor equivalent to increased inductance?

I know that back-EMF can be considered as a voltage source in series with the motor which is proportional to speed. This is the common understanding, and I totally get it. Before I understood this, I developed an alternate explanation on my own, and I wonder if it has any validity.

Think of this: an inductor resists change in current. A bigger inductor resists it more. A stalled motor resists change in current. A spinning motor resists it more.

A small inductor at a given current has some stored energy. A bigger inductor at the same current has more stored energy. A stalled motor at a given current has some stored energy. A spinning motor at the same current has more stored energy.

Hopefully you can see what a student might intuitively hypothesize: a motor's windings exhibit an inductance that increases with the motor's speed. Not because it's magically growing more turns of wire of course, but perhaps it's a sort of mechanical inductor, storing energy in the motor's momentum, rather than in a magnetic field. My intuitive understanding of an inductor is, after all, a flywheel. Maybe this is an inductor that actually is a flywheel.

Can this analogy be stretched further? In a resistive and inductive load, AC current lags behind AC voltage. Add more inductance, and current lags more. In a motor, current lags behind voltage. If the motor is spinning faster, does it lag more?

And if that much is true, can it be shown that back-EMF is equivalent to an inductance that increases with motor speed?

And if not, why? Intuitive examples would be appreciated first, then the math. I never seem to understand when presented in the opposite order.

Answer

Interesting. The back-emf (modeled as a voltage source proportional to speed) is not equivalent to an inductance that depends on speed. Furthermore, there is no possible L(w) you can come up with that will make that assertion true.

I will describe a simple experiment, but in essence I'll be saying that they can't be equivalent because upon a motor load change, an inductor dependent on speed L(w) will not affect the stationary state current (torque after all transients have died down, becoming a contradiction), while a voltage source dependent on speed v(w) will (which makes sense).

Assuming a DC motor, a simple proof is to imagine that the load on the motor gets reduced. Because there is less load, the motor speeds up. Also imagine we wait for some time so that all transients go away (t=inf.). Now let's see what happens with both models:

With the back-emf modeled as a voltage source, its voltage increases because speed increased. This means that the current decreases, because the difference between the power voltage source and the back-emf voltage got smaller. This means torque decreased, which makes sense because we reduced the load on the motor.

On the other hand, no matter what inductance value you give to the "back-emf inductor", the current on the motor would remain the same, because inductors are short-circuits in dc. But this does not make sense, because torque is proportional to current and if the current remains the same, torque remains the same, but we started this analysis saying that we reduced the load on the motor.