Auto Alternators As Motors

Sorry, after reading the whole thread I have to do something Germans call klugscheissen:
An induction motor is an asynchronous motor, as it usually runs not synchronous. If it's synchronous it has 0 torque and 0 current. The RPM vs power curve is (point) symmetric around that point. Apart from single phase motors with starter coil, they run as good as motors as as generators.
Synchronous motors have the RPM fixed to the frequency and permanent magnets. The field coil in a car alternator can be considered as (regulable and therefore extra power consuming) permanent magnet.
Well, I came here because I'm searching the math to calculate the kV, torque..., I'll get after converting an alternator before I do so. I didn't find that but at least I got into the idea of making an asynchronous rotor for the car alternator rather than putting rare earth magnets into it. Well I guess the Magnet with hal sensors is still the best at low RPM (which can be full throttle). So I don't know if I ever use that.
More klugscheissen:
A 50Hz motor survives 60Hz (if it does not get mechanically distroyed by the higher RPM) but vice versa the current get's to high if not in someway reduced (lower voltage, lower load (e.g. lower Schlupf (maybe slip in English, I don't know) eg. asynchronity e.g. difference between true and synchronous RPM e.g. an American motor rated at 400V, 60Hz 3400 (3600 synchronous) RPM should operate faster as about 2830 (3000 synchronous) RPM @ 50Hz and the same voltage and wiring (Δ vs. Y)). This is because the current in an inductor (coil) rises over the time and lower frequency means longer periodes.
Still hoping to find the math somewhere (could figure it out myself, but it would take a lot of time and I don't like reinventing the wheel.)

Greetings over the big pond
 
You will still need to power the rotor through the slip rings, otherwise the rotor won't turn when the stator is energized by the motor controller. I've seen some auto alternators turned into PM generators by mounting rare earth magnets in the rotor. Usually used in low RPM windmills. If you did that, then you would have a large PM brushless DC motor.

As far as converting a car alternator to a motor, remember that a car alternator is not very efficient in converting mechanical energy into electricity - so it might stand to reason that it won't be very efficient converting electrical energy to mechanical energy without significant modification.
What modification?
 
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