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Several years ago, I built a range extender for my electric bicycle using a weedwhacker motor and a dc motor with the shafts connected. It gave me about 50% more range but was extremely loud.
When you are accelerating, almost all of the power output of the range extender will likely be going to the motor, because when you hit the throttle the system voltage drops below charging voltage and your range extender/generator will not be able to hold the voltage above charging voltage under heavy acceleration. So make sure your battery charger can handle 100% of the output of the generator.
You might be able to build a transformer that can handle the amps better than using a battery charger. But it depends on how many amps your battery charger can handle, maybe you already have a good one.
I was quite impressed with my range extender, but wished that I had built it with more amp output to be able to run the vehicle entirely on the range extender. My range extender could push me to about 5 mph with no battery connected into the system. It would have been much better if it had a little more power.
I think that using an ac generator with a transformer and rectifier is the way to go. I had difficulty finding dc motors large enough in voltage and output to use as a generator when I was researching increasing the output. I'm not sure how well electric motors deal with pulse dc, but the battery system will level the pulses out a bit by holding a minimum voltage and acting as capacitors.
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