Reinoud,
Have you considered using stepper motors? This may be easier & cheaper, esp. for the lower powers you want.
That resistor of 220 ohm is a bit high. I'd give it a try with a 12V/.1A lamp, or 6V/.1A
You are using just one coil; I'm assuming you will be building an ordinary 9coils/12 magnets 3phase machine? If so, you get 3 times the AC voltage; in star, multiply by 1.7; As DC, you get 1.4 times as much as AC voltage.
Try calculating the internal resistance of your single coil and/or complete generator:
Measure unloaded voltage and loaded voltage (say, 8V unloaded, and 5V at .1A load)
R= (change in voltage)current
R= (8-5).1 = 30ohm.
The bigger & better your genny, the lower this internal resistance.
Anyhow, your 220 ohm resistor is way to high; it will seriously limit the current you can get out of the genny (in your case, 18mA). Try again with 5-10ohm, like someone else said. Or use a lightbulb, they also give a visual indication.
No worries, it'll take a while before you get the hang of designing and correctly sizing gennies, but it's definitely good fun (in my book).
Looking forward to new measurement results.
Peter (NL).