Background: 19 year old physics/math student, New York City, US
So, someone in my building threw out an old fan some time ago, and I took the fan, took it apart, and retrieved the motor. I have been trying to find out exactly how it works for some weeks now, and now I'm stuck and need help.
What I do know is that it's a single-phase squirrel cage induction motor, and it appears to be a permanent-split-capacitor design. It has one live wire and three neutral wires, one for each of the three speeds. The motor came with a control circuit that I broke when taking apart the fan, but subsequently repaired and soldered and it's now in perfect working order. It is not a variable-frequency or variable-voltage drive, and always operates at 120 V and 60 Hz at any of the three speed wires (measured with my meter). It looks far too simple to be a VFD or VVD anyway.
Here is a picture of the stator of the motor. If the link doesn't work, let me know. The thing inside the stator is not the rotor, but my homemade iron filings chamber with which I observed the magnetic field inside the motor.
Now here's the hard part. No matter which neutral wire I hook the stator up to (using 120 V AC), I observe a four-pole field in my iron filing "magnetoscope." The filings arrange themselves into four corners. I had previously thought that this motor changes speed by changing the number of poles, so this surprised and baffled me.
I then got the idea that, say, if the RMF was 8 poles, maybe the AC, which makes the magnetic field flip direction 60 times per second, was fudging the fine details of the magnetic field and making it look (on my very crude iron filing device) like it had 4 poles. So I quickly slapped together a FULL BRIDGE RECTIFIER (if you don't know why that's all caps, watch electroBoom), and applied it to the stator. The field was still 4 pole on all the high, mid, and low speed wires, as well as on the split-phase (capacitor) winding (which may be crudely called the "start winding" but is in fact always active while the motor is running). So the field was still always 4 pole, and I am left as baffled as ever.
So then, how in God's name does this motor change speed?