Well, now you are giving Jeremy the go ahead to talk about whirl!
You made me smile, Ta0.
What you describe seems like a resonance at 500 RPM and a 180 degree shift between both sides of the resonance frequency is common. I say this without thinking about the specifics in this case and without having read any whirl papers (not enough time in the day and I'm not very interested) but from resonances in general.
I have an idea for a simpler experiment which should help understanding, maybe tomorrow..
I don't think there is whirling here, because there is no vibration. The same like in unbalance wobble, the wobble is apparent, and the disk remains tilted always in the same direction, (at constant speed).
That direction, intuitively, should be that of the applied force, that of the air drag in this case.
But this happens only at low speed.
The simpler experiment I am thinking about is to use a simple unbalanced wheel, mounted in the lathe through the flexible shaft:
With the experience of the today experiment, I expect that, at low speed, the heavy side becomes pulled outwards, with centrifugal force working in the intuitive way.
At higher speed instead, I expect the behaviour to invert, and the heavy side to be pulled inwards, towards the rotational axis.
Maybe all of this could help understanding something about the slipping tops, like the tippe top.
What did you mark with a pencil circle and an arrow?
The drawing showing the positions of the center of rotation is just a little larger than the size of the hole in the middle of the disk, isn't it?
The circle is the side of the wheel where there is the plasic sheet, and the arrow is the direction of the air drag;
intuitively, the flexible shaft, and the wheel, should remain tilted towards that direction, while spinning;
but this happens only at low speed, (200, 290 and 425 RPM).
Yes, the drawn circle may be larger.. I drew it to contain all the dots and not in scale to the hole.