turboair model GR01N - when i remove fan from base it can spin noise free, as soon as i screw it back in it makes a loud whirring noise, seems to be more noisy the lower the speed
I would guess resonance to be the cause - as you say the fan is relatively quiet on it own but when screwed into the unit you get a noise. I can imagine the panels of the outer cover being made from very thin sheet metal and vibrating in sympathy with the fan. Perhaps if you glued some damping material to the larger, inside panels you might be able to reduce the noise.