For your consideration ...
Know exactly to what you are referring. Tired the same thing once before, on an older fan. Plastic used to hold the windings chipped and hard as a rock. The shaft bushings worn to the extend the fan rattles, vibrated at the high stetting from an up and down motion, or lateral motion, as the fan pushed air pulling the fan then bouncing back. Tired everything to make it quiet again. Cleaned, lubed, micro adjustments where possible, no joy. Even tried to find a used one of the same make and model on eBay, even if just to get the motor. Nope. It's not even made anymore since the old were made in a heavy duty way. But it's still usable, just not in a quiet setting. More for garage use now just to move the air. Though now, thinking about it, I might try packing in some water proof grease in those bushings to see if that'll quiet it down.