Out of the box, my Dyson TP01 had 2 sounds going on, a high-pitched plastic squeak and a metallic rattle like a bearing going out. Customer service were idiots and could only send me links to videos showing how to clean the exterior. This was after multiple attempts to get them to do ANYTHING.
I tore the fan down and found the plastic squeak. The motor sits in a ball (visible from the top) on foam (underneath only visible after completely disassembling) and there is a ring around the top of the motor cage with 4 flat spots that sit loosely on top of flanges from below. Adding some small strips of foam insulation tape between the motor and the ring stopped the plastic squeak.
I also ended up taking the whole thing down to the motor and while spinning with a drill, I added small amounts of synthetic grease to lubricate the motor bushings. This stopped the metallic rattle and the fan is super-quiet now.