You may not be observing a fast fan. Just a NOISY fan.
Fan bearings wear as they are used and get older. This increases the clearance between the fan shaft and the bore in the bearing sleeve. Once that clearance gets too large, this is what happens.
When you first start up a COLD system the fan makes a lot of noise because the shaft is "rattling around" in the sleeve. But as the bearings heat up from friction the shaft expands more than the sleeve, and the clearance gets narrower, until the noise stops. If you shut down and re-start right away with the fan still warmed up, you get no noise. But shut down for a long time to let it cool off, and the same story happens again. Over a long time, the length of the initial noise gets longer, until it always is noisy. After that the fan will simply seize up and not work at all.
The solution is to replace the fan. You cannot repair it. If this is a new thing and the initial noise is less than 5 minutes, it is not an emergency. But it WILL get worse, so plan to do the replacement some time.