With fans that do that I would suspect the bushings as well. Only way is to strip the fan apart ( mark the position of the end housings and the stator, as you need to put it back together exactly the same way) and clean out the old oil from the bearings and polish the shaft with some cloth, then relubricate with engine oil. Check the tolerance in the bush when out, you will find one end is going to be worn and tight, and as well look at float on the shaft forward and rear, as there are shims used to take up this float and they also either break or wear out.
I have had to resort to scrapping cheap motors to get the bushes and spacers to fix others, the bushes used to be made out of sintered bronze, but the newer ones are powder steel parts and are not as good at holding oil. Check as well the little felting ring outside the bush is not rotted, as it holds the oil reservoir that slowly seeps into the bush to lube it. Those as well you can grab from a scrapped cheap fan, as often there is no oil applied to them at all in manufacture aside from a single drop.