In praise of- sewing machine oil
I have been using sewing machine oil for well over a year now on noisy case and CPU fans with a 100% success rate.
The oil is ideal as it is designed for high speed motion and a fair number of references to use in PC fans exist on the internet- so when we had a spate of complaints about noisy machines I decided I hadn't anything to lose and gave it a try.
Remove the affected fan(s) completely from the computer (there is no need to remove the heatsink from the motherboard, just the fan).
On a fluid bearing fan you usually have to carefully remove a rubber bung (often underneath the label) with a pair of tweezers or a small flat head screwdriver and then you simply allow one to two small drops of the oil to soak into the bearing underneath.
Obviously it is worth cleaning excess dust off the fan blades whilst you do this to ensure it is evenly balanced.
Carefully re-install ensuring that you reconnect the fan to the motherboard.
The result for me has always been a near silent fan, however desperate it may have been sounding before.
Stand disclaimer, this has always worked for me, but I am not responsible if this wrecks your equipment.