How can the fans be disassembled without damage?

I have a fan that's very audibly grumbling while at idle speeds. I've opened the case and cleaned the fan blades and casings, with no result. I suspect there's dust/dirt in the actual bearings inside of the fan.

I've attempted to gently (but very forcefully) pry the fan piece with the blades away from its axle, to no avail. I fear that using more force would break it, but I can't tell how it's connected to know for sure.

I'd really like to fix this problem without dropping $50 on a replacement fan, if all I need is a cleaning.