If objects or trash has been inserted into the condenser fan through the intake grille of the unit, it’s possible the trash has wrapped itself around the fan axel or jammed the fan in some way. If debris binds up the fan and the fan fails to turn, but the motor continues to run, the result is a humming noise. Shut off power to the unit to prevent the motor from burning up before the fan can be fixed. To access the fan housing, you can remove panels on the central unit. Pull all foreign objects from the fan housing.
The fan axel spins by way of the ball bearings inside of the motor. If the bearings are grimy or jammed up, the fan might fail to spin or the spinning will be limited. The fan motor is trying to propel the fan to no avail, so the motor overworks and hums. You can remove top or side panels of the central air conditioner to access the fan housing, after power is shut off. If you give the fan a spin and it fails to spin freely, the bearings could be the cause. You can insert electrical motor oil into the lubrication ports on the motor and spin the fan around to work the oil into the ball bearings. The fan should spin freely.
The thermostat controls both the compressor and the fan component of the air conditioner. The compressor activates the cooling element and the fan blows the cold air out of the unit and into the home. If the thermostat wiring is incorrect or disconnected, this could cause the compressor to run without the fan. The humming noise would come from the compressor. You can lower the thermostat to test the reaction of the compressor and fan. If the fan fails to turn on but the compressor kicks in, the thermostat could be the culprit.
An incorrectly installed fan might slam against the fan housing, preventing it from turning and burning up the fan motor as a result. A fan that’s completely hung on the housing produces a humming noise from the motor, which is still activated. After panel removal, turn the fan to determine if it strikes the housing. If it does, uninstall the fan and reinstall it correctly.