The axle as you know is what the wheels of your mower are fitted to, the axles job is to support the weight of the mower, fix the drive assembly firmly to the mower and hold the wheels in place.
The genius of the trans-axle is that the outer case is the axle, it supports the weight of the mower and is fixed solidly to the chassis of the mower. Contained within the axle is the drive shafts and differential.
The differentials job is to allow one wheel to move independent of the other, this is useful when turning corners as the outer wheels of a mower travel further than the inner wheels.
The axle structure of a mower, doesn't give much trouble, and apart from removing grass and debris from the cooling fins, it's maintenance free.