What is the function of commutator in DC motor? why we don't use it in AC motors?

Commutator is simply a mechanical rectifier   used to reverse the direction of current every time  coil moves through the plane perpendicular to the magnetic field so as to To keep the torque on a DC motor from reversing its direction. For AC motor rectification is not required thus Commutator is not needed  rather a slip ring is used. 

For the DC motor the commutator is used to alternate the magnetic field created by the DC current, although, for AC motor the magnetic field is already alternated by the nature of the AC current.

an alternative magnetic field leads to a non zero average torque.

Cordially

During the rise of DC motors before, it is used where High Torque is needed. AC at that time is difficult to control specifically the frequency. Today AC can be controlled using the VFD. DC motors also has high maintenance and a lot of components to be checked. The commutator is such a converter used to convert from AC to DC current. Once the commutator is severely worn-out then it is useless.

commutator is used for the conversion of ac to dc and also from dc to ac, in case of dc motor's it is used to convert dc applied voltage into ac (changes polarity due to which current direction changes also polarity of pole changes with current direction) where as in ac motors no such conversion is needed, due to commutator and brushes dc motor's need more maintenance than ac motors.

1. Function of commutator:
2. To keep the torque on a DC motor from reversing every time the coil moves through the plane perpendicular to the magnetic field, a split-ring device called a commutator is used to reverse the current at that point.