Armeture has winding to produce magnet.my question is why doesnt rotar have winding and how it generate mag?

such types of motors are used in coolers

This type of motors are called asynchronous motors and the rotary magnetic field is produced by the coils of the stator by self-induction in the rotor coils.The rotor has a type of winding inside the iron core made by aluminum or copper bars that are shortcuts between them at the ends. Hope this help! Good luck!