Worm and gear transmission device in power-assisted steering system

An embodiment of the utility model discloses a worm and gear transmission device for a power-assisted steering system, which comprises a volute, a worm gear, a worm and two elastic retaining rings. The worm is provided with a thread and two supporting bearings, the thread is meshed with the worm gear, the two supporting bearings on two sides of the thread are used for mounting the worm on the volute, and the two elastic retaining rings are attached to the end faces, far away from the thread, of the two supporting bearings so as to clamp the worm between the two supporting bearings. The two elastic retaining rings of certain elasticity are disposed on the outer end faces of the two supporting bearings respectively, and elastic deformation of the elastic retaining rings can provide a certain axial gap for axial motion of the worm, so that the worm can meet the transmission requirement.