The feed device has a retaining disk (15) provided with perforations (18) for receiving and supporting the rear end of the guide tube (12) of the lathe. The retaining disk (15) is mounted on a supporting frame (16) so that it can rotate about the central axis of the spindle drum of the lathe. A sealing disk (26) arranged on the side of the retaining disk (15) remote from the spindle drum is coupled with the supporting frame (16) so as to remain fixed during rotation and is sealed from the retaining disk (15). Between the retaining disk (15) and the sealing disk (26) is a distributor channel (38) which is connected, on the one hand, to the openings in the guide tube (12) and, on the other hand, to a feed line for the damping fluid. A perforation (42) which can be closed by a closure element (43) and whose through flow diameter is at least approximately equal to the largest diameter of the workpieces, is advantageously arranged in the sealing disk (26) in alignment with one of the guide tubes.