A device for the fine machining of a circumferential workpiece surface arranged eccentrically relative to an axis of a workpiece. The device comprises a pressure mechanism configured to press a fine-machining tool against the circumferential workpiece surface. The device also includes a drive unit configured to drive an active section of the pressure mechanism via a first drive and a second drive. The first drive drives the active section in a movement plane that runs crosswise to the workpiece axis along a first movement trajectory. The second drive drives the active section along a second movement trajectory that is at an angle to the first movement trajectory.

In a method for machining a workpiece, a cutting tool is guided relative to the workpiece, with a vibration being superposed, the amplitude of which is at least 5 m. A supply circuit for a piezo actuator of a vibrating tool generates a voltage at the voltage output, which has a direct component and an alternating component. A supply system for a piezo actuator of a vibrating tool has the above-mentioned supply circuit which is connected to a secondary coil that is coupled to a primary coil.