A dental milling machine is provided with a tool which is guided in a chuck. A workpiece arm is mounted opposite the tool to be able to be moved at least in the direction of the spindle axis. With a control device it can be moved in relation to the workpiece, especially by means of a drive motor of the workpiece arm. The workpiece arm has an abutment element, whereby the control device moves the tool and the abutment element towards each other until they abut each other. The control device can be used to detect abutment of the abutment element with respect to the tool, in particular with respect to its tip, in particular by decelerating the (relative) movement of the tool and the abutment element towards each another, upon contact of the tool and the abutment element. This position may be signaled as a reference position and, especially may be stored.