Abstract: The present invention concerns a tool head comprising a machine connection for connecting the tool head to a machine tool, and a tool 5 portion which either has at least one geometrically defined cutting edge or has a receiving means for a tool insert having a geometrically defined cutting edge. To provide a tool head, like a drilling head, and a method with which highly precise machining is possible with very high feed speeds and good surface quality without the cutting edge being exposed to 10 a high rate of wear, it is proposed that there is a converter for converting electrical AC voltage into a mechanical vibration, wherein the converter is arranged, designed and connected to the tool portion so that the unit comprising the converter and the tool portion and possibly a tool insert 15 received in the receiving means can be excited to perform an ultrasonic vibration.