A machining unit, particularly for machining the surface of cylindrical cavities, has a tool-holder assembly, including an electric actuator for adjustment of the radial tool position. The control signals of the actuator are transmitted to said actuator by a stationary electronic control unit via a wireless communication system. Also provided on board the tool-holder assembly is a system for electrical supply of the actuator, constituted, for example, by one or more batteries or else by an electrical-generation microsystem that exploits a portion of the flow of the high-pressure lubricant-coolant that is fed into the machining area.