A spindle unit comprises a tool-cramping device to make more rigid a main spindle (2) of a machine tool and allow it to operate at high speeds. The main spindle (2) is a solid shaft of a very rigid material such as cemented carbide and is supported rotatably in a spindle head (1) by bearings (3) which generate only low heat. A tool-cramping device includes an adapter (8) attached to a front end of the main spindle (2), and a tool holder (12) carrying a rotary tool (10), with one of the adapter (8) and the tool holder (12) comprising a short columnar lug (9), and the other comprising a cylindrical bore which can be shrink-fitted tightly onto the lug (9). The member having the bore (13) therein is made of a material of a thermal expansion coefficient higher than that from which the other member is made. The tool-cramping device further comprises means for heating (14) and means for cooling (15) the member (12) having the bore (13) therein. <IMAGE>
