The machine tool has a main shaft (3) which is driven by an electric motor (4) and supported on a film of compressed air fed through channels in the body of the machine and controlled by a unit according to the machine loading. The machine housing (6) comprises a cylindrical bearing tube (61) and drive motor tube (62) with end plates (63,65). The motor drives the main shaft to rotate the cutting tool (2). Three bearing sections (71,72,73) have orifices (74) for the passage of air in a radial direction to support the main shaft. A flange section (3A) on the main shaft is controlled axially by air jets (75). Return air is extracted through a bore (78).
