Abstract: High speed cutting with machine tools is achieved with readily available bearings of a small diameter by mounting and presetting the cutting tool directly in a spindle of a spindle unit without employing a tool holder. Preferably, the spindle unit is small like a tool holder and can be easily changed with conventional kinds of tool changing apparatus. The elimination of the tool holder allows the conventional bearings to be kept small so that they may be operated at high speeds, e.g., 20,000 to 40,000 rpm, without excessive heat that would damage the bearings.