In the course of a machining of a workpiece with a tool, a drive spindle with a tilt table secured thereto of a tilt device provided on a work table of a machining center is rotated by a direct drive motor to control the relative angular position between the tool and the workpiece, and within a predetermined period of time in the course of a machining, the direct drive motor is rotated at a high speed with a spindle head and the work table of the machining center kept away to rotate the drive spindle and hence, the tilt table at a high speed, so that chips and cutting lubricant can be shaken from the workpiece and the tilt table.