Machine tool and control device

A machine tool comprising:

• a main spindle to which a workpiece is to be attached;
• a rotation mechanism that rotates the main spindle;
• a tool holder that holds a tool for cutting the workpiece;
• a movement mechanism that moves the main spindle and the tool holder relative to each other in a rotation axis direction of the main spindle;
• a vibration mechanism that vibrates the main spindle and the tool holder relative to each other in a vibration direction perpendicular to the rotation axis direction;
• and
• a control unit that controls the rotation mechanism and the vibration mechanism,
• wherein the machine tool cutting the workpiece by using the movement mechanism and the vibration mechanism so as to vibrate and move the workpiece and the tool relatively each other, while the rotation mechanism rotates the main spindle, and
• wherein the control unit driving the rotation mechanism and the vibration mechanism such that the tool is located at the same position in the vibration direction for each fixed rotation period of the main spindle and controlling the rotation mechanism and the vibration mechanism such that an outer circumferential surface or inner circumferential surface of the workpiece is machined into a substantially regular polygonal shape when viewed in the rotation axis direction.