Machine tool and cutting method

A method for cutting a workpiece having an inclined surface, the method comprising:

• a step of holding the workpiece and rotating the workpiece around an axis that extends in a Z direction;
• a step of adjusting a linear cutting blade of a cutting tool to cut the workpiece by inclining a direction of an edge of the linear cutting blade with respect to the Z direction when seen from an X direction, in which a depth of cutting of the workpiece is determined, and making a straight line on the inclined surface along the Z direction, when seen from the X direction, that is parallel to the edge of the linear cutting blade when seen from a Y direction perpendicular or substantially perpendicular to the Z direction and the X direction;
• and
• a step of cutting the workpiece while moving the cutting tool relative to the workpiece in a combined direction obtained by combining the Z direction, the X direction, and the Y direction;
• wherein
• the straight line on the inclined surface is inclined with respect to the Z direction when seen from the Y direction;
• a length of the edge of the linear cutting blade when seen from the Y direction is shorter than a length of the inclined surface when seen from the Y direction;
• and
• in the step of cutting the workpiece, the edge of the linear cutting blade cuts the workpiece while moving in the Y direction with respect to the workpiece, and while maintaining the edge of the linear cutting blade parallel to the straight line on the inclined surface when seen from the Y direction.

A machine tool that cuts a workpiece having an inclined surface or a curved surface, the machine tool comprising:

• a main spindle that holds and rotates the workpiece;
• a moving device that moves a cutting tool relative to the workpiece in a direction obtained by combining a Z direction parallel or substantially parallel with an axis of the main spindle, an X direction that is perpendicular or substantially perpendicular to the Z direction and determines a depth of cutting of the workpiece, and one of a Y direction perpendicular or substantially perpendicular to the Z direction and the X direction and an axis rotation direction parallel or substantially parallel with the Z direction, the cutting tool including a linear cutting blade to cut the workpiece;
• and
• a tool positioner that sets a direction of an edge of the cutting tool to an angle of the inclined surface or a tangent of the curved surface of the workpiece by inclining a direction of the edge with respect to the Z direction when seen from the Y direction in a state in which the direction of the edge is inclined with respect to the Z direction when seen from the X direction;
• wherein
• the tool positioner includes an angle setting mechanism that sets the angle of the edge with respect to the Z direction when seen from the Y direction.