A method for machining a workpiece, includes: rotating a rotary tool around a rotation axis, the rotary tool including at least one edge positioned on an outer periphery of the rotary tool around the rotation axis; relatively moving the rotary tool toward the workpiece in a first direction so that the at least one edge cuts the workpiece by a predetermined depth while the rotary tool is rotated around the rotation axis; and relatively moving the rotary tool with respect to the workpiece in a second direction that is substantially perpendicular to the first direction and that is inclined to a third direction substantially perpendicular to the rotation axis and the first direction.

Oscillation for a direct distance between the centers of a tool T and a workpiece W to meet l+a×l×(1−cos(Mωt)) and vertical oscillation to meet a×l×sin(Mωt) are applied alone or in combination with time t, where ω denotes an angular velocity of a workpiece, M denotes the number of sides of a polygon, and a denotes an adjustment parameter. Such oscillation enables adjustment as to how the machining surface is made concave or convex.

A control device that controls polygon turning to simultaneously rotate a workpiece and a tool and form a polygon on a surface of the workpiece acquires information on misalignment in the radial direction of a cutting tool attached to a tool body and generates pluses to correct the misalignment in the radial direction of the cutting tool. Furthermore, the control device outputs the pulses to an X-axis servo motor and moves a tool in the opposite direction to the misalignment in the radial direction of the cutting tool. Accordingly, the misalignment in the radial direction of the cutting tool is corrected, and thereby the precision of the polygon turning is improved.

A method for machining a workpiece, includes: rotating a rotary tool around a rotation axis, the rotary tool including at least one edge positioned on an outer periphery of the rotary tool around the rotation axis; relatively moving the rotary tool toward the workpiece in a first direction so that the at least one edge cuts the workpiece by a predetermined depth while the rotary tool is rotated around the rotation axis; and relatively moving the rotary tool with respect to the workpiece in a second direction that is substantially perpendicular to the first direction and that is inclined to a third direction substantially perpendicular to the rotation axis and the first direction.

Oscillation for a direct distance between the centers of a tool T and a workpiece W to meet l+al(1cos(Mt)) and vertical oscillation to meet alsin(Mt) are applied alone or in combination with time t, where denotes an angular velocity of a workpiece, M denotes the number of sides of a polygon, and a denotes an adjustment parameter. Such oscillation enables adjustment as to how the machining surface is made concave or convex.