Provided is a method of manufacturing an elbow, including: a first cutting step of cutting a material by relatively moving a cutting section of a cutting tool, which is formed of at least a part of a substantially spherical shape, along an inner side surface of the elbow to be finished in a direction from a first end surface to a second end surface of the material; and a second cutting step of cutting the material by relatively moving the cutting section along the inner side surface of the elbow to be finished in a direction from the second end surface to the first end surface of the material.

A cutting insert has first and second end surfaces, a peripheral side surface, a reference central axis A perpendicular to and passing through the two surfaces, and a cutting edge having at least one circular-arc-shaped cutting edge. A contact surface portion is formed in the second end surface. The arc-shaped cutting edge is part of virtual circle having a center E which is spaced apart from the central axis A. A longitudinal plane B includes the central axis A and the center E; a median plane C perpendicular to the central axis A passes midway between the two end surfaces; and a virtual plane D perpendicular to both the longitudinal plane B and the median plane C, intersects the circular-arc-shaped cutting edge and traverses the contact surface portion. In a cross-section along the virtual plane D, the contact surface portion is inclined relative to the median plane C.

A cutting insert has top and bottom surfaces opposing each other and a side surface connecting them. A part of an intersecting ridge between the top and side surfaces functions as a cutting edge. On the side surface, a side surface portion adjacent to the intersecting ridge portion opposing the cutting edge intersects the top surface at an acute angle. At least on a part of a bottom surface, an inclined surface gradually approaching the top surface with increasing distance from a side surface portion on a side opposite to a cutting edge is formed. This allows a part of the cutting resistance to act on the side surface portion. As a result, friction resistance between the side surface portion and the side surface of an insert seat becomes larger, thereby suppressing a shifting of the cutting insert when cutting.

Large diameter edges formed in arc shapes having curvature radii larger than a ball radius are provided. This allows improving surface roughness of a machined surface by cutting of a planar surface with the respective large diameter edges compared with cutting of a planar surface with a ball end cutting edge formed in an arc shape having a single curvature radius. Further, since the respective large diameter edges are formed in the arc shape, compared with cutting of a curved surface with linear cutting edges, surface roughness of a machined surface can be improved by cutting a curved surface with the respective large diameter edges. Accordingly, a pick feed during the cutting of the planar surface and the curved surface with the respective large diameter edges can be increased, and therefore machining efficiency in the cutting of both of the planar surface and the curved surface can be improved.

Large diameter edges formed in arc shapes having curvature radii larger than a ball radius are provided. This allows improving surface roughness of a machined surface by cutting of a planar surface with the respective large diameter edges compared with cutting of a planar surface with a ball end cutting edge formed in an arc shape having a single curvature radius. Further, since the respective large diameter edges are formed in the arc shape, compared with cutting of a curved surface with linear cutting edges, surface roughness of a machined surface can be improved by cutting a curved surface with the respective large diameter edges. Accordingly, a pick feed during the cutting of the planar surface and the curved surface with the respective large diameter edges can be increased, and therefore machining efficiency in the cutting of both of the planar surface and the curved surface can be improved.

Large diameter edges formed in arc shapes having curvature radii larger than a ball radius are provided. This allows improving surface roughness of a machined surface by cutting of a planar surface with the respective large diameter edges compared with cutting of a planar surface with a ball end cutting edge formed in an arc shape having a single curvature radius. Further, since the respective large diameter edges are formed in the arc shape, compared with cutting of a curved surface with linear cutting edges, surface roughness of a machined surface can be improved by cutting a curved surface with the respective large diameter edges. Accordingly, a pick feed during the cutting of the planar surface and the curved surface with the respective large diameter edges can be increased, and therefore machining efficiency in the cutting of both of the planar surface and the curved surface can be improved.

A cutting insert has first and second end surfaces, a peripheral side surface, a reference central axis A perpendicular to and passing through the two surfaces, and a cutting edge having at least one circular-arc-shaped cutting edge. A contact surface portion is formed in the second end surface. The arc-shaped cutting edge is part of virtual circle having a center E which is spaced apart from the central axis A. A longitudinal plane B includes the central axis A and the center E; a median plane C perpendicular to the central axis A passes midway between the two end surfaces; and a virtual plane D perpendicular to both the longitudinal plane B and the median plane C, intersects the circular-arc-shaped cutting edge and traverses the contact surface portion. In a cross-section along the virtual plane D, the contact surface portion is inclined relative to the median plane C.