A single-crystal diamond cutting tool is provided with a flank and a rake face, a cutting edge being provided at a boundary between the flank and the rake face, an inclined surface being provided at a location distant from the cutting edge, the inclined surface being contiguous to the rake face and inclined at 0.05 degrees or more and 80 degrees or less with respect to the rake face, the rake face having a roughness Ra of 1 .Math.m or less, the cutting edge being provided with a chamfered surface or round honing having a width of 1 .Math.m or less, the cutting edge having projections and depressions having a width of 100 nm or less and smaller than that of the chamfered surface or round honing.

In an embodiment, a cutting insert including a base member, a first face, a second face, a cutting edge, and a nose portion. The base member includes a coating layer on at least a part thereof. The first face has corner portions. The second face is adjacent to the first face. The cutting edge is on at least a part of the ridgeline portion of the first face and the second face, and includes first and second cutting edges. The first cutting edge is on the coating layer and has a C chamfered surface with a first width of 5 μm to 30 μm in the front view of the first face and a chamfer angle of 35° to 50°. The nose portion is at the corner portions between the first cutting edge and the second cutting edge.

A cutting tool according to an aspect of the present invention is a cutting tool for cutting a rotationally symmetrical surface of a rotating workpiece. The cutting includes the step of feeding the cutting tool in a direction inclined with respect to a rotational axis of the rotationally symmetrical surface, while holding the cutting tool in contact with the rotationally symmetrical surface. In the step of feeding the cutting tool, the cutting tool has a point that is in contact with the rotationally symmetrical surface and the point shifts as the cutting tool is fed. The cutting tool includes: a rake face; a flank face; and a cutting edge connecting the rake face and the flank face. The cutting edge as seen from above the flank face has a shape including at least one arc, and the arc has a radius of curvature of not less than 100 mm and not more than 500 mm.

A cutting tool for cutting a rotationally symmetrical surface of a rotating workpiece includes the step of feeding the cutting tool in a direction inclined with respect to a rotational axis of the rotationally symmetrical surface, while holding the cutting tool in contact with the rotationally symmetrical surface. In the step of feeding the cutting tool, the cutting tool has a point that is in contact with the rotationally symmetrical surface and the point shifts as the cutting tool is fed. The cutting tool includes: a rake face; a flank face; and a cutting edge connecting the rake face and the flank face. The cutting edge as seen from above the flank face has a shape including at least one arc, and the arc has a radius of curvature of not less than 100 mm and not more than 500 mm.

In an embodiment, a cutting insert including a base member, a first face, a second face, a cutting edge, and a nose portion. The base member includes a coating layer on at least a part thereof. The first face has corner portions. The second face is adjacent to the first face. The cutting edge is on at least a part of the ridgeline portion of the first face and the second face, and includes first and second cutting edges. The first cutting edge is on the coating layer and has a C chamfered surface with a first width of 5 m to 30 m in the front view of the first face and a chamfer angle of 35 to 50. The nose portion is at the corner portions between the first cutting edge and the second cutting edge.

A cutting tool includes: a cutting edge configured on an intersecting line of a rake surface and a flank; a breaker wall formed inside the cutting edge and protruding above the cutting tool; a boss part including a boss surface formed above the breaker wall; and a plurality of recessed parts formed in the boss part so as to extend toward the cutting edge. The width of the breaker wall in a direction in which the cutting edge extends along an intersecting line (including a virtual intersecting line or a virtual extension of the intersecting line) of the boss surface and the breaker wall, is greater than the width of a groove formed by the recessed part along the same intersecting line.