A cutting insert may include a first surface including a corner and a first side, a second surface, a third surface, an inclined surface located between the first surface and the third surface, a first ridgeline located on an intersection of the inclined surface and the first surface, and a second ridgeline located on an intersection of the inclined surface and the third surface. An imaginary straight line passing through a center of the first surface and a center of the second surface may be a central axis. In a cross section which is parallel to the central axis and is orthogonal to the first side, an imaginary straight line connecting the first ridgeline and the second ridge line may be a first straight line, and the inclined surface may include a first inclined surface located more away from the central axis than the first straight line.

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 insert includes a body made of a ceramic material. The body has a first surface, a second surface and at least one flank surface extending between the first surface and the second surface. The first surface includes a chip forming feature extending in a radially outwardly direction to a cutting edge and extending in a radially inwardly direction to an inner edge. The chip forming feature includes a front wall that slopes downward from the cutting edge radially inward toward a rounded bottom surface and a back wall that slopes upward from the rounded bottom surface radially inward to the inner edge. The chip forming feature can include an optional land surface between the cutting edge and the front wall.

Disclosed is a cutting insert having a generally polygonal shaped primary body including a primary body base connected to an opposing, generally parallel and similarly-shaped body face through a plurality of flank portions extending there between. The Cutting insert further includes at least one cutting protrusion merging therewith and extending away there from the primary body. The at least one cutting protrusion includes a protrusion base which is generally coplanar and merges with the primary body base. The at least one cutting protrusion further includes a rake face in a direction opposite to the protrusion base, and a protruding flank extending there between the protrusion base and the rake face. The at least one cutting protrusion further includes a tip flat extending between a rake front at a protrusion tip towards a rake root portion, adjacent the primary body.

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.

A cutting insert includes a body made of a ceramic material. The body has a first surface, a second surface and at least one flank surface extending between the first surface and the second surface. The first surface includes a chip forming feature extending in a radially outwardly direction to a cutting edge and extending in a radially inwardly direction to an inner edge. The chip forming feature includes a front wall that slopes downward from the cutting edge radially inward toward a rounded bottom surface and a back wall that slopes upward from the rounded bottom surface radially inward to the inner edge. The chip forming feature can include an optional land surface between the cutting edge and the front wall.

Disclosed is a cutting insert having a generally polygonal primary body having a primary body base connected to an opposing and similarly-shaped body face through a plurality of primary flank portions extending there between. The cutting insert further includes at least one cutting protrusion extending away from at least one of the primary flank portions, and merging therewith. The cutting protrusion includes a rake face coplanar and extending away from the adjacent primary flank portions, and an edge portion extended towards a cutting flank portion. The cutting protrusion further includes a tip flat extending between a rake front from a protrusion tip towards a rake root portion, adjacent one of the primary flank portions.