A cutting insert according to an embodiment of the present invention has a cutting edge having a first corner cutting edge, a flat cutting edge, a connecting edge, a major cutting edge, and a second corner cutting edge in the order named. The major cutting edge has an upwardly protruding curvilinear portion, a first straight line portion extending from the curvilinear portion toward the connecting edge, and a second straight line portion extending from the curvilinear portion toward the second corner cutting edge. The flat cutting edge and the major cutting edge have a straight line shape, and the connecting edge has an outwardly protruding curvilinear shape in a top view. The flat cutting edge, the connecting edge, and the first straight line portion are located on a straight line in a side view.

A cutting insert has a cutting edge having a first corner cutting edge, a flat cutting edge, a connecting edge, a major cutting edge, and a second corner cutting edge in the order named. The major cutting edge has an upwardly protruding curvilinear portion, a first straight line portion extending from the curvilinear portion toward the connecting edge, and a second straight line portion extending from the curvilinear portion toward the second corner cutting edge. The flat cutting edge and the major cutting edge have a straight line shape, and the connecting edge has an outwardly protruding curvilinear shape in a top view. The flat cutting edge, the connecting edge, and the first straight line portion are located on a straight line in a side view.

A cutting insert includes a first surface and a second surface each of which is polygonal and that face away from each other; a side surface that is continuous with the first surface and a side surface that is continuous with the second surface; a cutting edge formed along each of a ridge where the first surface and the side surface intersect and a ridge where the second surface and the side surface intersect; a bearing surface formed in each of a part the first surface and a part of the second surface adjacent to an insert center, the bearing surfaces disposed parallel to each other; and a recessed portion that separates the side surface that is continuous with the first surface from the side surface that is continuous with the second surface. The cutting edge includes three corner edges, a first cutting edge, and a second cutting edge, the first and second cutting edges being continuous with each other and located between each pair of the corner edges. A length of the first cutting edge is greater than that of the second cutting edge, an end portion of the first cutting edge adjacent to one of the corner edges is at a position higher than the bearing surface, and an end portion of the first cutting edge opposite to the end portion adjacent to the corner edge is at a position lower than the bearing surface. Each of the first surface, the second surface, and a cross section of the recessed portion has such a shape that outlines of the shape before and after rotation of the insert by 120 around the insert center are coincident with each other. The first surface and the second surface have the same shape, and the second cutting edge of the second surface is located at a corner at which the first cutting edge of the first surface is located.

A milling insert for shoulder milling having s a positive basic shape and includes an upper side having a rake surface, a lower side including a planar bottom surface, a side surface extending around the periphery of the milling insert, and a cutting edge formed between the side surface and the rake surface. The cutting edge has at least a major cutting edge portion, a corner radius cutting edge portion, a ramping cutting edge portion, and a surface wiping cutting edge portion. The side surface includes an upper set of primary clearance surfaces and a lower set of secondary clearance surfaces having a plurality of planar secondary clearance surfaces, wherein the upper set of primary clearance surfaces forms an overhang protruding with respect to the secondary clearance surfaces and extending around the entire upper periphery of the milling insert.

A double-sided milling cutting insert has a first cutting edge disposed at an intersection of a top side and a side surface and a second cutting edge disposed at an intersection of a bottom side and the side surface. Each of the first and second cutting edges contains three cutting edge portions which are useable by indexing. The cutting edge portions each have a cutting corner, a main cutting edge adjacent to one side of the cutting corner, and a wiper edge adjacent to the other side of the cutting corner. The main cutting edge and the wiper edge are each inclined towards a reference plane with increasing distance from the cutting corner such that the first and second cutting edges have the largest distance to the reference plane in the regions of the cutting corners. The side surface has main clearance surfaces, secondary clearance surfaces, and curved corner surfaces.

A cutting insert of the present invention includes an upper surface, a lower surface, a side surface, a cutting edge, and a mounting hole penetrating the upper surface and the lower surface, in which the cutting edge includes a main cutting edge, a corner cutting edge extending from the main cutting edge, and a sub-cutting edge extending from the corner cutting edge, the side surface includes a main cutting edge flank surface and a sub-cutting edge flank surface, the main cutting edge flank surface includes a first main cutting edge flank surface extending from the main cutting edge, and a second main cutting edge flank surface extending from the lower surface, the sub-cutting edge flank surface includes a first sub-cutting edge flank surface extending from the sub-cutting edge, and a second sub-cutting edge flank surface extending from the lower surface, the first sub-cutting edge flank surface and the second sub-cutting edge flank surface together form a stepped portion, and the second sub-cutting edge flank surface protrudes from an imaginary plane extending from the first sub-cutting edge flank surface.