An indexable cutting insert has upper and lower surfaces with a peripheral surface extending therebetween and having four side surfaces alternating with four corner surfaces. The side and corner surfaces intersect the upper surface to form side and corner cutting edges, respectively. Each side cutting edge includes a primary cutting edge adjoining one of the corner cutting edges at a first endpoint and a secondary cutting edge adjoining another one of the corner cutting edges at a second endpoint. In a top view, the four primary cutting edges define an imaginary first square, each primary cutting edge is tangential to its adjoining corner cutting edge, and each secondary cutting edge is curved and entirely located in one of four imaginary quadrants. The insert is removably secured in a rotary cutting tool such that one of the secondary cutting edges contains the axially forwardmost point of the insert's upper peripheral edge.

This cutting insert is provided with a lower surface of polygonal shape including side parts and a pair of corner parts, an upper surface, a lateral surface situated between the lower surface and the upper surface, a pair of corner cutting edges located at the pair of corners, and a main cutting edge located in a side portion. The main cutting edge is upwardly convex in shape, and in side view includes an upwardly convex curving portion, and a pair of linear portions respectively extending toward the pair of corner cutting edges from the curving portion. The top portion of the curving portion is positioned more toward the one of the corner cutting edges which, of the pair of corner cutting edges, is that contiguous to a working surface of a work material during cutting of the work material.

This cutting insert is provided with a lower surface of polygonal shape including side parts and a pair of corner parts, an upper surface, a lateral surface situated between the lower surface and the upper surface, a pair of corner cutting edges located at the pair of corners, and a main cutting edge located in a side portion. The main cutting edge is upwardly convex in shape, and in side view includes an upwardly convex curving portion, and a pair of linear portions respectively extending toward the pair of corner cutting edges from the curving portion. The top portion of the curving portion is positioned more toward the one of the corner cutting edges which, of the pair of corner cutting edges, is that contiguous to a working surface of a work material during cutting of the work material.

A polygonal cutting has opposing first and second end surfaces connected by a side surface, and a plurality of cutting edges formed between the end surfaces and the side surface. Each cutting edge is formed at corner and includes a corner cutting edge and a major cutting edge connected to the corner cutting edge. A rake surface formed along the cutting edge on first the end surface is inclined toward the second end surface. In a side view of the cutting insert, the major cutting edge includes an inclined part which is inclined so as to approach the second end surface from the corner cutting edge. A portion of the rake surface along the inclined part is formed such that an angle of inclination toward the second end surface increases toward the corner in a direction along the intersecting edge between the first end surface and the side surface.

A cutting insert has an upper surface, a lower surface, a side surface connecting the upper and lower surfaces. An intersecting edge between the upper surface and the side surface is provided with a cutting edge. The cutting edge has, in order, a second major cutting edge, a first major cutting edge, a corner cutting edge connected to these major cutting edges, and a flat cutting edge. An obtuse interior first angle () is formed by the second and first major cutting edges. A interior second angle () formed by the flat cutting edge and the first major cutting edge is larger than an interior third angle () formed by the flat cutting edge and the second major cutting edge. A land is provided adjacent to the first major cutting edge, a width of the land increasing toward the first corner cutting edge.

A polygonal cutting has opposing first and second end surfaces connected by a side surface, and a plurality of cutting edges formed between the end surfaces and the side surface. Each cutting edge is formed at corner and includes a corner cutting edge and a major cutting edge connected to the corner cutting edge. A rake surface formed along the cutting edge on first the end surface is inclined toward the second end surface. In a side view of the cutting insert, the major cutting edge includes an inclined part which is inclined so as to approach the second end surface from the corner cutting edge. A portion of the rake surface along the inclined part is formed such that an angle of inclination toward the second end surface increases toward the corner in a direction along the intersecting edge between the first end surface and the side surface.

A milling tool has single sided and indexable milling inserts having a round basic shape. Each milling insert has a plurality of tangentially spaced-apart and alternately usable cutting edges, which individually fall archedly from a first end, situated closest to an upper reference plane, to a lowest point, from which it again rises toward a second end. A reinforcing chamfer surface included in the cutting edge is formed with an increasing width in a direction from the first end of the cutting edge toward the second end.

A cutting insert has an upper surface (21), a lower surface (91) and a side surface (61) that connects the two surfaces. A cutting edge is formed at an intersecting edge between the upper surface (21) and the side surface (61). The cutting edge includes at least a major cutting edge (33), a corner edge (34) connected to the major cutting edge (33), and a curved wiper edge (35) located on the opposite side of the major cutting edge (33) across the corner edge (34). A first angle made by the major cutting edge (33) and the chord of the wiper edge (35) is 155<180, and a positive land is formed in the wiper edge (35). The cutting edge may further include an inner cutting edge (36) located on an opposite side of the corner edge (34) across the wiper edge (35).