A cutting insert may include a base including a first surface, a second surface and a lateral surface. The first surface may include a first corner, a second corner and a first side. The first side may include a first portion, a second portion, a third portion and a fourth portion in this order in a direction from the first corner to the second corner. An imaginary straight line being in contact with the first portion may be a reference line in a front view of the first surface. Inclination angles of the first portion, the second portion, the third portion and the fourth portion relative to the reference line may be respectively a first angle, a second angle, a third angle and a fourth angle. The third angle may be smaller than each of the second angle and the fourth angle.

A cutting insert includes a main body including a first face, a second face, and a third face. The second face includes a rake face. Among the outer-peripheral sides of the second face, the boundary portion with the first face is a main cutting edge. When viewed from the side where the first face is disposed, the main cutting edge includes a first straight portion, a second straight portion, and a curved portion. The first straight portion is located adjacent to a reference side. The second straight portion is arranged at a distance from the first straight portion. The curved portion connects the first straight portion and the second straight portion. A first intersection angle of the first straight portion with respect to the reference side is different from a second intersection angle of the second straight portion with respect to the reference side.

A cutting insert has a plate shape centered on an insert center axis. The cutting insert includes a front surface and a back surface facing an insert axial direction, an outer peripheral surface facing outward in an insert radial direction, and a cutting edge at an intersecting ridge line between the front surface and the outer peripheral surface. The back surface has a flat shape perpendicular to the insert center axis. The outer peripheral surface includes a flank surface coupled. The flank surface is inclined inward in the insert radial direction as extending in the insert axial direction from the front surface side to the back surface side. The front surface includes a rake surface. The rake surface is inclined from a back surface side to a front surface side in the insert axial direction as extending inward in the insert radial direction from the cutting edge.

A cutting insert includes a substrate and a cutting-edge insert. The substrate has, in a thickness direction of the substrate, a bottom surface, and a top surface opposite to the bottom surface. The top surface has a polygonal shape composed of a plurality of sides in a plan view as seen along the thickness direction. The top surface is provided with a projection projecting to a side opposite to the bottom surface along the thickness direction. The projection has a through-hole passing through the substrate along the thickness direction. The projection has a side surface contiguous to the top surface. The side surface is composed of a curved line protruding to a side opposite to the through-hole in the plan view as seen along the thickness direction.

A cutting insert includes first and second polygonal surfaces and a plurality of side surfaces. A corner edge that has a corner rake surface on the first polygonal surface is formed at a first corner portion, and a main cutting edge is formed from the corner edge to a second corner portion. The main cutting edge includes, at least on a corner edge side, a rake angle gradual increase region where a rake angle of a main rake surface gradually increases to a positive angle side as going from a first end portion of the corner edge toward a second corner portion side.

Chip discharge control is further improved. A cutting insert includes an upper surface, a lower surface, a screw hole having an axis penetrating from the upper surface to the lower surface, a peripheral side surface, and a major cutting edge, a wiper edge, and an inner edge formed in an intersecting region between the upper surface and the peripheral side surface. In a side view in which the peripheral side surface on which the inner edge is formed is seen from a direction perpendicular to the axis, the inner edge includes a recessed part recessed toward the lower surface, a length D.sub.L of the inner edge on one side of the recessed part in the side view is longer than a length D.sub.R of the inner edge on the other side of the recessed part, a lowest point of the inner edge is at a position lower than a flat part of the upper surface, and at least a part of the inner edge on the one side is at a position higher than the flat part of the upper surface. A cutting edge angle φ.sub.23L of the inner edge on the one side of the recessed part is larger than a half of a cutting edge angle φ.sub.23R of the inner edge on the other side of the recessed part.

A cutting insert for a shoulder milling tool has a trigonal shape and includes a first surface, a second surface, and a circumferential surface extending between the first surface and the second surface. The circumferential surface includes a countersunk circumferential waist portion. The circumferential surface has a first and a second clearance surface extending along a first and a second main cutting edge. Each of the first and second clearance surfaces forma a negative nominal clearance angle. Each of the first and second main cutting edges is arranged inside the countersunk circumferential waist portion, as seen in the view towards the first and second surfaces, respectively.

A cutting insert has an upper surface, a lower surface and a lateral surface. The upper surface has a first upper side, and a second upper side. The lower surface has a first lower side and a second lower side. The lateral surface has a first lateral surface, a second lateral surface, and a third lateral surface. The first lateral surface has a first concave part having a first constraining surface having a flat shape. The second lateral surface has a second concave part having a second constraining surface having a flat shape. The third lateral surface has a convex part. The first concave part and the second concave part are separated from each other by the convex part.

The invention relates to a cutting insert having a polygonal upper side. Cutting edges, which are alternately configured as roughing cutting edges and finishing cutting edges, are provided at the edges of the upper side. The finishing cutting edges define an incircle (K1) having a diameter that is enlarged in comparison to a nominal size of the cutting insert, and the roughing cutting edges define an incircle (K2) having a diameter that is reduced in comparison to the nominal size of the cutting insert. The invention further relates to a cutting tool having a tool body on which at least one such cutting insert is disposed.

To provide a cutting insert that is properly manufactured with ease of use. A cutting insert has a first end face, a second end face on the opposite side from the first end face, and a peripheral side surface that is parallel to a central axis connecting the center of the first end face and the center of the second end face and connects the first end face and the second end face. A first major cutting edge is formed on the outer edge of the first end face. A first flank facing the first major cutting edge is formed between the first major cutting edge and the peripheral side surface and has a negative clearance angle α with respect to the peripheral side surface. The peripheral side surface includes a first side surface facing the first flank. Between the first flank and the first side surface, a recess line is formed to extend along a virtual edge line where a virtual plane extending from the first flank and a virtual plane extending from the first side surface cross each other, and the recess line is formed with a notch on the virtual edge line.