A cutting insert may include a first surface, a second surface, a third surface, and a land surface. The first surface may include a first corner, a first side, and a second side. The land surface may be inclined relative to the first surface and the third surface. The land surface may include a first land surface connecting to the first corner. An imaginary flat surface orthogonal to a central axis connecting a center of the first surface and a center of the second surface may be a reference plane, a first inclination angle of a part of the first land surface which connects to a midportion of the first corner may be larger than a second inclination angle of a part of the first land surface which connects to an end portion at a side of the first side of the first corner.

A cutting part of a cutting insert may include a first surface including a corner, a first side, a first region, a second region and a third region. The first region may be located along the corner and the first side. The second region may be located at a more inner part than the first region. The third region may be located at a more inner part than the second region. A boundary between the corner and the first side may be a first point. A boundary between the first region and the second region may be a second point in a cross section that passes through the first point and is orthogonal to the first side. An imaginary straight line passing through the first point and the second point may be a first imaginary straight line. The first imaginary straight line may intersect with the third region.

A cutting insert comprises: a body; and a blade fixed to the body and made of a polycrystalline cubic boron nitride including 98.5% by volume or more of cubic boron nitride, the blade having a rake face and a flank face, the rake face and the flank face meeting each other and thus forming a ridge line which serves as a cutting edge, the rake face being provided with a land surface extending along the cutting edge, and a chip breaker disposed on a side opposite to the cutting edge with the land surface therebetween and also having a recess contiguous to the land surface.

A turning insert includes a top surface, an opposite bottom surface, and a reference plane located parallel to and between the top and the bottom surfaces. A nose portion includes a convex nose cutting edge, and a first and a second cutting edge. The nose cutting edge connects the first and second cutting edges. The first and second cutting edges form a nose angle of 71-85° relative to each other. The nose portion has a third convex cutting edge adjacent to the first cutting edge and a fourth cutting edge adjacent to the third convex cutting edge. The fourth cutting edge forms an angle of 10-30° relative to a bisector. The distance from at least a portion of the fourth cutting edge to the reference plane increases at an increasing distance from the nose cutting edge. A second protrusion is arranged between the nose cutting edge and the first protrusion.

A cutting insert includes a bottom surface, a top surface opposite to the bottom surface, and a cutting edge portion. The cutting edge portion is located on the same side as the top surface. The cutting edge portion is formed of a sintered material including cubic boron nitride particles. A volume ratio of the cubic boron nitride particles to the sintered material is more than or equal to 50 percent. The cutting edge portion includes a rake face, a flank face contiguous to the rake face, and a cutting edge located along a ridgeline between the rake face and the flank face. The rake face is inclined toward the bottom surface so that a distance from the rake face to the bottom surface decreases gradually toward the cutting edge.

A cutting insert includes a bottom surface, a top surface opposite to the bottom surface, and a cutting edge portion. The cutting edge portion is located on the same side as the top surface. The cutting edge portion is formed of a sintered material including cubic boron nitride particles. A volume ratio of the cubic boron nitride particles to the sintered material is more than or equal to 50 percent. The cutting edge portion includes a rake face, a flank face contiguous to the rake face, and a cutting edge located along a ridgeline between the rake face and the flank face. The rake face is inclined toward the bottom surface so that a distance from the rake face to the bottom surface decreases gradually toward the cutting edge.

A cutting insert (112) comprising a top surface (118), a bottom surface (120), and side surfaces (122) spanning there-between, said side surfaces (122) comprising one or more feed-facing side surfaces (122a) and one or more radial-facing side surfaces (122b). The top surface (118) is formed with one or more linear grooves, each constituting a chip breaker (125) and being disposed parallel to and adjacent one of said feed-facing side surfaces (122a). The chip breaker (125) is characterised by a constant profile along the entire length of its respective feed-facing surface (122a). Each of said feed-facing side surfaces (122a) is disposed at an acute feed-angle ( feed) with respect to the top surface (118), and each of said radial-facing side surfaces (122b) being disposed at an acute radial-angle ( radial) with respect to the top surface (118), the feed-angle ( feed) being greater than said radial-angle ( radial).

A cutting insert may include a first surface, a second surface, a third surface, and a land surface. The first surface may include a first corner and a first side. The land surface may be located between the first surface and the third surface. The land surface may include a first land surface connecting to the first corner, and a second land surface connecting to the first side. A width of the first land surface in a front view as viewed from a side of the first surface may be a first width, the first width at an end portion on a side of the second land surface may be larger than the width at a part connecting to a midportion of the first corner.

A cutting insert may include a first surface, a second surface, a third surface and a cutting edge. The first surface may include a corner, a first side, a first inclined surface located along the corner, a second inclined surface located further inside than the first inclined surface, a third inclined surface located along the first side, a fourth inclined surface located further inside the first surface than the third inclined surface, and a protruded part located further inside than the second inclined surface and the fourth inclined surface. An inclination angle of the protruded part may be smaller than an inclination angle of the second inclined surface in a cross section along a bisector of the corner. The inclination angle of the protruded part may be larger than a third inclination angle in a cross section orthogonal to the first side.

A polygonal cutting blade having a circular arc-shaped groove in a hole includes a blade body composed of an upper surface, a lower surface and a plurality of main side surfaces connecting the upper surface and the lower surface. The blade body has a central hole penetrating through the upper surface and the lower surface, and is centrally symmetrical about a central axis of the central hole. At least one set of positioning side surface comprised of adjacent two of the main side surfaces is provided. An inner surface of the central hole has at least one circular arc-shaped groove fitting with a fastening screw for fixing the cutting blade. The circular arc-shaped groove directly faces toward an intersection of the two main side surfaces of the set of positioning side surface. A groove central axis of the circular arc-shaped groove has an offset distance from the central axis.