A cutting insert is provided, comprising a top surface, a bottom surface, a plurality of side surfaces spanning therebetween, and a cutting edge formed at an intersection of the side surface and a forwardly-disposed portion of the top the surface. It further comprises a cooling cavity projecting into the insert, a top end thereof being disposed further forwardly than an open bottom end thereof. The cooling cavity defines at least one molding axis such that a solid element having the shape of the cooling cavity and completely inserted therein may be retracted intact therefrom along a linear path parallel to the molding axis. A circumscribing portion is formed on the side surfaces encircling the cutting insert. The circumscribing portion is formed parallel to the molding axis and has a non-zero height along its entire extent. The cutting insert does not extend beyond the circumscribing portion.

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.

In an embodiment, an insert includes an upper surface including a corner part, a lower surface, a side surface, and a cutting edge. The side surface is between the upper surface and the lower surface. The cutting edge is at least at a part of a first region in which the upper surface intersects with the side surface. The cutting edge includes a first cutting edge at the corner part, a second cutting edge, a third cutting edge, and a fourth cutting edge. The second cutting edge is next to the first cutting edge, and also next to the third cutting edge. The third and fourth cutting edges: each have a convex curvilinear shape with first and second radii of curvature, respectively; and extend downward and upward, respectively, in a side view as going farther from the second cutting edge. The second radius smaller than the first radius.

A cutting insert is provided, comprising a top surface, a bottom surface, a plurality of side surfaces spanning therebetween, and a cutting edge formed at an intersection of the side surface and a forwardly-disposed portion of the top the surface. It further comprises a cooling cavity projecting into the insert, a top end thereof being disposed further forwardly than an open bottom end thereof. The cooling cavity defines at least one molding axis such that a solid element having the shape of the cooling cavity and completely inserted therein may be retracted intact therefrom along a linear path parallel to the molding axis. A circumscribing portion is formed on the side surfaces encircling the cutting insert. The circumscribing portion is formed parallel to the molding axis and has a non-zero height along its entire extent. The cutting insert does not extend beyond the circumscribing portion.

A cutting insert in the present disclosure includes an upper surface, a lower surface, a side surface, and an edge. The upper surface includes a first corner part and a second corner part. The edge is located in a region which is located between the first corner part and the second corner part. The edge includes a first edge located at a side of the first corner part, a second edge located at a side of the second corner part, and a third edge located between the first edge and the second edge. The edge has a curvilinear shape being recessed toward the lower surface in a side view. Each of a radius of curvature R1 of the first edge and a radius of curvature R2 of the second edge is smaller than a radius of curvature R3 of the third edge in a side view.

A turning insert has two opposite main surfaces and a peripheral surface which extends therebetween and has N side surfaces, where 2<N<9. The insert has mirror symmetry about a mid-plane and 360/N degree rotational symmetry about a central axis perpendicular to the mid-plane. The insert has two main edges which each have N main cutting edges and N corner cutting edges. Each main cutting edge has two raised edge portions and a lowered edge portion. Each main surface has N main rake surfaces and N corner rake surfaces. Each main surface further has at least N convex island protrusions and N at least partially convex peninsula protrusions, any and all island protrusions associated with a given main rake surface being located between two adjacent peninsula protrusions, each pair of adjacent peninsula protrusions having at least one island protrusion located therebetween.

An insert according to an embodiment includes an upper surface including a corner part, a lower surface, a side surface, and a cutting edge. The cutting edge includes a first cutting edge located at the corner part, a second cutting edge adjacent to the first cutting edge, a third cutting edge adjacent to the second cutting edge, and a fourth cutting edge adjacent to the third cutting edge. Each of the third cutting edge and the fourth cutting edge has a concave curvilinear shape extending downward in a side view. A radius of curvature of the fourth cutting edge is smaller than a radius of curvature of the third cutting edge.

A cutting insert may include a first surface and a second surface. The first surface may include a first side, a first corner, a second corner, and a breaker part. The breaker part may include a first segment, a second segment, and a third segment. The first segment may be an inclined surface inclined so as to approach the second surface as going away from the first side. The third segment may be an inclined surface inclined so as to separate from the second surface as going away from the second segment. In a front view of the first surface, a maximum value at a side of the second corner may be greater than a maximum value at a side of the first corner in a distance from the first side to a top portion of the third segment on an orthogonal line with respect to the first side.

An insert of the present disclosure includes a first surface, a second surface connecting to the first surface, and a cutting edge located on at least a part of a ridgeline between the first surface and the second surface. The first surface includes, at a position away from the ridgeline, a groove extending from a first end part closest to the cutting edge to a second end part farthest away from the cutting edge. The groove includes an opening located in the first surface, and a bottom surface. The groove includes, at a position closer to the first end part than a half of a groove length, a first groove part where a groove depth increases as going from the second end part toward the first end part, and a second groove part where the groove depth decreases as going from the second end part toward the first end part. The first groove part is located closer to the second end part than the second groove part. A cutting tool of the present disclosure includes the insert.

A cutting insert includes an upper surface, a lower surface, a side surface, and a cutting edge. The upper surface includes a first side part, a second side part, and a corner part located between the first side part and the second side part. The side surface is located between the upper surface and the lower surface. The cutting edge is located at an intersection of the upper surface and the side surface. The cutting edge includes a first cutting edge located at the corner part, and a second cutting edge adjacent to the first cutting edge and located at the first side part. A height of the first cutting edge relative to the lower surface is constant. The second cutting edge is inclined toward the lower surface as going toward the corner part.