A vibration cutting insert includes a top surface having a rake face and a breaker face, a first side surface, a second side surface, and a bottom surface. In a cross section which includes a bisector of an angle formed between a first ridgeline and a second ridgeline when viewed in a direction from the top surface toward the bottom surface, and which is parallel to the direction from the top surface toward the bottom surface, a rake angle formed between the rake face and a plane parallel to the bottom surface has a positive angle. The angle formed between the first ridgeline and the second ridgeline is an acute angle. The rake face constitutes a cylindrical surface. The breaker face constitutes a flat surface.

A turning insert includes a top surface, an opposite bottom surface, a side surface connecting the top and bottom surfaces, and a cutting edge formed at an intersection between the top surface and the side surface. The cutting edge including a corner cutting edge, a first cutting edge, and a second cutting edge. The top surface having a first surface in the form of a depression, which borders at least a major portion of the corner cutting edge. The first and the second cutting edges subtending an angle which is 75-85. At least a part of the corner cutting edge is concave in a front view.

In accordance with various illustrative embodiments of the present disclosure, a rotationally symmetric surface of a workpiece is machined by a turning apparatus, wherein the workpiece is rotationally driven around a rotational axis, a cutting tool with a cutting edge positioned at the edge of a rake face is arranged relative to the workpiece, the cutting tool is brought into contact with the workpiece, and the cutting tool is advanced relative to the workpiece along a feed direction parallel to the rotational axis, the normal to the rake face being tilted relative to the feed direction, a first axis and a second axis, the first axis and the second axis are perpendicular to the feed direction and perpendicular to each other.

Indexable, double-sided turning inserts for turning operations and and a turning tool are provided with cutting edges at alternating corners on opposite sides of the insert. Chipbreaker structures can be provided without interfering with providing large supporting surfaces. When the insert is used in a cutting operation, chips from one of the cutting edges in use are unlikely to damage cutting edges that are not in use but are on adjacent corners.

Provided is a cutting tool for back turning capable of improving chipping resistance. A cutting tool wherein a wall surface of a chip breaker includes a first wall surface that is formed along a first ridgeline, and a reinforcing surface that is connected to the first wall surface and a first end surface at an end portion of the chip breaker on the side of a first cutting edge, and that forms an angle of 90 degrees or an obtuse angle with the first end surface.

Provided is a cutting insert that improves chip control performance. In a cutting insert for back turning process, a chip breaker wall face, of a chip breaker, facing the axial feed direction includes: when viewed from a first face side, a first wall face portion configured so that a ridgeline connecting a top portion of the chip breaker and the first wall face portion is a straight line; and a second wall face portion connected to the first wall face portion on a first cutting edge side and configured so that a ridgeline connecting the top portion of the chip breaker and the second wall face portion is closer to a second cutting edge side than the straight line.

An insert may include a base member and a resin layer located on the base member. The base member may include a first surface, a second surface, and a cutting edge. The first surface includes a rake surface region. The second surface may be adjacent to the first surface and includes a flank surface region. The cutting edge may be located in at least a part of a ridge line at which the first surface intersects with the second surface. The resin layer may not be located on the second surface but may be located on the first surface.

A cutting tool which allows for fracture resistance and cutting resistance to be improved at the same time is provided. A cutting tool according to the present invention is a cutting tool 1 comprising an end surface 10, first and second side surfaces 13, 14 which intersect with the end surface 10, a first cutting edge 20a in an intersecting edge between the end surface 10 and the first side surface 13, and a second cutting edge 20b in an intersecting edge between the end surface 10 and the second side surface 14, wherein: the first cutting edge 20a has a first honing surface 21a; and the second cutting edge 20b has a second honing surface 21b. A cross-sectional shape of the second honing surface 21b is different from a cross-sectional shape of the first honing surface 21a.

In an embodiment, a cutting insert includes an upper surface, a one or more side surfaces, and a cutting edge. The upper surface includes a first corner portion, and a first side that is adjacent to the first corner portion. The side surfaces are adjacent to the upper surface. The cutting edge is disposed on at least a portion of a section where the upper surface and the side surfaces intersect. The cutting edge includes first, second, third and fourth cutting edges. The first cutting edge is disposed at the first corner portion and has a convex curved shape. The second cutting edge is next to the first cutting edge, and has a linear shape. The third cutting edge is next to the second cutting edge, and has a convex curved shape. The fourth cutting edge is next to the third cutting edge on the first side.

A cutting insert of one aspect is provided with a top surface having a polygonal shape and including a corner portion, a first side and a second side, each extending from the corner portion, a bottom surface, a side surface, and a cutting edge. The cutting edge includes a corner cutting edge disposed in a position corresponding to the corner portion, and a first cutting edge disposed in a position corresponding to the first side. The top surface includes an inclined surface provided with a first inclined surface disposed along the first side, a second inclined surface disposed along the second side, and a third inclined surface disposed along the corner portion. An inclination angle of the first inclined surface is greater than an inclination angle of the second inclined surface.