There is provided a cutting insert having a low possibility that chips roughen a machined surface of a workpiece in back turning. The cutting insert includes a rake surface, a peripheral side surface, a front cutting edge which is provided on a ridge of the rake surface and the peripheral side surface, and a main cutting edge which is provided on the ridge so as to be continuous with the front cutting edge and has an extension direction which forms an obtuse angle with an extension direction of the front cutting edge, the main cutting edge is curved into a U shape over an entire length of an effective edge range which functions as a cutting blade, and the deepest point of the U shape is positioned in a range closer to a side of a corner than a position which divides a straight line connecting both ends of the main cutting edge at a ratio of 2:1 from the side of the corner positioned adjacent to the front cutting edge.

A cutting insert capable of performing front-turning and high feed back-turning according to one embodiment includes: an upper surface; a lower surface opposite to the upper surface in a vertical direction; a side portion configured to connect the upper surface and the lower surface; a mounting hole extending through the upper surface and the lower surface; and a plurality of cutting edges formed at edges where the upper surface meets the side portion, wherein the upper surface has one or more cutting corners, the plurality of cutting edges include a major cutting edge and a minor cutting edge extending from the cutting corner, and a representative inclination of the minor cutting edge used for high feed back-turning is greater than a representative inclination of the major cutting edge used for front-turning with respect to a virtual reference plane perpendicular to the vertical direction.

A cutting insert may include an upper surface, a lateral surface, and a cutting edge including a boundary between the upper surface and the lateral surface. The upper surface may include a first rising face that extends upward and a second rising face that is connected to an upper side of the first rising face and extends upward. The first rising face may include a first region that extends along a corner portion and a second region that extends along a side portion. The second rising face may include a third region connected to the first region and a fourth region connected to the second region. An entirety of a boundary between the first region and the third region may be positioned above the cutting edge. A boundary between the second region and the fourth region may include a portion disposed below the cutting edge.

A cutting insert, for producing a V-shaped profile in a workpiece by radial piercing relative to an axis of rotation of the workpiece, includes a reference plane and a V-shaped insertion region. The V-shaped insertion region includes, inter alia, two cutting edges in the reference plane, a rake face and a plurality of elongated chip-guiding depressions in the rake face, each extending in parallel with a depression axis of extent or extension axis in the reference plane, providing improved chip formation compared to the prior art. The depression axes of extent or extension axes each extend at a recess chip-guiding angle in a region of 0° to 45°. A method of using the cutting insert and the workpiece at a standstill and a machining method are also provided.

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.

A cutting insert includes a top face, a bottom face and a plurality of side walls extending between the top face and the bottom face. A central axis of the cutting insert extends through the top face and the bottom face. A peripheral cutting edge is defined at the juncture of each side wall and the top face. Each cutting edge includes a linear cutting edge portion having an end portion that connects to a concave cutting edge portion that curves inwardly in a plane that is perpendicular to a first plane containing the central axis, wherein at least one linear cutting edge portion and its corresponding end portion are parallel to the first plane containing the central axis.

Inclined surfaces are formed on a rake face and a recessed groove is formed in the central portion between the inclined surfaces. A groove width of the recessed groove gradually increases from the position of the end cutting edge toward the rear, then gradually decreases such that the recessed groove has a narrowest portion at a position P2 forward of the position P3 of an upper end of a breaker wall and rearward of a positive rake angle rear end position P1, and then gradually increases toward the rear up to the position P3 of the upper end of the breaker wall. The dimensional relation W1<W2<W3 holds, where W1 is the groove width at the end cutting edge, W2 is the groove width at the narrowest portion, and W3 is the groove width at the position P3 of the upper end of the breaker wall.

An indexable cutting insert for a cutting tool for material processing machines has a first axis of symmetry, at least one fastening bore passing through the indexable cutting insert parallel or coaxially to this first axis, two groups of main cutting edges, secondary cutting edges and cutting corners having a second axis of symmetry rotationally symmetrically opposite one another. At least the main cutting edges enclose an acute cutting edge angle with a plane oriented orthogonally to the first axis of symmetry. A cutting insert holder holds and fixes an indexable cutting insert. A recess for receiving the indexable cutting insert is on an elongated base body with polygonal cross-section. A support surface for supporting the indexable cutting insert is rotated about the base-body longitudinal axis and tilted about a second axis, a line of intersection between the rotated support surface and a plane perpendicular to the longitudinal axis.

A turning insert includes a top surface, an opposite bottom surface and a reference plane located parallel to and between the top surface and the bottom surface. A nose portion has a convex nose cutting edge, a first cutting edge 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 (α) of 71-85° relative to each other. The nose portion includes 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 (β) of 10-30° relative to a bisector. The distance from at least a portion of the fourth cutting edge to the reference plane increases as the distance from the nose cutting edge increases.

A cutting insert has cutting edges having the same shape and provided at respective corners of a polygon in rotational symmetry about the center axis of the polygon, is clamped in an upright position to a holder, and has a negative side rake angle on a rake face of a side cutting edge. A side cutting edge is present at an intersection ridge between a polygonal face and an outer peripheral face. The outer peripheral face includes a rake face of the cutting edge and a flank of an end cutting edge of another cutting edge different from the side cutting edge. The flank has a positive slope angle in opposition to a negative side rake angle of the side cutting edge. A breaker groove extending in a front-rear direction is formed in the rake face and cuts into the flank, in such a manner as to divide the rake face.