A cutting insert may include a first surface, a second surface, a first lateral surface, a second lateral surface, a first cutting edge and a second cutting edge. The first lateral surface may include a first inclined surface located along the first cutting edge, a second inclined surface located along the first inclined surface, a third inclined surface located along the second cutting edge, a fourth inclined surface located along the third inclined surface, and a flat surface located along the second inclined surface and the fourth inclined surface. A second inclination angle of the second inclined surface may be smaller than a first inclination angle of the first inclined surface. A fourth inclination angle of the fourth inclined surface may be larger than a third inclination angle of the third inclined surface.

A turning insert arranged for longitudinal turning of metal work pieces includes a nose cutting edge that slopes from a trailing cutting edge in direction towards a leading cutting edge. A turning tool is also disclosed.

A cutting insert has a seating surface, an outer peripheral surface, a top surface, and an attachment hole. The cutting edge includes a curved cutting corner edge portion, a first cutting edge portion, and a second cutting edge portion. The top surface includes a first rake face contiguous to the first cutting edge portion, a second rake face contiguous to the second cutting edge portion, and a third rake face contiguous to the cutting corner edge portion and also contiguous to the first and second rake faces. The third rake face has a first region contiguous to the first rake face and a second region contiguous to the second rake face. The first rake face and the first region each have a rake angle which is a positive angle. The second rake face and the second region each have a rake angle which is a negative angle.

A cutting tool comprises a substrate and a coating that coats the substrate, the coating including an -alumina layer, the -alumina layer including crystal grains of -alumina, the -alumina layer including a lower portion and an upper portion, the upper portion being occupied in area at a ratio of 50% or more by crystal grains of -alumina having (006) plane with a normal thereto having a direction within 15 with respect to a direction of a normal to the second interface, the lower portion being occupied in area at a ratio of 5% or more and less than 50% by crystal grains of -alumina having (012) plane, (104) plane, (110) plane, (113) plane, (116) plane, (300) plane, (214) plane and (006) plane each with a normal thereto having a direction within t 15 with respect to the direction of the normal to the second interface.

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 () 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 () 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 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.

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.

A cutting blade having a plurality of different coatings on surfaces thereof, including an upper surface, a lower surface, and a side surface connecting the upper surface and the lower surface, wherein the upper surface intersects the side surface to form at least one cutting edge unit, the cutting edge unit includes a main cutting edge and a secondary cutting edge, the upper surface includes at least one set of cutting planes, the cutting planes include a main cutting surface and a secondary cutting surface, the main cutting surface intersects the side surface to form the main cutting edge, the secondary cutting surface intersects the side surface to form the secondary cutting edge, a main coating is provided on the main cutting surface, a secondary coating is provided on the secondary cutting surface, and the main coating and the secondary coating are independent from each other.

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 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.