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 one or more 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. When viewed from directly above, 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 member comprising a cutting edge (S.sub.1,S.sub.2,S.sub.i) defining a cutting envelope and configured for removing material from a workpiece leaving therein a corner of angle . The cutting edge comprises a first cutting segment (S.sub.1) and a second cutting segment (S.sub.2) spaced from the first cutting segment (S.sub.2). Respective first and second imaginary tangents (T.sub.1,T.sub.2) of the first and second cutting segments (S.sub.1,S.sub.2) intersect one another at point O located outside the cutting envelope, forming an angle corresponding to angle , thereby defining a cutting frame at least a portion of which extends beyond the cutting envelope. The cutting edge further comprises an adjoining cutting segment (S.sub.i), extending between and bridging the first cutting segment (S.sub.1) and the second cutting segment (S.sub.2), and at least partially contained within the cutting frame. The cutting member further comprises at least one auxiliary cutting element (AT.sub.1,AT.sub.2) comprising an auxiliary cutting edge (CE,CE) extending generally along one of the imaginary tangents (T.sub.1,T.sub.2) and beyond the cutting envelope. The auxiliary cutting edge (CE,CE) does not intersect the other of the imaginary tangents (CE,CE) and/or a bisector (B) of the angle .

A method to form a surface on a metal work piece includes providing a turning insert having a first cutting edge, a second cutting edge and a convex nose cutting edge connecting the first and second cutting edges, a nose angle formed between the first and second cutting edges being less than or equal to 85; arranging the second cutting edge such that it forms a back clearance angle of more than 90 in a feed direction; positioning all parts of the turning insert ahead of the nose cutting edge in the feed direction; rotating the metal work piece around a rotational axis in a first direction; and moving the turning insert in a direction parallel to or at an angle less than 45 relative to the rotational axis, such that the surface at least partly is formed by the nose cutting edge.

A cutting insert according to one aspect of the present invention includes a polygonal columnar shape, and includes an upper surface, a lower surface and a side surface located between the upper surface and the lower surface, and a cutting edge is formed at an intersecting portion between the upper surface and the side surface, the upper surface includes a main portion of a convex shape including a flat upper end surface, a first projecting portion which projects from the main portion to a corner portion of the upper surface, and a pair of second projecting portions which each project from the first projecting portion to a periphery of the upper surface to interpose a region between a front end of the first projecting portion and the corner portion, and each of upper ends of the pair of second projecting portions is spaced part from the first projecting portion.

A straight line along the second line segment and a straight line along the fourth line segment form an acute angle. The straight line along the second line segment and the straight line along the third line segment form an obtuse angle. The straight line along the first line segment and the straight line along the fourth line segment form an obtuse angle. Each of the third curved portion and the fourth curved portion is larger in radius of curvature than the first curved portion and larger in radius of curvature than the second curved portion. In a direction perpendicular to the bottom surface, a distance between the top surface and the bottom surface is equal to a distance between the cutting edge and the bottom surface, or is shorter than the distance between the cutting edge and the bottom surface.

A tool includes, at least on its edge, a sintered cBN compact which includes cBN particles and a bonding phase, a plurality of flutes is formed on a rake face, each of the flutes having a starting end on the edge ridgeline and causing the edge ridgeline to be wavy, and the terminal end of the flute is disposed inwardly of the edge ridgeline. It is preferable that the flute width of the flute decreases with distance from the edge ridgeline, the flute depth of the flute decreases with distance from the edge ridgeline, and the rake face has a positive rake angle.

The present invention relates to a cutting insert having a cutting edge which is provided with a corner section that forms a convex arc shape when seen in a planar view from the direction facing the rake face and a pair of linear sections that are in contact with the corner section at the both ends thereof. The cutting edge is provided with a first region along the corner section, a second region along the linear section and a third region positioned between them, and a cross-sectional area of the insert main body on a cross-section orthogonal to the cutting edge in a range of width which is a radius R (mm) of the corner section is made largest in the third region, smallest in second region and between them in the first region in terms of size.

A turning insert includes a top surface, an opposite bottom surface, a reference plane located parallel to and between the top surface and the bottom surface, and a center axis extending perpendicular to the reference plane and intersecting the reference plane (RP), the top surface and the bottom surface. Side surfaces connect the top surface and the bottom surface. Three nose portions are formed symmetrically relative to the center axis. Each nose portion includes a first cutting edge, a second cutting edge and a convex nose cutting edge connecting the first) and second cutting edges. In a top view the first and second cutting edges on the same nose portion form a nose angle of 25-50 relative to each other. The distance from the first cutting edge to the reference plane varies in such a way that that this distance is decreasing at increasing distance from the nose cutting edge.

A method to form a surface on a metal work piece includes providing a turning insert having a first cutting edge, a second cutting edge and a convex nose cutting edge connecting the first and second cutting edges, a nose angle formed between the first and second cutting edges being less than or equal to 85; arranging the second cutting edge such that it forms a back clearance angle of more than 90 in a feed direction; positioning all parts of the turning insert ahead of the nose cutting edge in the feed direction; rotating the metal work piece around a rotational axis in a first direction; and moving the turning insert in a direction parallel to or at an angle less than 45 relative to the rotational axis, such that the surface at least partly is formed by the nose cutting edge.

A turning insert includes a top surface, a bottom surface, and side surfaces connecting the top and bottom surfaces. A reference plane is located parallel to and between the top surface and the bottom surface. A center axis intersects and extends perpendicular to the reference plane. Three nose portions are formed symmetrically around the center axis. Each nose portion has a first cutting edge, a second cutting edge and a convex nose cutting edge connecting the first and second cutting edges. As seen in in a top view, the first and second cutting edges on the same nose portion form a nose angle of 25-50. The first cutting edge includes a first sub-portion and a second sub-portion. A distance from the nose cutting edge to the first sub-portion is shorter than a distance from the nose cutting edge to the second sub-portion.