A cutting insert may include a first surface, a second surface, a third surface, and a land surface. The first surface may include a first corner and a first side. The land surface may be located between the first surface and the third surface. The land surface may include a first land surface connecting to the first corner, and a second land surface connecting to the first side. A width of the first land surface in a front view as viewed from a side of the first surface may be a first width, the first width at an end portion on a side of the second land surface may be larger than the width at a part connecting to a midportion of the first corner.

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.

An insert based on an aspect includes a first surface having a corner portion, a second surface, a third surface, and a cutting edge located on at least part of a portion on which the first surface and the third surface intersect. The cutting edge is provided with a first cutting edge located on the corner portion and a second cutting edge adjacent to the first cutting edge, and the third surface is provided with a first portion located along the first cutting edge and a second portion located along the second cutting edge. Additionally, the second portion includes a first region having a first end portion and a second end portion, and a second region having a third end portion and a fourth end portion. An inclination angle 212 at the second end portion is greater than an inclination angle 211 at the first end portion, and an inclination angle 222 at the fourth end portion is smaller than an inclination angle 221 at the third end portion.

A peeling plate has upper and lower sides, lateral faces extending between the upper and lower sides, and primary and secondary cutting edges at the transition from the lateral faces to the upper side. The peeling plate in a plan view of the upper side has the shape of a substantially regular n-gon, n being five or six, and n lateral edges lying between the n lateral faces. A primary cutting edge and a secondary cutting edge are formed at the transition from at least one lateral face to the upper surface, wherein active primary cutting edges and active secondary cutting edges are spaced apart from a lateral edge. The lateral edge at the transition to the upper side forming an active cutting corner to the respective active primary cutting edge and active secondary cutting edge.

A method for designing a cutting edge of a cutting element configured for removing material from a workpiece to leave therein a desired end profile (B22,B24,B26). The method comprises the steps of modeling a desired end profile (B22,B24,B26) of the workpiece, the profile having a longitudinal axis and being defined by a bottom surface (B12), a side surface (B16) and an adjustment surface (B14) extending therebetween; defining a lead profile plane (RP.sub.L) and an trail profile plane (RP.sub.T) spaced therefrom, each of the planes being oriented perpendicular to the longitudinal axis; determining a profile contour defined by the intersection line between the end profile (B22,B24,B26) and the lead profile plane (RP.sub.L). The contour profile includes a bottom contour, an adjoining contour and a side contour defined as the intersection lines between the lead profile plane (RP.sub.L) and the bottom surface (B12), the adjustment surface (B14) and the side surface (B16) respectively; designing a rake surface and a relief surface, the intersection line between which defines a cutting edge lying in the adjoining surface (B14) and spanning between the lead profile plane (RP.sub.L) and the trail profile plane (RP.sub.T). The cutting edge is designed such that in any reference plane (RP; FIG. 6A) oriented perpendicularly to the cutting edge, the intersection between each of the rake surface and the relief surface with the reference plane (RP) defines a respective rake line (RK; FIG. 7) and relief line (RF; FIG. 7), the angle (.sub.B) between the lines RK,RF) being equal to or smaller than a similar angle (.sub.B) taken along each of a plurality of similar reference planes (RP) disposed between the reference plane (RP.sub.n) and the lead profile plane (RP.sub.L).

A cutting insert according to an aspect includes a top surface and a side surface. At least a part of a ridge line where the top surface and the side surface intersects is a cutting edge. The cutting edge includes a first portion located at a corner portion, a second portion adjacent to the first portion, a third portion close to the second portion, a fourth portion close to the third portion, and a fifth portion adjacent to the fourth portion. When viewed from directly above, a curvature radius of the second portion is less than a curvature radius of the first portion, a curvature radius of the third portion is greater than the curvature radius of the first portion, and a curvature radius of the fourth portion is less than the curvature radius of the third portion.

A cutting insert includes a rake face, a flank face, a cutting edge formed at a ridge where the rake face and the flank face intersect, a land provided on the rake face along the cutting edge, a breaker groove provided in the rake face inside of the land, and a curved surface formed between a groove surface of the breaker groove and the land. A radius of curvature of the curved surface is 0.5 mm or greater.

A method to form a surface on a metal work piece includes providing a turning insert that has a nose angle formed between first and second cutting edges less than or equal to 85; providing a turning tool having a tool body with an insert seat in which the turning insert is mountable; arranging the orientation of the second cutting edge such that it forms a back clearance angle of more than 90 in a feed direction; rotating the metal work piece around a rotational axis in a first direction; moving the turning insert in a direction parallel to or at an angle less than 45 relative to the rotational axis; and setting the longitudinal axis of the tool body at an angle greater than zero but less than or equal to 90 relative to the rotational axis of the metal work piece.

In an embodiment, a cutting insert including a base member, a first face, a second face, a cutting edge, and a nose portion. The base member includes a coating layer on at least a part thereof. The first face has corner portions. The second face is adjacent to the first face. The cutting edge is on at least a part of the ridgeline portion of the first face and the second face, and includes first and second cutting edges. The first cutting edge is on the coating layer and has a C chamfered surface with a first width of 5 m to 30 m in the front view of the first face and a chamfer angle of 35 to 50. The nose portion is at the corner portions between the first cutting edge and the second cutting edge.