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 cutting insert includes: a polygonal shaped upper surface; a lower surface; a side surface connected to each of the upper and lower surfaces; and an upper cutting edge located at the intersection of the upper surface and the side surface. The upper surface alternately includes three major corners and three minor corners. The upper cutting edge includes: a corner cutting edge; a minor cutting edge inclined toward the lower surface as separating from the corner cutting edge at a first inclination angle; and a major cutting edge inclined toward the lower surface as separating from the minor cutting edge at a second inclination angle. The corner cutting edge, the minor cutting edge and the major cutting edge are located sequentially from a first major corner to each of first and second minor corners, both of which are adjacent to the first major corner.

In a cutting insert according to an embodiment of the present invention, an upper cutting edge includes, sequentially from a first corner to a second corner, a corner cutting edge, a minor cutting edge inclined as separating from the corner cutting edge at a first inclination angle on a basis of a vertical plane perpendicular to a central axis extending between upper and lower surfaces, and a major cutting edge inclined as separating from the minor cutting edge at a second inclination angle on the basis of the vertical plane so as to become more closer to the lower surface than the minor cutting edge. A cross section of a rake surface obtained by cutting an inwardly located end portion thereof along a direction of the central axis has a straight line shape or concave shape in a region crossing over at least a minor rake surface and a major rake surface. A cutting tool with the cutting insert, and a method of manufacturing a machined product by using the cutting tool are also provided.

A cutting element for use in a cutting operation, comprising a cutting edge (CE) capable of cutting out material from a workpiece during the operation, to form therein a workpiece corner of angle alpha. There exists at least one view of the cutting edge in which a portion of the cutting edge is delimitable by a first (L1) and a second (L2) line oriented tangentially to the portion of the cutting edge portion at respective tangency points A and B. The lines form therebetween a cutting angle corresponding to the workpiece corner angle alpha and have a vertex 0. For a bisector of the cutting angle intersecting the portion of the cutting edge at the point C, the projection C of the point C of the portion of the cutting edge on a line OL passing through the vertex 0 perpendicularly to the plane of the one view is located between projections A1 and B of the respective points A and B of the portion of the cutting edge on the line OL.

A cutting insert includes: a polygonal shaped upper surface; a lower surface; a side surface connected to each of the upper and lower surfaces; and an upper cutting edge located at the intersection of the upper surface and the side surface. The upper surface alternately includes three major corners and three minor corners. The upper cutting edge includes: a corner cutting edge; a minor cutting edge inclined toward the lower surface as separating from the corner cutting edge at a first inclination angle; and a major cutting edge inclined toward the lower surface as separating from the minor cutting edge at a second inclination angle. The corner cutting edge, the minor cutting edge and the major cutting edge are located sequentially from a first major corner to each of first and second minor corners, both of which are adjacent to the first major corner.