A cutting insert and a cutting tool having same are provided. The cutting insert includes an upper surface, a lower surface having a flat surface, side surfaces connecting to each of the upper surface and the lower surface, and cutting edges being formed by the upper surface and the side surfaces. A first cutting edge among the cutting edges is inclined downward. A major side surface among the side surfaces comprises a first major side surface connected to the upper surface so as to constitute the first cutting edge, and a second major side surface connected to the first major side surface and the lower surface. The first major side surface has a reversely positive surface, and the second major side surface has a reversely positive surface or a negative surface, and a minor side surface among the side surfaces has a positive surface or a negative surface.

A cutting insert and an indexable insert-type cutting tool includes a cutting edge (6A) formed on each of a pair of side ridge portions of at least one of the side faces, wherein an insert main body (1) is formed in the shape of having front-back inversion symmetry which is 180 rotationally symmetrical with respect to a line of symmetry (N) passing through the center of the side faces; a flank face adjacent to the cutting edge (6A) is formed on the side face in the vicinity of each of the pair of polygonal faces (2); each of the flank faces is formed in the shape of a twisted face; the pair of side ridge portions on which the cutting edge (6A) is formed intersect each other in such a manner that the second corner portion (B) of one side ridge portion protrudes outside the other side ridge portion.

A cutting insert comprises a first surface sequentially including a first and second inclined surface. The first inclined surface is inclined toward the second surface, going inward from the edge at a first inclined angle on a basis of a perpendicular plane perpendicular to a central axis extending between the first surface and a second surface. The second inclined surface, located more inward than the first inclined surface, is inclined toward the second surface at a second inclined angle different from the first inclined angle on the basis of the perpendicular plane. An intersecting part of the first inclined surface and the second inclined surface includes a first part located at a highest position in a region of the intersecting part along the second side surface. A cutting tool with the cutting insert, and a method of producing a machined product using the cutting tool are provided.

A cutting insert may include a first surface, a second surface and a lateral surface. The first surface may have a polygonal shape and may include a first corner, a second corner, a third corner, a first side and a second side. The lateral surface may include a first lateral surface and a second lateral surface. At least a part of the first lateral surface may be located between the first side and the second surface. At least a part of the second lateral surface may be located between the second side and the second surface. The first lateral surface may be located further outside than the first side in a front view of the first surface. The first lateral surface may include a first region located closer to the second lateral surface as coming closer to the second surface.

A cutting insert includes a first and a second pair of opposing side surfaces. As seen towards a first side surface, a first axial relief face and a first axial abutment face form part of a first surface grouping on a first side of a longitudinal plane. As seen towards a second side surface, a second axial relief face and a second axial abutment face form part of a second surface grouping on the first side of the longitudinal plane. The first axial abutment face forms a substantially flat surface and extends perpendicularly to a median plane of the insert. The second axial abutment face forms a substantially flat surface and extends perpendicularly to the median plane. A second side surface of the first pair of opposing side surfaces has a first and a second radial abutment face.

A cutting insert includes an upper surface, a lower surface, a side surface, and an upper cutting edge. The upper cutting edge includes a major cutting edge having an outwardly projecting curvilinear shape, and a minor cutting edge having a straight line shape and being continuous with the major cutting edge. The side surface includes a continuous inclined surface with the major cutting edge and is inclined outward from the upper surface to the lower surface with respect to a virtual straight line connecting the respective centers of the upper and lower surfaces. An inclination angle of the inclined surface with respect to a virtual straight line on the side surface increases from a portion of the inclined surface which is continuous with an end portion of the major cutting edge to a portion of the inclined surface which is continuous with a center of the major cutting edge.

A cutting insert in a non-limiting aspect of the present disclosure may include an upper surface having a polygonal shape and including a first side, a lower surface, and a lateral surface. The lateral surface may include a first lateral surface located between the first side and the lower surface. The first lateral surface may include a first region that is flat. The first region may include a first central region, a first upper region and a first lower region. The first upper region may be located closer to the upper surface than the first central region, and may have a larger width than the first central region. The first lower region may be located closer to the lower surface than the first central region, and may be a larger width than the first central region.