Chip discharge control is further improved. A cutting insert includes an upper surface, a lower surface, a screw hole having an axis penetrating from the upper surface to the lower surface, a peripheral side surface, and a major cutting edge, a wiper edge, and an inner edge formed in an intersecting region between the upper surface and the peripheral side surface. In a side view in which the peripheral side surface on which the inner edge is formed is seen from a direction perpendicular to the axis, the inner edge includes a recessed part recessed toward the lower surface, a length D.sub.L of the inner edge on one side of the recessed part in the side view is longer than a length D.sub.R of the inner edge on the other side of the recessed part, a lowest point of the inner edge is at a position lower than a flat part of the upper surface, and at least a part of the inner edge on the one side is at a position higher than the flat part of the upper surface. A cutting edge angle φ.sub.23L of the inner edge on the one side of the recessed part is larger than a half of a cutting edge angle φ.sub.23R of the inner edge on the other side of the recessed part.

A cutting insert for a shoulder milling tool has a trigonal shape and includes a first surface, a second surface, and a circumferential surface extending between the first surface and the second surface. The circumferential surface includes a countersunk circumferential waist portion. The circumferential surface has a first and a second clearance surface extending along a first and a second main cutting edge. Each of the first and second clearance surfaces forma a negative nominal clearance angle. Each of the first and second main cutting edges is arranged inside the countersunk circumferential waist portion, as seen in the view towards the first and second surfaces, respectively.

The invention relates to a cutting insert having a polygonal upper side. Cutting edges, which are alternately configured as roughing cutting edges and finishing cutting edges, are provided at the edges of the upper side. The finishing cutting edges define an incircle (K1) having a diameter that is enlarged in comparison to a nominal size of the cutting insert, and the roughing cutting edges define an incircle (K2) having a diameter that is reduced in comparison to the nominal size of the cutting insert. The invention further relates to a cutting tool having a tool body on which at least one such cutting insert is disposed.

Provided is a cutting insert configured to be able to realize downsizing of a cutting tool. A cutting insert includes: an upper surface and a lower surface facing each other and having a plurality of corner parts; a side surface connecting the upper surface and the lower surface and forming intersecting edges with the upper surface and the lower surface, respectively; and a through hole that has a central axis extending from the upper surface to the lower surface and that is formed for penetration from the upper surface to the lower surface. A corner cutting edge arranged at a position corresponding to a corner part of the upper surface, a minor cutting edge connected to a first end of the corner cutting edge, and a major cutting edge connected to a second end of the corner cutting edge are formed on the intersecting edge between the upper surface and the side surface. A flank of the corner cutting edge and a recessed part located on the lower surface side of the flank of the corner cutting edge are formed on the side surface.

A cutting insert includes a polygonal plate-shaped insert main body having two polygonal surfaces, a side surface having a flank, and a cutting edge to be formed in an intersection ridgeline portion between a rake face and the flank. The insert main body has a rotationally symmetrical shape with respect to an insert center line, and has a front-rear reversely symmetrical shape with respect to the polygonal surface. The cutting edge includes a corner cutting edge, a major cutting edge extending from an one end of the corner cutting edge, and a wiper cutting edge extending from an one end of the major cutting edge in a direction intersecting the major cutting edge at an obtuse angle. A first region is disposed where a clearance angle of the flank gradually decreases to a negative angle after continuously passing through 0° from a positive angle.

A double-sided cutting insert for milling has a first cutting edge formed at a transition from a top side to a circumferential lateral surface and a second cutting edge formed at a transition from a bottom side to the circumferential lateral surface. A reference plane (R) runs normal to an axis of symmetry (S). The cutting edges have main cutting edge portions and face cutting edge portions arranged in alternation, which extend between raised cutting corners and lowered cutting corners. The circumferential lateral surface has face free surfaces, which extend along the face cutting edge portion and which approach the axis of symmetry (S) with increasing distance from the associated face cutting edge portion. The circumferential lateral surface has main free surfaces, which extend along the main cutting edge portion and which move farther away from the axis of symmetry with increasing distance from the associated main cutting edge portion.

The invention relates to a cutting insert having a polygonal upper side. Cutting edges, which are alternately configured as roughing cutting edges and finishing cutting edges, are provided at the edges of the upper side. The finishing cutting edges define an incircle (K1) having a diameter that is enlarged in comparison to a nominal size of the cutting insert, and the roughing cutting edges define an incircle (K2) having a diameter that is reduced in comparison to the nominal size of the cutting insert. The invention further relates to a cutting tool having a tool body on which at least one such cutting insert is disposed.

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.

Provided is a cutting insert configured to be able to realize downsizing of a cutting tool. A cutting insert includes: an upper surface and a lower surface facing each other and having a plurality of corner parts; a side surface connecting the upper surface and the lower surface and forming intersecting edges with the upper surface and the lower surface, respectively; and a through hole that has a central axis extending from the upper surface to the lower surface and that is formed for penetration from the upper surface to the lower surface. A corner cutting edge arranged at a position corresponding to a corner part of the upper surface, a minor cutting edge connected to a first end of the corner cutting edge, and a major cutting edge connected to a second end of the corner cutting edge are formed on the intersecting edge between the upper surface and the side surface. A flank of the corner cutting edge and a recessed part located on the lower surface side of the flank of the corner cutting edge are formed on the side surface.

A rotary cutting method includes producing a processed product by rotary cutting of a workpiece by a rotary tool. The rotary tool has at least one cutting edge of which both of a first rake angle in a rotation radial direction and a second rake angle in a rotation axis direction are negative. The at least one cutting edge has a slanted face connected with a rake face forming the first and second rake angles. The slanted face is connected with the rake face at a ridge line. The slanted face faces a rotating direction of the rotary tool. An angle of the slanted face to the rotation axis direction is positive.