A vibration cutting insert includes a top surface having a rake face and a breaker face, a first side surface, a second side surface, and a bottom surface. In a cross section which includes a bisector of an angle formed between a first ridgeline and a second ridgeline when viewed in a direction from the top surface toward the bottom surface, and which is parallel to the direction from the top surface toward the bottom surface, a rake angle formed between the rake face and a plane parallel to the bottom surface has a positive angle. The angle formed between the first ridgeline and the second ridgeline is an acute angle. The rake face constitutes a cylindrical surface. The breaker face constitutes a flat surface.

A cutting edge includes a nose portion, a first cutting edge portion, and a second cutting edge portion. When a boundary between a first inclined portion and a first breaker portion, a boundary between a first step surface and a second breaker portion, a boundary between a second inclined portion and a third breaker portion, and a boundary between a second step surface and a fourth breaker portion are a first position, a second position, a third position, and a fourth position, respectively, the second position is higher than the first position and the fourth position is higher than the third position in a direction perpendicular to the seating surface, and a distance between the first position and the third position is greater than a distance between the second position and the fourth position in a direction parallel to the seating surface.

In an embodiment, an insert includes an upper surface including a corner part, a lower surface, a side surface, and a cutting edge. The side surface is between the upper surface and the lower surface. The cutting edge is at least at a part of a first region in which the upper surface intersects with the side surface. The cutting edge includes a first cutting edge at the corner part, a second cutting edge, a third cutting edge, and a fourth cutting edge. The second cutting edge is next to the first cutting edge, and also next to the third cutting edge. The third and fourth cutting edges: each have a convex curvilinear shape with first and second radii of curvature, respectively; and extend downward and upward, respectively, in a side view as going farther from the second cutting edge. The second radius smaller than the first radius.

A round double-sided cutting insert includes an insert peripheral surface that includes a plurality of angularly spaced apart indexing latches protruding therefrom and a plurality of cylindrical insert side abutment surfaces that circumferentially alternate with the plurality of indexing latches. An insert holder has a pocket peripheral surface which includes at least one indexing gap and a plurality of pocket side abutment surfaces that circumferentially alternate with the at least one indexing gap. When the cutting insert is releasably attached to the insert holder, to constitute a fastened position of a cutting tool, each of the plurality of pocket side abutment surfaces abuts a respective insert side abutment surface and each indexing gap has a respective indexing latch located therein.

There is provided a machining assembly and cutting insert for machining metal or like workpieces, wherein the cutting insert body has a cutting end. The cutting end comprises at least one cutting edge and at least one cutting lip formed adjacent the at least one cutting edge. The at least one cutting lip includes at least one cutting protrusion and associated chip cutting edge to split the chip formed by the at least one cutting edge, for producing chips during machining which are of a width that is sufficiently reduced to allow proper evacuation or removal.

A vibration cutting insert includes a top surface having a rake face and a breaker face, a first side surface, a second side surface, and a bottom surface. In a cross section which includes a bisector of an angle formed between a first ridgeline and a second ridgeline when viewed in a direction from the top surface toward the bottom surface, and which is parallel to the direction from the top surface toward the bottom surface, a rake angle formed between the rake face and a plane parallel to the bottom surface has a positive angle. The angle formed between the first ridgeline and the second ridgeline is an acute angle. The rake face constitutes a cylindrical surface. The breaker face constitutes a flat surface.

There is provided a cutting insert used for both drilling and turning. The cutting insert includes an insert main body having a front surface and a rear surface, the outline shapes of which are parallelogram shapes, peripheral side surfaces disposed on four sides of the insert main body, cutting edges provided on respective intersecting ridge lines between the front surface and the peripheral side surface and between the rear surface and the peripheral side surface of the insert main body, and a hole provided in the insert main body to incline with respect to the front surface and the rear surface, the hole being usable for attachment.

A round double-sided cutting insert includes an insert peripheral surface that includes a plurality of angularly spaced apart indexing latches protruding therefrom and a plurality of cylindrical insert side abutment surfaces that circumferentially alternate with the plurality of indexing latches. An insert holder has a pocket peripheral surface which includes at least one indexing gap and a plurality of pocket side abutment surfaces that circumferentially alternate with the at least one indexing gap. When the cutting insert is releasably attached to the insert holder, to constitute a fastened position of a cutting tool, each of the plurality of pocket side abutment surfaces abuts a respective insert side abutment surface and each indexing gap has a respective indexing latch located therein.

A cutting tool shim is to be disposed between a cutting insert and a holder and to be fixed to the holder. The ridgeline between the flank face and the rake face forms a cutting edge. The cutting edge includes an arc-shaped portion. A coolant supply path for jetting coolant to the arc-shaped portion is provided in the cutting tool shim, the coolant being supplied from the holder. The coolant supply path includes a lead-in port for leading the coolant from the holder to the coolant supply path, and a jetting port for arc-shaped portion for jetting the coolant to the arc-shaped portion. The jetting port for arc-shaped portion has a curved shape along the arc-shaped portion. The distance between the jetting port for arc-shaped portion and the arc-shaped portion is not less than 2.2 mm and not more than 8.1 mm.

In an embodiment, an insert includes an upper surface including a corner part, a lower surface, a side surface, and a cutting edge. The side surface is between the upper surface and the lower surface. The cutting edge is at least at a part of a first region in which the upper surface intersects with the side surface. The cutting edge includes a first cutting edge at the corner part, a second cutting edge, a third cutting edge, and a fourth cutting edge. The second cutting edge is next to the first cutting edge, and also next to the third cutting edge. The third and fourth cutting edges: each have a convex curvilinear shape with first and second radii of curvature, respectively; and extend downward and upward, respectively, in a side view as going farther from the second cutting edge. The second radius smaller than the first radius.