A cutting insert is mountable on a body. The cutting insert includes: a top surface; a bottom surface opposite to the top surface; a side surface contiguous to the top surface and the bottom surface; and a cutting edge formed at a ridgeline between the top surface and the side surface. The side surface has a first surface disposed adjacent to the cutting edge and a second surface contiguous to the first surface. When viewed in a cross sectional view parallel to the bottom surface, the second surface has a first position and a second position that are brought into abutment with the body when mounted on the body. Between the first position and the second position, an imaginary straight line extending through the first position and the second position is separated from the second surface.

A cutting insert including a first end surface, a second end surface and a peripheral side surface extending therebetween. The first and second end surfaces each having one substantially quadrangular portion and two substantially semicircular portions which are respectively joined to two opposing sides of the substantially quadrangular portion. An intersecting edge between each of the first and second end surfaces and the peripheral side surface is provided with a cutting edge. The cutting edge is formed in at least part of the substantially semicircular portion. At least part of a portion of the peripheral side surface which is adjacent to the substantially quadrangular portion of each of the first and second end surfaces, and at least part of a portion of the peripheral side surface which is adjacent to the substantially semicircular portion, each have a function of coming into contact with an insert seat.

A cutting insert according to an embodiment has a polygonal shaped upper surface, a lower surface, a side surface, and a cutting edge. The cutting edge has an arc-shaped first corner edge, an arc-shaped second corner edge, and a wiper edge located between the first corner edge and the second corner edge. The wiper edge has an arc-shaped first wiper edge and an arc-shaped second wiper edge located closer to the second corner edge than the first wiper edge. R0<R1<R2 is satisfied wherein R1 is a radius of curvature of the first wiper edge, R2 is a radius of curvature of the second wiper edge, and R0 is a radius of curvature of each of the corner edges in a top view.

An indexable cutting insert for face milling with high feed rates has: an upper side, a lower side with a smaller outer circumference than the upper side, and side surfaces connecting the upper and lower sides. Rounded cutting corners are formed at the transition between the side surfaces and the upper side. The cutting corners are connected via convexly arched cutting edges, each running convexly curved from one cutting corner to an adjacent cutting corner. Adjacent the cutting edges, the side surfaces have main flanks extending along the respective cutting edge in a continuously convexly curved manner from one cutting corner to an adjacent cutting corner. The main flanks extend in the direction of the lower side only over part of the height of the side surfaces and merge in a stepped manner into secondary surfaces which are set back inward.

A cutting insert has an upper surface, a lower surface and a lateral surface. The upper surface has a first upper side, and a second upper side. The lower surface has a first lower side and a second lower side. The lateral surface has a first lateral surface, a second lateral surface, and a third lateral surface. The first lateral surface has a first concave part having a first constraining surface having a flat shape. The second lateral surface has a second concave part having a second constraining surface having a flat shape. The third lateral surface has a convex part. The first concave part and the second concave part are separated from each other by the convex part.

A milling tool includes a tool body defining an insert pocket having a main seat floor, and lower, mid, and upper seat walls. A cutting insert having an insert body is disposed in the insert pocket. The insert body includes front and back faces, with first, second, and third main circumferential sides extending between the faces and about the circumference of the insert body. First, second, and third cutting corners are disposed between the main circumferential sides. Each of the main circumferential sides includes two side seating surfaces extending between adjacent cutting corners and having a transition corner disposed therebetween. One of the front or back surfaces engages the main seat floor. Three consecutive side seating surfaces engage the lower, mid, and upper seat wall, respectively. One of the lower, mid, and the upper seat walls or each of the side seating surfaces is generally planar, the other are convex.