A cutting insert includes a top face, a bottom face and a plurality of side walls extending between the top face and the bottom face. A peripheral cutting edge is defined at the juncture of each side wall and the top face. Each cutting edge includes a linear cutting edge portion and a concave cutting edge portion that curves inwardly in a plane that is perpendicular to a plane containing a central axis of the cutting insert. A radiused corner portion connects two adjacent cutting edges. Each linear cutting edge portion extends from one radiused corner portion to the concave cutting edge portion and the concave cutting edge portion extends from the linear cutting edge portion to another radiused corner portion.

A drill cutting insert has a cutting edge at a transition between a side surface and a top side which is formed with n identical cutting corners and n identical partial cutting edges with n{3, 4} extending between the cutting corners. Each of the n partial cutting edges has: adjoining a first cutting corner, a main lip which is straight in plan view of the top side; adjoining the other cutting corner, a secondary lip which is straight in plain view of the top side, and a transition section, via which the main lip and the secondary lip merge into one another and which has a convex section adjoining the main lip and a concave section adjoining the secondary lip. The main and secondary lips enclose on the outside an angle a <180 in plan view of the top side.

A cutting tool has an insert holder and a cutting insert releasably attached thereto. The cutting insert has an insert edge which includes two nose cutting edges and a convex corner cutting edge which extends therebetween. The two nose cutting edges form a nose angle. The insert edge also includes two mid-side edges which are located further from the corner cutting edge than the nose cutting edges. The two mid-side edges form a mid-side angle. The nose angle is less than the mid-side angle.

A cutting insert may include an upper surface, a lateral surface, and a cutting edge including a boundary between the upper surface and the lateral surface. The upper surface may include a first rising face that extends upward and a second rising face that is connected to an upper side of the first rising face and extends upward. The first rising face may include a first region that extends along a corner portion and a second region that extends along a side portion. The second rising face may include a third region connected to the first region and a fourth region connected to the second region. An entirety of a boundary between the first region and the third region may be positioned above the cutting edge. A boundary between the second region and the fourth region may include a portion disposed below the cutting edge.

A cutting insert includes a rake face, a flank face, and a cutting edge constituted of a ridgeline between the rake face and the flank face. The cutting edge has a first cutting edge portion for corner processing, a second cutting edge portion for low cut-in pulling processing, a third cutting edge portion for high cut-in pulling processing, a fourth cutting edge portion for finished-surface processing, a first connection cutting edge portion, a second connection cutting edge portion, and a third connection cutting edge portion. The fourth cutting edge portion is disposed between the first cutting edge portion and the second cutting edge portion. The second cutting edge portion is disposed between the fourth cutting edge portion and the third cutting edge portion. Each of the first cutting edge portion, the second cutting edge portion, and the fourth cutting edge portion has a curved shape.

A machining method for cutting process by making a workpiece (W) and a cutting tool (11) move relatively, characterized by using a cutting tool (11) comprising a cutting insert (28) having a first curved part (40a), a second curved part (40c) formed continuing from the first curved part (40a) and with a curvature smaller than the first curved part (40a), and a connecting part (40b) connecting the first curved part (40a) and the second curved part (40c) and by cutting while positioning the connecting part (40b) at the front end in the cut direction perpendicular to the direction of relative movement at the time of cutting.