A cutting insert of a substantially horizontal cylindrical segment shape is described. The cutting insert comprises top and bottom surfaces having a circular segment shape. The cutting insert further comprises a convex side. The cutting insert further comprises a flat side. The cutting insert further comprises a top cutting edge which is formed where the convex side and the top surface meet, and a bottom cutting edge which is formed where the convex side and the bottom surface meet. The cutting insert further comprises a hole extending from the convex side towards the flat side. The hole is positioned at a center of a surface of the flat side.

A cutting insert in a non-limiting aspect of the present disclosure may include an upper surface, a lower surface, a lateral surface and a cutting edge. The upper surface may include a first corner and a first side. The upper surface may further include a first protrusion and a second protrusion. The first protrusion may be extended toward the first corner. The second protrusion may be located between the first corner and the first protrusion. The first protrusion may include an inclined surface. The inclined surface may be located along the first side. The inclined surface may include a first surface and a second surface. The second surface may be located further away from the first corner than the first surface. The first surface and the second surface may be individually inclined upward as going away from the first side, and having a concave shape as a whole.

A turning insert has two opposite main surfaces and a peripheral surface which extends therebetween and has N side surfaces, where 2<N<9. The insert has mirror symmetry about a mid-plane and 360/N degree rotational symmetry about a central axis perpendicular to the mid-plane. The insert has two main edges which each have N main cutting edges and N corner cutting edges. Each main cutting edge has two raised edge portions and a lowered edge portion. Each main surface has N main rake surfaces and N corner rake surfaces. Each main surface further has at least N convex island protrusions and N at least partially convex peninsula protrusions, any and all island protrusions associated with a given main rake surface being located between two adjacent peninsula protrusions, each pair of adjacent peninsula protrusions having at least one island protrusion located therebetween.

A cutting insert of a substantially horizontal cylindrical segment shape may include top and bottom surfaces having a circular segment shape. The cutting insert may include a convex side and a flat side. The cutting insert may include a top cutting edge which is formed where the convex side and the top surface meet, and a bottom cutting edge which is formed where the convex side and the bottom surface meet. The cutting insert may include a hole extending from the convex side towards the flat side. The hole may be positioned at a center of a surface of the flat side.

A turning insert includes a top surface, an opposite bottom surface, a reference plane located parallel to and between the top surface and the bottom surface, and a center axis extending perpendicular to the reference plane and intersecting the reference plane (RP), the top surface and the bottom surface. Side surfaces connect the top surface and the bottom surface. Three nose portions are formed symmetrically relative to the center axis. Each nose portion includes a first cutting edge, a second cutting edge and a convex nose cutting edge connecting the first) and second cutting edges. In a top view the first and second cutting edges on the same nose portion form a nose angle of 25-50° relative to each other. The distance from the first cutting edge to the reference plane varies in such a way that that this distance is decreasing at increasing distance from the nose cutting edge.

A turning insert includes a top surface, an opposite bottom surface, and a reference plane located parallel to and between the top and the bottom surfaces. A nose portion includes a convex nose cutting edge, and a first and a second cutting edge. The nose cutting edge connects the first and second cutting edges. The first and second cutting edges form a nose angle of 71-85° relative to each other. The nose portion has a third convex cutting edge adjacent to the first cutting edge and a fourth cutting edge adjacent to the third convex cutting edge. The fourth cutting edge forms an angle of 10-30° relative to a bisector. The distance from at least a portion of the fourth cutting edge to the reference plane increases at an increasing distance from the nose cutting edge. A second protrusion is arranged between the nose cutting edge and the first protrusion.

Provided is a method for manufacturing a Fresnel lens mold by performing cutting process on a workpiece with a cutting tool, the Fresnel lens mold having a lens surface and an upright surface alternately arranged. The cutting tool has a first cutting edge having an arc shape with a radius r and a second cutting edge continuous to the first cutting edge. A machining apparatus repeatedly performs a first process of forming, with the first cutting edge, a lens mold surface serving as a mold of a lens surface of a Fresnel lens, and a second process of forming, with the second cutting edge, an upright mold surface serving as a mold of an upright surface of the Fresnel lens to manufacture the Fresnel lens mold.

A turning insert arranged for longitudinal turning of metal work pieces includes a nose cutting edge that slopes from a trailing cutting edge in direction towards a leading cutting edge. A turning tool is also disclosed.

A double-sided, polygonal cutting insert includes a first surface and a second surface opposite the first surface. A plurality of side surfaces extend between the first surface and the second surface. A plurality of primary concave cutting edges are formed at an intersection between the plurality of side surfaces and the first and second surfaces, and a plurality of convex wiper edges are formed at an intersection between the plurality of side surfaces and the first and second surfaces. Each wiper edge has a step extending radially outward from a respective side surface. The cutting insert is mounted in a cutting tool such that the primary cutting edge and a wiper edge contact a workpiece to produce a high-quality surface finish on the workpiece.

A double-sided, polygonal cutting insert includes a first surface and a second surface opposite the first surface. A plurality of side surfaces extend between the first surface and the second surface. A plurality of primary concave cutting edges are formed at an intersection between the plurality of side surfaces and the first and second surfaces, and a plurality of convex wiper edges are formed at an intersection between the plurality of side surfaces and the first and second surfaces. Each wiper edge has a step extending radially outward from a respective side surface. The cutting insert is mounted in a cutting tool such that the primary cutting edge and a wiper edge contact a workpiece to produce a high-quality surface finish on the workpiece.