A turning insert includes a top surface, an opposite bottom surface, a side surface connecting the top and bottom surfaces, and a cutting edge formed at an intersection between the top surface and the side surface. The cutting edge including a corner cutting edge, a first cutting edge, and a second cutting edge. The top surface having a first surface in the form of a depression, which borders at least a major portion of the corner cutting edge. The first and the second cutting edges subtending an angle θ which is 75-85°. At least a part of the corner cutting edge is concave in a front view.

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 cutting insert has a seating surface, an outer peripheral surface, a top surface, and an attachment hole. The cutting edge includes a curved cutting corner edge portion, a first cutting edge portion, and a second cutting edge portion. The top surface includes a first rake face contiguous to the first cutting edge portion, a second rake face contiguous to the second cutting edge portion, and a third rake face contiguous to the cutting corner edge portion and also contiguous to the first and second rake faces. The third rake face has a first region contiguous to the first rake face and a second region contiguous to the second rake face. The first rake face and the first region each have a rake angle which is a positive angle. The second rake face and the second region each have a rake angle which is a negative angle.

In an embodiment, a cutting insert including a base member, a first face, a second face, a cutting edge, and a nose portion. The base member includes a coating layer on at least a part thereof. The first face has corner portions. The second face is adjacent to the first face. The cutting edge is on at least a part of the ridgeline portion of the first face and the second face, and includes first and second cutting edges. The first cutting edge is on the coating layer and has a C chamfered surface with a first width of 5 μm to 30 μm in the front view of the first face and a chamfer angle of 35° to 50°. The nose portion is at the corner portions between the first cutting edge and the second cutting edge.

A cutting insert based on a non-limiting aspect has a first member and a second member joined to the first member. The second member has an upper surface and a side surface adjacent to the upper surface. The upper surface includes a first side, a second side and a corner. The upper surface has a first convex portion extending toward the corner, and a second convex portion extending from the first convex portion toward the first side. The second convex portion has a first end portion and a second end portion located closer to the corner than the first end portion. A first length from the first end to the first side is less than a second length from the second end portion to the first side in a top view.

A cutting insert may include a first surface, a second surface, a third surface, and a cutting edge. The first surface may include a first side part, a second side part, and a third side part. The cutting edge may be located at an intersection of the first surface and the third surface. The cutting edge may include a first cutting edge, a second cutting edge, and a third cutting edge. The third cutting edge may be located between the first cutting edge and the second cutting edge and have a convex curvilinear shape. The first cutting edge may be located asymmetrically relative to a bisector of an angle formed by the first side part and the second side part. The first surface may include a first inclined surface located along the first cutting edge and inclined toward the second surface at a first inclination angle.

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 cutting insert may include a first surface, a second surface, a third surface, and a land surface. The first surface may include a first corner and a first side. The land surface may be located between the first surface and the third surface. The land surface may include a first land surface connecting to the first corner, and a second land surface connecting to the first side. A width of the first land surface in a front view as viewed from a side of the first surface may be a first width, the first width at an end portion on a side of the second land surface may be larger than the width at a part connecting to a midportion of the first corner.

A cutting insert has a seating surface, an outer peripheral surface, a top surface, and an attachment hole. The cutting edge includes a curved cutting corner edge portion, a first cutting edge portion, and a second cutting edge portion. The top surface includes a first rake face contiguous to the first cutting edge portion, a second rake face contiguous to the second cutting edge portion, and a third rake face contiguous to the cutting corner edge portion and also contiguous to the first and second rake faces. The third rake face has a first region contiguous to the first rake face and a second region contiguous to the second rake face. The first rake face and the first region each have a rake angle which is a positive angle. The second rake face and the second region each have a rake angle which is a negative angle.

A turning insert includes a top surface, an opposite bottom surface and a reference plane located parallel to and between the top surface and the bottom surface. A nose portion has a convex nose cutting edge, a first cutting edge 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 includes 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 as the distance from the nose cutting edge increases.