A cutting tool according to an aspect of the present invention is a cutting tool for cutting a rotationally symmetrical surface of a rotating workpiece. The cutting includes the step of feeding the cutting tool in a direction inclined with respect to a rotational axis of the rotationally symmetrical surface, while holding the cutting tool in contact with the rotationally symmetrical surface. In the step of feeding the cutting tool, the cutting tool has a point that is in contact with the rotationally symmetrical surface and the point shifts as the cutting tool is fed. The cutting tool includes: a rake face; a flank face; and a cutting edge connecting the rake face and the flank face. The cutting edge as seen from above the flank face has a shape including at least one arc, and the arc has a radius of curvature of not less than 100 mm and not more than 500 mm.

To perform machining on a workpiece under wider variety of machining conditions. A first rising surface is adjacent to a cutting portion across a first surface, the first rising surface being inclined upward away from the first surface in a direction along a center axis and being away from the center axis toward a rear end of a main body. A second rising surface extends from a second surface toward the rear end of the main body, and is inclined upward away from the second surface in the direction along the center axis. In the direction along the center axis, a rear end of the first rising surface is closer to the rear end of the main body than a front end of the second rising surface.

A cutting tool 1 includes a cutting edge 2, a rake face 4 and a flank 5 and is used for cutting a surface of a cylindrical or columnar work W by a skiving process. The cutting tool 1 is configured to satisfy a relational expression:
tan.sup.1(cos /cos()tan.sup.1(cos.sup.1(r/r))<90
where denotes a rake angle, denotes an inclination angle of the cutting edge 2 with respect to the rotation axis A, denotes an angle between a feed direction of the cutting tool 1 and a direction orthogonal to a rotation axis A in a plane view of the cutting tool 1 and the work W, r denotes a radius of an outer circumferential surface of the work W before processing, and r denotes the radius of the outer circumferential surface of the work W after processing.

A rotary cutting tool insert according to one embodiment of the present invention includes: an annular rake face provided with at least one recess portion; and a cutting edge formed at an outer circumference of the rake face, the recess portion having a width of more than or equal to 1.2 mm and less than or equal to 3.0 mm in a circumferential direction of the rake face, a distance between the cutting edge and an end of the recess portion at the outer circumference side of the rake face being more than or equal to 0.1 mm and less than or equal to 0.5 mm. According to the rotary cutting tool insert according to the one embodiment of the present invention, roughness of a processed surface and vibration due to a cutting process can be prevented.

A cutting tool for cutting a rotationally symmetrical surface of a rotating workpiece includes the step of feeding the cutting tool in a direction inclined with respect to a rotational axis of the rotationally symmetrical surface, while holding the cutting tool in contact with the rotationally symmetrical surface. In the step of feeding the cutting tool, the cutting tool has a point that is in contact with the rotationally symmetrical surface and the point shifts as the cutting tool is fed. The cutting tool includes: a rake face; a flank face; and a cutting edge connecting the rake face and the flank face. The cutting edge as seen from above the flank face has a shape including at least one arc, and the arc has a radius of curvature of not less than 100 mm and not more than 500 mm.

A cutting tool 1 includes a cutting edge 2, a rake face 4 and a flank 5 and is used for cutting a surface of a cylindrical or columnar work W by a skiving process. The cutting tool 1 is configured to satisfy a relational expression:

tan.sup.1(cos /cos()tan.sup.1(cos.sup.1(r/r))<90

where denotes a rake angle, denotes an inclination angle of the cutting edge 2 with respect to the rotation axis A, denotes an angle between a feed direction of the cutting tool 1 and a direction orthogonal to a rotation axis A in a plane view of the cutting tool 1 and the work W, r denotes a radius of an outer circumferential surface of the work W before processing, and r denotes the radius of the outer circumferential surface of the work W after processing.

A guide pad for a cutting tool is formed with at least one sliding surface, which is convexly curved in a plane perpendicular to a longitudinal axis of the guide pad. Each sliding surface includes two convexly curved sliding sub-surfaces separated by a fluid conveying formation having a longitudinal extension in a direction in parallel to the longitudinal axis. The fluid conveying formation is planar or has a convexly curved shape in a direction perpendicular to the longitudinal axis having a larger radius of curvature than the radius of the sliding surface.

A holder and a cutting tool with the holder including an insertion hole at a front end part thereof, and a cutting insert that includes a cutting edge part and a shank part. The shank part has substantially a rod shape. A part of the shank part is immovably located in the insertion hole. The front end part of the holder includes a first curved surface part that becomes wider from a front end toward a back side when viewed from a side thereof. The first curved surface part includes: a curved line that extends from an edge of an opening of the insertion hole toward the back side; or a straight line that extends from the edge of the opening of the insertion hole and connects to a curved line that extends continuously from the straight line toward the back side without an angular part.

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 cutting insert includes an upper surface and a lower surface. The upper surface includes a first corner, a first side, a rake face, and a rising surface. The rising surface includes a first recessed portion recessed with respect to the first side, a first protruding portion located farther from the first corner than the first recessed portion, a second protruding portion located between the first protruding portion and the first side, and a first stepped portion located between the first protruding portion and the second protruding portion. The first protruding portion has a first front end portion located closest to the first side. A cross section orthogonal to the first side and including the first front end portion is a first cross section. At the first cross section, the second protruding portion is located closer to the lower surface than the first protruding portion.