In an end mill, eight peripheral cutting edges having a helical shape and a larger outer diameter than that of a shaft portion are in a cutting portion in a circumferential direction. For one peripheral cutting edge of the eight peripheral cutting edges, when a cut length of the peripheral cutting edge along an axial direction is L, a twist angle of the peripheral cutting edge is θ, and a circumferential distance at a lower end of the peripheral cutting edge between the peripheral cutting edge and another peripheral cutting edge adjacent to a tool rotation direction rear side of the peripheral cutting edge is a, n expressed by the following equation is approximately 1 for all of the eight peripheral cutting edges in at least a half region of the cut length from the lower end of the peripheral cutting edge.
n=(L×tan θ)/(2×a)

The present invention includes an end mill body which is formed of ceramic, a chip discharge flute which is formed on an outer periphery of the end mill body, a peripheral cutting edge which is formed on an intersection ridge line between a wall surface facing a tool rotation direction in the chip discharge flute and an outer peripheral surface of the end mill body, an end cutting edge which is formed on an intersection ridge line between the wall surface in the chip discharge flute and a tip surface of the end mill body, and a corner cutting edge which is positioned at a tip outer-peripheral part of the end mill body, connects an outer end of the end cutting edge and a tip of the peripheral cutting edge to each other, and has a convexly curved shape which is convex toward a tip outer-peripheral side of the end mill body.

A cutting insert of the present invention comprises: an upper surface and a lower surface; first and second lateral surfaces; first and second cutting edge parts; and corner cutting edges, wherein the first cutting edge part includes: a first main cutting edge for forming one end at a portion spaced farthest away from the corner cutting edge; a first sub-cutting edge connected to the corner cutting edge; and a first auxiliary cutting edge for connecting the first main cutting edge and the first sub-cutting edge so as to form a step between the same, and the first sub-cutting edge and the corner cutting edge form one straight line when viewed toward the first lateral surface, and are inclined upward in the direction opposite to the direction toward the lower surface while gradually going in the direction toward the second cutting edge part.

A cutting insert has opposing first and second end surfaces, and a peripheral side surface (connecting the end surfaces. A central axis penetrates the two end surfaces. The peripheral sure surface includes an outwardly inclined first side surface part related to a major cutting edge and a second side surface part related to a minor cutting edge. The outwardly inclined first side surface part gradually extends outward from the cutting insert, heading from the first end surface to the second end surface. When a second virtual plane, which is substantially perpendicular to the central axis and passes through the major cutting edge, is defined, an inwardly inclined part, on a back side of the cutting edge, of the second end surface is inclined so as to become more distant from the second virtual plane, heading from the outwardly inclined first side surface part to the central axis.

A cutting tool includes: a body extending along a longitudinal axis between a leading and trailing ends, the body having a clamping region disposed at or about the trailing end and a cutting region which extends toward the clamping region from the leading end of the body; a plurality of flutes defined in the body, each extending from the leading end toward the coupling portion; a plurality of peripheral cutting edges, each extending from the leading end toward the coupling portion along a corresponding flute of the plurality of flutes; and a plurality of end cutting edges disposed at the leading end, each end cutting edge extending from at or near the longitudinal axis outward along a corresponding flute. At least one end cutting edge is defined, in-part, by a plurality of rake faces which each extend from a corresponding portion of the one cutting edge into the corresponding flute.

A multi-flute ball end mill of the present invention includes: a shank portion configured to rotate about a rotational axis; a cutting edge portion; three or more ball edges formed on the cutting edge portion; gashes formed between the ball edges; peripheral cutting edges continuous with end portions of the ball edges on the shank portion side; and flutes formed between the peripheral cutting edges continuously with the gashes. The degree of curvature of the ball edges is 35% to 55%. Each of the gashes includes four faces of a rake face of each of the ball edges, a gash wall face, a first gash face, and a second gash face. The second gash face is formed such that the closer the second gash face is to the rotation center point, the more inwardly the second gash face enters a second face of each of the ball edges.

The present invention provides an end mill including: a shaft-shaped end mill main body; a chip discharge groove extending from a leading end to a trailing end in an axial direction of the end mill main body; a bottom blade which is provided at a leading end portion in the axial direction of the end mill main body and has a spherical shape in which a rotation locus around the axis has a center on the axis; and an outer peripheral blade which is provided along the chip discharge groove, and in which a rotation locus around the axis is convex outward. A curvature radius of the rotation locus of the outer peripheral blade is larger than a curvature radius of the rotation locus of the bottom blade. A twist angle of the outer peripheral blade is 20° or more.

A cutting insert has a plate shape centered on an insert center axis. The cutting insert includes a front surface and a back surface facing an insert axial direction, an outer peripheral surface facing outward in an insert radial direction, and a cutting edge at an intersecting ridge line between the front surface and the outer peripheral surface. The back surface has a flat shape perpendicular to the insert center axis. The outer peripheral surface includes a flank surface coupled. The flank surface is inclined inward in the insert radial direction as extending in the insert axial direction from the front surface side to the back surface side. The front surface includes a rake surface. The rake surface is inclined from a back surface side to a front surface side in the insert axial direction as extending inward in the insert radial direction from the cutting edge.

In an end mill body made of ceramic, a corner R rake face is formed in such a manner as to contain a point B and at least a region B, not a region A located on a side toward an end cutting edge. In other words, a first end portion of a cutting edge on a peripheral edge portion of the corner R rake face is formed on a peripheral edge of the region B of a corner R cutting edge, and a second end portion of the cutting edge reaches at least the point B. As a result, partial breakage of the corner R cutting edge is unlikely to occur in the course of cutting. That is, since the corner R rake face is formed in such a manner as to start from the first end portion located apart from a point A, which is the intersection of the end cutting edge and the corner R cutting edge, and such that the second end portion reaches the point B, a large cutting load is unlikely to be imposed on the starting point of the corner R rake face. Therefore, the corner R cutting edge is unlikely to be chipped.

A mirror finishing method for mirror-finishing a workpiece includes: a step of performing a first machining operation with a first tool which has a cylindrical portion made of polycrystalline diamond or cubic boron nitride at the tip of a shank thereof and further has a cutting edge formed by forming a linear groove on the cylindrical portion; and a step of, after the first machining operation has been performed, performing a second machining operation with a second tool which has a cylindrical portion made of polycrystalline diamond or cubic boron nitride at the tip of a shank thereof with no cutting edge on the cylindrical portion.