A cutting tool for performing cutting of a relatively rotating external workpiece while relatively feeding the same in a specified direction is configured to have: cutting sections that have a tool edge, a base section, which is provided as one piece with or separate from the cutting sections and is for holding the cutting sections, a chip-guiding wall, which starts near a tool edge, is formed on the outer circumferential surface of the base section so as to extend in the direction moving away from the tool edge, and is for interfering with chips from the external workpiece and guiding the chips in a direction away from the tool edge. Provided thereby is a cutting tool capable of smoothly discharging chips during cutting.

A cutting tool for performing cutting of a relatively rotating external workpiece while relatively feeding the same in a specified direction is configured to have: cutting sections that have a tool edge, a base section, which is provided as one piece with or separate from the cutting sections and is for holding the cutting sections, a chip-guiding wall, which starts near a tool edge, is formed on the outer circumferential surface of the base section so as to extend in the direction moving away from the tool edge, and is for interfering with chips from the external workpiece and guiding the chips in a direction away from the tool edge. Provided thereby is a cutting tool capable of smoothly discharging chips during cutting.

A cutting insert of one aspect is provided with a top surface having a polygonal shape and including a corner portion, a first side and a second side, each extending from the corner portion, a bottom surface, a side surface, and a cutting edge. The cutting edge includes a corner cutting edge disposed in a position corresponding to the corner portion, and a first cutting edge disposed in a position corresponding to the first side. The top surface includes an inclined surface provided with a first inclined surface disposed along the first side, a second inclined surface disposed along the second side, and a third inclined surface disposed along the corner portion. An inclination angle of the first inclined surface is greater than an inclination angle of the second inclined surface.

A method for designing a cutting edge of a cutting element configured for removing material from a workpiece to leave therein a desired end profile (B22,B24,B26). The method comprises the steps of modeling a desired end profile (B22,B24,B26) of the workpiece, the profile having a longitudinal axis and being defined by a bottom surface (B12), a side surface (B16) and an adjustment surface (B14) extending therebetween; defining a lead profile plane (RP.sub.L) and an trail profile plane (RP.sub.T) spaced therefrom, each of the planes being oriented perpendicular to the longitudinal axis; determining a profile contour defined by the intersection line between the end profile (B22,B24,B26) and the lead profile plane (RP.sub.L). The contour profile includes a bottom contour, an adjoining contour and a side contour defined as the intersection lines between the lead profile plane (RP.sub.L) and the bottom surface (B12), the adjustment surface (B14) and the side surface (B16) respectively; designing a rake surface and a relief surface, the intersection line between which defines a cutting edge lying in the adjoining surface (B14) and spanning between the lead profile plane (RP.sub.L) and the trail profile plane (RP.sub.T). The cutting edge is designed such that in any reference plane (RP; FIG. 6A) oriented perpendicularly to the cutting edge, the intersection between each of the rake surface and the relief surface with the reference plane (RP) defines a respective rake line (RK; FIG. 7) and relief line (RF; FIG. 7), the angle (.sub.B) between the lines RK,RF) being equal to or smaller than a similar angle (.sub.B) taken along each of a plurality of similar reference planes (RP) disposed between the reference plane (RP.sub.n) and the lead profile plane (RP.sub.L).

A method for designing a cutting edge of a cutting element configured for removing material from a workpiece to leave therein a desired end profile (B22,B24,B26). The method comprises the steps of modeling a desired end profile (B22,B24,B26) of the workpiece, the profile having a longitudinal axis and being defined by a bottom surface (B12), a side surface (B16) and an adjustment surface (B14) extending therebetween; defining a lead profile plane (RP.sub.L) and an trail profile plane (RP.sub.T) spaced therefrom, each of the planes being oriented perpendicular to the longitudinal axis; determining a profile contour defined by the intersection line between the end profile (B22,B24,B26) and the lead profile plane (RP.sub.L). The contour profile includes a bottom contour, an adjoining contour and a side contour defined as the intersection lines between the lead profile plane (RP.sub.L) and the bottom surface (B12), the adjustment surface (B14) and the side surface (B16) respectively; designing a rake surface and a relief surface, the intersection line between which defines a cutting edge lying in the adjoining surface (B14) and spanning between the lead profile plane (RP.sub.L) and the trail profile plane (RP.sub.T). The cutting edge is designed such that in any reference plane (RP; FIG. 6A) oriented perpendicularly to the cutting edge, the intersection between each of the rake surface and the relief surface with the reference plane (RP) defines a respective rake line (RK; FIG. 7) and relief line (RF; FIG. 7), the angle (.sub.B) between the lines RK,RF) being equal to or smaller than a similar angle (.sub.B) taken along each of a plurality of similar reference planes (RP) disposed between the reference plane (RP.sub.n) and the lead profile plane (RP.sub.L).

A cutting insert includes a base body and a coating layer, and also includes a rake surface, a flank surface, and a cutting edge located along an intersecting ridge therebetween. The rake surface includes an outer peripheral part and a middle part protruded relative to the outer peripheral part. The middle part includes a constraining surface. The outer peripheral part includes a first breaker part, a second breaker part, and the third breaker part adjacent to the constraining surface. The constraining surface is configured by the base body and the coating layer does not exist at the constraining surface. A skewness Rsk of a roughness curve at the constraining surface is ?1.5 ?m to ?0.5 ?m. A skewness Rsk at the third breaker part is ?0.2 ?m or less. The skewness Rsk at the constraining surface is smaller than the skewness Rsk at the third breaker part.

A cutting insert includes a base body and a coating layer, and also includes a rake surface, a flank surface, and a cutting edge located along an intersecting ridge therebetween. The rake surface includes an outer peripheral part and a middle part protruded relative to the outer peripheral part. The middle part includes a constraining surface. The outer peripheral part includes a first breaker part, a second breaker part, and the third breaker part adjacent to the constraining surface. The constraining surface is configured by the base body and the coating layer does not exist at the constraining surface. A skewness Rsk of a roughness curve at the constraining surface is ?1.5 ?m to ?0.5 ?m. A skewness Rsk at the third breaker part is ?0.2 ?m or less. The skewness Rsk at the constraining surface is smaller than the skewness Rsk at the third breaker part.

Inclined surfaces are formed on a rake face and a recessed groove is formed in the central portion between the inclined surfaces. A groove width of the recessed groove gradually increases from the position of the end cutting edge toward the rear, then gradually decreases such that the recessed groove has a narrowest portion at a position P2 forward of the position P3 of an upper end of a breaker wall and rearward of a positive rake angle rear end position P1, and then gradually increases toward the rear up to the position P3 of the upper end of the breaker wall. The dimensional relation W1<W2<W3 holds, where W1 is the groove width at the end cutting edge, W2 is the groove width at the narrowest portion, and W3 is the groove width at the position P3 of the upper end of the breaker wall.

Inclined surfaces are formed on a rake face and a recessed groove is formed in the central portion between the inclined surfaces. A groove width of the recessed groove gradually increases from the position of the end cutting edge toward the rear, then gradually decreases such that the recessed groove has a narrowest portion at a position P2 forward of the position P3 of an upper end of a breaker wall and rearward of a positive rake angle rear end position P1, and then gradually increases toward the rear up to the position P3 of the upper end of the breaker wall. The dimensional relation W1<W2<W3 holds, where W1 is the groove width at the end cutting edge, W2 is the groove width at the narrowest portion, and W3 is the groove width at the position P3 of the upper end of the breaker wall.

A cutting insert includes a main body including a first face, a second face, and a third face. The second face includes a rake face. Among the outer-peripheral sides of the second face, the boundary portion with the first face is a main cutting edge. When viewed from the side where the first face is disposed, the main cutting edge includes a first straight portion, a second straight portion, and a curved portion. The first straight portion is located adjacent to a reference side. The second straight portion is arranged at a distance from the first straight portion. The curved portion connects the first straight portion and the second straight portion. A first intersection angle of the first straight portion with respect to the reference side is different from a second intersection angle of the second straight portion with respect to the reference side.