JP7119933B2 - ball end mill - Google Patents

Description

In the present invention, a spherical cutting edge is formed on the outer periphery of the tip of an end mill body that rotates about the axis, and the locus of rotation about the axis is centered on the axis. It relates to a ball end mill extending from the side toward the rear end beyond a plane orthogonal to the axis at the center.

As a ball end mill used for tilting the main axis of a machine tool such as back chamfering of an undercut part of a mold or the like and 5-axis machining, Patent Document 1 discloses a tip end of an end mill body that rotates around an axis. A cutting edge having a spherical locus of rotation around the axis extends from the front end side to the rear end side in the axial direction so as to pass through the center of the spherical surface and cross a plane perpendicular to the axis. The cutting edge is formed so as to be twisted rearward in the rotational direction of the end mill as it goes toward the rear end side in the axial direction from the plane, while the axial rear end beyond the plane is twisted toward the rear end side. On the other hand, it is described that the torsion angle with respect to the axis is gradually reduced toward the rear end side.

Japanese Patent Application Laid-Open No. 2010-030023

By the way, the spherical cutting edge whose rotational locus about the axis is centered on the axis extends from the front end side of the end mill body toward the rear end side beyond the plane orthogonal to the axis line at the center. Ball end mills are often used exclusively for finishing machining because the outer circumference of the cutting edge, which has a spherical rotation locus, has a large radius from the axis, so the peripheral speed is high and the cutting edge is sharp. Also, the tip of the cutting edge closer to the tip of the end mill body than the outer periphery is often used exclusively for rough machining.

However, in such a ball end mill, if the cutting edge strength at the tip of the cutting edge is poor, the cutting edge will be chipped or fractured due to the large cutting resistance and cutting load that act as a result of thicker chips during rough machining. may occur and the tool life may be shortened. On the other hand, if the sharpness of the cutting edge is dull at the outer periphery of the cutting edge, it will not be possible to obtain good finished surface roughness and finished surface accuracy in finishing machining even at high peripheral speeds, and cutting resistance will increase. There is a risk that it will be lost.

The present invention has been made under such a background. In the extended ball end mill, the strength of the cutting edge is secured at the tip of the cutting edge to prevent chipping and breakage, while the outer periphery of the cutting edge can be given a sharp sharpness, which improves the finished surface roughness and surface accuracy. An object of the present invention is to provide a ball end mill capable of improving cutting resistance and reducing cutting resistance.

In order to solve the above-mentioned problems and achieve such objects, the present invention provides a chip discharger extending from the tip of the end mill body toward the rear end side on the outer periphery of the tip portion of the end mill body rotated about the axis. A groove is formed, and the trajectory of rotation about the axis line is centered on the axis line at the intersection ridge line between the wall surface of the chip discharge groove facing the end mill rotation direction and serving as the rake surface and the flank surface that intersects the rake surface. wherein the cutting edge extends from the front end side of the end mill body to the rear end side of the end mill body across a plane orthogonal to the axis at the center In a cross-section along the axis of the rotational trajectory of the cutting edge about the axis, a straight line connecting a point on the cutting edge and the center extends from the center to the tip side of the end mill body. Within the first angle range of 40° to 60° with respect to the extending axis, the radial rake angle of the cutting edge in a cross section passing through the one point and orthogonal to the axis is minimized. In a cross section along the axis of the locus of rotation of the blade about the axis, a straight line connecting a point on the cutting edge and the center forms a pinch with respect to the axis extending from the center toward the tip of the end mill body. In the second angle range of 80° to 100°, the radial rake angle of the cutting edge in the cross section passing through the one point and perpendicular to the axis is maximized.

In the ball end mill configured in this way, in a cross section along the axis of the spherical rotation locus, a straight line connecting a point on the cutting edge and the center extends from the center to the tip side of the end mill body. Radial rake angle of the cutting edge in a cross section perpendicular to the axis that passes through the one point in the first angle range of 40° to 60° with respect to the extending axis, that is, at the tip of the cutting edge is minimized, the edge angle of the cutting edge can be increased. Therefore, it is possible to secure the cutting edge strength of the cutting edge and prevent the occurrence of chipping and breakage even with a large cutting load during rough machining.

On the other hand, in the second angle range of 80° to 100°, that is, in the outer peripheral portion of the cutting edge, the radial rake angle of the cutting edge is maximized and sharpness can be achieved. Therefore, when the outer peripheral portion of the cutting edge is used for finishing, good finished surface roughness and finished surface accuracy can be obtained in combination with the fact that the peripheral speed is high due to the large radius from the axis. Cutting resistance can be reduced.

Here, if the position where the radial direction rake angle of the cutting edge is minimized is positioned closer to the tip side of the end mill body than the first angle range of the included angle of 40° to 60°, the cutting edge near the axis The radial rake angle at the tip of the blade becomes too small. Since the peripheral speed is slow at the tip near the axis in the angle range where the included angle is less than 40°, if the radial rake angle is too small, the cutting edge will rub against the work material, resulting in wear of the cutting edge. becomes significant. Furthermore, since the thickness of the chips generated by the cutting edge is small at the tip near the axis, the cutting load acting on the cutting edge is small. The rake angle may be greater than the minimum radial rake angle.

In addition, the position where the radial rake angle of the cutting edge is the smallest is located on the rear end side of the end mill body rather than the first angle range of 40° to 60° for the included angle, or the radial direction of the cutting edge If the position where the rake angle is maximized is located closer to the tip side of the end mill body than the second angle range of 80° to 100°, the tip of the cutting edge and the outer periphery The radial rake angle must be changed abruptly, which can lead to distortion of the rake face and increased cutting resistance.

Furthermore, if the position where the radial direction rake angle of the cutting edge is maximized is located on the rear end side of the end mill body relative to the second angle range of the included angle of 80° to 100°, the peripheral speed is high. Therefore, it is inefficient because the sharpest sharpness cannot be imparted to the outer peripheral portion of the cutting edge that is exclusively used for finishing.

The minimum radial rake angle of the cutting edge in the first angle range is preferably -15° or more. If the minimum radial rake angle of the cutting edge in the first angle range is as small as below -15°, the cutting load due to the cutting resistance acting when the tip of the cutting edge is used for rough machining increases. Therefore, even if the blade angle can be increased, chipping or breakage may occur. In order to more reliably prevent chipping and breakage of the cutting edge during rough machining at the tip, the minimum radial rake angle of the cutting edge in the first angle range should be -10° or more. is more desirable.

On the other hand, it is desirable that the maximum radial rake angle of the cutting edge in the second angle range is +15° or less. If the maximum radial rake angle of the cutting edge in this second angle range exceeds 15°, the cutting edge angle at the outer periphery of the cutting edge becomes too small, the edge strength is impaired, and the chip thickness is thin. Chipping and breakage may occur on the cutting edge even when used for . In order to more reliably prevent chipping and breakage of the cutting edge during finish machining of the outer peripheral portion, the maximum radial rake angle of the cutting edge in the second angle range should be +10° or less. more desirable.

In addition, as described above, at the tip of the cutting edge in the angle range where the included angle is less than 40°, the thickness of chips generated by the cutting edge is thin, so the cutting load acting on the cutting edge is small. The radial rake angle of the cutting edge in the first angle range may be gradually decreased from the front end side to the rear end side of the end mill body, reaching the minimum radial rake angle, and then gradually increasing. .

Furthermore, in order to ensure the sharpest sharpness in the vicinity of the outermost peripheral portion of the cutting edge where the included angle at which the peripheral speed is the highest is around 90°, the radial rake angle of the cutting edge in the second angle range is It is desirable that the radial rake angle gradually increases from the front end side toward the rear end side of the end mill body, reaches the maximum radial rake angle, and then gradually decreases.

As described above, according to the present invention, the cutting edge extends from the front end side of the end mill body toward the rear end side beyond the plane perpendicular to the axis at the center of the sphere formed by the rotation locus of the cutting edge. In the end mill, the edge strength can be secured at the tip of the cutting edge in the first angle range to prevent chipping and breakage, and the outer peripheral portion of the cutting edge in the second angle range has sharp sharpness. It can be applied to the cutting edge, making it possible to improve finished surface roughness and finished surface accuracy and reduce cutting resistance.

1 is a perspective view of a tip portion of an end mill body showing an embodiment of the present invention; FIG. 2 is a front view of the embodiment shown in FIG. 1; FIG. 2 is a side view of the embodiment shown in FIG. 1; FIG. VV cross-sectional view in FIG. is a cross-sectional view passing through one point on the blade and perpendicular to the axis of the end mill body) (however, the long cutting blades are shown positioned vertically). WW cross-sectional view in FIG. 2 is a cross-sectional view perpendicular to the axis of the end mill main body passing through one point on the cutting edge at a certain 50° position (however, the long cutting edges are shown positioned vertically). XX cross-sectional view in FIG. is a cross-sectional view passing through one point and perpendicular to the axis of the end mill body) (however, the long cutting blades are shown positioned vertically). YY cross-sectional view in FIG. is a cross-sectional view perpendicular to the axis of the end mill body passing through a point on the cutting edge at a certain 90° position (however, the long cutting edge is shown to be positioned above and below. Also, the coolant hole is illustration is omitted). ZZ cross-sectional view in FIG. (However, the long cutting edge is shown positioned vertically. The coolant hole is not shown.) . In the cross section along the axis of the locus of rotation about the axis of the cutting edge in the embodiment shown in FIG. FIG. 4 is a diagram showing the relationship between the included angle with respect to the extending axis and the radial rake angle in a cross section passing through one point on the cutting edge and perpendicular to the axis.

1 to 9 show one embodiment of the invention. In the present embodiment, the end mill main body 1 is integrally formed into a substantially columnar shape centering on the axis O from a hard material such as cemented carbide. The rear end portion of the end mill body 1 (upper right portion in FIG. 1; right side portion in FIG. 3) is formed into a cylindrical shank portion 2, and the tip portion of the end mill body 1 (in FIG. 1 A lower left portion (the left portion in FIG. 3) serves as a cutting edge portion 3 .

In such a ball end mill, the shank portion 2 is gripped by the main shaft of the machine tool and rotated about the axis O in the end mill rotation direction T, while the cutting edge portion 3 cuts the work material to form a die or the like. It is used for back chamfering of undercuts, 5-axis machining, etc., in which the main axis of the machine tool is inclined.

In the cutting edge portion 3, a plurality of (four in this embodiment) chip discharge grooves 4 twisted in the direction opposite to the end mill rotation direction T from the front end of the end mill body 1 toward the rear end are spaced apart in the circumferential direction. It is formed with an opening. Between the wall surfaces of these chip discharge grooves 4 facing the end mill rotation direction T and serving as the rake face 5 and the chip discharge grooves 4 adjacent in the circumferential direction, the distance from the tip inner periphery to the rear end outer periphery of the cutting edge portion 3 is provided. A cutting edge 7 is formed at each ridgeline portion that extends to the side and intersects with the flank 6 that intersects the rake face 5 .

These cutting edges 7 are formed in a spherical shape in which the locus of rotation about the axis O overlaps with each other and the locus of rotation about the axis O has a center C on the axis O. As shown in FIG. Furthermore, the locus of rotation formed by these cutting edges 7 around the axis O extends from the front end of the cutting edge portion 3 toward the rear end and extends beyond the plane P passing through the center C and perpendicular to the axis O. there is

In other words, in a ball end mill in which the locus of rotation of the bottom edge is usually hemispherical, in the cross section along the axis of the locus of rotation about the axis of the cutting edge, this locus of rotation is the rear end of the hemispherical bottom edge and its center. The included angle formed by the straight line connecting the above with respect to the axis extending from the center to the tip side of the end mill body is 90°. On the other hand, in this embodiment, the included angle θ formed by the straight line connecting the rear end of the cutting edge 7 and the center C with respect to the axis O extending from the center C to the tip side of the end mill body 1 is, for example, 120°. It is Therefore, the outer diameter of the tip portion of the shank portion 2 connected to the rear end of the cutting edge portion 3 is made smaller than the outer diameter at the position of the plane P perpendicular to the center C, which is the maximum outer diameter of the cutting edge 7. there is

Among the four cutting edges 7, two cutting edges 7 located on opposite sides with the axis O in between are long cutting edges 7a extending from the vicinity of the axis O at the tip of the cutting edge portion 3. As shown in FIG. On the other hand, the remaining two cutting edges 7 are spaced from the axis O to the outer peripheral side by notching the tip side portion (peripheral portion of the axis O) of the cutting edge portion 3 of the flank 6. A short cutting edge 7b extends toward the rear end side from the position of the cutting edge. The cutting edge portion 3 of the end mill main body 1 has a 180° rotationally symmetrical shape with respect to the axis O. As shown in FIG.

Further, in the chip discharging groove 4, a concave groove is formed by notching a wall surface facing the opposite side of the end mill rotation direction T of the chip discharging groove 4 from the rake face 5 in the tip side portion of the cutting edge portion 3. A gash 4a having a shape is formed. Therefore, on the tip end side of the cutting edge portion 3, for example, in the range where the included angle θ is 90° or less, the cutting edge 7 is positioned at the intersection ridge between the wall surface of the gash 4a facing the end mill rotation direction T and the flank surface 6. It is formed.

Furthermore, in this embodiment, the chip discharge groove 4 is twisted in the direction opposite to the end mill rotation direction T as it goes from the front end of the end mill body 1 toward the rear end side as described above, and the rake face 5 Since the cutting edge 7 extends in the direction opposite to the end mill rotation direction T from the tip inner periphery toward the rear end outer periphery, the cutting edge 7 also extends in the opposite direction to the end mill rotation direction T from the tip toward the rear end of the end mill body 1. twisted to the side. As a result, the cutting edge 7 is given a positive rake angle.

The radial rake angle α in the cross section passing through one point of the cutting edge 7 and perpendicular to the axis O is 1 The included angle θ formed by the straight line connecting the point and the center C with respect to the axis O extending from the center C to the tip side of the end mill body 1 is minimized within the first angle range A of 40° to 60°. In this embodiment, as shown in FIG. 9, which will be described later, the minimum radial rake angle α at one point on the cutting edge 7 where the included angle θ is approximately 55° is a negative angle of approximately −8.88°.

On the other hand, the radial rake angle α in the cross section passing through one point of the cutting edge 7 and perpendicular to the axis O is the same as A straight line connecting one point and the center C forms an included angle θ with respect to an axis O extending from the center C to the tip side of the end mill body 1 within a second angle range B of 80° to 100°, as shown in FIG. maximum as shown. In this embodiment, as shown in FIG. 9 described below, the maximum radial rake angle α shown in FIG. becomes a corner.

Here, FIG. 9 shows one point on the cutting edge 7 and the center C of the cutting edge 7 in a cross section along the axis O of the rotational trajectory of the cutting edge portion 3 about the axis O of the cutting edge 7 in this embodiment. with respect to the axis O extending from the center C of the cutting edge 7 to the tip side of the end mill body 1, and the radial rake in the cross section passing through one point on the cutting edge 7 and orthogonal to the axis O It is a figure which shows the relationship with angle (alpha) (degree).

As can be seen from FIG. 9, the radial rake angle α of the cutting edge 7 gradually decreases from the front end side to the rear end side of the end mill body 1 in the first angle range A, and reaches the minimum diameter. It becomes a directional rake angle α and then gradually increases. The radial rake angle θ of the cutting edge 7 in the second angle range gradually increases toward the rear end side of the end mill body 1 continuously from the first angle range A, reaching the maximum radial rake angle α. , and then gradually becomes smaller.

A coolant hole 8 is formed in the end mill main body 1 so as to extend from the rear end surface of the shank portion 2 along the axis O toward the tip side. At the center C of the cutting edge portion 3, the coolant holes 8 are branched into the same number as the chip discharge grooves 4 (four in this embodiment) and radially extend from the center C. A straight line connecting a point on the cutting edge 7 between the second angle range B and the center C forms an included angle θ with respect to the axis O extending from the center C to the tip side of the end mill body 1 is 60° to 60°. In an angle range of 80°, the chip discharge groove 4 is opened on the side of the rake face 5 of the wall surface facing away from the end mill rotation direction T. Here, the coolant hole 8 has a circular cross section.

In the ball end mill constructed in this manner, in a cross section along the axis O of the rotational trajectory of the spherical cutting edge 7, a straight line connecting a point on the cutting edge 7 and the center C extends from the center C to the end mill body 1. The radial rake angle of the cutting edge 7 in the cross section perpendicular to the axis O through the one point within the first angle range A in which the included angle θ formed with respect to the axis O extending to the tip side is 40 ° to 60 ° α becomes the minimum. Therefore, in the first angle range A, the edge angle of the cutting edge 7 can be increased to ensure edge strength.

Since the first angle range A is the tip of the cutting edge 7 that is used exclusively for rough machining, a large cutting force is generated when thick chips are generated during rough machining. The tool life can be extended by preventing the cutting edge 7 from chipping or breaking against the load.

On the other hand, the second angle range B in which the included angle θ is 80° to 100° is the outer peripheral portion of the cutting edge 7 used exclusively for finishing. At B, the radial rake angle α of the cutting edge 7 is maximized. For this reason, in the finishing process, it is possible to sharpen the sharpness, and since the radius from the axis O is large, the peripheral speed is high. , it is possible to reduce the cutting resistance.

Here, it is assumed that the position where the radial rake angle α of the cutting edge 7 is minimized is positioned closer to the tip side of the end mill body 1 than the first angle range A in which the included angle θ is 40° to 60°. , Since the distance from the axis O is short, the peripheral speed is slow and the cutting mode is such that the cutting edge rubs against the work material. As a result, the wear of the cutting edge 7 becomes significant, shortening the tool life. On the other hand, since chips generated by the cutting edge 7 at the tip near the axis O have a small thickness and the cutting load acting on the cutting edge 7 is small, the angle range of the included angle θ is less than 40°. The radial rake angle α of the blade 7 may be greater than the minimum radial rake angle.

Further, the position where the radial direction rake angle α of the cutting edge 7 is the smallest is located on the rear end side of the end mill body 1 with respect to the first angle range A in which the included angle θ is 40° to 60°, If the position where the radial rake angle α of the cutting edge 7 is maximized is positioned closer to the tip side of the end mill body 1 than the second angle range B in which the included angle θ is 80° to 100°, the cutting edge The radial direction rake angle α must be changed abruptly between the tip portion of 7 and the outer peripheral portion, and there is a risk that the rake face 5 will be distorted and the cutting resistance will increase.

Furthermore, it is assumed that the position where the radial rake angle α of the cutting edge 7 is maximized is located on the rear end side of the end mill body 1 with respect to the second angle range B in which the included angle θ is 80° to 100°. Since the peripheral speed is high, the outer peripheral portion of the cutting edge 7, which is exclusively used for finishing, cannot be given the sharpest sharpness, resulting in inefficiency.

The minimum radial rake angle α of the cutting edge 7 in the first angle range A is preferably −15° or more. If the minimum radial rake angle α of the cutting edge 7 in the first angle range A is as small as below −15°, the cutting load due to the cutting resistance acting when the tip of the cutting edge 7 is used for rough machining. becomes too large, chipping or breakage may occur even if the blade angle can be increased. Here, in order to more reliably prevent chipping and breakage at the tip of the cutting edge 7, the minimum radial rake angle α of the cutting edge 7 in the first angle range A should be -10° or more. It is more desirable to have

On the other hand, it is desirable that the maximum radial rake angle α of the cutting edge 7 in the second angle range B is +15° or less. If the maximum radial rake angle .alpha. Even when used for thin finishing, the cutting edge 7 may be chipped or damaged. Here, in order to more reliably prevent chipping and breakage of the cutting edge 7 at the outer peripheral portion, the maximum radial rake angle α of the cutting edge 7 in the second angle range B should be +10° or less. is more desirable.

Further, as described above, at the tip of the cutting edge 7 in the angle range where the included angle θ is less than 40° on the tip side of the first angle range A, the chips generated by the cutting edge 7 have a thickness of Since it is thin, the cutting load acting on the cutting edge 7 is small. For this reason, the radial rake angle α of the cutting edge 7 in the first angle range A gradually decreases from the front end side to the rear end side of the end mill body 1, reaching the minimum radial rake angle α. It suffices if it gradually increases.

Furthermore, in order to ensure the sharpest sharpness in the vicinity of the outermost peripheral portion of the cutting edge 7 where the included angle with the highest peripheral speed is around 90°, the radial rake angle of the cutting edge 7 in the second angle range B It is desirable that α also gradually increases from the front end side to the rear end side of the end mill body 1, reaches the maximum radial rake angle α, and then gradually decreases.

Furthermore, in this embodiment, coolant holes 8 are formed in the end mill main body 1 along the axis O, and the coolant holes 8 are branched at the center C of the cutting edge portion 3 in the same number as the chip discharge grooves 4. radiating from the center C. The branched coolant hole 8 is formed by a straight line connecting a point on the cutting edge 7 and the center C between the first angle range A and the second angle range B. In the angle range of 60 ° to 80 ° with respect to the axis O extending to the tip side, the chip discharge groove 4 is opened on the rake face 5 side of the wall surface facing the opposite side to the end mill rotation direction T. there is

Therefore, when coolant is supplied to the coolant hole 8 from the rear end side of the end mill body 1 during cutting, the coolant is jetted from the branched coolant hole 8 toward the tip side of the end mill body 1 slightly beyond the second angle range B. Let me. Here, as described above, the chip discharge groove 4 and the cutting edge 7 in this embodiment are twisted in the direction opposite to the end mill rotation direction T from the front end of the end mill body 1 toward the rear end side. As the end mill body 1 rotates, the coolant jetted to the tip side of the end mill body 1 flows into the chip discharge groove 4 toward the rear end side of the end mill body 1 beyond the angle range B of .

For this reason, according to the present embodiment, the coolant that has thus flowed into the second angle range B is supplied intensively to the outer peripheral portion of the cutting edge 7 near the included angle θ of 90° during finishing. By lubricating and cooling the outer peripheral portion of the cutting edge 7 and the cutting portion of the work material during finishing, the tool life can be further extended. In addition, since the coolant supplied to the outer peripheral portion of the cutting edge 7 in this way flows further into the rear end side of the end mill body 1, the chips can be efficiently discharged along with the coolant, thereby preventing the occurrence of chip clogging. It is possible to further reduce the cutting resistance.

However, the branching of the coolant hole 8 may not necessarily be at the center C of the cutting edge portion 3, and the number of the branched coolant holes 8 may not be the same as the number of the chip discharge grooves 4. The angle θ formed by a straight line connecting one point on the cutting edge 7 and the center C with respect to the axis O extending from the center C to the tip side of the end mill body 1 is in the range of 60° to 80°. , it may not be on the rake face 5 side of the wall surface of the chip discharge groove 4 facing the opposite side of the end mill rotation direction T.

In this embodiment, a case where the present invention is applied to a solid type ball end mill in which the cutting edge portion 3 of the end mill body 1 having the cutting edge 7 is formed integrally with the shank portion 2 has been described. The present invention can also be applied to a head-exchangeable ball end mill in which a head member having a cutting edge 3 is detachably attached to the tip of a shank 2 made of cemented carbide or steel. .

1 end mill body 2 shank portion 3 cutting edge portion 4 chip discharge groove 5 rake face 6 flank face 7 cutting edge 8 coolant hole O axis of end mill body 1 T rotation direction of end mill C sphere formed by the locus of rotation of cutting edge 7 around axis O Center P A plane passing through the center C and perpendicular to the axis O In a cross section along the axis O of the rotational trajectory of the cutting edge 7 around the axis O, a straight line connecting a point on the cutting edge 7 and the center C is the center C A first angle range B second angle range A included angle α formed with respect to the axis O extending from the end mill body 1 to the tip side of the end mill body 1 Radial direction rake angle of the cutting edge 7 in a cross section orthogonal to the axis O

Claims (7)

A chip discharge groove extending toward the rear end side from the front end of the end mill body is formed on the outer circumference of the tip portion of the end mill body that rotates about the axis, and the chip discharge groove faces the rotation direction of the end mill and serves as a rake face. A ball end mill in which a spherical cutting edge having a rotational trajectory about the axis centered on the axis is formed at an intersection ridge between a wall surface and a flank that intersects the rake face,
The cutting edge extends from the tip side of the end mill body toward the rear end side of the end mill body beyond a plane perpendicular to the axis at the center,
In a cross section along the axis of the locus of rotation of the cutting edge about the axis, a straight line connecting a point on the cutting edge and the center is with respect to the axis extending from the center to the tip side of the end mill body. Within a first angle range of 40° to 60°, the radial rake angle of the cutting edge in a cross section passing through the one point and perpendicular to the axis is minimized,
In a cross section along the axis of the locus of rotation of the cutting edge about the axis, a straight line connecting a point on the cutting edge and the center is with respect to the axis extending from the center to the tip side of the end mill body. A ball end mill characterized in that a radial rake angle of the cutting edge in a cross section passing through the one point and perpendicular to the axis is maximized within a second angle range of 80° to 100°. The ball end mill according to claim 1, wherein the minimum radial rake angle of the cutting edge in the first angle range is -15° or more. The ball end mill according to claim 1, wherein the minimum radial rake angle of the cutting edge in the second angle range is -10° or more. The ball end mill according to any one of claims 1 to 3, wherein the maximum radial rake angle of the cutting edge in the first angle range is +15° or less. The ball end mill according to any one of claims 1 to 3, wherein the maximum radial rake angle of the cutting edge in the second angle range is +10° or less. The radial rake angle of the cutting edge in the first angle range is characterized in that it gradually decreases toward the rear end side from the front end side of the end mill body, reaches the minimum radial rake angle, and then gradually increases. The ball end mill according to any one of claims 1 to 5. The radial rake angle of the cutting edge in the second angle range is characterized in that it gradually increases toward the rear end side from the front end side of the end mill body, reaches the maximum radial rake angle, and then gradually decreases. The ball end mill according to any one of claims 1 to 6.

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