Cutting insert

Abstract

This cutting insert has: a first surface; a second surface; and an outer peripheral surface. The first surface has a first seat surface. The second surface has a second seat surface. The second seat surface is opposite to the first seat surface. The outer peripheral surface is contiguous to each of the first and second surfaces. A ridgeline between the first surface and the outer peripheral surface forms a first ridgeline. The first ridgeline has a first supported part, a first connection part, a first cutting blade part, a second connection part, and a second supported part. The first cutting blade part is inclined in a direction from the first seat surface toward the second seat surface with respect to a surface parallel to the second seat surface. When viewed perpendicularly to the first seat surface, a first linear cutting blade, a second linear cutting blade, the first supported part, and the second supported part are linear, and the angle formed between the first linear cutting blade and the second linear cutting blade is larger than the angle formed between the first supported part and the second supported part.

Description

Cutting insert

[0001] The present disclosure relates to a cutting insert.

[0002] Japanese Patent Laid-Open Publication No. 7-308807 (Patent Document 1) describes a throw-away insert in which the cutting edge has an inclination angle in the direction away from the corner portion in the range of 8° to 30°.

[0003] Japanese Patent Application Publication No. 7-308807

[0004] The cutting insert according to the present disclosure comprises a first surface, a second surface, and an outer peripheral surface. The first surface includes a first seating surface. The second surface includes a second seating surface. The second seating surface is opposite the first seating surface. The outer peripheral surface is continuous with each of the first surface and the second surface. A ridgeline between the first surface and the outer peripheral surface forms a first ridgeline. The first ridgeline includes a first supported portion, a first connecting portion, a first cutting edge portion, a second connecting portion, and a second supported portion. The first connecting portion is continuous with the first supported portion. The first cutting edge portion is continuous with the first connecting portion. The first cutting edge portion is opposite the first supported portion with respect to the first connecting portion. The second connecting portion is continuous with the first cutting edge portion. The second connecting portion is opposite the first connecting portion with respect to the first cutting edge portion. The second supported portion is continuous with the second connecting portion. The second supported portion is located opposite the first cutting edge portion with respect to the second connection portion. The first cutting edge portion is inclined in a direction from the first seating surface to the second seating surface with respect to a plane parallel to the second seating surface. If the connection point between the first connection portion and the first cutting edge portion is defined as the first connection point and the connection point between the first connection portion and the first supported portion is defined as the second connection point, the distance between the first connection point and the second seating surface in the direction from the first seating surface to the second seating surface is shorter than the distance between the second connection point and the second seating surface. The first cutting edge portion has a first straight cutting edge, a corner cutting edge, and a second straight cutting edge. The first straight cutting edge is connected to the first connection portion. The corner cutting edge is connected to the first straight cutting edge. The corner cutting edge is located opposite the first connection portion with respect to the first straight cutting edge. The second straight cutting edge is connected to each of the corner cutting edge and the second connection portion. When viewed perpendicularly to the first seating surface, the first straight cutting edge, the second straight cutting edge, the first supported portion, and the second supported portion are each linear, and the angle between the first straight cutting edge and the second straight cutting edge is greater than the angle between the first supported portion and the second supported portion.

[0005] FIG. 1 is a first perspective schematic view showing the configuration of a cutting insert according to this embodiment. FIG. 2 is a second perspective schematic view showing the configuration of a cutting insert according to this embodiment. FIG. 3 is an enlarged perspective schematic view showing region III in FIG. 1. FIG. 4 is a plan schematic view showing the configuration of a cutting insert according to this embodiment. FIG. 5 is an enlarged schematic view showing a first ridge line in region V in FIG. 4. FIG. 6 is a bottom schematic view showing the configuration of a cutting insert according to this embodiment. FIG. 7 is an enlarged schematic view showing a second ridge line in region VII in FIG. 6. FIG. 8 is a side schematic view showing the configuration of a cutting insert according to this embodiment. FIG. 9 is a cross-sectional schematic view taken along line IX-IX in FIG. 8. FIG. 10 is a longitudinal sectional schematic view taken along line X-X in FIG. 4. FIG. 11 is a longitudinal sectional schematic view taken along line XI-XI in FIG. 4. FIG. 12 is a longitudinal sectional schematic view taken along line XII-XII in FIG. 4. Fig. 13 is a schematic diagram showing a state in which a workpiece is being turned using a cutting insert whose cutting edge is parallel to the seating surface. Fig. 14 is a first schematic diagram showing the outer shape of the cutting insert as viewed along the direction of the main motion. Fig. 15 is a schematic diagram showing a state in which a workpiece is being turned using a cutting insert whose cutting edge is inclined with respect to the seating surface. Fig. 16 is a second schematic diagram showing the outer shape of the cutting insert as viewed along the direction of the main motion. Fig. 17 is a cross-sectional schematic diagram showing a state in which the cutting insert is attached to a holder. Fig. 18 is a longitudinal sectional schematic diagram showing a first modified example of the cutting insert according to this embodiment. Fig. 19 is a longitudinal sectional schematic diagram showing a second modified example of the cutting insert according to this embodiment.

[0006] [Problem to be Solved by the Present Disclosure] In some cutting inserts, the cutting edge is inclined relative to the seating surface to improve the sharpness of the cutting edge. When cutting a workpiece, the cutting insert is placed on a holder so that the flank of the cutting insert is inclined in a direction away from the workpiece. Therefore, when comparing a case in which the cutting edge is inclined relative to the seating surface of the cutting insert with a case in which the cutting edge is parallel to the seating surface of the cutting insert, the shape of the cutting edge when viewed in the direction of the main movement during cutting is different.

[0007] If the shape of the cutting edge seen in the direction of the main motion is different, the shape of the machined surface of the cut workpiece will also be different. Therefore, if the cutting insert used for cutting is changed from a cutting insert whose cutting edge is parallel to the seating surface to a cutting insert whose cutting edge is inclined relative to the seating surface, it may not be possible to use the existing holder and existing machining program.

[0008] The object of the present disclosure is to provide a cutting insert that can be used with existing holders and existing machining programs even when the cutting insert used for cutting is changed from a cutting insert whose cutting edge is parallel to the seating surface to a cutting insert whose cutting edge is inclined relative to the seating surface.

[0009] [Effects of the Present Disclosure] According to the present disclosure, even if the cutting insert used for cutting is changed from a cutting insert whose cutting edge is parallel to the seating surface to a cutting insert whose cutting edge is inclined relative to the seating surface, it is possible to provide a cutting insert that can be used with existing holders and existing machining programs.

[0010] [Outline of the embodiment] First, an outline of the embodiment of the present disclosure will be described.

[0011] (1) A cutting insert according to the present disclosure has a first surface, a second surface, and an outer peripheral surface. The first surface has a first seating surface. The second surface has a second seating surface. The second seating surface is opposite the first seating surface. The outer peripheral surface is connected to each of the first surface and the second surface. A ridge line between the first surface and the outer peripheral surface forms a first ridge line. The first ridge line has a first supported portion, a first connecting portion, a first cutting edge portion, a second connecting portion, and a second supported portion. The first connecting portion is connected to the first supported portion. The first cutting edge portion is connected to the first connecting portion. The first cutting edge portion is opposite the first supported portion with respect to the first connecting portion. The second connecting portion is connected to the first cutting edge portion. The second connecting portion is opposite the first connecting portion with respect to the first cutting edge portion. The second supported portion is connected to the second connecting portion. The second supported portion is located opposite the first cutting edge portion with respect to the second connection portion. The first cutting edge portion is inclined in a direction from the first seating surface to the second seating surface with respect to a plane parallel to the second seating surface. If the connection point between the first connection portion and the first cutting edge portion is defined as the first connection point and the connection point between the first connection portion and the first supported portion is defined as the second connection point, the distance between the first connection point and the second seating surface in the direction from the first seating surface to the second seating surface is shorter than the distance between the second connection point and the second seating surface. The first cutting edge portion has a first straight cutting edge, a corner cutting edge, and a second straight cutting edge. The first straight cutting edge is connected to the first connection portion. The corner cutting edge is connected to the first straight cutting edge. The corner cutting edge is located opposite the first connection portion with respect to the first straight cutting edge. The second straight cutting edge is connected to each of the corner cutting edge and the second connection portion. When viewed perpendicularly to the first seating surface, the first straight cutting edge, the second straight cutting edge, the first supported portion, and the second supported portion are each linear, and the angle between the first straight cutting edge and the second straight cutting edge is greater than the angle between the first supported portion and the second supported portion.

[0012] Therefore, when comparing a cutting insert in which the cutting edge is parallel to the seating surface with the cutting insert according to this embodiment, the difference in the shape of the cutting edge as viewed in the direction of the main motion can be reduced, so that existing holders and existing machining programs can be used.

[0013] (2) According to the cutting insert described in (1) above, the outer peripheral surface may have a flank surface, a connecting surface, and a supported surface. The flank surface may be continuous with the first cutting edge portion. The connecting surface may be continuous with both the flank surface and the first connecting portion. The supported surface may be continuous with both the connecting surface and the first supported portion. In a cross section parallel to the first bearing surface and intersecting with the connecting surface, the connecting surface may be recessed toward the inside of the outer peripheral surface with respect to the supported surface. This prevents the connecting surface from coming into contact with the holder.

[0014] (3) According to the cutting insert described in (2) above, the ridge line between the second surface and the outer peripheral surface may form a second ridge line. The second ridge line may have a second cutting edge portion. The second cutting edge portion may be continuous with the flank surface. The first cutting edge portion and the second cutting edge portion may be symmetrical with respect to an imaginary plane positioned at an equal distance from each of the first and second bearing surfaces. This can improve the tool life of the cutting insert.

[0015] (4) According to the cutting insert described in (1) above, the outer peripheral surface may have a flank. The flank may be continuous with the first cutting edge portion. A ridgeline between the second surface and the outer peripheral surface may form a second ridgeline. The second ridgeline may have a second cutting edge portion. The second cutting edge portion may be continuous with the flank. The first cutting edge portion and the second cutting edge portion may be symmetrical with respect to an imaginary plane positioned at an equal distance from each of the first and second bearing surfaces. This can improve the tool life of the cutting insert.

[0016] (5) According to the cutting insert described in (3) or (4) above, in a cross section perpendicular to the first bearing surface and including a bisector of the angle between the first straight cutting edge and the second straight cutting edge, when viewed perpendicular to the first bearing surface, if a tangent to the flank of the first cutting edge portion is defined as a first tangent, a portion of the first tangent to the first cutting edge portion in a direction from the first bearing surface to the second bearing surface may be inclined inwardly from the outer circumferential surface with the first cutting edge portion as a fulcrum relative to a line passing through the first cutting edge portion and perpendicular to the second bearing surface, and if a tangent to the flank of the second cutting edge portion is defined as a second tangent, a portion of the second tangent to the second cutting edge portion in a direction from the second bearing surface to the first bearing surface may be inclined inwardly from the outer circumferential surface with the second cutting edge portion as a fulcrum relative to a line passing through the second cutting edge portion and perpendicular to the first bearing surface. This makes it possible to prevent wear of the flank due to contact between the flank and the workpiece.

[0017] (6) According to the cutting insert described in any one of (3) to (5), the flank may have a first flank portion, a second flank portion, and an intermediate surface. The first flank portion may be continuous with the first cutting edge portion. The second flank portion may be continuous with the second cutting edge portion. The intermediate surface may be continuous with each of the first flank portion and the second flank portion. The intermediate surface may be located between the first flank portion and the second flank portion. In a cross section perpendicular to the first cutting edge portion, the first flank portion may be inclined inwardly from the outer circumferential surface with respect to a line passing through the first cutting edge portion and perpendicular to the second bearing surface, with the first cutting edge portion as a fulcrum, and the second flank portion may be inclined inwardly from the outer circumferential surface with respect to a line passing through the second cutting edge portion and perpendicular to the first bearing surface, with the second cutting edge portion as a fulcrum. This effectively prevents wear of the flank caused by contact between the flank and the workpiece.

[0018] [Details of the embodiment] Hereinafter, details of the embodiment of the present disclosure (also referred to as the present embodiment) will be described with reference to the drawings. Note that the same or corresponding parts in the following drawings are given the same reference numerals, and their description will not be repeated. For convenience of explanation, the scale of each component in the drawings has been adjusted appropriately.

[0019] Fig. 1 is a first perspective schematic view showing the configuration of a cutting insert 100 according to this embodiment. As shown in Fig. 1, the cutting insert 100 mainly has a first surface 1, an outer peripheral surface 3, and an inner peripheral surface 9. The cutting insert 100 is used in a state held by a holder (not shown).

[0020] The inner peripheral surface 9 is continuous with the first surface 1. The inner peripheral surface 9 forms a through hole 8. The outer peripheral surface 3 is located outside the inner peripheral surface 9. The outer peripheral surface 3 is continuous with the first surface 1. The ridge line between the first surface 1 and the outer peripheral surface 3 forms a first ridge line 10. The first ridge line 10 is annular.

[0021] The first ridge 10 has a first ridge portion 4, a second ridge portion 5, a first corner portion 19, and a second corner portion 29. The first ridge portion 4 and the second ridge portion 5 face each other. The first corner portion 19 connects the first ridge portion 4 and the second ridge portion 5. The second corner portion 29 connects the first ridge portion 4 and the second ridge portion 5. The first corner portion 19 and the second corner portion 29 face each other.

[0022] The first ridge portion 4 has a first supported portion 11, a first connecting portion 12, a first cutting edge portion 13, a second connecting portion 14, and a second supported portion 15. The first supported portion 11 is continuous with a first corner portion 19. The first supported portion 11 is a portion that is supported by a holder (not shown).

[0023] The first connecting portion 12 is continuous with the first supported portion 11. The first connecting portion 12 is located on the opposite side of the first corner portion 19 from the first supported portion 11. From another perspective, on the first ridge line 10, the first supported portion 11 is located between the first corner portion 19 and the first connecting portion 12.

[0024] The first cutting edge portion 13 is continuous with the first connecting portion 12. The first cutting edge portion 13 is located opposite the first supported portion 11 with respect to the first connecting portion 12. From another perspective, on the first ridge line 10, the first connecting portion 12 is located between the first supported portion 11 and the first cutting edge portion 13. The first cutting edge portion 13 functions as a cutting edge.

[0025] The second connecting portion 14 is continuous with the first cutting edge portion 13. The second connecting portion 14 is located opposite the first connecting portion 12 with respect to the first cutting edge portion 13. From another perspective, the first cutting edge portion 13 is located between the first connecting portion 12 and the second connecting portion 14 on the first ridge line 10.

[0026] The second supported portion 15 is continuous with the second connecting portion 14 and the second corner portion 29. On the first ridge line 10, the second supported portion 15 is located between the second connecting portion 14 and the second corner portion 29. The second supported portion 15 is located on the opposite side of the first cutting edge portion 13 with respect to the second connecting portion 14. From another perspective, on the first ridge line 10, the second connecting portion 14 is located between the first cutting edge portion 13 and the second supported portion 15. The second supported portion 15 is a portion that is supported by a holder (not shown).

[0027] The second ridge portion 5 has substantially the same configuration as the first ridge portion 4. From another perspective, the first ridge 10 has two first supported portions 11, two first connecting portions 12, two first cutting edge portions 13, two second connecting portions 14, and two second supported portions 15. The first corner portion 19 is continuous with each of the first supported portions 11 of the first ridge portion 4 and the second supported portions 15 of the second ridge portion 5. The second corner portion 29 is continuous with each of the first supported portions 11 of the second ridge portion 5 and the second supported portions 15 of the first ridge portion 4.

[0028] The first surface 1 has a first bearing surface 51 and a first rake surface 52. The first bearing surface 51 is flat. The first bearing surface 51 is continuous with the inner peripheral surface 9. The first rake surface 52 is continuous with the first cutting edge portion 13.

[0029] Fig. 2 is a second perspective schematic view showing the configuration of the cutting insert 100 according to this embodiment. As shown in Fig. 2, the cutting insert 100 has a second surface 2. The second surface 2 is continuous with each of the outer peripheral surface 3 and the inner peripheral surface 9. The ridge line between the second surface 2 and the outer peripheral surface 3 forms a second ridge line 30. The second ridge line 30 is annular.

[0030] The second ridge 30 has a third ridge portion 6, a fourth ridge portion 7, a third corner portion 39, and a fourth corner portion 49. The third ridge portion 6 and the fourth ridge portion 7 face each other. The third corner portion 39 connects the third ridge portion 6 and the fourth ridge portion 7. The fourth corner portion 49 connects the third ridge portion 6 and the fourth ridge portion 7. The third corner portion 39 and the fourth corner portion 49 face each other.

[0031] The third ridge portion 6 has a third supported portion 31, a third connecting portion 32, a second cutting edge portion 33, a fourth connecting portion 34, and a fourth supported portion 35. The third supported portion 31 is continuous with a third corner portion 39. The third supported portion 31 is a portion that is supported by a holder (not shown).

[0032] The third connecting portion 32 is continuous with the third supported portion 31. The third connecting portion 32 is located on the opposite side of the third corner portion 39 from the third supported portion 31. From another perspective, on the second ridge line 30, the third supported portion 31 is located between the third corner portion 39 and the third connecting portion 32.

[0033] The second cutting edge portion 33 is continuous with the third connecting portion 32. The second cutting edge portion 33 is located opposite the third supported portion 31 with respect to the third connecting portion 32. From another perspective, on the second ridge line 30, the third connecting portion 32 is located between the third supported portion 31 and the second cutting edge portion 33. The second cutting edge portion 33 functions as a cutting edge.

[0034] The fourth connecting portion 34 is continuous with the second cutting edge portion 33. The fourth connecting portion 34 is located opposite the third connecting portion 32 with respect to the second cutting edge portion 33. From another perspective, on the second ridge line 30, the second cutting edge portion 33 is located between the third connecting portion 32 and the fourth connecting portion 34.

[0035] The fourth supported portion 35 is continuous with each of the fourth connecting portion 34 and the fourth corner portion 49. On the second ridge line 30, the fourth supported portion 35 is located between the fourth connecting portion 34 and the fourth corner portion 49. The fourth supported portion 35 is located on the opposite side of the second cutting edge portion 33 with respect to the fourth connecting portion 34. From another perspective, on the second ridge line 30, the fourth connecting portion 34 is located between the second cutting edge portion 33 and the fourth supported portion 35. The fourth supported portion 35 is a portion that is supported by a holder (not shown).

[0036] The fourth ridge portion 7 has substantially the same configuration as the third ridge portion 6. From another perspective, the second ridge 30 has two third supported portions 31, two third connecting portions 32, two second cutting edge portions 33, two fourth connecting portions 34, and two fourth supported portions 35. The third corner portion 39 is continuous with each of the third supported portions 31 of the third ridge portion 6 and the fourth supported portions 35 of the fourth ridge portion 7. The fourth corner portion 49 is continuous with each of the third supported portions 31 of the fourth ridge portion 7 and the fourth supported portions 35 of the third ridge portion 6.

[0037] The second surface 2 has a second bearing surface 61 and a second rake surface 62. The second bearing surface 61 is flat. The second bearing surface 61 is continuous with the inner peripheral surface 9. The second rake surface 62 is continuous with the second cutting edge portion 33.

[0038] Fig. 3 is an enlarged perspective schematic view showing region III in Fig. 1. As shown in Fig. 3, the outer peripheral surface 3 has a first supported surface 71, a first connecting surface 72, a flank surface 73, a second connecting surface 74, and a second supported surface 75.

[0039] The first supported surface 71 is continuous with each of the first supported portion 11 and the fourth supported portion 35. From another perspective, the first supported portion 11 is formed by the ridgeline between the first supported surface 71 and the first surface 1. The fourth supported portion 35 is formed by the ridgeline between the first supported surface 71 and the second surface 2 (see FIG. 2). The first supported surface 71 is flat. The first supported surface 71 is a surface that is supported by a holder (not shown).

[0040] The first connection surface 72 is continuous with the first supported surface 71. The first connection surface 72 is continuous with each of the first connection portion 12 and the fourth connection portion 34. From another perspective, the first connection portion 12 is formed by the ridge line between the first connection surface 72 and the first surface 1. The fourth connection portion 34 is formed by the ridge line between the first connection surface 72 and the second surface 2 (see FIG. 2 ).

[0041] The flank 73 is continuous with the first connecting surface 72. In the circumferential direction, the flank 73 is opposite the first supported surface 71 with respect to the first connecting surface 72. In this specification, the circumferential direction refers to the direction along the first ridge 10 from the first connecting portion 12 toward the second connecting portion 14 via the first cutting edge portion 13.

[0042] The flank 73 is continuous with each of the first cutting edge portion 13 and the second cutting edge portion 33. From another perspective, the first cutting edge portion 13 is formed by the ridge line between the flank 73 and the first surface 1. The second cutting edge portion 33 is formed by the ridge line between the flank 73 and the second surface 2 (see FIG. 2 ).

[0043] The second connection surface 74 is continuous with the relief surface 73. In the circumferential direction, the second connection surface 74 is located opposite the first connection surface 72 with respect to the relief surface 73. The second connection surface 74 is continuous with each of the second connection portion 14 and the third connection portion 32. From another perspective, the second connection portion 14 is formed by the ridge line between the second connection surface 74 and the first surface 1. The third connection portion 32 is formed by the ridge line between the second connection surface 74 and the second surface 2 (see FIG. 2 ).

[0044] The second supported surface 75 is continuous with the second connecting surface 74. In the circumferential direction, the second supported surface 75 is located on the opposite side of the relief surface 73 from the second connecting surface 74. The second supported surface 75 is continuous with each of the second supported portion 15 and the third supported portion 31. From another perspective, the second supported portion 15 is formed by the ridgeline between the second supported surface 75 and the first surface 1. The third supported portion 31 is formed by the ridgeline between the second supported surface 75 and the second surface 2 (see FIG. 2 ).

[0045] 3 , the first connection surface 72 has a first connection surface portion 81, a second connection surface portion 82, a third connection surface portion 83, and a fourth connection surface portion 84. The first connection surface portion 81 is continuous with the first supported surface 71. The second connection surface portion 82 is continuous with the first connection surface portion 81. In the circumferential direction, the second connection surface portion 82 is located opposite the first supported surface 71 with respect to the first connection surface portion 81.

[0046] The third connection surface portion 83 is continuous with the second connection surface portion 82. In the circumferential direction, the third connection surface portion 83 is located opposite the first connection surface portion 81 with respect to the second connection surface portion 82. The fourth connection surface portion 84 is continuous with both the third connection surface portion 83 and the flank surface 73. In the circumferential direction, the fourth connection surface portion 84 is located opposite the second connection surface portion 82 with respect to the third connection surface portion 83. In the circumferential direction, the fourth connection surface portion 84 is located between the third connection surface portion 83 and the flank surface 73.

[0047] The second connection surface 74 has a fifth connection surface portion 85, a sixth connection surface portion 86, a seventh connection surface portion 87, and an eighth connection surface portion 88. The fifth connection surface portion 85 is continuous with the second supported surface 75. The sixth connection surface portion 86 is continuous with the fifth connection surface portion 85. In the circumferential direction, the sixth connection surface portion 86 is located opposite the second supported surface 75 with respect to the fifth connection surface portion 85.

[0048] The seventh connection surface portion 87 is continuous with the sixth connection surface portion 86. In the circumferential direction, the seventh connection surface portion 87 is located opposite the fifth connection surface portion 85 with respect to the sixth connection surface portion 86. The eighth connection surface portion 88 is continuous with both the seventh connection surface portion 87 and the flank surface 73. In the circumferential direction, the eighth connection surface portion 88 is located opposite the sixth connection surface portion 86 with respect to the seventh connection surface portion 87. In the circumferential direction, the eighth connection surface portion 88 is located between the sixth connection surface portion 86 and the seventh connection surface portion 87.

[0049] The flank 73 has a first flank portion 76, a second flank portion 77, and an intermediate surface 89. The first flank portion 76 is continuous with the first cutting edge portion 13. In the circumferential direction, the first flank portion 76 is continuous with each of the first connecting surface 72 and the second connecting surface 74. The second flank portion 77 is continuous with the second cutting edge portion 33. In the circumferential direction, the second flank portion 77 is continuous with each of the first connecting surface 72 and the second connecting surface 74.

[0050] The intermediate surface 89 is located between the first flank portion 76 and the second flank portion 77. The intermediate surface 89 is continuous with each of the first flank portion 76 and the second flank portion 77. In the circumferential direction, the intermediate surface 89 is continuous with each of the first connecting surface 72 and the second connecting surface 74.

[0051] The intermediate surface 89 has a first intermediate surface portion 78, a second intermediate surface portion 79, and a third intermediate surface portion 80. The first intermediate surface portion 78 is continuous with the first clearance surface portion 76. The second intermediate surface portion 79 is continuous with the second clearance surface portion 77. The third intermediate surface portion 80 is located between the first intermediate surface portion 78 and the second intermediate surface portion 79. The third intermediate surface portion 80 is continuous with each of the first intermediate surface portion 78 and the second intermediate surface portion 79.

[0052] Fig. 4 is a schematic plan view showing the configuration of the cutting insert 100 according to this embodiment. Fig. 4 shows the configuration of the cutting insert 100 as viewed perpendicularly to the first bearing surface 51. As shown in Fig. 4, when viewed perpendicularly to the first bearing surface 51 (hereinafter also referred to as a plan view), the outer shape of the cutting insert 100 is, for example, a rhombus.

[0053] The first cutting edge portion 13 has a first straight cutting edge 16, a first corner cutting edge 17, and a second straight cutting edge 18. The first straight cutting edge 16 is continuous with the first connecting portion 12. In a plan view, the first straight cutting edge 16 is linear.

[0054] The first corner cutting edge 17 is continuous with the first straight cutting edge 16. The first corner cutting edge 17 is located on the opposite side of the first connecting portion 12 from the first straight cutting edge 16. From another perspective, the first straight cutting edge 16 is located between the first connecting portion 12 and the first corner cutting edge 17 on the first ridge line 10. In plan view, the first corner cutting edge 17 is curved. Specifically, in plan view, the first corner cutting edge 17 is arc-shaped.

[0055] The second straight cutting edge 18 is continuous with each of the first corner cutting edge 17 and the second connecting portion 14. On the first ridge line 10, the second straight cutting edge 18 is located between the first corner cutting edge 17 and the second connecting portion 14. The second straight cutting edge 18 is located opposite the first straight cutting edge 16 with respect to the first corner cutting edge 17. From another perspective, on the first ridge line 10, the first corner cutting edge 17 is located between the second straight cutting edge 18 and the first straight cutting edge 16.

[0056] In plan view, the second straight cutting edge 18 is linear. In plan view, the bisector of the angle formed by the first straight cutting edge 16 and the second straight cutting edge 18 is defined as a first bisector 131.

[0057] In a plan view, the first supported portion 11 is linear. In a plan view, the first connecting portion 12 is curved and recessed toward the inside of the first ridge 10. In a plan view, the second supported portion 15 is linear. In a plan view, the second connecting portion 14 is curved and recessed toward the inside of the first ridge 10.

[0058] An axis passing through the center of the inner peripheral surface 9 is defined as the central axis O. The first bisector 131 intersects with the central axis O. The shape of the first ridge 10 may be, for example, two-fold symmetric with respect to the central axis O. From another perspective, the shape of the first ridge portion 4 rotated 180° around the central axis O may coincide with the shape of the second ridge portion 5.

[0059] The shape of the cutting insert 100 may be, for example, two-fold symmetric with respect to the central axis O. The shape of the outer peripheral surface 3 (see FIG. 3 ) may be, for example, two-fold symmetric with respect to the central axis O. In a plan view, the shape of the first ridge line 10 may be line-symmetric with respect to the first bisector 131. In a plan view, the shape of the first surface 1 may be line-symmetric with respect to the first bisector 131.

[0060] Figure 5 is an enlarged schematic diagram showing the first ridge line 10 within region V in Figure 4. In Figure 5, black dots without reference numbers indicate connection points between components. As shown in Figure 5, in a plan view, the angle between the first straight cutting edge 16 and the second straight cutting edge 18 is defined as a first angle θ1. In a plan view, the angle between the first supported portion 11 and the second supported portion 15 is defined as a second angle θ2.

[0061] The first angle θ1 is greater than the second angle θ2. The value obtained by subtracting the second angle θ2 from the first angle θ1 is, for example, 0.25° or greater and 5° or less. The second angle θ2 is not particularly limited, but is, for example, 80°. The second angle θ2 may be, for example, 35°, 55°, 60°, or 90°.

[0062] In plan view, the first bisector 131 intersects with the first corner cutting edge 17. The point where the first bisector 131 intersects with the first corner cutting edge 17 in plan view is defined as a first vertex 141. The connection point between the first connection portion 12 and the first cutting edge portion 13 is defined as a first connection point 91. The connection point between the first connection portion 12 and the first supported portion 11 is defined as a second connection point 92.

[0063] The first connecting portion 12 has a first curved portion 21, a second curved portion 22, a first straight portion 23, and a third curved portion 24. The first curved portion 21 is smoothly connected to the first supported portion 11. The first curved portion 21 is formed by the ridge line between the first connecting surface portion 81 (see FIG. 3 ) and the first surface 1. In a plan view, the first curved portion 21 is convex outward from the first ridge line 10. In a plan view, the first curved portion 21 is, for example, arc-shaped.

[0064] The second curved portion 22 is smoothly connected to the first curved portion 21. The second curved portion 22 is formed by the ridge between the second connection surface portion 82 (see FIG. 3 ) and the first surface 1. In plan view, the second curved portion 22 is concave toward the inside of the first ridge 10. In plan view, the second curved portion 22 has, for example, an arc shape. In plan view, the radius of curvature of the second curved portion 22 is larger than the radius of curvature of the first curved portion 21.

[0065] The first straight portion 23 is smoothly connected to the second curved portion 22. The first straight portion 23 is formed by the ridge line between the third connecting surface portion 83 (see FIG. 3 ) and the first surface 1. In plan view, the first straight portion 23 is linear. In plan view, the first straight portion 23 is inclined inward of the first ridge line 10 with respect to the first straight cutting edge 16.

[0066] The third curved portion 24 is smoothly connected to each of the first straight portion 23 and the first cutting edge portion 13. The third curved portion 24 is formed by the ridge line between the fourth connecting surface portion 84 (see FIG. 3 ) and the first surface 1. In a plan view, the third curved portion 24 is convex outward from the first ridge line 10. In a plan view, the third curved portion 24 is, for example, arc-shaped. In a plan view, the radius of curvature of the third curved portion 24 is smaller than the radius of curvature of the second curved portion 22.

[0067] In a plan view, an imaginary line (first imaginary line 111) overlapping the first supported portion 11 intersects with the first connection portion 12. The intersection (first intersection 151) of the first imaginary line 111 and the first connection portion 12 is, for example, on the first straight line portion 23. The portion of the first connection portion 12 between the second connection point 92 and the first intersection 151 is recessed with respect to the first imaginary line 111. In a plan view, the first connection point 91 is located outside the first ridge line 10 with respect to the first imaginary line 111.

[0068] The connection point between the second connection portion 14 and the first cutting edge portion 13 is a third connection point 93. The connection point between the second connection portion 14 and the second supported portion 15 is a fourth connection point 94. The second connection portion 14 has a fourth curved portion 25, a fifth curved portion 26, a second straight portion 27, and a sixth curved portion 28.

[0069] The fourth curved portion 25 is smoothly connected to the second supported portion 15. The fourth curved portion 25 is formed by the ridge line between the fifth connecting surface portion 85 (see FIG. 3 ) and the first surface 1. In plan view, the fourth curved portion 25 is convex outward from the first ridge line 10. In plan view, the fourth curved portion 25 is, for example, arc-shaped.

[0070] The fifth curved portion 26 is smoothly connected to the fourth curved portion 25. The fifth curved portion 26 is formed by the ridge line between the sixth connecting surface portion 86 (see FIG. 3 ) and the first surface 1. In plan view, the fifth curved portion 26 is concave toward the inside of the first ridge line 10. In plan view, the fifth curved portion 26 has, for example, an arc shape. In plan view, the radius of curvature of the fifth curved portion 26 is larger than the radius of curvature of the fourth curved portion 25.

[0071] The second straight portion 27 is smoothly connected to the fifth curved portion 26. The second straight portion 27 is formed by the ridge line between the seventh connecting surface portion 87 (see FIG. 3 ) and the first surface 1. In a plan view, the second straight portion 27 is linear. In a plan view, the second straight portion 27 is inclined inward of the first ridge line 10 with respect to the second straight cutting edge 18. In a plan view, the angle formed between the first straight portion 23 and the second straight portion 27 (third angle θ3) is smaller than both the first angle θ1 and the second angle θ2.

[0072] The sixth curved portion 28 is smoothly connected to each of the second straight portion 27 and the first cutting edge portion 13. The sixth curved portion 28 is formed by the ridge line between the eighth connecting surface portion 88 (see FIG. 3 ) and the first surface 1. In a plan view, the sixth curved portion 28 is convex outward from the first ridge line 10. In a plan view, the sixth curved portion 28 is, for example, arc-shaped. In a plan view, the radius of curvature of the sixth curved portion 28 is smaller than the radius of curvature of the fifth curved portion 26.

[0073] In a plan view, an imaginary line (second imaginary line 112) that overlaps the second supported portion 15 intersects with the second connection portion 14. The intersection (second intersection 152) of the second imaginary line 112 and the second connection portion 14 is, for example, on the second straight line portion 27. The portion of the second connection portion 14 between the fourth connection point 94 and the second intersection 152 is recessed with respect to the second imaginary line 112. In a plan view, the third connection point 93 is located outside the first ridge line 10 with respect to the second imaginary line 112.

[0074] Fig. 6 is a bottom schematic view showing the configuration of the cutting insert 100 according to this embodiment. Fig. 6 shows the configuration of the cutting insert 100 as viewed perpendicularly to the second bearing surface 61. As shown in Fig. 6, when viewed perpendicularly to the second bearing surface 61 (hereinafter also referred to as a bottom view), the outer shape of the cutting insert 100 is, for example, a rhombic shape.

[0075] The second cutting edge portion 33 has a third straight cutting edge 36, a second corner cutting edge 37, and a fourth straight cutting edge 38. The third straight cutting edge 36 is continuous with the third connecting portion 32. In a bottom view, the third straight cutting edge 36 is linear.

[0076] The second corner cutting edge 37 is continuous with the third straight cutting edge 36. The second corner cutting edge 37 is located on the opposite side of the third connecting portion 32 from the third straight cutting edge 36. From another perspective, the third straight cutting edge 36 is located between the third connecting portion 32 and the second corner cutting edge 37 on the second ridge line 30. In bottom view, the second corner cutting edge 37 is curved. Specifically, in bottom view, the second corner cutting edge 37 is arc-shaped.

[0077] The fourth straight cutting edge 38 is continuous with each of the second corner cutting edge 37 and the fourth connecting portion 34. On the second ridge line 30, the fourth straight cutting edge 38 is located between the second corner cutting edge 37 and the fourth connecting portion 34. The fourth straight cutting edge 38 is located opposite the third straight cutting edge 36 with respect to the second corner cutting edge 37. From another perspective, on the second ridge line 30, the second corner cutting edge 37 is located between the fourth straight cutting edge 38 and the third straight cutting edge 36.

[0078] In the bottom view, the fourth straight cutting edge 38 is linear. In the bottom view, the bisector of the angle formed by the third straight cutting edge 36 and the fourth straight cutting edge 38 is the second bisector 132. The second bisector 132 intersects with the central axis O.

[0079] In bottom view, the third supported portion 31 is linear. In bottom view, the third connecting portion 32 is curved and recessed toward the inside of the second ridge 30. In bottom view, the fourth supported portion 35 is linear. In bottom view, the fourth connecting portion 34 is curved and recessed toward the inside of the second ridge 30.

[0080] The shape of the second ridge line 30 may be, for example, two-fold symmetric with respect to the central axis O. From another perspective, the shape of the third ridge line portion 6 rotated 180 degrees around the central axis O may coincide with the shape of the fourth ridge line portion 7.

[0081] In bottom view, the shape of the second ridge line 30 may be line-symmetric with respect to the second bisector 132. In bottom view, the shape of the second surface 2 may be line-symmetric with respect to the second bisector 132.

[0082] Figure 7 is an enlarged schematic diagram showing the second ridge line 30 located within region VII in Figure 6. In Figure 7, black dots without reference numbers indicate connection points between components. As shown in Figure 7, in a plan view, the angle between the third straight cutting edge 36 and the fourth straight cutting edge 38 is a fourth angle θ4. In a plan view, the angle between the third supported portion 31 and the fourth supported portion 35 is a fifth angle θ5.

[0083] The fourth angle θ4 is greater than the fifth angle θ5. The value obtained by subtracting the fifth angle θ5 from the fourth angle θ4 is, for example, 0.25° or greater and 5° or less. The fifth angle θ5 is not particularly limited, but is, for example, 80°. The fifth angle θ5 may be, for example, 35°, 55°, 60°, or 90°.

[0084] In bottom view, the second bisector 132 intersects with the second corner cutting edge 37. The point where the second bisector 132 and the second corner cutting edge 37 intersect in bottom view is defined as a second vertex 142. The connection point between the third connection portion 32 and the second cutting edge portion 33 is defined as a fifth connection point 95. The connection point between the third connection portion 32 and the third supported portion 31 is defined as a sixth connection point 96.

[0085] The third connection portion 32 has a seventh curved portion 41, an eighth curved portion 42, a third straight portion 43, and a ninth curved portion 44. The seventh curved portion 41 is smoothly connected to the third supported portion 31. The seventh curved portion 41 is formed by the ridge line between the fifth connection surface portion 85 (see FIG. 3 ) and the second surface 2. In a bottom view, the seventh curved portion 41 is convex outward from the second ridge line 30. In a bottom view, the seventh curved portion 41 is, for example, arc-shaped.

[0086] The eighth curved portion 42 is smoothly connected to the seventh curved portion 41. The eighth curved portion 42 is formed by the ridge between the sixth connecting surface portion 86 (see FIG. 3 ) and the second surface 2. In a bottom view, the eighth curved portion 42 is concave toward the inside of the second ridge 30. In a bottom view, the eighth curved portion 42 has, for example, an arc shape. In a bottom view, the radius of curvature of the eighth curved portion 42 is larger than the radius of curvature of the seventh curved portion 41.

[0087] The third straight portion 43 is smoothly connected to the eighth curved portion 42. The third straight portion 43 is formed by the ridge line between the seventh connecting surface portion 87 (see FIG. 3 ) and the second surface 2. In bottom view, the third straight portion 43 is linear. In bottom view, the third straight portion 43 is inclined inward of the second ridge line 30 with respect to the third straight cutting edge 36.

[0088] The ninth curved portion 44 is smoothly connected to the third straight portion 43. The ninth curved portion 44 is formed by the ridge between the eighth connecting surface portion 88 (see FIG. 3 ) and the second surface 2. In a bottom view, the ninth curved portion 44 is convex outward from the second ridge 30. In a bottom view, the ninth curved portion 44 has, for example, an arc shape. In a bottom view, the radius of curvature of the ninth curved portion 44 is smaller than the radius of curvature of the eighth curved portion 42.

[0089] In bottom view, an imaginary line (third imaginary line 113) overlapping the third supported portion 31 intersects with the third connection portion 32. An intersection (third intersection 153) of the third imaginary line 113 and the third connection portion 32 is located, for example, on the third straight line portion 43. A portion of the third connection portion 32 between the sixth connection point 96 and the third intersection 153 is recessed with respect to the third imaginary line 113. In bottom view, the fifth connection point 95 is located outward from the third imaginary line 113.

[0090] The connection point between the fourth connection portion 34 and the second cutting edge portion 33 is a seventh connection point 97. The connection point between the fourth connection portion 34 and the fourth supported portion 35 is an eighth connection point 98. The fourth connection portion 34 has a tenth curved portion 45, an eleventh curved portion 46, a fourth straight portion 47, and a twelfth curved portion 48.

[0091] The tenth curved portion 45 is smoothly connected to the fourth supported portion 35. The tenth curved portion 45 is formed by the ridge line between the first connecting surface portion 81 (see FIG. 3 ) and the second surface 2. In bottom view, the tenth curved portion 45 is convex outward from the second ridge line 30. In bottom view, the tenth curved portion 45 is, for example, arc-shaped.

[0092] The eleventh curved portion 46 is smoothly connected to the tenth curved portion 45. The eleventh curved portion 46 is formed by the ridge between the second connection surface portion 82 (see FIG. 3 ) and the second surface 2. In a bottom view, the eleventh curved portion 46 is concave toward the inside of the second ridge 30. In a bottom view, the eleventh curved portion 46 has, for example, an arc shape. In a bottom view, the radius of curvature of the eleventh curved portion 46 is larger than the radius of curvature of the tenth curved portion 45.

[0093] The fourth straight portion 47 is smoothly connected to the eleventh curved portion 46. The fourth straight portion 47 is formed by the ridge line between the third connecting surface portion 83 (see FIG. 3 ) and the second surface 2. In a bottom view, the fourth straight portion 47 is linear. In a bottom view, the fourth straight portion 47 is inclined toward the inside of the second ridge line 30 with respect to the fourth straight cutting edge 38. In a bottom view, the angle formed by the third straight portion 43 and the fourth straight portion 47 (sixth angle θ6) is smaller than each of the fourth angle θ4 and the fifth angle θ5.

[0094] The twelfth curved portion 48 is smoothly connected to the fourth straight portion 47. The twelfth curved portion 48 is formed by the ridge between the fourth connecting surface portion 84 (see FIG. 3 ) and the second surface 2. In a bottom view, the twelfth curved portion 48 is convex outward from the second ridge 30. In a bottom view, the twelfth curved portion 48 is, for example, arc-shaped. In a bottom view, the radius of curvature of the twelfth curved portion 48 is smaller than the radius of curvature of the eleventh curved portion 46.

[0095] In bottom view, an imaginary line (fourth imaginary line 114) that overlaps with the fourth supported portion 35 intersects with the fourth connection portion 34. The intersection (fourth intersection 154) of the fourth imaginary line 114 and the fourth connection portion 34 is, for example, on the fourth straight line portion 47. The portion of the fourth connection portion 34 between the eighth connection point 98 and the fourth intersection 154 is recessed with respect to the fourth imaginary line 114. In bottom view, the seventh connection point 97 is located outward from the fourth imaginary line 114.

[0096] Fig. 8 is a schematic side view showing the configuration of the cutting insert 100 according to this embodiment. Fig. 8 shows the configuration of the cutting insert 100 as viewed along the arrow A in Fig. 4. The direction of the arrow A is the direction from the outer peripheral surface 3 toward the central axis O along the first bisector 131.

[0097] 8 , the second seating surface 61 is opposite the first seating surface 51. The second seating surface 61 may be parallel to the first seating surface 51. The direction from the first seating surface 51 to the second seating surface 61 is defined as a first direction 101. Conversely, the direction from the second seating surface 61 to the first seating surface 51 is defined as a second direction 102. The first direction 101 is perpendicular to the first seating surface 51. The second direction 102 is perpendicular to the first seating surface 51.

[0098] 8 shows an imaginary plane 99. The imaginary plane 99 is located at an equal distance from each of the first seating surface 51 and the second seating surface 61. In other words, in the first direction 101, the distance between the first seating surface 51 and the imaginary plane 99 is equal to the distance between the second seating surface 61 and the imaginary plane 99.

[0099] As shown in Fig. 8 , the first cutting edge portion 13 and the second cutting edge portion 33 may be symmetrical with respect to an imaginary plane 99. Therefore, the number of cutting edges of the cutting insert 100 is increased. This can improve the tool life of the cutting insert 100. The shape of the cutting insert 100 may be symmetrical with respect to the imaginary plane 99. Specifically, the first surface 1 and the second surface 2 may be symmetrical with respect to the imaginary plane 99. The first ridge line 10 and the second ridge line 30 may be symmetrical with respect to the imaginary plane 99. The shape of the outer peripheral surface 3 may be symmetrical with respect to the imaginary plane 99.

[0100] In the first direction 101, the distance (first distance D1) between the first connection point 91 and the second seating surface 61 is shorter than the distance (second distance D2) between the second connection point 92 and the second seating surface 61. From another perspective, in the first direction 101, the first connection point 91 is located between the second connection point 92 and the second seating surface 61.

[0101] Similarly, in the first direction 101, the distance between the third connection point 93 and the second seating surface 61 is shorter than the distance between the fourth connection point 94 and the second seating surface 61. From another perspective, in the first direction 101, the third connection point 93 is located between the fourth connection point 94 and the second seating surface 61. The distance between the third connection point 93 and the second seating surface 61 in the first direction 101 may be the same as the first distance D1. The distance between the fourth connection point 94 and the second seating surface 61 in the first direction 101 may be the same as the second distance D2.

[0102] The first cutting edge portion 13 is inclined in the first direction 101 with respect to a plane parallel to the second bearing surface 61, except for the first vertex 141. Specifically, the distance between the first cutting edge portion 13 and the second bearing surface 61 in the first direction 101 decreases with increasing distance from the first vertex 141. In this specification, the state in which the cutting edge portion is inclined with respect to a plane, except for one point on the cutting edge portion, is also simply referred to as "the cutting edge portion is inclined with respect to the plane." In Figure 8, the first line 60 indicates a plane parallel to the second bearing surface 61.

[0103] In the first direction 101, the distance (third distance D3) between the fifth connection point 95 and the first seating surface 51 is shorter than the distance (fourth distance D4) between the sixth connection point 96 and the first seating surface 51. From another perspective, in the first direction 101, the fifth connection point 95 is located between the sixth connection point 96 and the first seating surface 51.

[0104] Similarly, in the first direction 101, the distance between the seventh connection point 97 and the first seating surface 51 is shorter than the distance between the eighth connection point 98 and the first seating surface 51. From another perspective, in the first direction 101, the seventh connection point 97 is located between the eighth connection point 98 and the first seating surface 51. The distance between the seventh connection point 97 and the first seating surface 51 in the first direction 101 may be the same as the third distance D3. The distance between the eighth connection point 98 and the first seating surface 51 in the first direction 101 may be the same as the fourth distance D4.

[0105] The second cutting edge portion 33 is inclined in the second direction 102 with respect to a plane parallel to the first bearing surface 51, except for the second vertex 142. Specifically, the distance between the second cutting edge portion 33 and the first bearing surface 51 in the first direction 101 decreases with increasing distance from the second vertex 142. In FIG. 8 , a second line 70 indicates a plane parallel to the first bearing surface 51.

[0106] In the first direction 101, the first ridge line 10 is between the first seating surface 51 and the second seating surface 61. In the first direction 101, the second ridge line 30 is between the first seating surface 51 and the second seating surface 61.

[0107] When viewed along the first bisector 131 (hereinafter also referred to as a side view), the first connection portion 12 is recessed in the first direction 101. In the side view, the second connection portion 14 is recessed in the first direction 101. In the side view, the third connection portion 32 is recessed in the second direction 102. In the side view, the fourth connection portion 34 is recessed in the second direction 102.

[0108] In a side view, the first supported portion 11 is linear. In a side view, the second supported portion 15 is linear. In a side view, the third supported portion 31 is linear. In a side view, the fourth supported portion 35 is linear.

[0109] Figure 9 is a schematic cross-sectional view taken along line IX-IX in Figure 8. In Figure 9, black dots without reference symbols indicate connection points between components. The cross section shown in Figure 9 is a cross section that is parallel to the first seating surface 51 and intersects with the first connecting surface 72. The cross section that is parallel to the first seating surface 51 and intersects with the first connecting surface 72 is referred to as a first cross section CS1. The first cross section CS1 is a cross section seen in a first direction 101.

[0110] As shown in Fig. 9 , in the first cross section CS1, the first connecting surface 72 is recessed toward the inside of the outer peripheral surface 3 with respect to the first supported surface 71. Fig. 17 is a schematic cross-sectional view showing a state in which the cutting insert 100 is attached to the holder 210. Fig. 17 shows the cutting insert 100 and the holder 210 in a cross section parallel to the first bearing surface 51. As shown in Fig. 17 , the holder 210 usually has a first support surface 211, a second support surface 212, and an undercut surface 213. The first supported surface 71 is supported by the first support surface 211. The second supported surface 75 is supported by the second support surface 212. The undercut surface 213 faces the undercut surface 73.

[0111] 17 , even when the cutting insert 100 according to this embodiment is attached to a holder to which a cutting insert having a cutting edge 201 parallel to the seating surface is attached, the first connecting surface 72 can be prevented from contacting the first supporting surface 211 of the holder 210. This allows stable contact between the first supported surface 71 and the first supporting surface 211. As a result, the cutting insert 100 can be stably fixed to the holder 210.

[0112] 9 , in the first cross section CS1, the first connecting surface 72 is recessed toward the inside of the outer peripheral surface 3 with respect to an imaginary line (a fifth imaginary line 115) that overlaps with the first supported surface 71. In the first cross section CS1, a part of the first connecting surface 72 that is continuous with the relief surface 73 may be located outside the outer peripheral surface 3 with respect to the fifth imaginary line 115.

[0113] In the first cross section CS1, the first connection surface portion 81 is smoothly connected to the first supported surface 71. In the first cross section CS1, the first connection surface portion 81 has, for example, an arc shape. In the first cross section CS1, the first connection surface portion 81 is convex outward from the outer peripheral surface 3.

[0114] In the first cross section CS1, the second connection surface portion 82 is smoothly connected to the first connection surface portion 81. In the first cross section CS1, the second connection surface portion 82 is, for example, arc-shaped. In the first cross section CS1, the radius of curvature of the second connection surface portion 82 is larger than the radius of curvature of the first connection surface portion 81. In the first cross section CS1, the second connection surface portion 82 is concave toward the inside of the outer peripheral surface 3.

[0115] In the first cross section CS1, the third connection surface portion 83 is smoothly connected to the second connection surface portion 82. In the first cross section CS1, the third connection surface portion 83 is, for example, linear. In the first cross section CS1, the third connection surface portion 83 is inclined clockwise with respect to the fifth virtual line 115.

[0116] In the first cross section CS1, the fourth connection surface portion 84 is smoothly connected to each of the third connection surface portion 83 and the flank surface 73. In the first cross section CS1, the fourth connection surface portion 84 is, for example, arc-shaped. In the first cross section CS1, the radius of curvature of the fourth connection surface portion 84 is smaller than the radius of curvature of the second connection surface portion 82. In the first cross section CS1, the fourth connection surface portion 84 is convex outward from the outer peripheral surface 3.

[0117] 9 , in the first cross section CS1, the second connecting surface 74 is recessed toward the inside of the outer peripheral surface 3 with respect to the second supported surface 75. Specifically, in the first cross section CS1, the second connecting surface 74 is recessed toward the inside of the outer peripheral surface 3 with respect to an imaginary line (a sixth imaginary line 116) that overlaps with the second supported surface 75. In the first cross section CS1, a portion of the second connecting surface 74 that is continuous with the relief surface 73 may be located outside the outer peripheral surface 3 with respect to the sixth imaginary line 116.

[0118] In the first cross section CS1, the fifth connection surface 85 is smoothly connected to the second supported surface 75. In the first cross section CS1, the fifth connection surface 85 has, for example, an arc shape. In the first cross section CS1, the fifth connection surface 85 is convex outward from the outer peripheral surface 3.

[0119] In the first cross section CS1, the sixth connection surface portion 86 is smoothly connected to the fifth connection surface portion 85. In the first cross section CS1, the sixth connection surface portion 86 has, for example, an arc shape. In the first cross section CS1, the radius of curvature of the sixth connection surface portion 86 is larger than the radius of curvature of the fifth connection surface portion 85. In the first cross section CS1, the sixth connection surface portion 86 is concave toward the inside of the outer peripheral surface 3.

[0120] In the first cross section CS1, the seventh connecting surface 87 is smoothly connected to the sixth connecting surface 86. In the first cross section CS1, the seventh connecting surface 87 is, for example, linear. In the first cross section CS1, the seventh connecting surface 87 is inclined counterclockwise with respect to the sixth virtual line 116.

[0121] In the first cross section CS1, the eighth connecting surface portion 88 is smoothly connected to each of the seventh connecting surface portion 87 and the flank surface 73. In the first cross section CS1, the eighth connecting surface portion 88 is, for example, arc-shaped. In the first cross section CS1, the radius of curvature of the eighth connecting surface portion 88 is smaller than the radius of curvature of the sixth connecting surface portion 86. In the first cross section CS1, the eighth connecting surface portion 88 is convex outward from the outer peripheral surface 3.

[0122] Fig. 10 is a schematic vertical cross-sectional view taken along line X-X in Fig. 4. Fig. 10 shows a cross section that includes the first bisector 131 and is perpendicular to the first bearing surface 51. The cross section that includes the first bisector 131 and is perpendicular to the first bearing surface 51 is designated as the second cross section CS2. The second cross section CS2 is perpendicular to the first corner cutting edge 17. The second cross section CS2 is a cross section seen along the first cutting edge portion 13 in a direction from the second straight cutting edge 18 toward the first straight cutting edge 16. In Fig. 10, black dots indicate connection points between components.

[0123] 10 , in the second cross section CS2, a line that passes through the first corner cutting edge 17 and is perpendicular to the second bearing surface 61 is defined as a seventh imaginary line 117. The seventh imaginary line 117 passes through the second corner cutting edge 37 and is perpendicular to the first bearing surface 51. From another perspective, the seventh imaginary line 117 passes through both ends of the flank surface 73.

[0124] In the second cross section CS2, the relief surface 73 is recessed inward of the outer peripheral surface 3 with respect to the seventh imaginary line 117. The intermediate surface 89 is located, for example, in a direction perpendicular to the first direction 101 with respect to the seventh imaginary line 117 and toward the inside of the outer peripheral surface 3.

[0125] In the second cross section CS2, the first flank portion 76 is inclined inward of the outer peripheral surface 3 with respect to the seventh imaginary line 117, with the first corner cutting edge 17 as a fulcrum. This effectively prevents the flank 73 from excessively scraping against the workpiece (not shown) near the first cutting edge portion 13. This effectively prevents wear of the flank 73 due to contact between the flank 73 and the workpiece. In the second cross section CS2, the tangent to the flank 73 at the first corner cutting edge 17 is defined as a first tangent line 121. The first tangent line 121 is inclined counterclockwise around the first corner cutting edge 17 with respect to the seventh imaginary line 117.

[0126] The first tangent 121 has a first portion 161 and a second portion 162. The first portion 161 is in the first direction 101 relative to the first corner cutting edge 17. In the second cross section CS2, the first portion 161 is inclined inward of the outer peripheral surface 3 with respect to the seventh imaginary line 117, with the first corner cutting edge 17 as a fulcrum. This prevents excessive abrasion between the flank 73 and the workpiece near the first cutting edge portion 13. This prevents wear of the flank 73 due to contact between the flank 73 and the workpiece. The second portion 162 is in the second direction 102 relative to the first corner cutting edge 17. The second portion 162 is continuous with the first portion 161 at the first corner cutting edge 17.

[0127] In the second cross section CS2, the second flank portion 77 is inclined inward of the outer peripheral surface 3 with respect to the seventh imaginary line 117, with the second corner cutting edge 37 as a fulcrum. This effectively prevents excessive abrasion between the flank 73 and the workpiece near the second cutting edge portion 33. This effectively prevents wear of the flank 73 due to contact between the flank 73 and the workpiece. In the second cross section CS2, the tangent to the flank 73 at the second corner cutting edge 37 is a second tangent line 122. The second tangent line 122 is inclined clockwise around the second corner cutting edge 37 with respect to the seventh imaginary line 117.

[0128] The second tangent 122 has a third portion 163 and a fourth portion 164. The third portion 163 is in the second direction 102 relative to the second corner cutting edge 37. In the second cross section CS2, the third portion 163 is inclined inward of the outer peripheral surface 3 with respect to the seventh imaginary line 117, with the second corner cutting edge 37 as a fulcrum. This prevents excessive abrasion between the flank 73 and the workpiece near the second cutting edge portion 33. This prevents wear of the flank 73 due to contact between the flank 73 and the workpiece. The fourth portion 164 is in the first direction 101 relative to the second corner cutting edge 37. The fourth portion 164 is continuous with the third portion 163 at the second corner cutting edge 37.

[0129] Figure 11 is a schematic vertical cross-sectional view taken along line XI-XI in Figure 4. The cross-section shown in Figure 11 is perpendicular to the first straight cutting edge 16. The cross-section perpendicular to the first straight cutting edge 16 is designated as the third cross-section CS3. The third cross-section CS3 is a cross-section seen in the direction from the second straight cutting edge 18 toward the first straight cutting edge 16 along the first cutting edge portion 13. In Figure 11, black dots indicate connection points between components.

[0130] 11 , in the third cross section CS3, the flank 73 is recessed inward of the outer peripheral surface 3 with respect to a line (an eighth imaginary line 118) that passes through the first straight cutting edge 16 and is perpendicular to the second bearing surface 61. The eighth imaginary line 118 passes through the fourth straight cutting edge 38 and is perpendicular to the first bearing surface 51.

[0131] In the third cross section CS3, the first flank portion 76 is inclined inward of the outer peripheral surface 3 with respect to the eighth imaginary line 118, with the first straight cutting edge 16 as a fulcrum. In the third cross section CS3, a tangent to the flank 73 at the first straight cutting edge 16 (a third tangent line 123) is inclined counterclockwise around the first straight cutting edge 16 with respect to the eighth imaginary line 118.

[0132] The third tangent 123 has a fifth portion 165 and a sixth portion 166. The fifth portion 165 is in the first direction 101 relative to the first straight cutting edge 16. In the third cross section CS3, the fifth portion 165 is inclined toward the inside of the outer peripheral surface 3 with respect to the eighth imaginary line 118, with the first straight cutting edge 16 as a fulcrum. The sixth portion 166 is in the second direction 102 relative to the first straight cutting edge 16. The sixth portion 166 is continuous with the fifth portion 165 at the first straight cutting edge 16.

[0133] In the third cross section CS3, the second flank portion 77 is inclined inward of the outer peripheral surface 3 with respect to the eighth imaginary line 118, with the fourth straight cutting edge 38 as a fulcrum. In the third cross section CS3, the tangent line (fourth tangent line 124) of the flank 73 at the fourth straight cutting edge 38 is inclined clockwise around the fourth straight cutting edge 38 with respect to the eighth imaginary line 118.

[0134] The fourth tangent 124 has a seventh portion 167 and an eighth portion 168. The seventh portion 167 is in the second direction 102 relative to the fourth straight cutting edge 38. In the third cross section CS3, the seventh portion 167 is inclined toward the inside of the outer peripheral surface 3 with respect to the eighth imaginary line 118, with the fourth straight cutting edge 38 as a fulcrum. The eighth portion 168 is in the first direction 101 relative to the fourth straight cutting edge 38. The eighth portion 168 is continuous with the seventh portion 167 at the fourth straight cutting edge 38.

[0135] Figure 12 is a schematic vertical cross-sectional view taken along line XII-XII in Figure 4. The cross-section shown in Figure 12 is perpendicular to the second straight cutting edge 18. The cross-section perpendicular to the second straight cutting edge 18 is designated as a fourth cross-section CS4. The fourth cross-section CS4 is a cross-section seen in a direction from the second straight cutting edge 18 toward the first straight cutting edge 16 along the first cutting edge portion 13. In Figure 12, black dots indicate connection points between components.

[0136] 12 , in the fourth cross section CS4, the flank 73 is recessed inward of the outer peripheral surface 3 with respect to a line (a ninth imaginary line 119) that passes through the second straight cutting edge 18 and is perpendicular to the second bearing surface 61. The ninth imaginary line 119 passes through the third straight cutting edge 36 and is perpendicular to the first bearing surface 51.

[0137] In the fourth cross section CS4, the first flank portion 76 is inclined inward of the outer peripheral surface 3 with respect to the ninth imaginary line 119, with the second straight cutting edge 18 as a fulcrum. In the fourth cross section CS4, the tangent to the flank 73 at the second straight cutting edge 18 (fifth tangent line 125) is inclined counterclockwise around the second straight cutting edge 18 with respect to the ninth imaginary line 119.

[0138] The fifth tangent 125 has a ninth portion 169 and a tenth portion 170. The ninth portion 169 is in the first direction 101 relative to the second straight cutting edge 18. In the fourth cross section CS4, the ninth portion 169 is inclined toward the inside of the outer peripheral surface 3 with respect to the ninth imaginary line 119, with the second straight cutting edge 18 as a fulcrum. The tenth portion 170 is in the second direction 102 relative to the second straight cutting edge 18. The tenth portion 170 is continuous with the ninth portion 169 at the second straight cutting edge 18.

[0139] In the fourth cross section CS4, the second flank portion 77 is inclined inward of the outer peripheral surface 3 with respect to the ninth imaginary line 119, with the third straight cutting edge 36 as a fulcrum. In the fourth cross section CS4, the tangent to the flank 73 at the third straight cutting edge 36 (sixth tangent line 126) is inclined clockwise around the third straight cutting edge 36 with respect to the ninth imaginary line 119.

[0140] The sixth tangent 126 has an eleventh portion 171 and a twelfth portion 172. The eleventh portion 171 is in the second direction 102 relative to the third straight cutting edge 36. In the fourth cross section CS4, the eleventh portion 171 is inclined inward of the outer peripheral surface 3 with respect to the ninth imaginary line 119, with the third straight cutting edge 36 as a fulcrum. The twelfth portion 172 is in the first direction 101 relative to the third straight cutting edge 36. The twelfth portion 172 is continuous with the eleventh portion 171 at the third straight cutting edge 36.

[0141] 10 to 12 , each of the second cross section CS2, the third cross section CS3, and the fourth cross section CS4 is a cross section perpendicular to the first cutting edge portion 13. Hereinafter, the second cross section CS2, the third cross section CS3, and the fourth cross section CS4 will also be referred to as a cross section perpendicular to the first cutting edge portion 13.

[0142] In a cross section perpendicular to the first cutting edge portion 13, the flank 73 is recessed toward the inside of the outer peripheral surface 3. In a cross section perpendicular to the first cutting edge portion 13, the first flank portion 76 is linear. In a cross section perpendicular to the first cutting edge portion 13, the second flank portion 77 is linear.

[0143] In a cross section perpendicular to the first cutting edge portion 13, the first intermediate surface portion 78 has, for example, an arc shape. The first intermediate surface portion 78 is smoothly connected to, for example, the first flank surface portion 76. In a cross section perpendicular to the first cutting edge portion 13, the second intermediate surface portion 79 has, for example, an arc shape. The second intermediate surface portion 79 is smoothly connected to, for example, the second flank surface portion 77. In a cross section perpendicular to the first cutting edge portion 13, the third intermediate surface portion 80 has, for example, a linear shape. The third intermediate surface portion 80 is smoothly connected to each of the first intermediate surface portion 78 and the second intermediate surface portion 79.

[0144] In a cross section perpendicular to the first cutting edge portion 13, the first rake face 52 is inclined in a first direction 101 relative to the first bearing surface 51, with the first cutting edge portion 13 as a fulcrum. In a cross section perpendicular to the first cutting edge portion 13, the second rake face 62 is inclined in a second direction 102 relative to the second bearing surface 61, with the second cutting edge portion 33 as a fulcrum.

[0145] Next, the effects of the cutting insert 100 according to this embodiment will be described. Fig. 13 is a schematic diagram showing a state in which a workpiece is being turned using a cutting insert whose cutting edge is parallel to the seating surface. Fig. 13 shows a cutting insert whose cutting edge 201 is parallel to the seating surface. From another perspective, the cutting edge 201 is parallel to the contour line 202 of the seating surface.

[0146] 13 , when cutting a workpiece 209, the cutting insert is attached to a holder 210. Specifically, for example, the cutting insert is positioned so that a side surface 205 of the cutting insert is inclined in a direction away from the workpiece 209. In FIG. 13 , arrow B indicates the inclination direction of the side surface 205.

[0147] The workpiece 209 rotates along the arrow R. The cutting insert is moved along the feed direction F. The cutting edge 201 comes into contact with the workpiece 209, thereby turning the workpiece 209. In FIG. 13 , the arrow C indicates the direction of the main motion. Specifically, the direction of the arrow C is the direction of the relative motion between the cutting insert and the workpiece 209, excluding the component of the feed direction F.

[0148] Fig. 14 is a first schematic diagram showing the outline of the cutting insert as viewed along the direction of the main motion. A workpiece 209 and a holder 210 are not shown in Fig. 14. As shown in Fig. 14, when viewed along the direction of the main motion, a contour line 202 of the seating surface of the cutting insert is positioned in the inclination direction of the side surface 205 (arrow B) relative to the cutting edge 201.

[0149] 15 is a schematic diagram showing a state in which a workpiece is being turned using a cutting insert whose cutting edge is inclined with respect to the seating surface. As shown in FIG. 15, in some cutting inserts, the cutting edge 201 is inclined with respect to the seating surface in order to improve the sharpness of the cutting edge 201. In this case, the distance between the cutting edge 201 and the contour line 202 becomes shorter with increasing distance from the tip of the cutting edge 201.

[0150] 16 is a second schematic diagram showing the outline of the cutting insert as viewed along the direction of the main motion. In FIG. 16, a virtual line 204 indicates the cutting edge 201 of the cutting insert, the cutting edge being parallel to the seating surface. From another perspective, the virtual line 204 corresponds to the cutting edge 201 in FIG. 14.

[0151] 16, when the cutting edge 201 is inclined relative to the seating surface, the position of the cutting edge as viewed in the direction of the primary motion is different from when the cutting edge 201 is parallel to the seating surface (see FIG. 14). Specifically, when the cutting edge 201 is inclined relative to the seating surface, the angle formed by the two straight portions of the cutting edge 201 (cutting edge angle θ9) is smaller than when the cutting edge 201 is parallel to the seating surface.

[0152] For this reason, the shape of the machined surface of the cut workpiece may differ between when the cutting edge 201 is parallel to the seating surface and when the cutting edge 201 is inclined relative to the seating surface. Therefore, when using a cutting insert in which the cutting edge 201 is inclined relative to the seating surface, the shape of the machined surface may be adjusted by changing the holder 210 or the machining program. In this case, an existing holder or an existing machining program that is used when using a cutting insert in which the cutting edge 201 is parallel to the seating surface cannot be used.

[0153] According to the cutting insert 100 of this embodiment, the first cutting edge portion 13 is inclined in a direction (first direction 101) from the first seating surface 51 toward the second seating surface 61 with respect to a plane parallel to the second seating surface 61. When viewed perpendicularly to the first seating surface 51, the angle formed between the first straight cutting edge 16 and the second straight cutting edge 18 is larger than the angle formed between the first supported portion 11 and the second supported portion 15.

[0154] Therefore, when the cutting insert 100 is attached to the holder, the angle (cutting edge angle θ9) between the first straight cutting edge 16 and the second straight cutting edge 18 as viewed in the direction of the main motion during cutting can be prevented from becoming excessively small. As a result, when comparing a cutting insert in which the cutting edge 201 is parallel to the seating surface with the cutting insert 100 according to this embodiment, the difference in the shape of the cutting edge as viewed in the direction of the main motion can be reduced. Therefore, even if the cutting insert used for cutting is changed from a cutting insert in which the cutting edge is parallel to the seating surface to a cutting insert in which the cutting edge is inclined with respect to the seating surface, an existing holder and an existing machining program can be used.

[0155] According to the cutting insert 100 of this embodiment, the first cutting edge portion 13 is inclined in the first direction 101 with respect to a plane parallel to the second seating surface 61, thereby improving the sharpness of the first cutting edge portion 13.

[0156] (Modifications) Fig. 18 is a schematic vertical cross-sectional view showing a first modification of the cutting insert 100 according to this embodiment. The cross section shown in Fig. 18 corresponds to the cross section shown in Fig. 10. As shown in Fig. 18, in the cross section perpendicular to the first cutting edge portion 13, the intermediate surface 89 may be curved. In the cross section perpendicular to the first cutting edge portion 13, the intermediate surface 89 may be arc-shaped.

[0157] Fig. 19 is a schematic vertical cross-sectional view showing a second modified example of the cutting insert 100 according to this embodiment. The cross-section shown in Fig. 19 corresponds to the cross-section shown in Fig. 10 . As shown in Fig. 19 , in the cross-section perpendicular to the first cutting edge portion 13, a part of the intermediate surface 89 may be convex outward from the outer circumferential surface 3. In the cross-section perpendicular to the first cutting edge portion 13, the third intermediate surface portion 80 may overlap with the seventh imaginary line 117.

[0158] In a cross section perpendicular to the first cutting edge portion 13, the first intermediate surface portion 78 may be inclined outward from the outer peripheral surface 3 relative to the first flank surface portion 76. In a cross section perpendicular to the first cutting edge portion 13, the second intermediate surface portion 79 may be inclined outward from the outer peripheral surface 3 relative to the second flank surface portion 77.

[0159] The above describes a configuration in which the cutting insert 100 has two first cutting edge portions 13 and two second cutting edge portions 33. From another perspective, the above describes a configuration in which the number of cutting edges of the cutting insert 100 is four. However, the configuration of the cutting insert 100 according to the present disclosure is not limited to the above configuration.

[0160] Specifically, the cutting insert 100 may not have the second cutting edge portion 33. From another perspective, the number of cutting edges of the cutting insert 100 may be two. The second surface 2 may be planar. In a plan view, the shape of the cutting insert 100 may be, for example, three-fold symmetric with respect to the central axis O. From another perspective, the number of cutting edges of the cutting insert 100 may be three or six.

[0161] The embodiments disclosed herein are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined by the claims, not by the above description, and is intended to include meanings equivalent to the claims and all modifications within the scope thereof.

[0162] 1 First surface, 2 Second surface, 3 Outer peripheral surface, 4 First ridge portion, 5 Second ridge portion, 6 Third ridge portion, 7 Fourth ridge portion, 8 Through hole, 9 Inner peripheral surface, 10 First ridge, 11 First supported portion, 12 First connecting portion, 13 First cutting edge portion, 14 Second connecting portion, 15 Second supported portion, 16 First straight cutting edge, 17 First corner cutting edge, 18 Second straight cutting edge, 19 First corner portion, 21 First curved portion, 22 Second curved portion, 23 First straight portion, 24 Third curved portion, 25 Fourth curved portion, 26 Fifth curved portion, 27 Second straight portion, 28 Sixth curved portion, 29 Second corner portion, 30 Second ridge, 31 Third supported portion, 32 Third connecting portion, 33 Second cutting edge portion, 34 Fourth connecting portion, 35 Fourth supported portion, 36 Third straight cutting edge, 37 Second corner cutting edge, 38 Fourth straight cutting edge, 39 Third corner portion, 41 Seventh curved portion, 42 Eighth curved portion, 43 Third straight portion, 44 Ninth curved portion, 45 Tenth curved portion, 46 Eleventh curved portion, 47 Fourth straight portion, 48 Twelfth curved portion, 49 Fourth corner portion, 51 First bearing surface, 52 First rake face, 60 First line, 61 Second bearing surface, 62 Second rake face, 70 Second line, 71 First supported surface, 72 First connecting surface, 73 Relief surface, 74 Second connecting surface, 75 Second supported surface, 76 First relief surface portion, 77 Second relief surface portion, 78 First intermediate surface portion, 79 Second intermediate surface portion, 80 Third intermediate surface portion, 81 First connecting surface portion, 82 Second connecting surface portion, 83 Third connecting surface portion, 84 Fourth connection surface portion, 85 Fifth connection surface portion, 86 Sixth connection surface portion, 87 Seventh connection surface portion, 88 Eighth connection surface portion, 89 Intermediate surface, 91 First connection point, 92 Second connection point, 93 Third connection point, 94 Fourth connection point, 95 Fifth connection point, 96 Sixth connection point, 97 Seventh connection point, 98 Eighth connection point, 99 Virtual plane, 100 Cutting insert, 101 First direction, 102 Second direction, 111 First virtual line, 112 Second virtual line, 113 Third virtual line, 114 Fourth virtual line, 115 Fifth virtual line, 116 Sixth virtual line, 117 Seventh virtual line, 118 Eighth virtual line, 119 Ninth virtual line, 121 First tangent, 122 Second tangent, 123 Third tangent, 124 Fourth tangent, 125 Fifth tangent, 126 Sixth tangent, 131 First bisector, 132 Second bisector, 141 First vertex, 142 Second vertex, 151 First intersection, 152 Second intersection, 153 Third intersection,154 4th intersection, 161 1st section, 162 2nd section, 163 3rd section, 164 4th section, 165 5th section, 166 6th section, 167 7th section, 168 8th section, 169 9th section, 170 10th section, 171 11th section, 172 12th section, 201 Cutting edge, 202 Outline, 204 Imaginary line, 205 Side, 209 Workpiece, 210 Hollow, 211 1st support surface, 212 2nd support surface, 213 Escape groove surface, CS1 1st section, CS2 2nd section, CS3 3rd section, CS4 4th section, D1 1st distance, D2 2nd distance, D3 3rd distance, D4 ​​4th distance, F Feed direction, O Center axis, θ1: 1st angle, θ2: 2nd angle, θ3: 3rd angle, θ4: 4th angle, θ5: 5th angle, θ6: 6th angle, θ9: Cutting edge angle.

Claims

1. A tool comprising: a first surface including a first seating surface; a second surface including a second seating surface opposite the first seating surface; and an outer peripheral surface connected to each of the first surface and the second surface, wherein the ridge line between the first surface and the outer peripheral surface forms a first ridge line, and the first ridge line includes: a first supported portion; a first connecting portion connected to the first supported portion; a first cutting edge portion connected to the first connecting portion and located on the opposite side of the first supported portion with respect to the first connecting portion; a second connecting portion connected to the first cutting edge portion and located on the opposite side of the first connecting portion with respect to the first cutting edge portion; and a second supported portion connected to the second connecting portion and located on the opposite side of the first cutting edge portion with respect to the second connecting portion, wherein the first cutting edge portion is inclined in a direction from the first seating surface toward the second seating surface with respect to a plane parallel to the second seating surface, a cutting insert, wherein, when a connection point between the first connection portion and the first cutting edge portion is defined as a first connection point and a connection point between the first connection portion and the first supported portion is defined as a second connection point, a distance between the first connection point and the second seating surface in a direction from the first seating surface to the second seating surface is shorter than a distance between the second connection point and the second seating surface, the first cutting edge portion has: a first straight cutting edge continuing to the first connection portion; a corner cutting edge continuing to the first straight cutting edge and located on the opposite side of the first connection portion from the first straight cutting edge; and a second straight cutting edge continuing to each of the corner cutting edge and the second connection portion, when viewed perpendicularly to the first seating surface, each of the first straight cutting edge, the second straight cutting edge, the first supported portion, and the second supported portion is linear, and an angle formed between the first straight cutting edge and the second straight cutting edge is greater than an angle formed between the first supported portion and the second supported portion.

2. A cutting insert as described in claim 1, wherein the outer peripheral surface has a flank surface continuing to the first cutting edge portion, a connecting surface continuing to each of the flank surface and the first connecting portion, and a supported surface continuing to each of the connecting surface and the first supported portion, and in a cross section parallel to the first seating surface and intersecting with the connecting surface, the connecting surface is recessed toward the inside of the outer peripheral surface with respect to the supported surface.

3. A cutting insert as described in claim 2, wherein the ridge line between the second surface and the outer peripheral surface forms a second ridge line, the second ridge line has a second cutting edge portion continuing to the flank surface, and the first cutting edge portion and the second cutting edge portion are symmetrical with respect to an imaginary plane positioned at an equal distance from each of the first and second seating surfaces.

4. A cutting insert as described in claim 1, wherein the outer peripheral surface has a flank surface continuing to the first cutting edge portion, the ridge line between the second surface and the outer peripheral surface forms a second ridge line, the second ridge line has a second cutting edge portion continuing to the flank surface, and the first cutting edge portion and the second cutting edge portion are symmetrical with respect to an imaginary plane positioned at an equal distance from each of the first and second seating surfaces.

5. A cutting insert as described in claim 3 or claim 4, wherein in a cross section perpendicular to the first seating surface and including a bisector of the angle between the first straight cutting edge and the second straight cutting edge, when viewed perpendicular to the first seating surface, if a tangent to the flank of the first cutting edge portion is defined as a first tangent, a portion of the first tangent to the first cutting edge portion in a direction from the first seating surface toward the second seating surface is inclined inwardly to the outer peripheral surface with the first cutting edge portion as a fulcrum with respect to a straight line passing through the first cutting edge portion and perpendicular to the second seating surface, and if a tangent to the flank of the second cutting edge portion is defined as a second tangent, a portion of the second tangent to the second cutting edge portion in a direction from the second seating surface toward the first seating surface is inclined inwardly to the outer peripheral surface with the second cutting edge portion as a fulcrum with respect to a straight line passing through the second cutting edge portion and perpendicular to the first seating surface.

6. A cutting insert according to any one of claims 3 to 5, wherein the flank has: a first flank portion continuous with the first cutting edge portion; a second flank portion continuous with the second cutting edge portion; and an intermediate surface continuous with each of the first flank portion and the second flank portion and located between the first flank portion and the second flank portion; and in a cross section perpendicular to the first cutting edge portion, the first flank portion is inclined inwardly of the outer peripheral surface with respect to a straight line passing through the first cutting edge portion and perpendicular to the second seating surface, with the first cutting edge portion as a fulcrum; and the second flank portion is inclined inwardly of the outer peripheral surface with respect to a straight line passing through the second cutting edge portion and perpendicular to the first seating surface, with the second cutting edge portion as a fulcrum.

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