Cutting insert, cutting tool, and method for manufacturing cut workpiece
The cutting insert's unique land surface configuration addresses chatter vibrations and limited engagement angles by minimizing contact and improving chip discharge, resulting in enhanced durability and flexibility in cutting processes.
Patent Information
- Application Number
- PCT/JP2025/005293
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-03-22
- Filing Date
- 2025-02-18
- Publication Date
- 2025-09-25
AI Technical Summary
Existing cutting inserts with planar land surfaces experience large chatter vibrations and limited engagement angles, reducing the degree of freedom in cutting processes.
The cutting insert design features a first land surface with a convex curve, a second land surface with a convex curve, and a third land surface with a concave curve, each with specific radii of curvature, reducing contact with the workpiece and enhancing chip discharge, thereby minimizing chatter vibrations and increasing the degree of freedom in cutting.
The innovative design reduces chatter vibrations, improves cutting edge durability, and enhances chip discharge, allowing for more flexible cutting angles and improved machining accuracy.
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Figure JP2025005293_25092025_PF_FP_ABST
Abstract
Description
Cutting insert, cutting tool, and method for manufacturing machined product
[0001] The present disclosure relates to cutting inserts, cutting tools, and methods for manufacturing machined workpieces.
[0002] The cutting tool and the manufacturing method of the cutting workpiece are applied to cutting of a workpiece. The cutting may include, for example, turning and milling. The milling may include, for example, shoulder milling and face milling.
[0003] Examples of cutting inserts for cutting tools used when cutting a workpiece include cutting inserts (chips) described in Patent Documents 1 and 2. The cutting inserts described in Patent Documents 1 and 2 have a land surface located along the cutting edge. The land surface described in Patent Document 1 has a planar configuration that points upward as it moves away from the cutting edge. The land surface described in Patent Document 2 has a planar configuration that points downward as it moves away from the cutting edge.
[0004] Japanese Patent Publication No. 2011-110635 and Japanese Patent Publication No. 2-095508
[0005] In one non-limiting aspect of the present disclosure, a cutting insert has an upper surface, a lower surface, a side surface connected to the upper surface and the lower surface, and a cutting edge located at an intersection of the upper surface and the side surface. The upper surface has a land surface located along the cutting edge and a rake surface connected to the land surface and approaching the lower surface as it moves away from the land surface. The land surface, in a cross section perpendicular to the cutting edge, has a first land surface having a convex curve shape connected to the side surface, a second land surface having a convex curve shape connected to the first land surface and approaching the lower surface as it moves away from the first land surface, and a third land surface having a concave curve shape connected to the second land surface and approaching the lower surface as it moves away from the first land surface. In the cross section, the radius of curvature of the first land surface is smaller than the radius of curvature of the second land surface.
[0006] 11. A plan view showing a schematic configuration of a cutting insert according to embodiment 1 of the present disclosure. A first side view showing a schematic configuration of a cutting insert according to embodiment 1 of the present disclosure. A second side view showing a schematic configuration of a cutting insert according to embodiment 1 of the present disclosure. A perspective view showing a schematic configuration of a cutting insert according to embodiment 1 of the present disclosure. A V-V sectional view of FIG. 1. An enlarged view of region VI shown in FIG. 5. A diagram geometrically explaining a first land surface. A diagram geometrically explaining a second land surface. A diagram geometrically explaining a third land surface. A X-X sectional view of FIG. 1. A front view showing a schematic configuration of a cutting tool according to embodiment 2 of the present disclosure. A perspective view showing a schematic configuration of a cutting tool according to embodiment 2 of the present disclosure. A diagram viewed from the tip side showing a schematic configuration of a cutting tool according to embodiment 2 of the present disclosure. An enlarged view of range XIV of FIG. 11. A perspective view showing step D1 in a method of manufacturing a machined product according to embodiment 3 of the present disclosure. A perspective view showing step D2 in a method of manufacturing a machined product according to embodiment 3 of the present disclosure. A perspective view showing step D3 in a method of manufacturing a machined product according to embodiment 3 of the present disclosure.
[0007] The land surfaces described in Patent Documents 1 and 2 are both planar and are represented by straight lines in a cross-sectional view. Therefore, when performing cutting using cutting inserts having these land surfaces, depending on the engagement angle, the land surface may come into full contact with the workpiece. In this case, a large cutting load is momentarily applied to the cutting insert, which may cause large chatter vibrations. In other words, to avoid large chatter vibrations, it is necessary to limit the engagement angle, which may reduce the degree of freedom in cutting.
[0008] The cutting insert in the above embodiment is likely to avoid the occurrence of large chatter vibrations while ensuring the degree of freedom in cutting processing.
[0009] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The following describes an embodiment of the present disclosure. For convenience of explanation, the same reference numerals are used to designate components having the same functions as those previously described, and the description thereof may not be repeated.
[0010] [Embodiment 1] Fig. 1 is a plan view showing a schematic configuration of a cutting insert 101 according to embodiment 1 of the present disclosure. Fig. 2 is a first side view showing a schematic configuration of the cutting insert 101 according to embodiment 1 of the present disclosure. Fig. 3 is a second side view showing a schematic configuration of the cutting insert 101 according to embodiment 1 of the present disclosure. Fig. 4 is a perspective view showing a schematic configuration of the cutting insert 101 according to embodiment 1 of the present disclosure. Fig. 2 shows a side view along the short direction of the cutting insert 101, and Fig. 3 shows a side view along the long direction of the cutting insert 101.
[0011] The cutting insert 101 may have an upper surface 1, a lower surface 2, a side surface 3, and a cutting edge 4. The side surface 3 may be connected to the upper surface 1 and the lower surface 2. The cutting edge 4 may be located at the intersection of the upper surface 1 and the side surface 3.
[0012] The upper surface 1 may have a land surface 5 and a rake surface 6. The land surface 5 may be located along the cutting edge 4. The rake surface 6 may be connected to the land surface 5. The rake surface 6 may approach the lower surface 2 as it moves away from the land surface 5. In this application, the term "along" does not necessarily mean that the two members extend parallel to each other, but may also mean that the two members extend at an angle of 5° or less to each other.
[0013] The land surface 5 may have a first land surface 7 , a second land surface 8 , and a third land surface 9 in a cross section perpendicular to the cutting edge 4 .
[0014] Fig. 5 is a cross-sectional view taken along line V-V in Fig. 1. Fig. 6 is an enlarged view of region VI shown in Fig. 5. Fig. 7 is a diagram geometrically explaining the first land surface 7. Fig. 8 is a diagram geometrically explaining the second land surface 8. Fig. 9 is a diagram geometrically explaining the third land surface 9. Fig. 10 is a cross-sectional view taken along line X-X in Fig. 1. The cross section perpendicular to the cutting edge 4 may be any one of the V-V cross section and the X-X cross section in Fig. 1.
[0015] The first land surface 7 may be connected to the side surface 3. The first land surface 7 may be convexly curved. The second land surface 8 may be connected to the first land surface 7. The second land surface 8 may approach the lower surface 2 as it moves away from the first land surface 7. The second land surface 8 may be convexly curved. The third land surface 9 may be connected to the second land surface 8. The third land surface 9 may approach the lower surface 2 as it moves away from the first land surface 7. The third land surface 9 may be concavely curved.
[0016] In a cross section perpendicular to the cutting edge 4 , the radius of curvature R7 of the first land surface 7 may be smaller than the radius of curvature R8 of the second land surface 8 .
[0017] In the above cross section, because the second land surface 8 is a convex curve, the second land surface 8 is less likely to come into contact with the workpiece, and the heat generated by contact with the workpiece can be reduced. As a result, restrictions on the engagement angle with the workpiece can be reduced, increasing the degree of freedom in cutting processing. Also, in the above cross section, the thickness of the cutting insert 101 near the cutting edge 4 can be increased compared to when the second land surface 8 is straight. This improves the durability of the cutting edge 4. Furthermore, because the second land surface 8 has a relatively large radius of curvature and a gentle convex curve, the durability of the land surface 5 as a whole can be improved.
[0018] In addition, in the above cross section, the first land surface 7 has a convex curve, which improves the durability of the cutting edge 4. Furthermore, the first land surface 7 has a relatively small radius of curvature and a sharp convex curve, which improves the sharpness of the cutting edge 4. This makes it easier to avoid the occurrence of large chatter vibrations.
[0019] Furthermore, because the third land surface 9 has a concave curve in the cross section, chips generated by the cutting edge 4 are easily released when they flow toward the rake face 6. Specifically, the third land surface 9, which has a concave curve, allows chips to curl appropriately while suppressing welding, making it difficult for chips to contact the rake face 6. This reduces chip clogging and improves chip discharge. Furthermore, when the land surface 5 has the third land surface 9 that has a concave curve in the cross section, it is easy to avoid the chips from coming into strong contact with the rake face 6 when they flow toward the rake face 6, and wear on the rake face 6 is less likely to progress. This also reduces restrictions on the engagement angle with the workpiece, thereby increasing the degree of freedom in cutting.
[0020] From the above viewpoint, the cutting insert 101 can easily avoid the occurrence of large chatter vibrations while ensuring the degree of freedom in cutting processing.
[0021] In a cross section perpendicular to the cutting edge 4, the radius of curvature R9 of the third land surface 9 may be larger than the radius of curvature R7 of the first land surface 7. In this case, the thickness of the cutting insert 101 in the vicinity of the cutting edge 4 can be increased, thereby improving the durability of the cutting edge 4. In addition, since the third land surface 9 is configured to be gently curved, chips are less likely to clog the third land surface 9.
[0022] In a cross section perpendicular to the cutting edge 4, the radius of curvature R9 of the third land surface 9 may be larger than the radius of curvature R8 of the second land surface 8. In this case, the thickness of the cutting insert 101 in the vicinity of the cutting edge 4 can be further increased. Therefore, the durability of the cutting edge 4 is further improved.
[0023] At least a portion of the first land surface 7 may be located above the second land surface 8. This allows the first land surface 7, whose cross section perpendicular to the cutting edge 4 is a sharp convex curve, to more easily bite into the workpiece, thereby improving sharpness. As shown in FIG. 6 , in this embodiment, the upper end 5 a of the land surface 5 is located on the first land surface 7. Therefore, at least a portion of the first land surface 7, including the upper end 5 a, is located above the second land surface 8. Furthermore, because the upper end 5 a of the land surface 5 is located on the first land surface 7, the first land surface 7 of the land surface 5 more easily bites into the workpiece. The first land surface 7, which has a relatively small radius of curvature, more easily bites into the workpiece, thereby improving sharpness of the cutting edge 4.
[0024] The second land surface 8 may be inclined downward as it moves away from the first land surface 7. This makes it less likely that the second land surface 8 will come into full contact with the workpiece, thereby reducing cutting resistance.
[0025] An imaginary line passing through the center 10 of the upper surface 1 and the center 11 of the lower surface 2 is the central axis 12, an imaginary plane perpendicular to the central axis 12 is the reference plane 13, and the length of the land surface 5 in a direction parallel to the reference plane 13 in a cross section perpendicular to the cutting edge 4 is the width. In this case, the width W8 of the second land surface 8 may be larger than the width W7 of the first land surface 7. This can increase the strength of the cutting edge 4.
[0026] The width W9 of the third land surface 9 may be larger than the width W8 of the second land surface 8. When the width W9 of the third land surface 9, whose cross section perpendicular to the cutting edge 4 is a concave curved surface, is relatively large, the cutting insert 101 can be made smaller while facilitating the flow of chips toward the rake face 6.
[0027] In a cross section perpendicular to the cutting edge 4, the rake face 6 may be linear with an inclination angle greater than that of a tangent to the land surface 5 at the boundary between the first land surface 7 and the second land surface 8. This improves chip discharge performance. Here, as shown in Figures 5 and 10, the inclination angle of the rake face 6 with respect to the reference plane 13 may be θ.
[0028] In the example shown in FIG. 1 , the top surface 1 is polygonal, specifically rectangular. The outer edge of the rectangular top surface 1 has four corners and four sides. Of the four corners, two (the lower right corner and the upper left corner in FIG. 1 ) are positioned relatively higher, and the remaining two (the lower left corner and the upper right corner in FIG. 1 ) are positioned relatively lower. The two corners positioned relatively higher are usually called major corners. This is because the major corners are the parts of the outer edge of the top surface 1 that bite into the workpiece and play a major role in cutting the workpiece. For convenience, the lower right corner in FIG. 1 , which is one of the major corners, will be referred to as major corner 1a, and the corner located at the upper right in FIG. 1 and adjacent to major corner 1a will be referred to as minor corner 1b.
[0029] In the example shown in FIG. 1 , the heights of the four corners are different, so each of the four sides is inclined in side view. For example, in FIG. 1 , the side extending from the major corner 1a toward the minor corner 1b is inclined in side view so as to approach the lower surface 2 as it moves from the major corner 1a toward the minor corner 1b. As shown in FIG. 1 , the X-X cross section is a cross section of a region farther from the major corner 1a than the V-V cross section. Therefore, the height of the cutting edge 4 shown in the X-X cross section is lower than the height of the cutting edge 4 shown in the V-V cross section. When the cutting edge 4 is inclined in this way, the cutting edge 4 is less likely to come into full contact with the workpiece, improving the durability of the cutting edge 4.
[0030] Here, the rake face 6 may have a region in which the inclination angle θ decreases with increasing distance from the main corner 1a. In the example shown in Figures 5 and 10, the inclination angle θ in the X-X cross section, which is a region relatively far from the main corner 1a, is smaller than the inclination angle θ in the V-V cross section, which is a region relatively close to the main corner 1a. When the rake face 6 has the above configuration, chip discharge performance is improved.
[0031] If the rake face 6 has a region where the inclination angle θ decreases with increasing distance from the main corner 1a, the rake face 6 will have a spiral shape in this region. This will make it easier for chips to curl spirally in the direction away from the main corner 1a. This will improve chip discharge performance as described above.
[0032] On the side extending from the major corner 1a to the minor corner 1b, the radius of curvature R7 of the first land surface 7, the radius of curvature R8 of the second land surface 8, and the radius of curvature R9 of the third land surface 9 may each be constant or may vary.
[0033] 5 and 10, the radius of curvature R7 of the first land surface 7 may be constant. In this case, the variation in sharpness of the cutting edge 4 located along the above-mentioned side can be minimized. Therefore, the occurrence of large chatter vibrations can be easily avoided.
[0034] 5 and 10, the radius of curvature R9 of the third land surface 9 in the X-X cross section, which is a region relatively far from the main corner 1a, may be larger than the radius of curvature R9 of the third land surface 9 in the V-V cross section, which is a region relatively close to the main corner 1a. In this case, chip discharge performance is improved.
[0035] Because the radius of curvature R9 of the third land surface 9 in the X-X cross section, which is a region relatively far from the main corner 1a, is relatively large, chips flowing through this region tend to be braked relatively strongly. On the other hand, because the radius of curvature R9 of the third land surface 9 in the V-V cross section, which is a region relatively close to the main corner 1a, is relatively small, chips flowing through this region tend not to be braked relatively strongly. Due to the difference in the braking of chips in these regions, chips tend to curl spirally in a direction away from the main corner 1a. This improves chip dischargeability as described above.
[0036] Examples of materials for the cutting insert 101 include cemented carbide and cermet.
[0037] Examples of cemented carbide compositions include WC-Co, WC-TiC-Co, and WC-TiC-TaC-Co. WC-Co may be produced by adding cobalt (Co) powder to tungsten carbide (WC) and sintering the mixture. WC-TiC-Co may be produced by adding titanium carbide (TiC) to WC-Co. WC-TiC-TaC-Co may be produced by adding tantalum carbide (TaC) to WC-TiC-Co.
[0038] The cermet may be a sintered composite material in which a ceramic component is combined with a metal. Specifically, the cermet may be a cermet containing a titanium compound as a main component. Examples of the cermet containing a titanium compound as a main component include titanium carbide (TiC) and titanium nitride (TiN).
[0039] The cutting insert 101 is not limited to the example configuration shown in Fig. 1. For example, when viewed from the top surface 1, it may have a configuration that is a mirror image of the cutting insert 101 shown in Fig. 1.
[0040] [Embodiment 2] Fig. 11 is a front view showing a schematic configuration of a cutting tool 201 according to embodiment 2 of the present disclosure. Fig. 12 is a perspective view showing a schematic configuration of the cutting tool 201 according to embodiment 2 of the present disclosure. Fig. 13 is a view showing a schematic configuration of the cutting tool 201 according to embodiment 2 of the present disclosure, as viewed from the tip 15 side. Fig. 14 is an enlarged view of range XIV in Fig. 11 .
[0041] The cutting tool 201 may have a holder 14 and a cutting insert 101. The holder 14 may have a pocket 17 extending from a leading end 15 toward a trailing end 16 and located on the side of the leading end 15. The cutting insert 101 may be located in the pocket 17.
[0042] The cutting tool 201 has a cutting insert 101 that ensures freedom of cutting processing while easily avoiding the occurrence of large chatter vibrations, so that the workpiece can be cut with excellent processing accuracy, and a machined product with a highly accurate processed surface can be manufactured.
[0043] The cutting tool 201 is not limited to the example configuration shown in Fig. 11. For example, when viewed from the rear end 16, the cutting tool 201 may have a configuration that is a mirror image of the cutting tool 201 shown in Fig. 11.
[0044] [Embodiment 3] Figure 15 is a perspective view showing step D1 in a method for manufacturing a machined product 401 according to embodiment 3 of the present disclosure. Figure 16 is a perspective view showing step D2 in a method for manufacturing a machined product 401 according to embodiment 3 of the present disclosure. Figure 17 is a perspective view showing step D3 in a method for manufacturing a machined product 401 according to embodiment 3 of the present disclosure. The method for manufacturing the machined product 401 may include steps D1 to D3.
[0045] Step D1 is a step of rotating the cutting tool 201. The cutting tool 201 may be rotated around a rotation axis A of the cutting tool 201. In the example shown in Fig. 15 , the rotation direction of the cutting tool 201 is clockwise as viewed from the rear end 16 side. When a cutting tool 201 having a configuration that is a mirror image of the example shown in Fig. 15 is used, the rotation direction of the cutting tool 201 may be counterclockwise as viewed from the rear end 16 side.
[0046] Step D2 is a step of bringing the cutting tool 201 into contact with the workpiece 301. At least one of the rotating cutting tool 201 and the workpiece 301 may be moved to bring the cutting tool 201 and the workpiece 301 relatively close to each other. The cutting edge 4 of the cutting insert 101 of the cutting tool 201 may be brought into contact with the workpiece 301 to cut the workpiece 301. Examples of materials for the workpiece 301 include carbon steel, alloy steel, stainless steel, cast iron, and non-ferrous metals.
[0047] Step D3 is a step of separating the cutting tool 201 from the workpiece 301. At least one of the cutting tool 201 and the workpiece 301 may be moved to separate the cutting tool 201 from the workpiece 301, thereby obtaining a machined product 401.
[0048] The manufacturing method of the machined product 401 uses a cutting tool 201 having a cutting insert 101 that is likely to avoid the occurrence of large chatter vibrations while ensuring the degree of freedom in cutting. Therefore, according to the manufacturing method of the machined product 401, the workpiece 301 can be cut with excellent machining accuracy, and the machined product 401 having a highly accurate machined surface can be obtained.
[0049] If cutting processing is to be continued after step D3, the cutting tool 201 is kept rotating and the process of contacting the cutting edge 4 of the cutting insert 101 of the cutting tool 201 with different locations on the workpiece 301 is repeated.
[0050] Although the manufacturing methods of the cutting insert 101, the cutting tool 201, and the machined product 401 have been exemplified above, this aspect is not limited to the above-described embodiments, and any method may be used as long as it does not deviate from the gist of this aspect.
[0051] [Summary] A cutting insert according to aspect 1 of the present disclosure has an upper surface, a lower surface, a side surface connected to the upper surface and the lower surface, and a cutting edge located at an intersection of the upper surface and the side surface, the upper surface has a land surface located along the cutting edge, and a cutting surface connected to the land surface and approaching the lower surface as it moves away from the land surface, the land surface has, in a cross section perpendicular to the cutting edge, a first land surface having a convex curved shape connected to the side surface, a second land surface having a convex curved shape connected to the first land surface and approaching the lower surface as it moves away from the first land surface, and a third land surface having a concave curved shape connected to the second land surface and approaching the lower surface as it moves away from the first land surface, and in the cross section, a radius of curvature of the first land surface is smaller than a radius of curvature of the second land surface.
[0052] In a cutting insert according to a second aspect of the present disclosure, in the first aspect, the radius of curvature of the third land surface is larger than the radius of curvature of the first land surface in the cross section.
[0053] In a cutting insert according to a third aspect of the present disclosure, in the second aspect, the radius of curvature of the third land surface is larger than the radius of curvature of the second land surface in the cross section.
[0054] A cutting insert according to a fourth aspect of the present disclosure is the cutting insert of any one of the first to third aspects, wherein at least a portion of the first land surface is located above the second land surface.
[0055] A cutting insert according to a fifth aspect of the present disclosure is the cutting insert of any one of the first to fourth aspects, wherein the second land surface slopes downward with increasing distance from the first land surface.
[0056] A cutting insert according to aspect 6 of the present disclosure is, in any one of aspects 1 to 5, such that an imaginary line passing through the center of the upper surface and the center of the lower surface is a central axis, an imaginary plane perpendicular to the central axis is a reference plane, the length of the land surface in a direction parallel to the reference plane in the cross section is a width, and the width of the second land surface is greater than the width of the first land surface.
[0057] A cutting insert according to a seventh aspect of the present disclosure is in accordance with the sixth aspect, wherein the width of the third land surface is greater than the width of the second land surface.
[0058] A cutting insert according to aspect 8 of the present disclosure is any one of aspects 1 to 7, wherein in the cross section, the cutting face is a straight line having a larger inclination angle than the tangent to the land surface at the boundary between the first land surface and the second land surface.
[0059] A cutting tool according to aspect 9 of the present disclosure is any of aspects 1 to 8, and includes a holder extending from the front end to the rear end and having a pocket located on the front end side, and the cutting insert located in the pocket.
[0060] A manufacturing method for a machined product according to aspect 10 of the present disclosure is similar to aspect 9, and includes the steps of rotating the cutting tool, bringing the cutting tool into contact with a workpiece, and moving the cutting tool away from the workpiece.
[0061] The invention according to the present disclosure has been described above based on the drawings and examples. However, the invention according to the present disclosure is not limited to the above-described embodiments. In other words, the invention according to the present disclosure can be modified in various ways within the scope of the present disclosure, and embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the invention according to the present disclosure. In other words, it should be noted that a person skilled in the art could easily make various modifications or corrections based on the present disclosure. It should also be noted that these modifications or corrections are included in the scope of the present disclosure.
[0062] REFERENCE SIGNS LIST 1 Upper surface 2 Lower surface 3 Side surface 4 Cutting edge 5 Land surface 6 Rake face 7 First land surface 8 Second land surface 9 Third land surface 10 Center of upper surface 11 Center of lower surface 12 Central axis 13 Reference surface 14 Holder 15 Tip 16 Rear end 17 Pocket 101 Cutting insert 201 Cutting tool 301 Workpiece 401 Machined product R7 Radius of curvature of first land surface R8 Radius of curvature of second land surface R9 Radius of curvature of third land surface W7 Width of first land surface W8 Width of second land surface W9 Width of third land surface
Claims
1. A cutting insert having an upper surface, a lower surface, a side surface connected to the upper surface and the lower surface, and a cutting edge located at the intersection of the upper surface and the side surface, wherein the upper surface has a land surface located along the cutting edge, and a cutting surface connected to the land surface and approaching the lower surface as it moves away from the land surface, wherein the land surface, in a cross section perpendicular to the cutting edge, has: a first land surface having a convex curve connected to the side surface; a second land surface having a convex curve connected to the first land surface and approaching the lower surface as it moves away from the first land surface; and a third land surface having a concave curve connected to the second land surface and approaching the lower surface as it moves away from the first land surface, wherein in the cross section, the radius of curvature of the first land surface is smaller than the radius of curvature of the second land surface.
2. The cutting insert according to claim 1, wherein, in the cross section, the radius of curvature of the third land surface is larger than the radius of curvature of the first land surface.
3. The cutting insert according to claim 2, wherein the radius of curvature of the third land surface is larger than the radius of curvature of the second land surface in the cross section.
4. The cutting insert according to any one of claims 1 to 3, wherein at least a portion of the first land surface is located above the second land surface.
5. A cutting insert according to any one of claims 1 to 4, wherein the second land surface slopes downward as it moves away from the first land surface.
6. A cutting insert according to any one of claims 1 to 5, wherein an imaginary line passing through the center of the upper surface and the center of the lower surface is a central axis, an imaginary plane perpendicular to the central axis is a reference plane, the length of the land surface in a direction parallel to the reference plane in the cross section is a width, and the width of the second land surface is greater than the width of the first land surface.
7. The cutting insert according to claim 6, wherein the width of the third land surface is greater than the width of the second land surface.
8. A cutting insert according to any one of claims 1 to 7, wherein in the cross section, the cutting surface is a straight line having an inclination angle greater than that of a tangent to the land surface at the boundary between the first land surface and the second land surface.
9. A cutting tool comprising: a holder extending from a front end to a rear end and having a pocket located on the front end side; and a cutting insert according to any one of claims 1 to 8 located in the pocket.
10. A method for manufacturing a machined product, comprising the steps of: rotating the cutting tool according to claim 9; bringing the cutting tool into contact with a workpiece; and separating the cutting tool from the workpiece.
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