Cutting insert, cutting tool, and method of manufacturing machined product

1. A cutting insert, comprising:

an upper surface comprising:

a first side part;

a second side part; and

a corner part located between the first side part and the second side part;

a lower surface located on a side of the cutting insert opposite to the upper surface;

a side surface located between the upper surface and the lower surface; and

a cutting edge located at an intersection of the upper surface and the side surface, wherein

the upper surface further comprises a first surface configured as a land surface bordering the cutting edge, a second surface configured as a rake surface which is located further inward than and bordering the first surface and only inclined toward the lower surface as going farther from the first surface, and a third surface which is located further inward than and bordering the second surface;

the first surface extending from the cutting edge to the second surface;

the second surface extending from the first surface to the third surface;

the cutting edge comprises a first cutting edge located at the corner part and a second cutting edge located at the first side part;

the first surface comprises a first region bordering the first cutting edge, a second region adjacent to the first region and bordering the cutting edge, and a third region which is adjacent to the second region and bordering the second cutting edge;

a width of the first region in a direction perpendicular to the cutting edge in the first region, a width of the second region in a direction perpendicular to the cutting edge in the second region, and a width of the third region in a direction perpendicular to the cutting edge in the third region define corresponding widths of the first surface from the cutting edge to the second surface;

the width of the second region is less than each of the width of the first region and the width of the third region;

the second surface comprises a fourth region located further inward than and bordering the first region, a fifth region located further inward than and bordering the second region, and a sixth region located further inward than and bordering the third region;

a width of the fourth region in a direction perpendicular to the cutting edge in the fourth region, a width of the fifth region in a direction perpendicular to the cutting edge in the fifth region, and a width of the sixth region in a direction perpendicular to the cutting edge in the sixth region define corresponding widths of the second surface from the first surface to the third surface;

the width of the fifth region in the direction perpendicular to the cutting edge in the fifth region is greater than each of the width of the fourth region in the direction perpendicular to the cutting edge in the fourth region and the width of the sixth region in the direction perpendicular to the cutting edge in the sixth region;

a maximum inclination angle of the fourth region and a maximum inclination angle of the sixth region have a greater inclination angle than a maximum inclination angle of the fifth region;

the first surface is inclined toward the lower surface as going farther from the cutting edge;

every inclination angle of the first surface is less than every inclination angle of the second surface; and

every inclination angle of the third surface is less than every inclination angle of the second surface.

2. The cutting insert according to claim 1 , wherein the second region comprises:

a first portion which is adjacent to the first region and borders the first cutting edge, and

a second portion which is adjacent to the third region and borders the second cutting edge.

3. The cutting insert according to claim 2 , wherein

a width of the first portion in a direction perpendicular to the cutting edge in the first portion decreases as going farther from the first region, and

a width of the second portion in a direction perpendicular to the cutting edge in the second portion decreases as going farther from the third region.

4. The cutting insert according to claim 3 , wherein

a decrement of the width of the first portion is greater than a decrement of the width of the second portion.

5. The cutting insert according to claim 1 , wherein

the width of the third region in the direction perpendicular to the cutting edge in the third region is greater than the width of the first region in the direction perpendicular to the cutting edge in the first region.

6. The cutting insert according to claim 1 , wherein

the maximum inclination angle of the sixth region is equal to the maximum inclination angle of the fourth region.

7. The cutting insert according to claim 1 , wherein

an inclination angle of the second region is less than an inclination angle of the first region and greater than an inclination angle of the third region.

8. The cutting insert according to claim 7 , wherein

an inclination angle of the first surface decreases as going farther from the corner part, from the first region to the third region.

9. The cutting insert according to claim 7 , wherein

a decrement of the inclination angle in the second region is lower than a decrement of the inclination angle in the first region, and is higher than a decrement of the inclination angle in the third region.

10. The cutting insert according to claim 1 , wherein

a length of the second region along the cutting edge is greater than a length of the first region along the cutting edge and is smaller than a length of the third region along the cutting edge.

11. A cutting tool, comprising:

the cutting insert according to claim 1 ; and

a holder designed to attach the cutting insert to the holder.

12. A method of manufacturing a machined product, comprising:

rotating a workpiece;

bringing the cutting tool according to claim 11 into contact with the workpiece being rotated; and

moving the cutting tool away from the workpiece.

13. The cutting insert according to claim 1 , wherein

the fifth region has a single inclination angle throughout an entirety of the fifth region equal to the maximum inclination angle of the fifth region.