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

1. A cutting insert, comprising:

an upper surface;

a lower surface located on a side opposite to the upper surface;

a front lateral surface located between the upper surface and the lower surface; and

a rear lateral surface located between the upper surface and the lower surface and located on a side opposite to the front lateral surface,

the upper surface comprising

a first upper cutting edge located on an intersection with the front lateral surface, and

an upper constraining surface which is located closer to the rear lateral surface than the first upper cutting edge, and which is contactable with a holder,

the lower surface comprising a lower constraining surface contactable with the holder,

the lower constraining surface comprising a lower protrusion extended from a side of the front lateral surface toward the rear lateral surface,

the lower protrusion comprising

a first region located on a side opposite to the upper constraining surface,

a second region located closer to the front lateral surface than the first region, and

a third region located closer to the rear lateral surface than the first region, wherein

a wedge angle of the first region is a first angle, a wedge angle of the second region is a second angle and a wedge angle of the third region is a third angle in a cross section orthogonal to an extending direction of the lower protrusion, and

the first angle is smaller than each of the second angle and the third angle.

2. The cutting insert according to claim 1 , wherein

the second angle is smaller than the third angle.

3. The cutting insert according to claim 1 , wherein

the upper constraining surface comprises an upper protrusion extended from a side of the front lateral surface toward the rear lateral surface, and

the upper protrusion is extended parallel to the lower protrusion.

4. The cutting insert according to claim 3 , wherein

a wedge angle of the upper protrusion is a fourth angle in a cross section orthogonal to an extending direction of the upper protrusion, and

the first angle is smaller than the fourth angle.

5. The cutting insert according to claim 4 , wherein

the third region comprises a first portion located on a side opposite to the upper constraining surface, and

the third angle at the first portion is identical with the fourth angle.

6. The cutting insert according to claim 1 , wherein

the first region comprises

a first top having a convex curved surface shape, and

a first inclined surface that is flat and connects to the first top along an extending direction of the lower protrusion,

a width of the first top in the extending direction of the lower protrusion is a first width, and a width of the first inclined surface in the extending direction of the lower protrusion is a second width, and

a maximum value of the first width is larger than a maximum value of the second width.

7. The cutting insert according to claim 1 , wherein

the second region comprises

a second top having a convex curved surface shape, and

a second inclined surface that is flat and connects to the second top along an extending direction of the lower protrusion,

a width of the second top in the extending direction of the lower protrusion is a third width, and a width of the second inclined surface in the extending direction of the lower protrusion is a fourth width, and

a maximum value of the third width is smaller than a maximum value of the fourth width.

8. A cutting tool, comprising:

a holder which has a plate shape extended from a first end to a second end and comprises a pocket located on a side of the first end; and

the cutting insert according to claim 1 , the cutting insert being located in the pocket.

9. A method for manufacturing a machined product, comprising:

rotating a workpiece;

bringing the cutting tool according to claim 8 into contact with the workpiece being rotated; and

moving the cutting tool away from the workpiece.