1. A ball screw comprising:
a threaded shaft having a spiral threaded groove at an outer circumferential surface;
a nut having a threaded groove which faces the threaded groove of the threaded shaft at an inner circumferential surface;
a plurality of balls rotatably loaded in a spiral ball raceway constituted by both of the threaded grooves; and
a ball circulation groove which returns and circulates the balls from an end point to a start point of the ball raceway,
wherein the nut is formed by concaving a part of the inner circumferential surface of the nut to form the ball circulation groove constituted by a concaved groove, and forming the threaded groove in the inner circumferential surface of the nut to be connected with an end part of the ball circulation groove, and
wherein at least a part of a edge portion constituted by both of side surfaces of the ball circulation groove and a surface which continue from each of the side surfaces and which extend in an axial direction is formed to be rounded.
2. The ball screw according to claim 2, further comprising a lubricant reservoir which can hold a lubricant and the lubricant reservoir is constituted by a dented part

formed by denting a part of an inner surface of the concaved groove.
3. The ball screw according to claim 3,
wherein the ball circulation groove comprises: both of
the end parts connecting with the ball raceway; and an intermediate part between the both of the end parts, and wherein an area of a cross-section of the lubricant reservoir cut along a plane perpendicular to a length direction of the ball circulation groove is larger at a part adjacent to the intermediate part than a part adjacent to the end parts.
4. The ball screw according to claim 3, wherein the ball circulation groove is curved, and the lubricant reservoir arranged at an inside in the radial direction of the curve of ball circulation groove is larger in the area of the cross-section cut along a plane perpendicular to the length direction of the ball circulation groove than a lubricant reservoir arranged at an outside in the radial direction of the curved ball circulation groove.
5. The ball screw according to claim 3, wherein the concaved groove constituting the ball circulation groove and the dented part constituting the lubricant reservoir are formed simultaneously.

6. The ball screw according to claim 2 or claim 3,
wherein an arithmetic average roughness Ra2 of a surface of
the ball circulation groove is greater than 0 µm to equal to
or smaller than 1.6 µm.
7. The ball screw according to claim 7,
wherein a press method using a die of a cam mechanism
is performed, the cam mechanism comprising:
a cam driver inserted into a nut blank having a cylindrical shape and moving in an axial direction; and
a cam slider arranged between the nut blank and the cam driver and formed with a projecting part corresponding to the ball circulation groove, a movement of the cam driver causing the projecting part to move in a radial direction of the nut, wherein an arithmetic average roughness Ra1 of a surface of the projecting part is equal to or greater than 0.01 µm to equal to or smaller than 0.2 µm, so as to push against the inner circumferential surface of the nut blank by the projecting part and thereby to form the ball circulation groove at the inner circumferential surface of the nut blank.
8. The ball screw according to claim 2 or claim 3,
wherein the ball circulation groove comprises a concaved
groove formed by concaving a part of the inner circumferential
surface of the nut, and
wherein a surface hardness of the threaded groove of the nut is equal to or greater than HRC 58 to equal to or smaller than HRC 62, a surface hardness of the both of the end parts
Amendment under Article 34 PCT Rule

connecting with the ball raceway in the ball circulation groove is equal to or greater than HRC 58 to equal to or smaller than HRC 62, and a surface hardness of the intermediate part between both of the end parts in the ball circulation groove is equal to or smaller than HV 550.
9. The ball screw according to claim 2 or claim 3,
wherein only both of the end parts in the ball circulation
groove and the threaded groove of the nut are subjected to
induction heat treatment.
10. The ball screw according to claim 2 or claim 3,
wherein the nut is formed by deburring the boundary part of
the ball circulation groove and the ball raceway by at least
one of brushing and blasting.
11. The ball screw according to claim 2 or claim 3,
wherein following three conditions A, B, and C are satisfied,
condition A: the ball circulation groove comprises a concaved groove formed by concaving a part of the inner circumferential surface of the nut,
condition B: the ball circulation groove comprises both of the end parts connecting with the ball raceway, an intermediate part arranged between the both of the end parts, and a curved part which connects the end parts and the intermediate parts, and has a substantially letter S shape, and

condition C: an edge part of the curved part in the edge part of the concaved groove is curved, and the edge part at the outside in the radial direction of the curve is formed in a shape in which a plurality of arcs different in radius of curvature are smoothly connected.
12. The ball screw according to claim 2 or claim 3,
wherein the ball circulation groove comprises both of the end
parts connecting with the ball raceway, and an intermediate
part arranged between the both of the end parts, and
wherein a groove width of the intermediate part is narrower than a groove width of the end parts.
13. The ball screw according to claim 2 or claim 3,
wherein following three conditions D, E, and F are satisfied,
condition D: the ball circulation groove comprises a concaved groove formed by concaving a part of the inner circumferential surface of the nut,
condition E: the ball circulation groove comprises both of the end parts connecting with the ball raceway, and two curved parts arranged between the both of the end parts and curved in opposite directions to each other, and has a substantially letter S shape, and
condition F: edge parts of the two curved parts in the edge part of the concaved groove are curved, and the edge part at the outside in the radial direction of the curve is formed in a shape in which a plurality of arcs different in radius of curvature are smoothly connected.

14. The ball screw according to claim 2 or claim
3, wherein following three conditions G, H, and I are
satisfied,
5 condition G: the ball circulation groove comprises a
concaved groove formed by concaving a part of the inner
circumferential surface of the nut,
condition H: the ball circulation groove comprises both
of the end parts connecting with the ball raceway, and two 0 curved parts arranged between the both of the end parts and
curved in opposite directions to each other, and forms a
substantially letter S shape, and
condition I: edge parts of the two curved parts in the
edge part of the concaved groove are curved and the edge part 5 at the outside in the radial direction of the curve and the
inside in the radial direction of the curve are formed in a
single arc shape.
15. The ball screw according to claim 2 or claim 3,
0 wherein the ball circulation groove comprises a concaved
groove formed by concaving a part of the inner circumferential surface of the nut, and
wherein at least a part in the length direction of the ball circulation groove has a cross-sectional shape of a 5 substantially letter V shape, when cut along a plane perpendicular to the length direction.

16. The ball screw according to claim 16, wherein the
ball circulation groove comprises both of the end parts
connecting with the ball raceway and an intermediate part
between the both of the end parts, and
wherein at least one of the intermediate part and the end parts has a cross-sectional shape of a substantially letter V shape, when cut along a plane perpendicular to the length direction of the ball circulation groove.
17. The ball screw according to claim 16, wherein a
bottom part of the concaved groove constituting the ball
circulation groove is provided with a lubricant reservoir.