Ball screw

A ball screw comprising:

• a ball screw shaft including a helical groove;
• a ball nut including a helical groove;
• and
• a plurality of balls placed between the helical groove of the ball screw shaft and the helical groove of the ball nut,
• the ball nut being provided with a recirculation groove that is connected to one end and the other end of the helical groove of the ball nut to recirculate the balls, wherein
• a recirculation trajectory of the recirculation groove is formed on the basis of a groove cross-sectional trajectory curve representing a trajectory along which the balls are recirculated in a groove cross-section of the ball screw shaft, and a longitudinal trajectory curve representing a trajectory along which the balls are recirculated in a virtual plane where a trajectory length ω of the groove cross-sectional trajectory curve is an H-axis and a helical trajectory length Fv(ω) is a V-axis,
• the helical trajectory length Fv(ω) of the longitudinal trajectory curve from a turn start point is set as a helical trajectory length Fv(ω) of the recirculation trajectory of the recirculation groove from the turn start point,
• a principal normal direction coordinate Fn(ω) of the groove cross-sectional trajectory curve is set as a principal normal direction coordinate Fn(ω) to the helical trajectory length Fv(ω) of the recirculation trajectory of the recirculation groove, and
• a binormal direction coordinate Fb(ω) of the groove cross-sectional trajectory curve is set as a binormal direction coordinate Fb(ω) to the helical trajectory length Fv(ω) of the recirculation trajectory of the recirculation groove.