Abstract: Due to the raceway profile has a significant influence on the contact performance of ball screws, the contact performance of second-order closely matched raceway ball screws compared to conventional ball screws was investigated. Initially, the second-order approximate curve of the ball was derived based on the close contact theory in contact geometry, and a novel second-order closely matched raceway profile for ball screws was proposed. Secondly, an equivalent model of a ball screw with a closely matched raceway profile was established, followed by finite element analysis and photoelastic experiments to evaluate the distribution of contact stress in the ball screw. Finally, stress distribution fringe patterns for different raceway profiles were obtained through photoelastic experiments, validating the superiority of closely matched raceways in achieving stress distribution uniformity within the contact region. The results demonstrate that, compared to conventional Gothic arch ball screws, the design of second-order closely matched raceways significantly increases the contact area, reduces contact stress concentration, smoothens the stress gradient in the contact region, and effectively enhances the load-carrying capacity and service life of ball screw assemblies.