The　maximum　axial　contact　stiffness　optimization　model　of　double-nut　ball　screws　was　established.　The　coupling　association　of　the　normal　force　of　raceway　with　the　variation　of　the　contact　angle　based　on　Hertzian　theory　was　considered.　The　optimal　axial　contact　stiffness　can　be　determined　by　using　ISIGHT　integrated　MATLAB　with　the　NLPQL　(quadratic　sequence　planning　method)　method　in　terms　of　the　contact　angle　and　curvature　ratio.　The　results　showed　that　within　a　specified　range　with　a　gradually　increasing　curvature　ratio,　the　contact　angle　increased,　whereas　ball　screw　axial　contact　stiffness　first　increased　and　then　decreased.　The　axial　contact　stiffness　was　increased　by　13.3%　after　optimization.　©　2021　IEEE.