The　prestretching　of　ball　screw　can　effectively　increase　the　positioning　accuracy,　but　high　value　of　prestretching　can　lead　to　the　bearing　excessive　heat　and　affects　its　life,　thus　the　research　of　optimal　prestretching　has　important　significance.　Optimal　prestretching　of　ball　screw　which　influenced　by　the　axial　load　and　temperature　increase　which　is　related　to　the　axial　load,　need　meet　the　requirement　of　the　ball　screw　to　be　in　the　state　of　tension　under　the　maximum　axial　load.　The　deformation　of　ball　screw　under　the　axial　load　is　named　as　load　deformation　and　the　deformation　due　to　the　thermal　is　named　as　thermal　deformation.　The　optimal　prestretching　is　used　to　compensate　the　maximum　load　deformation(MLD)　and　the　maximum　thermal　deformation　(MTD).　In　order　to　insure　the　axial　stiffness　of　the　ball　screw　to　be　stable,　the　axial　load　of　ball　screws　is　not　more　than　three　times　the　preload.　So　the　three　times　preload　of　ball　screw　is　as　the　maximum　axial　load.　The　optimal　prestretching　is　the　sum　of　the　MLD　and　MTD.　The　temperature　distribution　and　thermal　deformation　has　been　obtained　when　the　ball　screw　reach　thermal　equilibrium.　Combined　with　thermal-mechanical　coupling　analysis,　the　optimal　prestretching　has　been　obtained　for　the　different　axial　load　and　different　preload.　The　analysis　results　show　that　the　MTD　plays　a　main　role　influencing　the　optimal　prestretching,　and　the　MLD　occupies　the　optimal　prestretching　maximum　to　10.61%.