Axial　stiffness　of　ball　screws　has　great　effects　on　accuracy　of　positioning,　dynamic　characteristic　and　transmission　efficiency.　Axial　contact　stiffness　modeling　of　ball　screws　is　the　key　problem　in　dynamic　analysis　of　ball　screws.　Aiming　at　obtaining　axial　stiffness　of　ball　screws　considering　microscopic　fractal　characteristics　of　contact　surfaces,　a　new　analytical　method　is　proposed　to　estimate　axial　contact　stiffness　of　ball　screws　and　combine　the　minimum　excess　principle　with　Mandelbort　(MB)　fractal　theory　in　this　research.　The　minimum　excess　principle　is　employed　to　conduct　normal　stress　analysis.　And　the　Mandelbort　fractal　theory　is　adopted　to　obtain　contact　stiffness　in　ball　screws.　The　effectiveness　of　the　proposed　method　is　validated　by　the　self-designed　experiment.　The　comparison　between　theoretical　results　and　experimental　results　demonstrates　that　axial　contact　stiffness　of　ball　screws　could　be　obtained　by　the　proposed　method.　Copyright　©　by　HIGH　TECHNOLOGY　LETTERS　PRESS.