Accurate　modeling　of　the　contact　stiffness　of　bolted　joints　is　therefore　crucial　to　predict　the　dynamic　performance　of　CNC　machine　tools.　This　paper　presents　a　contact　stiffness　model　of　a　bolted　joint　based　on　multi-scale　theory.　The　model　uses　a　series　of　stacked　three-dimensional　sine　waves　to　describe　the　multiple　scales　of　roughness　of　the　contact　surface,　and　each　frequency　level　is　considered　a　layer　of　asperities,　stacked　iteratively　on　top　of　each　other.　The　relationship　between　the　contact　area　ratio　and　frequency　level　can　be　deduced.　Moreover,　the　contact　stiffness　at　each　frequency　level　can　be　regarded　as　a　spring　in　series　in　the　model,　therefore,　the　total　stiffness　can　be　obtained　by　summing　the　contact　stiffness　at　each　frequency　level.　The　influences　of　contact　load,　material　characteristic　parameters　and　multi-scale　parameters　on　the　contact　stiffness　model　are　analyzed　by　mathematical　simulation.　An　experimental　setup　consisting　of　the　section　beam　specimen　was　used　to　validate　the　numerical　model　of　the　bolted　joint　for　the　case　of　equal　pre-tightening　forces.　The　relative　error　between　the　multi-scale　natural　frequencies　and　experimental　frequencies　was　less　than　9.94%,　suggesting　the　multi-scale　model　can　be　effectively　used　in　predicting　the　dynamic　characteristics　of　CNC　machine　tools.　©　2019,　Jilin　University　Press.　All　right　reserved.