Considering　the　time-varying　vibration　characteristics　of　the　ball　screw　caused　by　the　continuous　movement　of　the　nut,　this　paper　takes　the　form　of　a　hollow　screw　shaft　structure　containing　multiple　tuned　mass　dampers　(MTMD)　to　achieve　the　lateral　multi-mode　vibration　control　of　the　screw　shaft.　The　screw　shaft　is　modeled　as　an　Euler　Bernoulli　beam　with　elastic　supports　at　both　ends　and　the　position　of　the　nut.　Each　tuned　mass　damper　(TMD)　is　connected　to　the　screw　shaft　via　an　elastic　spring　and　a　viscous　damping　element.　After　establishment　of　the　lateral　dynamic　model　of　the　screw　shaft　which　taking　into　account　the　changing　positon　of　the　nut　and　the　multiple　resonant　responses　of　the　shaft,　the　optimum　design　parameters　of　each　TMD　can　be　determined　using　a　numerical　optimization　algorithm　based　on　the　mode　summation　method.　The　multiple　resonant　responses　of　the　screw　shaft　installed　with　the　optimally　designed　MTMD　are　analyzed　to　demonstrate　the　robust　design　of　the　MTMD　for　the　lateral　time-varying　vibration　control　of　the　screw　shaft.　Theoretical　studies　and　experimental　results　show　that　the　proposed　design　method　of　the　MTMD　can　remarkably　improve　the　lateral　dynamic　stiffness　of　the　screw　shaft.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.