This　paper　investigates　and　analyzes　the　performances　of　several　types　of　tuned　mass　damper　(TMD)　including　common　single　TMD(STMD),　multiple　tuned　mass　dampers　(MTMD)　and　dual　tuned　mass　dampers　(DTMD)　on　the　machining　chatter　control.　Considering　the　special　nature　of　the　machining　stability　problem,　the　optimal　design　parameters　of　the　dampers　are　defined　as　those　that　minimize　the　magnitude　of　the　real　part　of　the　FRF　of　the　damped　machining　system.　This　paper　demonstrates　the　performance　of　the　optimally　designed　different　TMDs　for　machining　stability　improvement　by　calculating　the　stability　diagrams　for　the　turning　processes.　The　calculation　results　show　that　a　more　than　60%　improvement　in　the　critical　limiting　cutting　depth　can　be　obtained　for　the　optimally　designed　MTMD　(2　TMDs)　compared　to　the　optimally　designed　STMD,　and　a　more　than　20%　improvement　for　the　optimally　designed　DTMD　compared　to　the　optimally　designed　MTMD(2　TMDs).