The　tuned　mass　damper(TMD)　has　been　successfully　applied　to　the　vibration　control　in　machining,　while　the　most　widely　adopted　tuning　is　equal　peaks,　which　splits　the　magnitude　of　the　frequency　response　function(FRF)　into　equal　peaks.　However,　chatter　is　a　special　self-excited　problem　and　a　chatter-free　machining　is　determined　by　FRF　at　the　cutting　zone.　A　TMD　tuning　aiming　at　achieving　the　maximum　chatter　stability　is　studied,　and　it　is　formulated　as　an　optimization　problem　of　maximizing　the　minimum　negative　real　part　of　FRF.　By　employing　the　steepest　descend　method,　the　optimum　frequency　and　damping　ratio　of　TMD　are　obtained,　and　they　are　compared　against　the　equal　peaks　tuning.　The　advantage　of　the　proposed　tuning　is　demonstrated　numerically　by　comparing　the　minimum　point　of　the　negative　real　part,　and　is　further　verified　by　damping　a　flexible　mode　from　the　fixture　of　a　turning　machine.　A　TMD　is　designed　and　placed　on　the　fixture　along　the　vibration　of　the　target　mode　after　performing　modal　analysis　and　mode　shape　visualization.　Both　of　the　above　two　tunings　are　applied　to　modify　the　tool　point　FRF　by　tuning　TMD　respectively.　Chatter　stability　chart　of　the　turning　shows　that　the　proposed　tuning　can　increase　the　critical　depth　of　cut　37%　more　than　the　equal　peaks.　Cutting　tests　with　an　increasing　depth　of　cut　are　conducted　on　the　turning　machine　in　order　to　distinguish　the　stability　limit.　The　tool　vibrations　during　the　machining　are　compared　to　validate　the　simulation　results.　The　proposed　damping　design　and　optimization　routine　are　able　to　further　increase　the　chatter　suppression　effect.