Optimization of multiple tuned mass dampers to suppress machine tool chatter

Chatter is more detrimental to machining due to its instability than forced vibrations. This paper presents design and optimal tuning of multiple tuned mass dampers (TMDs) to increase chatter resistance of machine tool structures. Chatter free critical depth of cut of a machine is inversely proportional to the negative real part of frequency response function (FRF) at the toolworkpiece interface. Instead of targeting reduction of magnitude, the negative real part of FRF of the machine is reduced by designing single and multiple TMD systems. The TMDs are designed to have equal masses, and their damping and stiffness values are optimized to improve chatter resistance using minimax numerical optimization algorithm. It is shown that multiple TMDs need more accurate tuning of stiffness and natural frequency of each TMD, but are more robust to uncertainties in damping and input dynamic parameters in comparison with single TMD applications. The proposed tuned damper design and optimization strategy is experimentally illustrated to increase chatter free depth of cuts.