Optimization of multiple tuned mass dampers for chatter suppression in turning

Multiple tuned mass dampers (TMDs) are superior to the single TMD with the same mass in the bandwidth and effectiveness for vibration control, and the most adopted optimization methods for TMDs are H_∞ or H₂ (i.e. minimization of the amplitude or root mean squared value of the vibration). However, the chatter vibration in the machine tool is a special self-excited problem. Especially for turning, the chatter-free depth of cut is only determined by the negative real part of the relative frequency response function (FRF) between the tool and workpiece. The objective function of multiple TMDs damping the primary structure was formulated (i.e. maximizing the most negative point of tool point FRF), and the minimax approach was employed to optimize the stiffness and damping of each TMD. The advantage of the proposed method was validated by tuning three TMDs on a specially designed fixture of a turning machine after performing the modal test. The cutting tests demonstrate that the tuning method can further increase the chatter suppression performance of multiple TMDs, and the chatter free depth of cut can be increased 52% more than the H_∞ method.