The most common tunings for the TMD in the field of vibration suppression are H∞ and H2. However, regenerative machine tool chatter is a complex problem with many variations, which therefore requires a new tuning for the optimum chatter suppression. The real part based tuning is investigated numerically by employing the minimax numerical approach, which aims to maximize the minimum real part of the primary structure under the harmonic excitation. The performances of multiple TMDs system are discussed. A face milling case is employed to verify the benefits of multiple TMDs in increasing the chatter free depth of cut. It is concluded that multiple TMDs configuration are more effective than single TMD in chatter control.