Chatter stability limits in end milling with anisotropic flexible tools

Self-excited chatter vibration in end milling is caused by the regeneration and mode coupling mechanisms. In order to avoid chatter vibration, both mechanisms need to be investigated. Past researches have shown that the mode coupling effect in end milling can be suppressed by using cutting tools with anisotropic dynamic characteristics. However, it is difficult to apply previously developed analytical models for predicting the chatter stability limits in end milling with the anisotropic tools. Hence, suitable conditions for chatter suppression and the overall phenomena have not been clarified thoroughly yet. This paper proposes a new analytical model to predict chatter stability limits in end milling with tools that have anisotropic transfer functions. The model considers the anisotropic tool to vibrate steadily in a rotating coordinate system rather than in an inertial coordinate system. The cutting process is formulated in this rotating coordinate system, and variation in the transfer function of the anisotropic tool with respect to the spindle speed is considered. Fundamental cutting tests have been conducted to verify the proposed model. Experimentally identified stability limits agreed closely with the predictions. Furthermore, analytical investigations have shown that the transfer function of the cutting tool changes considerably with the spindle speed. This affects the chatter stability prediction significantly. Using the proposed model, it is concluded that higher stability limits can be achieved only at low spindle speed conditions by using anisotropic tools. However, the number of flutes on the tool is limited to be less than three, and they need to be arranged at suitable positions. The effect of the cutter helix also needs to be negligible.