Robust prediction of chatter stability in milling based on the analytical chatter stability

A major obstacle that limits the productivity in machining operations is the presence of machine tool chatter. Machining is a dynamic process and chatter behavior depends upon a number of different aspects including spindle speeds, material properties, tool geometry, and even the location of tool respect to the rest of machine. Many of the traditional models used to predict chatter stability lobes assume that parameters such as natural frequency, stiffness, and cutting coefficients remain constant. In reality, these parameters vary and they affect the chatter stability. The uncertainty in these parameters can be taken into consideration by employing the robust stability theory into a two degree of freedom milling model. Utilizing the Edge theorem and the Zero Exclusion condition, a robust chatter stability model, based on the analytical chatter stability milling model, is developed. This improves the reliability compared to the projected pseudo single degree of freedom model. The method is verified experimentally for milling operations while considering a changing natural frequency and cutting coefficient.