Self-excited chatter, an instability of the cutting process in combination with the machine structure, is a basic performance limitation of a machine tool. A theory is developed which permits calculation of borderlines of stability for a structure having n-degrees of freedom and assuming no dynamics in the cutting process. Harmonic solutions of the system characteristic equation are found using a special chart, and the resulting data are used to plot a stability chart. However, an infinite number of such stability charts exists for a given machine because the structure dynamics vary with cutting-force orientation. This fact makes a simpler index of chatter performance desirable. A simple stability criterion is proposed which states that the directional cutting stiffness must be less than one half the minimum directional dynamic stiffness of the structure for each force orientation to assure chatter-free performance at all spindle speeds. Thus chatter-free performance can be fundamentally identified with adequate structural dynamic stiffness for all cutting-force orientations. Such a broad requirement for dynamic stiffness is difficult to meet in the design stage since structural characteristics are not easily predicted and controlled. Machine testing with continual improvements in the structure to increase dynamic stiffness is currently the best way to combat chatter.

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