Critical Review of Chatter Vibration Models for Milling

Abstract

The pioneering scalar chatter stability models were introduced by (1957), and (1958) almost at the same period but independent of each other. Tlusty proposed the following chatter stability expression:

$$ a_{lim} = \frac{{ - 1}} {{2K_s G_0 (\omega )}} $$

(1)

where a _lim is the critical depth of cut without chatter, K _s[N/m ²] is the cutting coefficient representing the hardness of the material and the tool geometry influence, and G _o[m/N] is the negative real part of the frequency response function of the structure oriented in the direction of chip thickness. Tobias’s (Tobias and Fiswick 1958; Tobias 1965) model is similar except that he considered the cutting coefficient as a complex number with dependency on effective cutting speed and chip thickness. Tobias also introduced the stability lobes (Tobias and Fiswick 1958) which show the stable spindle speed and depth of cut combinations using the phase relationship between the vibration waves left on the cut surface and natural modes of the structure. The basic chatter theory presented by Tlusty and lobes introduced by Tobias had a fundamental impact in guiding the design of machine tools and the selection of productive cutting conditions. Although the theory was based on orthogonal cutting conditions, where the machining system is continuous without time varying dynamics, researchers and engineers used it with great success by simple adjustments based on intuitions and experience. (Merritt 1965) reformulated the orthogonal chatter theory based on Nyquist’s Stability law. Tlusty (Koenigsberger and Tlusty 1967) introduced orientation of the cutting forces, average number of teeth in cut and flexibilities in the direction of chip which allowed application of the staler chatter theory to practical turning, milling and shaping operations.