The stability of periodic cutting operations, the dynamics of which are described by linear differential-difference equations with periodic coefficients, is studied. A new stability theory that uses parametric transfer functions and Fourier analysis to obtain the characteristic equation of such systems is experimentally verified. The theory is applied to single-point turning of a compliant work piece with two degrees-of-freedom. The theoretical predictions of both the critical depth of cut for chatter-free turning and the corresponding chatter frequency were found to be in good agreement with the measurements obtained from actual chatter tests under various surface speeds.

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