Traditional regenerative stability theory predicts a set of optimally stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted ρ) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of ρ becomes small. The results of the theory are supported by numerical simulation and experiment. It is anticipated that the theory will be relevant for choosing optimal machining parameters in high-speed peripheral milling operations where the radial depth of cut is only a small fraction of the tool diameter.

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The purpose of this study is an evaluation of the statistical variance in the once-per-revolution sampled audio signal during milling as a chatter indicator. It is shown that, due to the synchronous and asynchronous nature of stable and unstable cuts, respectively, once-per-revolution sampling leads to a tight distribution of values for stable cuts, with a corresponding low variance, and a wider sample distribution for unstable cuts, with an associated high variance. A comparison of stability maps developed using: 1) analytic techniques, and 2) the variance from once-per-revolution sampled timedomain simulations is provided and good agreement is shown. Experimental agreement between the well-known Fast Fourier Transform (FFT) chatter detection method, that analyzes the content of the FFT spectrum for chatter frequencies, and the new variance-based technique is also demonstrated.

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