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The paper considers applying the residue theory in obtaining mathematical models for autocorrelation functions of vibroacoustic oscillations in a machine dynamic system during the cutting process. It shows that these models are analogous to experimental data and reflects their practical application for assessing the dynamic quality of machine tools and setting a processing mode. Calculating the dynamic system stability margin is carried out automatically according to the oscillation index obtained from a real amplitude-frequency characteristic of the dynamic system. This characteristic, in its turn, is determined from the identified transfer function. The article considers the construction of a theoretical model for the autocorrelation function of vibroacoustic oscillations of a grinding machine dynamic system, that would be equivalent to the autocorrelation function obtained from experimental data. Such a model would be feasible to use to calculate the dynamic system transfer function of the machine with a subsequent evaluation of its stability margin. It substantiates applying the dynamic system stability margin of the machine as an informative characteristic based on measuring vibroacoustic oscillations during the cutting process to evaluate the technological system quality and stating an appropriate processing mode to achieve the required part surface quality. It is shown that the identification of transfer function under the established conditions by the autocorrelation function of vibroacoustic oscillations during cutting enables us, based on the maximum stability margin of the dynamic system, to determine the machine with the highest dynamic quality and set the cutting mode, which ensures high processing quality and reduces tool wear.

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