Modelling and practical application of autocorrelation functions of vibroacoustic oscillations in a machine dynamic system

Abstract

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.

Identification of the Model of the Dynamic System of a Milling Machine Based on the Study of Vibroacoustic Characteristics

“…In the article [7], the authors concluded, that by registering vibroacoustic vibrations during cutting, one could then calculate the autocorrelation function, and then, after performing the appropriate mathematical processing according to the methods of the theory of automatic control, form the corresponding estimates correlated with the dynamic state of the technological system. The article [8] is devoted to obtaining a simple expression for determining the transfer function of a closed dynamic system of a lathe by an experimental and analytical method. The transfer function can be calculated if an analytical expression for the autocorrelation function of the output signal is obtained, for example, by identification by the experimentally recorded vibroacoustic vibrations of the cutter of a lathe.…”