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.
Part machining on the lathes with automated tools is a complex process that depends on the properties of the lathe dynamic system. Oscillations in processing the main parts determine the dynamic quality of the lathes, quality of the surface layer and resistance of the cutting tool, therefore, it is necessary to identify the methods to control the operation mode. Increased efficiency of the process is provided by the forced cutting modes, which can lead to the deterioration of processing quality and premature wear of a cutting tool. Theoretical definition of rational cutting modes causes certain difficulties, so the experimental search for a solution to the problem is most urgent. In order to select rational cutting modes on the lathes and grinding machines, it is proposed to use the stability margin of the lathe dynamic system (DS), which should be determined from the transfer function of DS using the autocorrelation function (ACF) of oscillations. A condition for identification of the lathe DS is a preliminary identification of ACF, which can be implemented using oscillation records during cutting. Pre-filtering of oscillations is carried out to exclude low-frequency range containing frequencies caused by oscillations of lathe system elements and to save frequencies associated with the cutting process. Cut modes are assigned to the highest stability margin, which ensures high surface quality. There is an unambiguous ana-lytical relationship between the oscillation index and the damping coefficient of the ACF, which makes it possible to calculate the α coefficient, by the value of which it is possible to estimate the stability margin of the ET in different cutting modes and select the most appropriate one. Studying the lathe oscillations in processing high-precision parts makes it possible to control the technological mode, using the oscillation level as one of the indicators of its quality.
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