OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 coupled to the geometric characteristics of the formed surface and wear [17–21]. Most studies are limited to the problem of estimating wear as the main factor affecting the output properties [22–24]. Here, we note the modeling of evolutionary changes in the DCS that we proposed earlier [25, 26]. In this system, wear evolution and quality parameters are represented as a Volterra’s integral equation of the second kind with respect to the phase trajectory of irreversible transformations in terms of work done. Thus, the evolution of properties and parameters reveals the complete DCS. However, its use requires significant computing resources. In this paper, we will limit ourselves to the problem of wear diagnosis based on the analysis of vibroacoustic emission (VAE) [27–47]. To measure VAE, piezoelectric transducers, force sensors, noncontact laser and other measuring systems are used to determine the vibrations of a certain DCS coordinate in the frequency range (10 Hz…600 kHz). The measured sequences undergo preliminary processing using integral transformations, primarily Fourier transformations [26], Wavelet transformations [37], HilbertHuang transformations [36], Volterra transformations [3, 37, 28], etc. Methods of complexing measurable sequences of various physical nature are used [48]. In contrast to previous studies, this paper focuses on the construction of an information sign space (ISS), which considers the sensitivity of parameters’ variations to wear changes, their noise immunity, and ease of formation in diagnostic systems. Two frequency ranges are considered separately. The low-frequency range is within (1.0–1.5) kHz, and the high-frequency range is above 2.0 kHz. This division is due to the peculiarities of mathematical modeling of the DCS as a channel through which information about the force interactions formed during processing is transmitted. The purpose of the work is to develop a method for diagnosing cutting tool wear by determining the information space of features formed on the basis of studying changes in the frequency characteristics of the dynamic cutting system caused by wear development. To achieve this purpose, the following tasks must be undertaken. – to develop an analytical method for determining the information space of the low- and high-frequency ranges; – to perform mathematical modeling and to conduct digital simulations, and full-scale experiments; – to determine the parameters of the information space within the considered frequency ranges and a method for their evaluation. Methods Methodology for experimental wear assessment A generalized parameter for assessing the tool’s condition is the wear on its flank face. Therefore, let us consider an algorithm for the experimental assessment of flank wear, which is defined by the height of the flank wear land (Fig. 1). The configuration of the wear mark on the flank face varies, and only in some cases does it approximate a rectangle, as shown in Fig. 1, a. Therefore, we will define the wear assessment as the height of an equivalent rectangle, w = S0/(tp (0) – X 1 *), where S 0 is the surface area of the wear trace on the flank face of the tool, and X1 * is the elastic deformation under equilibrium conditions. The area S 0 is estimated using a grid (Fig. 1, c). It has been previously shown [2, 3, 26, 47] that the properties of dynamic contact stiffness (DCS) are influenced by dynamic connection parameters, and changes in these parameters are manifested as variations in vibration spectra. The parameters of this connection are dependent on wear, and it is convenient to analyze the interdependence of the vibration spectrum and wear independently within two frequency ranges. In the low-frequency range (ωH ∈ (0,ω0)), the model can be represented as a finite-dimensional spatial discrete model [47]. This is a frequency range whose upper limit is defined by the natural frequencies of the tool and workpiece subsystems. We will interpret the frequency range above ω0 as the high-frequency range (ωB ∈ (ω0,∞). Methodology for analytical determination of the information space in the low-frequency range The previously derived DCS model [47] is considered. We will limit our analysis to the case of machining a non-deformable workpiece. Then, the equation of the perturbed dynamic system response (DSR) can be written as:
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