OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 3 2024 cutting zone. In the frequency range (10–2,000) Hz the changes of macro-interactions are studied, and in the frequency range (20–600) kHz the processes of micro-contact interactions on the tool faces and in the area of primary plastic deformation are displayed. The evaluation of the state of friction nodes, including the contact between the auxiliary flank of the tool and the workpiece, is of independent importance [20, 21]. It is noted that the development of wear causes a change in the statistical properties of VAE in the friction node. Studies have been carried out to assess the state of machine nodes using the vibration signal during cutting [22, 23], as well as the quality of parts manufacturing [24, 25]. Special attention is paid to tool wear assessment [26–29]. Measurement transducers for vibration analysis of dynamic cutting system (DCS) are analyzed. Piezoelectric transducers [26, 27], laser systems [28, 29], non-contact electrical transducers such as magnetoelectric, induction, capacitive ones, etc. are considered. The construction of diagnostic systems includes methods of primary signal processing and the construction of information space in which the decisive recognition rules are considered. Typically, the Fourier transform [26–28] and wavelet transforms [29] of vibration sequences, auto regression spectral analysis [2, 30–33], various functionals over sequences, including algorithms for self-tuning or learning filters [34–36] are considered. The Hilbert-Huang transform [43] is also used. These transformations define the initial information processing. Further, neuro-fuzzy modelling algorithms [29], Bayesian classification rules [14, 37] are used to obtain the information model. The increase of diagnostics efficiency due to complexing of signals of different physical nature is considered [38–42]. Here, the systems of joint processing of information on forces and VAE [38, 39], as well as on temperature and VAE [40, 41] are widely spread. In all cases, two problems are considered in the development of vibroacoustic diagnostics systems. The first problem is related to the construction of the information space, and the secondly, to the definition of the rules with the help of which it is possible to provide clustering on the basis of wear in the information space. Therefore, intuitively or experimentally, the dependence of DCS on wearability is analyzed. A lot of research has been devoted to the modelling of DCS. It is considered as a unity of subsystems interacting through cutting [44–47]. The interaction is modelled by dynamic coupling representing the dependence of forces on state coordinates [45, 46], first of all, on elastic deformations [6, 17, 24, 25]. This takes into account the regeneration of the deformation trace left on the previous turn of the workpiece [48-50], the lag of forces with respect to deformations [45, 51, 52], and the nonlinear dependence of forces on state coordinates [52–54]. The above list is far from exhausting the research in the field of DCS. It should be noted that these studies focus on the problem of stability, formation of attracting sets of deformations, its bifurcations, and so on. However, when solving the problems of diagnostics, it is necessary to consider DCS as a channel through which the information about force interactions is transmitted, in which the properties of the wear-dependent perturbation are manifested. Moreover, the properties of this channel also depend on wear, since the change in wear causes a change in the parameters of the dynamic coupling formed by cutting. There is a paper that considers the influence of parameter fluctuations on the stability of DCS [55]. However, the changes in these parameters are considered in quasi-statics, and its relationship with wear is not disclosed. The analysis shows that the next stage of the study of dynamic wear monitoring methods is related to the solution of two problems. Firstly, it is necessary to analyze the frequency properties of DCS as a channel through which information about force interactions is transmitted, for example, in the region of the auxiliary flank of the tool. Moreover, the frequency properties of this channel depend on wear. It also affects the noise immunity of the wear information transmission. Secondly, it is necessary to provide models of the power emission itself, taking into account its dependence on wear. These two problems determine the purpose of the research presented in this paper. Research methodology Mathematical modeling. Problem statement. Let us consider the DCS model, which is based on our previously obtained ideas [17, 24, 25]. In contrast to earlier studies, we will consider it perturbed by additive power noise 1 2 3 { , , } T f f f = f(t) 2 2 ( , , ) ( ) d X dX m h cX F L V X f t dt dt Σ + + = + , (1)
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