OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 about the diagnostic characteristics in the vibroacoustic emission (VAE) signals. Machining was performed on a modernized 1K62 lathe, equipped with adjustable spindle and feed drives. Instead of the carriage, a STD.201-1 measuring system was installed to determine forces, vibration, and temperature. Parameters are given in Table 1. The total mass is m = 0.015 kg∙s2/mm. The dynamic couple parameters are provided in Table 2. The resonant frequencies of the tool subsystem are Ω0,1 = 130 Hz, Ω0,1 = 174 Hz, Ω0,1 = 236 Hz. Ta b l e 1 Matrices of speed coefficients and elasticity of the tool subsystem c1,1 (kg/mm) c2,2 (kg/mm) c3,3 (kg/mm) h1,1 (kg∙s/mm) h2,2 (kg∙s/mm) h3,3 (kg∙s/mm) 4,500 1,500 750 1.3 1.1 0.8 c1,2 = c2,1 (kg/mm) c1,3 = c3,1 (kg/mm) c2,3 = c3,2 (kg/mm) h1,2 = h2,1 (kg∙s/mm) h1,3 = h3,1 (kg∙s/mm) h2,3 = h3,2 (kg∙s/mm) 200 150 80 0.6 0.5 0.4 Ta b l e 2 Dynamic coupling parameters ρ (kg/mm2) ρф (kg/mm2) Ω (s −1) T(0) (s) ς k T k(T) (s /m) k (S) χ 1 χ2 χ3 100–1,000 20 5–50 0.0001 1–7 0.2 5 0.1 0.4 0.51 0.76 The spectra are studied based on numerical modeling in the Matlab-Simulink software package, as well as experimentally by direct measurement of the vibroacoustic emission (VAE) during the cutting process. Let us consider the spectra of deformation oscillations X ∈ ℜ(3) X calculated as responses to “white” noise. The spectra in Fig. 2, a and b differ from the spectrum in Fig. 2, c by angular coefficients χ = χ χ χ 1 2 3 { , , } T . The examples are selected to illustrate the following properties of the spectra. 1. Resonances (shown as round, unshaded points) and antiresonances (shown as shaded points) can be distinguished in the spectrum. In real systems, they remain virtually unchanged when the parameters of the dynamic connection formed by the cutting process vary. 2. In the case of kinematic disturbances (Fig. 2, a), periodic spikes are superimposed on the spectra. The distance between them is equal to the rotation frequency of the workpiece. In the case of force disturbances, the peaks are normalized (Fig. 2, b). They are also normalized in the high-frequency range. Therefore, in the actual measured spectrum, significant variations in level are detected as the frequency increases, but resonance frequencies are usually observed. 3. Peaks at all resonances may not appear, or they may appear to a lesser extent (Fig. 2, c). This behavior is determined by the structure of the elasticity matrices c coefficients χ. It is known that the angular coefficients change as wear increases. For example, forces in the direction normal to the flank face increase faster [51], which is reflected in the redistribution of amplitudes at resonance frequencies. 4. Wear development causes an increase in the parameters ρ and T(0), as well as a change in the angular coefficients χ. An increase in ρ causes a shift in the roots of the characteristic polynomial of the linearized variation equation, such that some roots move toward the imaginary axis, and an increase in ρ always leads to a loss of stability. An increase in T(0) has a contradictory effect. On the one hand, an increase in T(0) contributes to self-excitation, and on the other hand, it leads to additional damping. 5. As wear progresses, due to changes in the parameters of dynamic coupling, the system may lose its equilibrium stability, and various attracting sets of deformations may form in the vicinity of the trajectory,
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