OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 a b c Fig. 2. Typical examples of autospectra: a – spindle rotation frequency of 10.0 Hz, disturbances applied to feed rate variations; b – spindle rotation frequency of 100 Hz, disturbances applied to cutting force module; c – spectral changes depending on the direction of deformation displacements in space ℜ(3) X with bifurcations possibly observed along the trajectory. In this case, the normalized vibration spectrum is practically independent of perturbations and is determined by the properties of the DCS. An example of the influence of parameter ρ on the dispersion-normalized spectrum for value X ∈ ℜ(3) X is shown in Fig. 3. Experiments show that for 0.1 C-Mn-2 Ni-Mo-V steel under conditions of feed rate 0 ( ) p S = 0.1 mm, cutting depth 0 ( ) p t = 1.5 mm, and cutting speed 0 3 ( ) V = 1.2 m/s, as wear on the rake face increases to 0.6 mm, a monotonic increase in ρ from 100 kg/mm² to 160 kg/mm² is observed. This corresponds to the transformation of the spectrum shown in Fig. 4. Note the special features of the spectrum changes. There is a redistribution of the intensity of oscillations in frequency ranges located near the natural frequencies. Let us denote them by Ai,s, i, s = 1, 2, 3. Here, i is the resonance number, and s is the number of directions of oscillations in space ℜ(3) X . As ρ increases, not only does the amplitude at frequency Ω3 increase, but the quality factor of this mode also increases. At ρ = 160 kg/mm2 a single oscillator with a common frequency Ω 3 is formed. Analysis shows that when ρ = 145 kg/mm2, the equilibrium loses stability and self-oscillations are formed. More details on the formation of attracting sets of deformations can be found in our works [2, 3, 25, 26]. As the roots of the characteristic polynomial approach the imaginary axis, the quality factor of the oscillator representing this pair of complex conjugate roots increases. Here are some examples of how the ratio of amplitudes at resonances changes with ρ (Fig. 4). The point of instability is marked with a red dotted line, to the right of which a delta-shaped spectrum δ(ω − Ω3) is formed, so all coefficients increase indefinitely. A rougher but more interference-resistant estimate is the average frequency of the spectrum ω(C) in the X ∈ ℜ(3) X directions. With increasing wear, primarily due to an increase in the parameter T (0), a shift of the
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