OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 3 2024 Let us consider the frequency response obtained on the basis of the calculation of auto spectrums of deformations (Fig. 4) at force perturbation in the form of “white” noise. Light round dots indicate resonances, dark dots indicate antiresonances. The following peculiarities of the frequency response change should be noted. 1. At small values of the parameter ρ, three bursts are noticeable in the spectrum, which correspond to the resonances of the subsystem ω0,i. In between are the antiresonances. At ρ > (30–50) kg/mm2, comb spectra are superimposed on the amplitude change, the distance between the bursts of which is equal to the workpiece rotation frequency of 10 Hz. Its level increases with increasing ρ. At ρ > 400 kg/mm2 the spacing between bursts starts to level off and the dispersion of the spectrum increases. At ρ = 550 kg/mm2 the system loses stability. It forms auto oscillations, and SX,X(ω) transforms into δ(ω – ω0)-shaped spectrum with frequency ω0 = const. At further increase of ρ, independent of the perturbation, different attracting sets of deformations are formed, the frequency properties of which do not depend on small perturbations. We have analyzed them in an unperturbed system earlier [17, 24, 25, 51, 52, 60]. 2. The redistribution of amplitude bursts at the resonances, changes in its goodness of fit and some shift of frequencies are observed. These changes are influenced by the initial parameters. The time constant T(0), a b Fig. 5. An example of a VAE spectrum obtained from measuring vibration accelerations in the X1 direction: a – wear w = 0.1 mm; b – wear w = 0.6 mm Ta b l e 1 Matrices of speed coefficients and elasticity of the tool subsystem 1,1, kg/mm ñ 2,2 kg/mm , ñ 3,3 kg/mm , ñ 1,1 kg s/mm , h ⋅ 2,2 kg s/mm , h ⋅ 3,3 kg s/mm , h ⋅ 4,500 1,500 750 1.3 1.1 0.8 1,2 2,1, kg / mm ñ ñ = 1,3 3,1, kg / mm ñ ñ = 2,3 3,2, kg / mm ñ ñ = 1,2 2,1, kg s / mm h h = ⋅ 1,3 3,1, kg s / mm h h = ⋅ 2,3 3,2, kg s / mm h h = ⋅ 200 150 80 0.6 0.5 0.4 Ta b l e 2 Dynamic link options 2 , kg/mm ρ 0, kg/mm ρ 1 , s- Ω (0), T s ς T k ( ), s/m T k ( ) S k 1 χ 2 χ 3 χ 100–1,000 20 5–50 0.0001 1–7 0.2 5.0 0.1 0.4 0.51 0.76
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