OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 4 2) If ρ(ν) increases. Then it follows from (9) that the properties of the system change fundamentally. In particular, at resonances the amplitude bursts decrease. Moreover ρ < ρmax, where ρmax is the maximum permissible value at which the system is stable. The value of ρmax depends on technological modes and system parameters. The value of ρmax decreases with increasing the cutting depth tP (0). The value of ρ max also depends on T(0) and 0 1 ( ) ω F X W j . 3) If the usual turning condition tP (0) » S P (0) is satisfied, the main influence on the frequency response is [ ] { } 0 2 ( ) (0) , 0 Mod ( ) 1 exp( ) 1 ρ ω ω + - ω - v P F X t W j Tj T j . Then there exists such a set of frequencies ω∈ ∆ω, in which [1 – exp(–Tjω)]ω∈Δω = 0. This is because the operator [1 – exp(–Tjω)] periodically converges to zero as the frequency increases. Therefore, the set ω∈Δω is defined by the rotational frequency of the workpiece and multiples of it. This property leads to transformation of monotonically varying frequency characteristics to the characteristics of the comb filter type. As a result of the study of the mathematical model, it is necessary to draw an important conclusion for further analysis: variations in the parameters of the dynamic coupling formed by cutting are reflected in changes in the frequency characteristics of the DCS, i.e. the channel through which information about force interactions in the cutting zone is transmitted. Example of frequency response. Let’s consider the change of AFC at variation ̅ρ and T(0), for turning a shaft R = 42.0 mm made of 0.1 % C-1 % Mn-2 % Ni-0.5 % Mo-0.05 % V steel (20 MnMoNi 5 5 (DIN), A 508-3 (AISI)). The frequency response is investigated on the basis of numerical modelling in the Matlab-Simulink software package, as well as experimentally on the basis of direct measurement of VAE in the cutting process (fig. 4, 5). In modeling, a force disturbance in the form of white noise is considered. Technological modes without deformations and perturbations: feed SP (0) = 0.1 mm; depth t P (0) = 2 mm and cutting speed VP (0) = (0.5-3.8) m/s. The generalized mass is m = 0,015 kg∙s2/mm. Machining was carried out on a modernized 1K62 machine tool equipped with adjustable spindle and feed drives. Instead of a slide, a measuring system STD.201-1 was installed to determine forces, vibration and temperature. The parameters of model are given in Table 1, Table 2. Fig. 4. Examples of changes in auto-spectra of strain depending on the pressure of chips on the leading edge of the tool
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