OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 { } { } − + = ρ − − − × ξ − ξ ξ ∫ 3 2 (0) (0) (0) (0) 3 1 1 2 / ( , ) [ ( )] ( ) ( ) , t X p X P t T T dF dt F V V t X k X t T V V d (2) where { } ρ = ρ + µ −ς − 3 0 3 1 exp[ ( )] X V V is the chip pressure, kg/mm2; ρ 0 is the pressure in the area of low cutting speed region on the tool’s rake face; μ is the dimensionless parameter; ς is the steepness coefficient, s/m; T(0) is the chip formation time constant, s; k p is the dimensionless trail regeneration coefficient ( 〈 〈〈 0 1 p k ). Forces Φ2, Φ3 can be expressed as: ( ) { } ∗ ∗ = + ρ − ς υ − υ = + ρ − ς υ − υ (0) 2 0 1 (0) 3 0 1 Ô ( ) exp ( ) ; Ô ( ) exp ( ) , P T T P k F t X t k k F k t X t Ô Ô Ô Ô (3) where ρф is the force per unit contact length on the tool flank face, representing stiffness, kg/mm; ς is a parameter depending on the rear angle á and wear; kT is the friction coefficient; kΦ is the dimensionless coefficient of elastic recovery. Equations (1)-(3) constitute a numerical model of the DCS. The model’s adequacy was validated by comparing the results of digital simulations and full-scale experiments, which were conducted using continuous vibration monitoring measurement systems. The parameters of the dynamic connection equation, particularly the chip pressure on the rake face of the tool, were refined using both theoretical material [49] and force measurements during the cutting process [50]. For this purpose, a STD.201-1 system was used instead of the support to measure the dynamic loads on the tool along the {X1, X2, X3} axes. The hardware interface of the test bench consists of a set of electronic units manufactured by National Instruments: NI9234, NI-9237, and NI-9219, with a sampling frequency of up to 25 kHz. The accuracy of the analytical simulation results is limited by the zone of steady-state tool wear and the onset of accelerated wear, where the influence of random processes in the cutting zone reduces the accuracy of classical analytical nonlinear models. Here, we leverage previously developed mathematical tools to construct a space of wear characteristics. It is important to note that the parameters of the dynamic connection p(w) = {p1(w), p2(w),… pn(w)} formed during cutting depend on wear. Let experimentally determined trajectories be given as p(w) = = {p1(w), p2(w),… pn(w)}. For the sequence w = {w1, w2,…wk}, we calculate the spectra ω 1 1 , ( ) X X S , ù 2 2 , ( ) X X S and ù 3 3 , ( ) X X S in the space ℜ(3) X as Fourier transforms of the diagonal elements of the correlationmatricesofthetimeseriesofdeformations = ∈ ℜ = ( )( ) ( ) ( ) ( ) (3) 1 2 3 { ( ), ( ), ( )} , 1, 2, ... . i i i T X X t X t X t i k i X t Consequently, we obtain a set of deformation spectra for each set of parameters corresponding to each wear state w = {w1, w2,…wk}. Results and Discussion Example of determining the parameters of the information space in the low-frequency range If the perturbations f0(t) are small and the equilibrium is asymptotically stable, then the forces Φ in Equation (1) can be neglected. In this case, the main parameters influencing the formation of the spectra are the variations in ρ and T(0). Consider the turning of a shaft with a diameter of D = 84.0 mm, made of 0.1 C-Mn-2 Ni-Mo-V steel. The investigations were carried out as part of the implementation of a commercial contract with Atommash (Volgodonsk). The machining conditions were based on the technological process for manufacturing a real “blow-off pipe” type detail for rough turning. The technological parameters were as follows: feed rate Sp = 0.1 mm; depth of cut tp = 2 mm; and cutting speed V3 = (0.5…3.8) m/s. During the investigation, the range of cutting speeds was expanded in order to obtain more complete information
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