OBRABOTKAMETALLOV Vol. 27 No. 3 2025 technology modes. To measure tool vibrations, a stand consisting of three A603C01 accelerometers, an LCard E20-10 analog-to-digital converter (ADC) with an input signal sampling frequency of up to 10 MHz, and a BTK-2-010 ICP converter for amplifying and proportionally converting vibration acceleration signals into alternating voltage with a frequency range of 0.1–50,000 Hz (Fig. 1) was used. The signal sampling frequency was 10 kHz per channel. Signals were recorded using L-Graph II software, and experimental data processing and identification of the parameters of the digital model of the cutting process were performed using Matlab and Simulink software. a b Fig. 1. General view of the equipment for the study: a – vibration accelerometers (1); b – continuous vibration monitoring system of the tool: ADC E20-10 (2) and ICP transducer VTK-2-010 (3) The dynamic cutting system model is represented as a set of three interconnected subsystems. The first subsystem controls the movement of the cutting tool relative to the workpiece, i.e., it sets the cutting parameters and the inertial-dissipative properties of the system. The second subsystem models the elastic deformations and cutting forces acting on the tool. The third subsystem implements a block for simulating uncontrolled disturbances, the source of which are kinematic disturbances from the machine’s drive system and spindle runout [25]. When modeling the dynamics of the machining process, the values of the cutting speed V, feed rate s, and cutting depth t were determined as follows: for each parameter, the value was determined by the sum of the value set by the control system (V0, s0, t0), deformation displacements H = {HX,HY,HZ}, mm, and deformation displacement rates η = dH/dτ = {ηX,ηY,ηZ}, mm/s, as well as vibration disturbances Δ = {ΔX,ΔY,ΔZ}, mm. Vibration disturbances are periodic functions of time and can be represented as: = ∆ = ∆ τ = ω τ ν τ = ∆ τ = ω ω τ ∑ ∑ 1 1 ( ) sin( ), ( ) / cos( ), k i n n n k i i n n n n A d d A (1) where An, ωn are the amplitudes and frequencies of the oscillators disturbing the movement of the tool in the directions of movement i = {X,Y,Z}, determined experimentally. The final representation of the cutting modes was modeled as follows: ( ) ∆ τ ∆ τ−τ = − η + ν = − η + ν τ = − + ∆ ∫ 0 0 0 ; ; , Z Z x X X Y Y V V s V d t t H (2)
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