OBRABOTKAMETALLOV technology Vol. 27 No. 3 2025 where τ0 =1/Ω is the time of one rotation of the part, s; Ω is the rotation frequency of the part, Hz; Vx is the feed speed, Vx = s0·Ω, mm/s. The maximum contact temperature on the rake face was calculated for each combination of V, s, and t values that they take at the moments of fluctuations due to tool vibrations using the Chichinadze-Shucheva analytical dependence [15]: ω ω = + + − ⋅ ⋅ − ⋅ ⋅ ⋅ × + π 3 2 01 02 1 1 1 1 2 2 2 2 2 2 2 2 1 3 1 1 2 2 1 1 2 exp C C C C C l l l l T k a k a k a rfc k a l k m V V V V k a V − λ × λ ⋅ + π ⋅ 1 2 1 1 1 2 2 , C m l a V (3) where ω01 is the maximum volumetric density of the heat source from friction forces in the tool body, W/m3; ω = − − 0 02 1 exp H H m m q kt T t h k T is the initial density of the heat source in the material being processed, W/m3; q 0 is the specific friction power for the front surface, W/m2; k 1, k2 are the heat absorption source localization coefficients for the tool and the material being processed, respectively, m–1; a 2 is the thermal conductivity coefficient of the workpiece, m²/s; λ1, λ 2 are the thermal conductivity coefficient of the solid alloy and the workpiece material, respectively, W/m·°C; Vc is the chip feed rate on the front surface, m/s; τk is the average tangential stresses on the front surface, Pa; Tm is the melting point of the workpiece material, oC; k is the temperature coefficient, oC; k = 7.143·10–4· T m; h is the average thickness of the plastically deformed layer in the chip, m; TH is the temperature difference within the plastically deformed layer, oC; l 1 is the length of the SPD zone on the rake face, m; α = λ 1 1 1 1 1 m A P , А1 is the tribocontact area on the SPD zone, m2; P 1 is the perimeter of tribocontact on the SPD zone, m; α1 is the heat transfer coefficient of the tool material, m2/°C. The average thickness of the SPD zone is determined by the empirical relationship [26]: τ = λ 1 2 . k m l h T (4) To account for the influence of cutting force variations during fluctuations on the values of parameters τk and h, the average shear stress on the rake face was determined as τk = FXY/Ak, Pa, where FXY is the resultant cutting force for the longitudinal (X) and radial (Y) directions, and Ak is the total contact area between the chip and the rake face, defined as Ak =2·l1·b. The values of the contact length l1 and the width of the cut layer b were determined using the methods [27] and [28], respectively. Results and Discussion The data on oscillatory accelerations recorded by vibration sensors were analyzed and processed. The oscillation velocity and displacement of the tool relative to the workpiece were calculated. Fig. 2 shows the vibration characteristics of the cutting process in the longitudinal direction, which is responsible for variations in the area of the cut layer. Based on the spectral characteristics of the data from the measuring system, the dominant frequency components of the system and kinematic disturbances were established.
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