OBRABOTKAMETALLOV technology Vol. 27 No. 2 2025 By transforming the integrands using the integration by parts method, we obtain: 0 x x S y x x x R x x R R x x y x x x R x x R R d c c c b b 2 2 2 0 0 0 II 2 II II 2 II 2 0 0 0 0 1 ( ) arcsin + 2 1 + + arcsin 2 ñ c c c c c c x x y x x x R x x R R b b a a II 2 II II 2 II 2 0 0 0 0 1 arcsin . 2 c c c (2) To optimize the calculations, the y-axis of the coordinate system should be drawn through the center of the rounding radius of the cutting plate, where the coordinates х0 and х0 II will be equal to zero, and the difference between the coordinates y0 and y0 II reflects the feed per revolution. Thus, taking into account equation (1) and (2), the calculated values of cutting force for the studied samples are presented in Table. Ta b l e 1 Technological parameters of the finishing boring process Fu, mm/rpm Sс, mm2 Рс, N/mm2 AISI 5140 / ENAW-2024 Р, N AISI 5140 / ENAW-2024 0.05 0.004987 1500/700 7.4805/3.4909 0.075 0.007456 1500/700 11.184/5.2192 0.1 0.009896 1500/700 14.844/6.9272 By modeling the situation with the unevenness of the allowance based on the calculation formula for determining the area of the cut layer, we can conclude that unevenness of the allowance of 0.1 mm leads to an increase in cutting force by a factor of 2 compared to the nominal value for finishing and, as a consequence, to an increase in the magnitude of the error. Thus, at the stage of preliminary adjustment of the boring cutter, it is necessary to estimate the diametrical size of the hole along the entire length of the processing using a measuring probe. If deviations in the position of the hole axis center are detected in the range of 0.05 to 0.1 mm, it is recommended to perform a preliminary pass (semifinished boring). This additional pass will eliminate the unevenness of the allowance exceeding the calculated values, taking into account the size and shape tolerance. This method allows minimizing the number of passes depending on the accuracy of the axis positioning at the previous pass. The next step was to determine the magnitude of the radial displacement of the tool axis during fine boring of holes. At the moment the cutting tool cuts into the workpiece material, a cutting force begins to act on the boring bar in the contact zone. The tool holder, as shown in Fig. 8, is a conical surface with a cutting plate fixed to its end. This scheme is a system with variable stiffness with one degree of freedom, at the extreme point of which a cutting force (P) acts: Fig. 8.Schematic of the boring process dynamics
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