OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 4 2022 3. To reduce the uncertainty ΔD(iT) for variations c, it is reasonable to carry out machining with small feeds. However, at small feeds commensurate with the tool radius at its apex, the stabilizing effect of the motion direction formed on the workpiece is leveled out. Therefore, the magnitude of the feed from below is also limited [57]. These methods do not eliminate the need for matching the CNC program with the law of change of stiffness. If the set of paths SP (0)(iT,V P) is calculated, then it is additionally necessary to select from this set those, for which the condition of minimum wear intensity is satisfi ed. The solution to this problem is described in suffi cient detail in [58]. The paths (7) are calculated under the assumption that the subsystem of “fast” motions is asymptotically stable. Under this condition (7), there is an attractor that has the property of attraction in the entire state space. In this connection, it is additionally necessary to analyze the subsystem of “fast” motions for asymptotic stability. Example of CNC program matching with a change in part stiffness. The problem of matching TEE with changing system properties has a wide range of applications: matching TEE with evolutionary changes in system properties due to the work of forces in the cutting zone; matching TEE with an a priori specifi ed law of changing the stiffness of the workpiece; matching TEE with the development of tool wear, etc. As an example, the longitudinal turning of the fuel pump nozzle fi tting of a diesel engine is considered (length L0 = 144 mm (Fig. 1, b), diameter D = 18 mm, material – hot-rolled bar made of steel 45 (STATE STANDARD 2590-2006) with diameter D = 25 mm. The tools used were tool systems with interchangeable 15 % (WC + TiC) + 6 % Co (HS123) square inserts and MR TNR 2020 K11 toolholders. Tool geometry: back rake angle γ = 15°, cutting edge angle φ = 90°, front clearance angle α = 6o. Parameters of the tool elastic system and dynamic coupling are given in Table 1, Table 2. Generalized mass m = 0.5∙10–3 kg∙s2/mm. To determine the law of variation of the radial stiffness along the axis of the workpiece, we can use the laws of bending vibrations of rods [59]. This information is easier and more accurate to obtain experimentally (Fig. 1, a). The law c(Y)(L 2) should be supplemented by its agreement with the change in the reduced mass along L2. This is due to the fact that the natural frequencies of the bending vibrations of the shaft remain constant at all values of L2 [4–6, 46]. Ta b l e 1 Matrices of velocity coeffi cients and elasticity of the tool subsystem c1,1, kg/mm c2,2, kg/mm c3,3, kg/mm h1,1, kg∙s/mm h2,2, kg∙s/mm h3,3, kg∙s/mm 2,000 1,000 1,000 1.3 1.1 0.8 1,2 2,1, êã/ìì ñ ñ 1,3 3,1, êã/ìì ñ ñ 2,3 3,2, êã/ìì ñ ñ 1,2 2,1, êã ñ/ìì h h 1,3 3,1, êã ñ/ìì h h 2,3 3,2, êã ñ/ìì h h c1,2 = c2,1, kg/mm c1,3 = c3,1, kg/mm c2,3 = c3,2, kg/mm h1,2 = h2,1, kg∙s/mm h1,3 = h3,1, kg∙s/mm h2,3 = h3,2, kg∙s/mm 100 150 80 0.6 0.5 0.4 Ta b l e 2 Dynamic link options ρ, kg/mm2 ζ, (mm/s)–1 T (0), s μ χ 1 χ2 χ3 300 0.1 0.0001–0.0005 0.5 0.7 0.5 0.5
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