OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 2 2024 Results and its discussion The accuracy of the mathematical modeling of deformations does not guarantee the adequacy of its transformation into the part geometry. If it is possible to determine X(t), the trajectories L(Φ), V(Φ)(t) are determined on the basis of (1) when L(t), V(t) are given. To analyze the adequacy of transformation forming motions into geometric topology, it is necessary to compare the two topologies C(L, X) and (L, X) since the “skeletal” geometric topology is a direct geometric representation of the trajectory L(Φ)(t), V(Φ)(t) on the part surface. Note that if a geometric topology is specified, then any accepted engineering practice estimates of the geometric quality of the part can be calculated from it. A profile and contour measuring station T4HD by IMTS/Triebworx (the error does not exceed 0.01 µm in the range: diameter up to 200 mm and width of the controlled surface 20 mm) was used to measure the relief and surface morphology. The device allows measuring irregularities up to half of the circumference length. The measurement of X1(t) and R(t) (fig. 6) allows spectral analysis of the vibrational displacements X1(t) and profile function R(t) in the unity of the auto and cross spectrum, as well as the coherence function 1 2 , ( ) X R K ω . To evaluate the surface morphology, a three-dimensional microscope Contour ELITE (manufactured by BRUKER) was used, which allows obtaining photographs and surface relief with high resolution (in the horizontal plane of the order of 160 nm) (fig. 7). For vibration measurements, sensors made by Bruel and Kjerr and certified AP35D transducers with digital output were used. An integration operation was used to a b c Fig. 6. Variation of coherence functions between vibrational displacements and profile function
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