OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 with each mode vary depending on the values and combinations of the elastic parameters. The geometric parameters of grinding wheels have a decisive influence on the shapes of the modes, the sequence of their manifestation, and the corresponding frequencies. Table 3 summarizes the natural frequencies and their corresponding modes in the order of their manifestation for grinding wheel No. 3 – GW 1 600×50×305 25A F60 L 7 V 50 2 class GOST R 52781-2007. Ta b l e 3 Occurrence order of grinding wheel natural oscillations modes* No. 1 2 3 4 5 6 7 f, Hz 544.59 544.62 1187.6 1429.7 1429.71 1451.8 1451.81 Mode Repeated modes Repeated modes Repeated modes No. 8 9 10 11 12 13 14 f, Hz 1983.3 1983.5 2555.5 2555.51 3440.4 3440.8 3503.5 Mode Repeated modes Repeated modes Repeated modes No. 15 16 17 18 19 20 * – GW 1 600×50×305 25А F60 L 7 V 50 2 class GOST Р 52781-2007 f, Hz 3508.8 3508.81 3850.0 3850.1 4503.5 4503.51 Mode Repeated modes Repeated modes Repeated modes Thus, a pair of the lowest modes are bending modes with two nodal diameters, f₁ and f₂ (n = 2, s = 0), followed by the bending mode f₃ with one nodal circle (n = 0, s = 1), called the “umbrella” mode in the literature [21]. This result agrees with the analytical calculations of vibration modes of grinding wheels by B. A. Glagovsky and I. B. Moskovenko [22]. In the study of vibrations of discs with a central axial hole, the letters n and s denote the number of nodal diameters and nodal circles, respectively. The grinding wheels considered in this study belong to this category. The bending modes manifested in pairs f₄ and f₅ (n = 3, s = 0), f₁₀ and f₁₁ (n = 4, s = 0), and f₁₇ and f₁₈ (n = 5, s= 0) are similar and differ only in the number of nodal diameters. The pairs f₈ and f₉ (n = 1,
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