OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Amodel of a grinding wheel was developed that allows parametric control over its geometry and elastic parameters. The following equation expresses the relationship between the natural frequencies of a grinding wheel’s vibrations and its geometric dimensions, shape, and elastic parameters: ( , ) i i E f F a = ν ρ where Fi(a, ν) is the shape factor, which depends on the body’s geometrical dimensions and shape (a = f(D, d, H)), Poisson’s ratio (ν), and the mode of oscillation. The model parameters are summarized in Table 2. Fig. 3. Spectral composition of grinding wheel No.3 natural vibrations Ta b l e 2 Grinding wheel model parameters Symbol Description Geometrical model parameters D GW outer diameter d GW inner diameter H GW height Elastic parameters of model material ν Poisson’s ratio Е Young’s modulus ρ density The calculation of eigenmodes and oscillation frequencies was carried out for each variant of the grinding wheel (GW) parameters – D, d, H, ν, E, and ρ – in order to determine the agreement with the experimentally obtained frequencies. The comparison is presented in the section “Comparison of experimental and calculated spectral compositions of grinding wheels”. Results and Discussion Eigenmodes of Grinding Wheel Vibration Computer modeling has shown that the order in which eigenmodes of grinding wheel vibrations manifest remains unchanged over a wide range of values of ν, E, and ρ. The natural frequency values associated
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