OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 The order of eigenmodes’ manifestation changes significantly as a result of calculating them under these specified boundary conditions. The bending mode with the highest values of modal participation coefficients and modal masses becomes the lowest and most significant mode, featuring a nodal circle coinciding with the end region — the “umbrella” mode. The participation of this mode in the overall dynamics of the grinding wheel vibrations is much greater (more than 30 times) than that of the others and, accordingly, it generates the most powerful acoustic wave. Comparison of experimental and calculated spectral compositions of grinding wheels In figs. 5, a–k, the black lines show the spectral compositions obtained experimentally using the method described in section “Experimental study of natural vibrations of grinding wheels”. These graphs illustrate the distribution of the natural frequencies of grinding wheels with the studied characteristics. During computer modeling and the modal analysis process, the values of Poisson’s ratio (ν) and Young’s modulus (E) were adjusted to align the calculated frequency values (shown in the graphs as red vertical lines) with the experimental frequencies. The parametric optimization problem was solved using the fitting method. A perfect fit can only be achieved when the real geometric dimensions of the grinding wheels exactly match their modeled counterparts. The frequencies coincide at a satisfactory level. The deviation of the calculated frequencies from the experimental values does not exceed 5 %. Consequently, the values of the integral elastic parameters, ν and E, were obtained for each grinding wheel considered: 1. 25А F36 L – ν = 0.25; Е = 51.25 GPa; 7. 25А F60 P – ν = 0.225; Е = 54 GPa; 2. 25А F46 L – ν = 0.215; Е = 46 GPa; 8. 25А F60 S – ν = 0.2; Е = 67.5 GPa; 3. 25А F60 L – ν = 0.18; Е = 41.5 GPa; 9. 14А F60 L – ν = 0.25; Е = 41.2 GPa; 4. 25А F80 L – ν = 0.17; Е = 40 GPa; 10. 64С F60 L – ν = 0.26; Е = 43 GPa; 5. 25А F120 L – ν = 0.16; Е = 45.5 GPa; 11. 92А F60 L – ν = 0.27; Е = 53 GPa. 6. 25А F60 N – ν = 0.22; Е = 48 GPa; Thus, although labor-intensive, this approach to determining ν and E is recognized as effective. The agreement between the calculated and experimental frequencies allows us to conclude that the simulated values of Poisson’s ratio and Young’s modulus of the grinding wheels correspond to those of their prototypes. Therefore, the main objective of this work has been achieved. Currently, work is underway to develop a mathematical model of the sound pressure generated during grinding and a methodology for predicting the grinding wheel service life based on acoustic indices. This model requires taking into account the actual elasticity parameters of grinding wheels and establishing a relationship between these parameters and the wheels’ characteristics. The values of ν and E obtained during this study were used as parameters to develop a sound pressure model of the grinding process. Preliminary results show the model’s qualitative agreement with, and adequacy to, the experimental acoustic data obtained during the grinding process study. Dependence of integral elastic parameters on grinding wheel characteristics The study of grinding wheels No. 1, No. 2, No. 3, No. 4, and No. 5 determined the influence of abrasive grain size on the elastic parameters, ν and E. Poisson’s ratio decreases as the abrasive grain size decreases. Young’s modulus decreases until the grain size reaches 0.2 mm; thereafter, the trend reverses and begins to increase. However, there is insufficient data to conclude whether the increase in Young’s modulus will continue as the grain size is further reduced. Fig. 6 shows graphs reflecting this dependence in terms of granularity versus Poisson’s ratio and granularity versus Young’s modulus. Next, regression equations and curves were obtained using MS Excel. The regression curves constructed from the experimental data are expressed by second-degree polynomial
RkJQdWJsaXNoZXIy MTk0ODM1