OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 these frequencies. The closest values are observed when considering the NVF of GW 1 and the frequencies during grinding with a straight profile wheel: 2,062 Hz and 2,150 Hz, respectively. In the event of a similar comparison of GW 2, the frequency difference is more significant: natural vibrations – 2,337 Hz: and grinding – 2,070 Hz. It can thus be confirmed that the source of the acoustic signal during grinding is the grinding wheel. Informative frequencies for the processes using GW 1 and GW 2 are, respectively: fGW1 = 2,050 – 2,250 Hz; (2,150 ± 100 Hz); and fGW2 = 1,970–2,170 Hz (2,070 ± 100 Hz). As a result, we found that when studying the relationship between the acoustic characteristics of the grinding process and the tool cutting capacity for various process conditions (tool profile, the periodic vertical feed to the depth t, and the duration of processing), the dominant natural vibration frequencies of the grinding wheels need to be taken into account, since it can be used to determine the informative frequencies. Mathematical modeling of the sound level parameter during grinding with the tools of various profiles If we have data available on the dynamics of the acoustic signal during grinding, we can develop regression models (2, 3) which describe the dependence of the sound level (β, dB) on the processing time (T, min) and the periodic vertical feed to the depth t (St, mm/double stroke) for each of the wheels. 1 38.6 128.7 0.096 ; GW t S T β = − + + (2) 2 36.05 75.9 0.29 . GW t S T β = − + + (3) The statistical significance of the equations was verified using the determination coefficient and Fisher’s criterion. With regard to equation (2), the determination coefficient is R2 = 0.46, and for equation (3) R2 = 0.63. The calculated value of Fisher’s criterion for equation (2) F GW1 = 36.5, and for equation (3) FGW2 = 73.4. The table values of the criterion for the equations coincide, since during statistical processing it has an equal number of the degrees of freedom: Ftabl = 3.07. Since in both cases, the actual value of Fisher’s criterion significantly exceeds the critical (tabulated) value, we can conclude that the determination coefficients are statistically significant and the regression equations are statistically reliable. In addition the coefficients at St and t are jointly significant. Mathematical models (2) and (3) describe the dependence of the acoustic parameter – the sound level of a certain frequency on the periodic vertical feed to the depth t and the processing time. The models have both similarities and considerable differences. Analysis showed that the periodic vertical feed to the depth t (St, mm/double stroke) has a greater influence on the sound level (similar to [28]) as compared to the processing time (T, min). At the same time, the processing time factor is more important for equation (3) than for equation (2). Thus, GW 2 processing time has a greater influence on the sound level than GW 1 processing time. The applied significance of these models lies in the possible prediction of the sound level, in the aims of monitoring current cutting capacity in the ranges of St from 0.01 to 0.02 mm/double stroke, and the processing time from 0 to 15 minutes. The mathematical models thus obtained for determining the acoustic parameters (amplitude of the sound level) can be used correctly, only if the informative frequencies, for which these models were developed, match. Roughness study. The roughness of the workpieces was studied at the end of the processing cycle which lasted for 15 minutes. The results of the measurements are presented in the graphs of Figure 13. We established the dependence of the arithmetic mean deviation of the sample profile (Ra, µm) on the periodic vertical feed to the depth t (St, mm/double stroke). The graphs show that the surface roughness formed by profile wheel GW 2 is always much higher than when compared to the processing using GW 1. Thus, measurements in the direction of the longitudinal feed VS differ by 20 %, and measurements taken perpendicular to the VS direction – by 70 %. The roughness also increases with an increase in the periodic vertical feed to the depth t. Although the values for GW 2 exceed those for GW 1 for the measurements taken along the VS direction, it increases more slowly (depend
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