OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 cell sizes of the upper and lower sieves (Wm) for each fraction (refer to Table 1). The strength of the correlation coefficients was evaluated using the Chaddock scale. The Spearman’s rank correlation coefficient (ρ) between grain length (l) and grain width (b) does not exceed 0.3. The average ρ value for the l-b relationship is 0.21 for roller-press grinding and 0.25 for rotary grinding. The correlation strength between the grain shape factor (l/b) and grain length (l) is significantly higher, with an average ρ value exceeding 0.7. The strength of the relationship between the shape factor (l/b) and grain width for the selected fractions ranges from −0.35 to −0.50, indicating an inverse relationship where the shape factor decreases as grain width increases. Based on the absolute values of the correlation coefficients, the strength of the relationship between grain length (l) and width (b) falls into the “weak” category, while the relationship between grain width (b) and shape factor (l/b) is categorized as “moderate”. The correlation coefficients between grain length (l) and shape factor (l/b) are at the lower end of the “strong” relationship category, ranging from 0.69 to 0.84 with an average of 0.76. In accordance with the established scale for ρ, this indicates a strong correlation. The grinding method does not appear to have a significant effect on the correlation strength. We explored the feasibility of modeling the relationships between geometric parameters using a standard set of functional dependencies within Microsoft Excel. Table 4 presents the constant values and coefficients of determination (R2) for the approximations of the relationships between the geometric grain parameters, based on the following dependencies: l = a1b; (1) l/b = a2b + c1; (2) l/b = a3l; (3) l/b = a4l+ c2. (4) Ta b l e 4 Constant coefficients and confidence coefficients for approximating the relationship between geometric parameters of grains Roller-press grinding Fraction l = a1b l/b = a2b + c l/b = a3l l/b = a4l+ c2 а1 R 2 a 2 c R 2 a 3 R 2 a 4 c2 R 2 1 1.39 0.10 –0.00044 2.54 0.16 0.00054 0.65 0.00037 0.065 0.72 2 1.34 0.10 –0.00046 2.25 0.17 0.00053 0.55 0.00044 0.247 0.57 3 1.37 0.10 –0.00079 2.30 0.13 0.00087 0.69 0.00078 0.141 0.70 4 1.35 0.20 –0.0017 2.49 0.22 0.0015 0.55 0.00135 0.145 0.56 5 1.37 0.15 –0.0029 2.41 0.19 0.0029 0.55 0.00255 0.176 0.54 R2m – 0.13 – – 0.17 – 0.58 – – 0.63 Rotary grinding Fraction l = a1b l/b = a2b + c l/b = a3l l/b = a4l + c2 а1 R 2 a 2 c R 2 a 3 R 2 a 4 c2 R 2 1 1.33 0.15 –0.00037 2.31 0.17 0.00038 0.64 0.00035 0.138 0.64 2 1.32 0.21 –0.00051 2.30 0.21 0.00053 0.56 0.00046 0.188 0.57 3 1.29 0.13 –0.00075 2.16 0.20 0.00089 0.47 0.00070 0.277 0.51 4 1.32 0.25 –0.0015 2.32 0.24 0.0015 0.49 0.00129 0.219 0.51 5 1.31 0.21 –0.0029 2.31 0.24 0.0029 0.45 0.00238 0.243 0.48 R2m – 0.19 – – 0.21 – 0.52 0.54
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