OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 For grains produced by roller-press and rotary grinding, the accuracy of the approximation using the linear dependence l =a1b (1) does not exceed 0.25, indicating a weak correlation. Similarly, modeling the dependence of the shape factor (l/b) on grain width (b) using equation (2) yielded low approximation accuracy. A significant improvement in R2 was achieved using a direct proportional relationship (3), with average approximation reliability coefficients of 0.58 and 0.52 for grains produced by roller-press and rotary grinding, respectively. Replacing the proportional relationship with a linear one (4) resulted in only a marginal increase in approximation reliability. As an illustration, fig. 5 depicts the regression relationships between the geometric parameters of fraction 3 grains produced by roller-press grinding (figs. 5, a; 5, b) and rotary grinding (figs. 5, c; 5, d). The data points in figs. 5, a and 5, b were approximated using a direct proportional relationship (l = a1b), while those in figs. 5, b and 5, c were approximated using a linear relationship (l/b = a2b + c). It is worth noting that following roller-press grinding, the relative proportion of grains with a length exceeding, for example, 4,650 μm (fig. 5, a), is significantly higher than that after rotary grinding (fig. 5, c), which affects the shape factor. The number of grains with a shape factor l/b > 2 is 3.5 times greater after roller-press grinding than after rotary grinding (figs. 5, b and 5, d). Similar trends are observed in other fractions. Fig. 6 illustrates the dependence of the shape factor on grain length for each of the five fractions. Within the range of l/b values from 2 to 4, the distribution density of needle-shaped grains obtained by roller-press grinding (fig. 6, a) is substantially higher than that of those produced by rotary grinding (fig. 6, b). In the larger fractions (1–3) obtained by roller-press grinding (fig. 6, a), grains with a shape factor exceeding 3 are absent. Grains with a shape factor exceeding 3 are absent in all fractions produced by rotary grinding (fig. 6, b). a b с в Fig. 5. Regression relationships between geometric parameters of grains in fraction 2: a, b – roller-press grinding; c, d – rotary grinding
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