## 4 Results and Discussion
### Parameter Identification of the Pneumatic Classification Process  
This section describes the analysis of the impact of the loading and unloading time for material in a layer on the quality of pneumatic classification. The presented pneumatic classification process is cyclic and divided into two main stages (2 and 3 in Figure 5). At stage 2, the material is fed into the body by a dosing device. At stage 3, the gradual unloading of granular material accumulated in a suspended layer occurs. In the process of feeding, the operating time of the dosing device significantly impacts the separation efficiency. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Mass (g)**} & \multicolumn{2}{c}{**Fraction (mm)**} \\ \cline{3-4}  & & **0.16–0.20** & **0.40–0.63** \\ \hline Starting mixture & 1129 & 575 & 554 \\ Concentration (\%) & 100 & 51 & 49 \\ Fine fraction tank & 591 & 563 & 29 \\ Concentration (\%) & 100 & 95 & 5 \\ Coarse fraction & 526 & 23 & 504 \\ Concentration (\%) & 100 & 4 & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of river sand separation. Figure 4: Estimation of the separation efficiency for the process of pneumatic classification. At the initial stage 1 (continuous loading), the material is continuously fed into the pneumatic classificator. This mode reduces the total time of the process, but the separation efficiency does not exceed 60%. Consequently, the loss of the main fraction reaches 40%. At the first stage (operating area), there is a decrease in the losses of the main fraction before loading the material layer. Reducing the loss occurs until 20 s before reloading, and then the process proceeds to the next stage (flow fracture area). At this stage, losses of the main fraction increase. The loading time additionally affects the total time of the process. To optimize the time \(T\) for additional loading of various materials, the following dependence is proposed based on the obtained experimental data:  
\[T=a\cdot\left(\frac{D_{c}}{D_{f}}\right)^{-n}, \tag{7}\]  
where \(D_{c}\) and \(D_{f}\) are particle sizes of a coarse and fine fraction (mm), and \(a\) and \(n\) are experimental constants. This dependence (Figure 6) shows that the greater the ratio of coarse and fine fractions is, the lower the time it takes to reload the rotating layer is. Additionally, the closer the boundary of the separated fractions is, the more time is required to reload the material. Increasing the feeding time reduces the total time of the process, but negatively impacts the separation efficiency since it increases the loss of the main fraction and its contamination by the fine fraction. Additionally, an oversaturating mixture in the rotating layer gradually falls down. This fact leads to the overlap of gas flow at the inlet. As a result, the gas flow removes coarse and fine fractions. Based on the obtained data, optimal time limits should be selected for each cycle of loading that affects energy loss and the efficiency of the process. Thus, a mathematical model for evaluating  
Figure 5: Losses of the main fraction during the pneumatic classification process: 1—continuous loading; 2—operating area; 3—flow fracture. Figure 6: Experimental results and the corresponding approximation curve. the parameters of Equation (7) is proposed. This model is based on using quasi-linear regression analysis [25].