# Study on the Population Balance Dynamics Simulation of Grinding under Impact Crushing
## 3 Results and Discussion
### The Population Balance Dynamics Simulation of Grinding under Impact Crushing of PyrrIhotite
#### 3.2.3 Calculation of the Selection Function  
The calculation process for the selection function is the same as that in Section 3.1.3. By batch grinding the test data, the relationship between the particle size selection function \(S_{i}\) and time for the pyrrhotite with different feed particle sizes is calculated as shown in Figure 7.  
According to Figures 2 and 7, the selection functions for each particle size of pyrrhotite and quartz have similar characteristics. The selection function of each particle size shows  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Particle Size/mm**} & \multicolumn{10}{c}{**Nominal Particle Size/mm**} \\ \cline{2-11}  & **2.8118** & **2.003** & **1.4163** & **1.0015** & **0.7141** & **0.5050** & **0.3571** & **0.2522** & **0.1783** & **0.1261** & **0.0892** & **0.0630** & **0.0449** \\ \hline \(-3.35+2.36\) & 0.0001 & & & & & & & & & & \\ \(-2.36+1.7\) & 0.0012 & 0.0000 & & & & & & & & & \\ \(-1.7+1.18\) & 0.0096 & 0.0012 & 0.0001 & & & & & & & & \\ \(-1.18+0.85\) & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & & & & & & \\ \(-0.85+0.60\) & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0002 & & & & & & \\ \(-0.6+0.425\) & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0001 & & & & & \\ \(-0.425+0.3\) & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & & & \\ \(-0.3+0.212\) & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & & \\ \(-0.212+0.15\) & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & & \\ \(-0.15+0.106\) & 0.1007 & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & \\ \(-0.106+0.075\) & 0.0835 & 0.1007 & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 & & \\ \(-0.075+0.053\) & 0.0540 & 0.0835 & 0.1007 & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0001 & \\ \(-0.053+0.038\) & 0.0427 & 0.0540 & 0.0835 & 0.1007 & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 \\ \(-0.038+0.013\) & 0.0600 & 0.0427 & 0.0540 & 0.0835 & 0.1007 & 0.1202 & 0.1299 & 0.1063 & 0.0657 & 0.0010 & 0.0858 & 0.0096 & 0.0012 & 0.0000 \\ \hline \hline \end{tabular}
\end{table}
Table 9: The \(\mathbf{b}_{ij}\) matrix of pyrrhotite under impact crushing.  
Figure 7: The relationship curve between the \(S_{i}\) and time of pyrrhotite: (**a**) \(-3.35+2.36\) mm, (**b**) \(-2.36+1.7\) mm, (**c**) \(-1.7+1.18\) mm.  
an overall downward trend over time, with the selection function of the coarse particle size being higher than that of the fine particle size. Moreover, the selection functions of the fine particle sizes are all small, and their changes over time are not particularly significant. And the selection functions of the fine particle sizes are even close to zero, indicating that the probability of them being selected for breakage is minimal. At the same time, Figure 7 further reveals that the selection function diminishes with a decrease in feed particle size.