# Experimental Research into the Efficiency of an Electromagnetic Mill
## 6 EMM Efficiency and Grinding Quality
The relation of this coefficient to the loading level of the WC or the WS layer height was approximated based on physical considerations and analysis of the experimental data from a quality point of view (Figure 7). The final shape of the relation \(k_{kr}(L_{n})\) will of course require additional experimental studies. The results of mathematical experimentation and calculated values of the average number of impacts and their impulse are presented in Table 3. It should be noted that the numbers of experiments given in Table 3 correspond to numbers of experiments in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No. of** & **Efficiency** & **Quality** & **Layer** & **Number** & **WS** & **Average** & **Average** & **Adjusted** \\
**Experiment** & **[g/s]** & **Quality** & **Height of Mix in** & **of Mill-** & **Particle** & **Impacts in** & **Impacts in** & **Force Impulse** \\
**m** & **WC [m]** & **WC [m]** & **WC [m]** & **WC [m]** & **WC [m]** & **WC [m]** & **WC [m]** & **WC [m]** \\ \hline
1 & 2.2833 & 0.4672 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(8.394\times 10^{-4}\) & \(1.214\times 10^{-4}\) \\
2 & 1.4417 & 0.4682 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(1.679\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
3 & 1.0778 & 0.5000 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(2.518\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
4 & 0.8667 & 0.5433 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(3.358\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
5 & 0.7167 & 0.5628 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(4.197\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
6 & 0.6139 & 0.6651 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(5.037\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
7 & 0.5357 & 0.7556 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(5.876\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
8 & 0.6024 & 0.4822 & 0.031 & 53 & 156 & 27.98 & \(1.071\times 10^{-4}\) & \(5.876\times 10^{-5}\) & \(1.214\times 10^{-4}\) \\
9 & 0.7381 & 0.4226 & 0.031 & 24 & 234 & 27.00 & \(2.556\times 10^{-4}\) & \(5.670\times 10^{-5}\) & \(2.897\times 10^{-4}\) \\
10 & 0.7810 & 0.7287 & 0.031 & 13 & 307 & 54.15 & \(1.668\times 10^{-4}\) & \(1.137\times 10^{-5}\) & \(1.890\times 10^{-4}\) \\
11 & 0.6583 & 0.2595 & 0.028 & 15 & 175 & 15.67 & \(9.247\times 10^{-5}\) & \(1.880\times 10^{-5}\) & \(9.273\times 10^{-4}\) \\
12 & 0.8250 & 0.3889 & 0.029 & 29 & 168 & 21.21 & \(1.083\times 10^{-4}\) & \(2.545\times 10^{-5}\) & \(1.134\times 10^{-4}\) \\
13 & 0.9333 & 0.3929 & 0.035 & 93 & 137 & 41.31 & \(9.303\times 10^{-5}\) & \(4.957\times 10^{-5}\) & \(1.212\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of computational studies of the grinding process. Figure 7: The relation between the adjustment coefficient and the WC load level. To extend the capability of the analysis of the obtained data, regression analysis was utilized, similar to the one described earlier (3)-(11). Proposed methods of fitting data (18)-(20) resulted in the reduction in the number of independent variables to three. Those are millstone diameter \(d_{m}\), average number of millstone impacts \(k_{st}\) and the adjusted force impulse of those impacts \(S_{sk}\). The Taylor polynomial used in regression of efficiency \(P_{m}\) and quality \(Q_{m}\) is expressed in scalar notation:  
\[Y=c_{1}+c_{2}x_{1}+c_{3}x_{2}+c_{4}x_{3}+c_{5}\frac{x_{1}^{2}}{2!}+c_{6}x_{1}x _{2}+c_{7}x_{1}x_{3}+c_{8}\frac{x_{2}^{2}}{2!}+c_{9}x_{2}x_{3}+c_{10}\frac{x_{3} ^{2}}{2!} \tag{22}\]  
Regression coefficients \(\stackrel{{\rightarrow}}{{c}}\) are displayed in Table 4.  
Figure 8 presents the relations of efficiency \(P_{m}\) and quality \(Q_{m}\) to two technological indicators--duration and millstone diameter. The other independent variables were assumed to be constant. The values obtained here allow for a comparison with values obtained directly from the experiment.