# A Study of Magnetic Mill Productivity
## 10 Verification of the Model Using a Physical Experiment
Figure 14: Laboratory setup for studying the MM: 1—inductor with PM; 2—working chamber; 3—driving engine; 4—supervision system; 5—support arrangements of the supporting and rotating device; 6—tripod; 7—illumination lamp; 8—bed plate. The duration of the video recording in real time was \(\approx\)2.5 s. The obtained video recording was used to determine characteristics of the movement of millstones in real conditions of conducting a physical experiment. Specialized software Tracker 5.1 (OSP) [34] was used to process the results of this experiment, in particular to monitor the behavior of millstones in real time, their reference to the coordinate system, size calibration, determination of positions, values of velocity projections, etc. Time alignment of the calculation process with the experimental process took place with the help of the initial condition obtained on the basis of analysis of the video recording of the experiment, using the aforementioned Tracker software. This condition contains information about the initial inclination of the axis \(+d\) of the magnetic system of the inductor (\(\gamma_{i}=-115.0^{\circ}\), Figure 2), the initial positions of the five millstones for \(t\) = 0 s, and their linear velocities at that moment. All this information is presented in Table 1.  
A comparison of five frames of the video recording and images obtained on the basis of the calculation, corresponding to the moments of time 0.0 s, 0.03 s, 0.06 s, 0.09 s, and 0.12 s, is shown in Figure 15. The numbering of millstones (from 1 to 5) is conventionally shown there. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of the** & **Radius Vector** & **Angular Coordinate of the** & **Angle of Rotation** & **Module of the** & **Direction of the** \\
**Millstone** & \(\mathbf{r_{m}}\)**, \(\mathbf{m}\)** & **Coordinate of the** & \(\mathbf{\alpha_{m}}^{\circ}\) & **Velocity Vector** & **Velocity Vector** \\  & & **Millstone \(\mathbf{\gamma_{m}}^{\circ}\)** & \(\mathbf{\alpha_{m}}\)**, \(\mathbf{m/s}\) & \(\mathbf{\alpha_{v}}^{\circ}\) \\ \hline
1 & 0.0361 & \(-141.2\) & \(-35\) & 0.7066 & \(104.4\) \\
2 & 0.0325 & 126.9 & \(-25\) & 1.9329 & \(-59.9\) \\
3 & 0.0513 & 82.7 & 45 & 0.4190 & \(-68.4\) \\
4 & 0.0252 & 79.1 & 100 & 2.0095 & \(-105.7\) \\
5 & 0.0242 & 12.5 & 100 & 1.3913 & \(-101.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial condition. Figure 15: _Cont._  
Direct analysis of the video recording of the process showed that the direction of rotation of a millstone around its own axis is opposite to the direction of rotation of the inductor field. This is due to several reasons. Firstly, it is due to the relatively large difference between the rotation frequency of the field and the rotation frequency of the mill around the WC axis. The second reason is the displacement of the rotation axis of each millstone relative to the inductor axis, as a result of which the force effect on the opposite ends of the millstone is different both in magnitude and direction. The trajectories of millstones with numbers 1, 3 and 5 obtained by experimental and calculation methods are compared in Figure 16. The graphs in the polar coordinate system show hodographs of the vector \(\overline{r_{m}}\) and the radius vector of the point of application of one of the pair of forces \(\overline{F_{o}}\), namely point 1 (Figure 2). This dependence reflects the rotational movement of the millstone around its own center of mass. Figure 15: Positioning of millstones in the WC at moments of time: (**a,f**) 0.0 s; (**b,g**) 0.03 s; (**c,h**) 0.06 s; (**d,i**) 0.09 s; (**e,j**) 0.12 s; determined on the basis of the experiment (**a–e**); based on the calculation (**f–j**). As can be seen from this comparison, the calculated trajectories mainly reflect the characteristic features of the behavior of ferromagnetic millstones in a rotating magnetic field. A movement around the center of the WC in the direction of rotation of the magnetic field and rotation around an axis passing through the center of mass is observed.