# Experimental Research into the Efficiency of an Electromagnetic Mill
## 4 Analysis of Results of the Experiment  
The experimental study primarily focused on the quantitative analysis of the relation between a set of technological indicators of the grinding process and its efficiency. An experiment forms the most suitable way of verifying the validity of the assumptions that were utilized and to verify the results of the mathematical modeling of the dynamic process inside the working chamber of the mill based on a two-dimensional approach to the process. A natural mineral, calcium carbonate (CaCO\({}_{3}\)) was identified as the grinding medium. Its average density is 2540 kg/m\({}^{3}\) and hardness on the Mohs scale is 4.3 \(\div\) 4.5. Particles of this material had the average size of 2 \(\div\) 5 mm before grinding. A four-dimensional space of the experiment factors was established, namely: \(t_{z}\)--grinding duration; \(d_{m}\)--millstone diameter; \(m_{m}\)--millstone mass; \(m_{WS}\)--grinding substance mass. Discreet values of those factors are: \(t_{z}\) = 60 s, 120 s, 180 s, 240 s, 300 s, 360 s, 420 s; \(d_{m}\) = 2 mm, 3 mm, 4 mm (the ratio of the mill length to its diameter was 10 in all cases); \(m_{m}\) = 50 g, 100 g, 200 g, 400 g, 800 g; \(m_{WS}\) = 50 g, 100 g, 200 g, 400 g, 600 g.  
On the basis of those values, research was conducted in a 22-step plan of the experiment. The obtained results (including the mass of the fractions of ground WS and mass of the unground leftovers) are presented in Table 1. Measurements no. 1 to 7 demonstrate quantitative variations of the individual fractions depending on the duration of the grinding process in the conditions of constant ratios of millstones and ground substance for a 2:1 ratio of ground substance to millstones. In experiments no. 8 to 10, the dependence of the distribution of masses in individual fractions in relation to the dimensions of the millstones was examined for a constant grinding time equal to 420 s and for a constant ratio of ground mass and millstones of 2:1. Experiments no. 11 to 16 indicate the dependence of the mass distribution in individual fractions on the number of millstones and their size at  
Figure 2: Basic electrical diagram. a constant mass of ground substance and grinding time. Experiments no. 17 to 22 examined the dependence of the mass distribution in individual fractions on the amount of the ground substance and the dimensions of the millstones at a constant mass of millstones and grinding time. Figure 3 shows the distribution of the WS fraction recorded after experiment no. 10 in an illustrative form (Table 1). It presents the distribution of WS fraction prior to grinding (fraction \(2\div 5\) mm, weight 400 g) and individual fractions after grinding: fraction \(>2\) mm, weight 72 g; fraction \(1\div 2\) mm, weight 22 g; fraction \(0.5\div 1\) mm, weight 11 g; fraction \(0.25\div 0.5\) mm, weight 56 g; fraction \(<0.25\) mm, weight 239 g. A set of sieves presented in Figure 1c was used for the selection of the mentioned fractions. The obtained experiment results are non-deterministic. In order to analytically describe this particular set of results regression analysis was utilized, which is used on functions defined by tables (TF). It represents the dependence of the field of the electrodynamic force acting on the grinding medium in the center of WC, on parameters such as the phase \(\varphi\) of the resultant EMM of the inductor winding, the length of the radius of the location of the center of mass of the grinding medium \(r_{m}\) and inclination angle of this radius \(\gamma_{m}\). In order to approximate each particular table function, an analytical expression describing the function is used, for a function closest to the TF giving its properties (power polynomials, trigonometric polynomials, elementary or special functions). However, in this case (TF Table 1), no information for any such function exists; therefore, power polynomials are commonly utilized. For a TF with one or more independent variables, a Taylor series forms the most appropriate one.