## 2 Materials and Methods
### Abrasion Energy Input (Mechanical Work) and Power Estimation  
The mechanical work done by the machines was estimated theoretically. It was also attempted to calculate the mechanical work from the power draw measurements. The effective net power draw was determined as the difference between the measured idling (no load) power draw of the machines and the power draw of the filled machines (with charge). This estimation was determined according to the assumption that the total power draw (\(P\)) is a sum of the net (effective) power draw (\(P_{NET}\)), used for the comminution process, and the idling/no load power draw (\(P_{NL}\)) (Equation (4)). \[P=P_{NL}+P_{NET} \tag{4}\]  
The power draw was measured using the energy consumption meter \"VOLTCRAFT SEM6000\". This consumption meter measures the power, voltage, current, and frequency that are feeding a machine. When measuring power draw, the measurements started after the shift from star to delta transformation, meaning that the beginning power tends to be higher to start the initial motion of the machine. The mechanical work (energy) estimated for the abrasion machines (both micro-Deval and Los Angeles) was used for initiating particle motion, sound, temperature rise, abrasion, etc. That is why the estimated energy/mechanical work was taken into consideration as the energy/mechanical work to which a particle was subjected. In the abrasion machines, energy levels were considered to stay constant throughout the whole cycle. The mechanical work (energy) used by both machines was also approximated theoretically. The theoretical calculation was simplified as described below (Equations (5)-(8)). For the micro-Deval apparatus, mechanical work was considered to be a result of the rotational kinetic energy (\(E_{k}\)) of the charge (including steel charge and a rock particle) inside the drum. For the calculation, all of the charge (water, steel balls, and rock particle) was considered as a whole, with an equally distributed mass. Buoyancy was neglected. It was assumed that there is no friction between the steel balls, and between the steel balls and the drum lining. Also, due to the absence of friction, the material was assumed to be rolling around the lowest point of the drum's cross section. \[W=W_{rot}=E_{k}*\Delta\phi \tag{5}\]  
where: \(W\)--mechanical work (J); \(W_{rot}\)--mechanical work introduced by rotation (J); \(E_{k}\)--kinetic energy (J); \(\Delta\phi\)--angular displacement (-);  
\[E_{k}=1/2*I*\omega^{2} \tag{6}\]  
where: \(I\)--moment of inertia (of charge) (kg/m\({}^{2}\)); \(\omega\)--angular velocity (rad/s);  
\[I=m*{r_{m}}^{2} \tag{7}\]  
where: \(m\)--mass (of the charge) (kg); \(r_{m}\)--distance from the centre of the drum cross section to the centre of mass of charge (m);  
\[\Delta\phi=\Delta d/r \tag{8}\]  
where: \(\Delta d\)--linear displacement (on the perimeter of the drum cross section) (m); \(r\)--radius of the drum's cross section (m). For the Los Angeles machine, the mechanical work was considered to be a result of the kinetic energy of the impact when a material drops to the toe of a drum, and the rotational kinetic energy of the charge inside the drum (Equations (9)-(12)). Due to the low filling of the drum (0.35% in first cycle, up to 0.28% in fifth cycle), it was taken into consideration that all of the material inside of the drum was lifted by the lifter/shelf and was carried on it for half of the rotation until it reached the highest point of the drum's cross section (shoulder), when it dropped and impacted the toe of the drum. For the other half of the rotation, until it was collected again by the lifter, the material was under the influence of rotational kinetic energy.