How much energy it takes to break an ore, and what Axb says about hardness.
-Specific energy Ecs (kWh/t)
-Impact energy (J)
-Impact speed (m/s)
-Expected t10 (%)
-Axb (true)
-Hardness class (indicative)
-Axb fitted from your drops
-Drops recorded
The science
In a drop-weight test a known mass falls from a known height onto a rock particle. The energy delivered is m g h; dividing by the particle mass gives the specific comminution energy Ecs, converted with 1 kWh/t = 3600 J/kg. The impact speed is sqrt(2 g h).
The product is characterised by t10, the percentage passing one tenth of the parent size. Napier-Munn and co-workers at the JKMRC fitted t10 = A (1 - exp(-b Ecs)). At low energy the slope is A b, the number called Axb: the lower it is, the harder the ore resists impact breakage and the more energy a SAG mill needs.
The simulation draws noisy measurements around the true curve and re-fits A and b by least squares. More drops across a wide range of energies recover the parameters better; with few points or high noise the fit wanders, as in a real test programme.
Honest simplifications: one size class, a single particle per drop, the full drop energy attributed to the particle, a schematic power-law shape for the product size curve anchored only at t10, and indicative hardness bands rather than a standard.