Crushing efficiency

The ratio of surface energy created by crushing to the energy absorbed by the solid is the crushing efficiency ɳ_c. if e_s is the surface energy per unit area, in feet times pound force per square foot, and A_wb and A_wa are the areas per unit mass of product and feed, respectively, the energy absorbed by a unit mass of the material W_n is

W_n = e_s(A_wb- A_wa)/ ɳ_c

The surface energy created by fracture is small in comparison with the total mechanical energy stored in the material at the time of rupture, and most of the latter is converted into heat. Crushing efficiencies are therefore low.

The energy absorbed by the solid W_n is less than that fed to the machine. Part of the total energy input W is used to overcome friction in the bearings and other moving parts, and the rest is available for crushing. The ratio of the energy absorbed to the energy input is ɳ_m, the mechanical efficiency. Then, if W is the energy input,

W = W_n/ ɳ_m = e_s(A_wb- A_wa)/ ɳ_c ɳ_m

If ṁ is the feed rate, the power required by the machine is

P = W ṁ = ṁ e_s(A_wb- A_wa)/ ɳ_c ɳ_m