Bond’s law

Bond postulated that work required to form particles of size Dp from very large feed is proportional to the square root of the surface-to-volume ratio of the product, Sp/Vp. By relation Sp/Vp = 6/ɸsDp, from which it follows that

P/ ṁ = Kb/(Dp)^0.5

Where Kb is a constant that depends on the type of machine and on the material being crushed. To use this equation, a work index Wi is defined as the gross energy requirement in kilowatt-hours per ton of feed needed to reduce a very large feed to such a size that 80% of the product passes a 100-µm screen. This definition leads to a relation between Kb and Wi. If Dp is in millimeters, P in kilowatts, and ṁ in tons per hour,

Kb = 0.3162 Wi

If 80% of the feed passes a mesh size of Dpa millimeters and 80% of the product a mesh of Dpb millimeters, it follows

P/ ṁ = 0.3162 Wi [1/(Dpb)^0.5 - 1/(Dpa)^0.5]

Rittinger’s and Kick’s laws

Rittinger's law states that work required in crushing is proportional to the new surface created. In other words, crushing efficiency is constant and for a given machine and feed material is independent of the sizes of feed and product. Rittinger’s law is written as-

P/ ṁ = Kr(1/Dsb – 1/Dsa)

Kick proposed another law based on stress analysis of plastic deformation within the elastic limit, which states that the work required for crushing a given mass of material is constant for the same reduction ratio, that ia, the ration of the initial particle size to the final particle size. This leads to the relation

P/ ṁ = Kk ln(Dsa/Dsb)