Mathematical Sizing of Grinding Mills Using Bond's Equation

A common method use in ill sizing involves work index numbers based on the Bond testes. The following mathematical relationship for estimating mill power requirements applies:

Where:

W = Kilowat hours per short ton.
W_i = Constant known as the Work Index.
P₈₀ = Size in microns 80% of the feed passes.
F₈₀ = Size in microns 80% of the feed passes.

W_i can be obtained from laboratory batch test, or its value can be approximated form prior experience with related materials.

The following data can be used to illustrate the Bond method in sizing a ball mill operating in closed circuit.

Work index = 13.0
Feed Size is 95.99% minus ½”
Product Size is 75% minus 200 mesh
Capacity = 60 stph

First convert to 80% passing.

From the table on the opposite page select 8500 microns as the F₈₀ size for 99% passing 75% the P80 size can be determined from a distribution curve or approximated form the Gates-Gaudin-Schumann relationship as follows:

The horsepower calculated for an overflow ball mill corresponds to an 11’ 6” x 15’ mill, 11’ 6” is the diameter inside the shell, and the diameter inside the liners, D, is 11’ 0”.

A series of correction factors are considered in the Bond method. Some of the more common ones are shown on the previous page.