Optimal Ball Size Tool

The Optimal Ball Size tool is designed to estimate the ideal make-up ball size for any given grinding application. This estimation is based on empirical correlations independently proposed by Ettore Azzaroni and Allis Chalmers. In cases where the ideal ball size is not commercially available, this tool also allows for designing a mix recharge policy (with a maximum of two different make-up sizes) to maintain the same ideal ball charge area.

To determine the ideal size (diameter) of balls to be continuously recharged into a grinding mill for maximum performance, the following two independent empirical correlations have been proposed in the literature:

Ettore Azzaroni's Formula: (3rd ARMCO-Chile Symposium, Nov. 10-14, 1980)

Allis Chalmers' Formula: (Mineral Processing Plant Design, Chapter 12, SME of AIME, 1980)

Where:

• dR*: Ideal Make-up Ball Size, inches
• F80: 80% Passing Size in the Fresh Feed Stream, microns.
• ρm: Ore Density, t/m³.
• BWi: Bond's Work Index of the ore, kWh/t (metric).
• N: Rotational Mill Speed, rpm.
• Nc: Rotational Mill Speed, as a percentage of the Mill Critical Speed.
• D: Effective Mill Diameter, feet.