A new general formula to predict the specific energy of grinding in ball mills and vertimills


Published in Proceedings of the IMPC2020 Congress, SAIMM


Since 1952, Bond’s equation has been used as a standard to predict the specific energy of grinding for a given duty. The Bond’s equation considers that the exponent is constant for all conditions. Hukki, in 1961, pointed out that the exponent is a function of the particle size, and concluded that the Bond’s equation applies successfully for an intermediate range of sizes; out of this range the Bond’s equation leads to high error as demonstrated in this paper.

More recently, in 2004, S. Morrell presented a new formula in which the exponents vary with the feed and product size. This paper is based on Hukki’s approach and presents a new general formula, in which the exponent varies only with the feed particle size. This new equation has been proven in 82 observable cases in Peru and other countries around the world, involving ball mills and vertimills in different configurations over a wide range of feed and product sizes, work indices and mill diameters; in most cases, the predicted value has an error less than 10% with regards to the observed value and no need for any correction factor.


Grinding, specific energy, particle size, work index, variable exponen


The author would like to thank Metso:Outotec for allowing the publication of this paper


R.V. Pechea*

aAuthor, Chief Process Metallurgist, Metso:Outotec, Lima-Peru*Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

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