The last 90 years have generated a considerable volume of technical literature on the subject of grinding mill power and its prediction. It is therefore surprising that in all this time there have been no published models for predicting grinding mill power draw which have been validated using a published wide range of comprehensive industrial scale data.
Notwithstanding this lack of data, the majority of models have placed limited emphasis on the internal dynamics of mills and have relied on simple assumptions which consider the charge to take up a fixed position and shape. In recent years laboratory based studies (Liddell, 1986) have shown that these assumptions do not hold over a wide range of operating conditions, and bring into doubt the ability of existing models to accurately predict grinding mill power draw.
To remedy this deficiency a research programme was therefore undertaken to:
• provide a large compehensive data base of the power draws of industrial scale ball, semi-autogenous (SAG) and autogenous (AG)
• use these data to develop mathematical models which can accurately predict the power draw of industrial grinding mills over a wide
range of operating and design conditions
The approach which was adopted utilized a glass fronted laboratory mill, operating under a range of speeds and fillings, to provide data on the movement of a charge in a grinding mill. The position of critical points in the charge and the velocity of particles within the charge were measured with the aid of photographic techniques. These measurements were then related
mathematically to the operating conditions using empirical techniques.
The equations which were developed from this exercise were incorporated in a theoretical approach to the prediction of power draw. The resultant model explicitly described the effects of the mill discharge mechanism (i.e. grate or overflow), as well as the shape of the end sections (i.e. planar or conical). The model made no specific distinction between ball, semi-autogenous (SAG) or autogenous (AG) mills except by virtue of their charge density and/or discharge mechanism. Two further models were developed, one of which was more complex in nature but which additionally accounted for the effect of grinding media size distribution on power draw. The other model was an empirical version with a very simple form yet similar predictive performance to the other two.
Data were collected from a wide range of wet industrial grinding mills to calibrate and verify the model. In
total 76 data sets were generated covering the power draws of ball, SAG and AG mills in the range 7 - 7900 kW. All three models were found to predict the power draw of the mills in the data base with a high degree of accuracy. This contrasted with the results from testing a number of existing published models, none of which were found to be entirely satisfactory.