Advanced Powder Technology, Available online 19 October 2013.

V.K. Gupta, Shivani Sharma.

Department of Fuel and Mineral Engineering, Indian School of Mines, Dhanbad 826 004, India

**Abstract**

With a view to developing a sound basis for the design and scale-up of ball mills, a large amount of data available in the literature were analyzed for variation of the two key mill performance parameters: power specific values of the ‘absolute breakage rate of the coarsest size fraction’, *S*^{*}, and ‘absolute rate of production of fines’, *F*^{*}, with some of the important operating and design variables such as the mill speed, ball load, particle load, ball diameter and mill diameter. In general, values of both the mill performance parameters were found to vary significantly with the mill operating conditions. The nature and relative magnitude of variation for the two parameters also differed significantly. Moreover, the effect of any particular variable on the *S*^{*} and *F*^{*} values was found to be significantly different for different sets of operating conditions. It has been emphasized that, as the purpose of grinding is to produce fine particles, the mill design and scale-up work should be based mainly on the *F*^{*} parameters. Moreover, it is not correct to regard the *S*^{*} values to be independent of the mill design and operating variables as a general rule, especially for a fine analysis of the performance of the grinding systems.

**Additional Information**

In this paper, energy consumption in the ball mill grinding operation has been analyzed under different operating conditions in terms of two key performance parameters: (i) mill power specific absolute grinding rate of the coarsest size fraction of particles, S*, and (ii) mill power specific absolute rate of production of the ground product that is finer than a specified size, F*. The operating variables considered are: mill speed, ball load, particle load, ball diameter and mill diameter. The materials studied are: quartz, limestone, dolomite and two types of cement clinker. Important findings are described below:

- In general, both the performance parameters vary significantly (20-40%) with the mill operating variables. However, they do not vary in the same proportion. The effect of mil speed, ball load and mill diameter is relatively more pronounced for F*. The opposite is true for the effect of particle load and ball diameter on S* and F*.
- The effect of any particular operating variable on S* and F* is different for different materials. Soft materials and fine particles are ground more energy efficiently on lower mill speeds. And, the effect of ball diameter on F* is relatively less pronounced in case of hard materials.
- For a given material, the effect of any particular operating variable on S* and F* is different for different combinations of values of the other operating variables.
- Results obtained in the case of wet mode of grinding differ from those obtained in the case of dry mode of grinding. For example, in the case of wet grinding of limestone, the effect of mill speed on F* was found to be significantly less pronounced than that observed for S*.
- In view of the above mentioned observations, it is not possible to develop a general quantitative correlation which is valid for all materials and for all possible combinations of values of the mill operating variables.
- It is proposed that for any given material, the optimum values of various operating variables should be established by carrying out some well designed experiments in a laboratory ball mill. These experiments should cover the likely range of operating variables for the production mill. And, the best combination of the values of the operating variables would be the one that gives the highest value for F*.