Summary
The grinding processes in ball mills are far too complex for an exact mathematical description. The well known, simple Comminu-tion Laws and the phenomenological Population Balance Model provide equations for an estimation of the dependence between feed size, energy consumption and product size distribution. Important parameters like ball size, mill filling or mill speed, however, are not included in these equations. A more detailed quantitative description of the comminution processes seems necessary. For this purpose, the complex grinding process was split into several fundamental processes:
a) Singleparticle fragmentation: the basic process in grinding.
b) Fragmentation under packed bed conditions: packing structure determines the distribution of comminution energy flowing into individual single particles in the bed.,
c) Fragmentation by an impacting ball: a packed bed with position-dependent loading intensity is formed during impact.
d) Comminution in a ball mill:if the kinetic energy distribution of the balls in the mill would be known, then the comminution process could be described in terms of a) to c). '
Experimental and theoretical investigations as well as evaluation of published experimental data gave following results:
a) Based on fracture mechanics, Weibull flaw size distribution statistics and Hertz-theory of contact forces, simple equations have been derived for the probability of breakage, mass specific comminution energy and fragment size distribution of singlepar-ticles. The theory contains a few parameters to be determined experimentally and was tested successfully on published experimental data.
b) The contact energy distribution of particle assemblies under packed,bed conditions has been determined experimentally using packed beds of polished soft steel balls. Combining this distribution with the single particle fragmentation theory according to a), allows the prediction of the fraction of broken particles in packed bed experiments. The theoretical predictions were verified with experiments carried out on glass spheres.
c) The fragmentation of particle assqnblies between a stationary and an impacting ball was studied in detail with simple equipment at the University of Karlsruhe and with the ultra fast load cell of the University of Utah. Both investigations provide evidence that the height of the particle bed is reduced to only 1 to 2 particle layers when comminution begins to be effective. This has to be taken into account in further modeling.
d) The mathematical description of ball mill grinding in terms of processes a) to c) is the final aim of the theoretical development. This, however, was beyond the scope of this research project.