Self-Similarity In Particle Bed Comminution

The progress in comminution is often described by the specific surface area and the energy utilization or the brakeage ratio and breakage function. The principal mechanisms of size reduction are therefore, well known. All four parameters share a common disadvantage: They are limited in describing the behavior of a feed material with fine particles and a wide particle size distribution. An alternative is to describe the progress in comminution with ? The particle size distributions Q(x) before and after the stress or ? The particle concentration ratio pcr(x), which combines these two states. In the case of a self-similar fracture behavior, (in short: self-similarity) the progress in comminution can be simplistically described by the relationship between a reference particle size and the stress intensity. Self-similarity means self-similar breakage functions of geometrically similar particles of the same strength, a certain stress situation and stresses up to the breakage point. Self-similar breakage functions show the same curve at different stress intensities when the fragment size x is normalized with a reference particle size xNorm. This behavior was demonstrated for single particle comminution repeatedly and unequivocally. In the field of particle bed comminution, these results differ in literature. Therefore, the self-similarity in particle bed comminution was systematically investigated at the Institute of Mechanical Process Engineering and Mineral Processing of the TU Bergakademie Freiberg as part of a research project. Limestone, quartz, silicon carbide and glass beads, were examined with a hydraulic press. The particle sizes covered monodisperse fractions in the range of 1-1000 µm, bimodal mixtures of these fractions and polydisperse fractions. The results obviously show that there is no self-similar fracture behavior in the case of glass beads, quartz and silicon carbide. Statements on the self-similarity of limestone are much more difficult: Only some of the investigated limestone fractions show a similar clear, non-self-similar behavior. Self-similar curves appear particularly for fine monodisperse fractions as well as bimodal mixtures, which stressed with pressures above 200 MPa. Considering the measurement accuracy of particle size analysis the coincidence of the curves can be explained by the fact that progress in comminution almost ends above 200 MPa. At this point, a hydrostatic stress state is reached in the particle bed which is known from the literature. This stress state inhibits further fractures. Overall, it has been verified for the investigated materials that there?s no self-similar fracture behavior in particle bed comminution. One reason for the diverse opinions in literature is that there are three types of particles after the comminution in the particle bed: ? Particles which are stressed below their breaking point, ? Particles which are stressed right up to the break point, and ? Particles which are stressed beyond their breaking point.