Theoretical Prediction of Energy Consumption and Particle Size Distribution in grinding and drilling of brittle materials

Abstract

Based on physical assumptions, simple equations have been derived for the probability of breakage of particles, for the dependence of fragmentation energy on particle size and for the fragment size distributions as a function of mass-specific energy. The particles were considered as spheres, and Hertz theory of the stress distribution at the contact between a sphere of brittle material and a flat surface was applied in combination with Weibull statistics of failure. The predicted dependence of the probability of breakage on particle size and mass-specific energy agrees well with experimentally obtained data for singleparticle experiments, even if the particles were not spherical. The resulting fragment size distribution could be predicted by the application of fracture mechanics. The theory can also be applied to rock drilling, where the breaking material is considered as a flat surface and the drilling tool as being of spherical shape. In both comminution and drilling, the experimental results agree fairly well with the theory.

The Investigation of Breakage Probability of Irregularly Shaped Particles by Impact tests

“…[15][16][17] . Based on Rumpf s similarity principle, Weichert 18,19) introduced the Weibull statistics 20) to the field of comminution to describe the breakage probability of brittle spheres. The breakage probability P can be described as a function of mass-related energy Wm:…”

“…By varying exponent z in a relevant interval between 1.5 and 2.5, see Weichert 18) , the gamma function varies slightly from 0.885 to 0.905. In the future consideration, the gamma function will be assumed to be constant and equal to 0.9.…”

“…3. According to Weichert 18) , the Weibull exponent z varies between 1.5 and 2.7 for relevant materials. Based on this fact, the three values of z (lower -1.5, middle -2, and upper -2.7) were used for the simulation.…”

Characterization of Nanocrystalline Oxide Powders Prepared by CO₂ Laser Evaporation

“…Weichert [22], for instance, investigated the dependencies of the mean specific breakage energy on the particle size. His results for glass spheres of sizes in the range from 10 J.tm to 10 mm, can be extrapolated to fictitious particles of 10 mm.…”

Breakage Probability of Irregularly Shaped Particles by Impact Stressing

“…Zerkleinerungsarbeit als Bruchwahrscheinlichkeit darzustellen. Als Kurvenparameter lassen sich die Partikelgröße und eine stoffabhängige Konstante quantifizieren [1,2]. Diese Darstellungsmethode basiert auf der Weibull-Verteilung [3] und der Hertz-HuberTheorie [4,5] und wurde ursprünglich nur für die Kontaktdeformation und den Bruch elastischer Kugeln entwickelt.…”