The effect of damage on breakage kinetics

Algorithms are developed for describing the batch grinding kinetics of particles with a distribution of strengths subjected to repeated impacts of a known specific impact energy (as in a hammer mill). It is shown that the critical number of (equal) impacts required to produce sufficient damage that the final impact will cause disintegrative fracture isTc=least integer≥E(1)ENβ,1≤E(1)EN≤51/βleast integer≥E(1)51/β−1/γENγ,E(1)EN≥51/β1,E(1)EN≤1whereβ=0.62α0.59γ=β+(5.5)(10−3)α2.32where E(1) is the particle strength defined as the specific impact energy required to fracture the particle in one impact, EN is the applied specific impact energy, and α is the damage accumulation coefficient. The amount of unbroken feed left from a feed of a single 2 sieve interval was calculated as a fraction of grinding time, assuming literature values of the distribution of strengths of a limestone. If a weak impact is used and no allowance is made for damage accumulation, then it is predicted that some fraction will always remain unbroken. If damage accumulation is included, the strongest material will eventually break. First-order breakage kinetics was not predicted in either case.