Analyzing the influence of Cerchar abrasiveness index on particle size distribution in ball milling based on multifractal theory

This study investigates the influence of cerchar abrasiveness index (CAI) on the multifractal parameters of particle size distribution (PSD) in the ball milling from both global and local perspectives. The results indicate that with increase of CAI, the generalized dimension spectrum parameters D(0) and D(1) exhibit three distinct stages, and the concentration of PSD gradually decreases. The variations in singular spectrum parameters Delta alpha and Delta f reveal that, for CAI below 1.0, the main variation in milling is dominated by large particle, and the local heterogeneity changes are not significant. As the CAI exceeds 1.0, variability of particle sizes approaches each other, and the local heterogeneity shows a trend of increasing and then decreasing. As CAI increases, the point of maximum heterogeneity in PSD becomes more concentrated towards the later stages of milling. Finally, the micro-mechanisms of differences in CAI and multifractal parameters were discussed by considering mineralogical composition and bond work index of individual minerals.