Abstract: The population balance model is the most commonly used framework for simulating the operation of ball mills. However,accurately characterizing the variation of breakage rate parameters with operational conditions remains challenging. Based on the framework of the population balance model,mathematical modeling was conducted on the ball milling test results of a tungsten ore to explore the effects of feed rate,feed particle size,media distribution,and ball filling rate on the breakage rate.A neural network-based nonlinear model was established using experimental data to map the relationship between breakage rate and these key parameters.The results indicate that the breakage rate increases with rising mill rotation speeds but decrea sing with increasing feed rates.Larger steel balls enhance the breakage rate of coarse particles,while smaller steel balls improve the breakage rate of fine particles.Three feed samples with coarse,medium,and fine particle size distributions were prepared. Under the same grinding conditions,different feed size distributions exhibited varying breakage rates.However,as grinding pro gressed,the coarse particle size distribution converged toward that of the standard feed.An increase in fine particle content was found to enhance the breakage rate of coarse particles.The predictive model based on neural networks shows strong consistency with experimental validation data,the coefficient of determination R²=0.961,confirming its reliable forecasting capability.

Key words: ball mill,population balance model,breakage rate,neural network