In the past, most of the Population Balance Model-based ball mill scale-up studies were carried out using a mono-size ball charge and a single size fraction of the particulate material as the starting feed. It was reported that the breakage distribution parameters were independent of the mill diameter, specific breakage rate parameters varied with mill diameter as D^γ, and the mill diameter exponent γ was independent of particle size. However, in the industrial grinding operations, we have significantly broad size distributions for both the grinding media and the particulate contents of the mill. Therefore, experimental data generated under these conditions were taken from the literature and analyzed. These data pertain to the dry and wet batch grinding of limestone, quartz, and ores of vanadium and pyrochlore. Our analysis of the data showed that in contrast to the findings of the earlier researchers, the breakage distribution parameters were not independent of the mill diameter, and the value of γ for the specific breakage rate parameters varied with particle size in the case of multicomponent ores. Because of these complications, a single parameter, the specific rate of production of material that is finer than a specified size, was used as the basis for scale-up. It was found that the value of the mill diameter scale-up factor varied quite significantly with the breakage properties of the material, the size distribution of the particulate contents of the mill, the size of the desired product, and the mode of grinding (dry/wet). Therefore, ball mill scale-up models presently available need to be modified in light of these new findings.

过去，大多数基于群体平衡模型的球磨机放大研究都是使用单一尺寸的球装料和单一尺寸的颗粒材料作为起始进料进行的。据报道，破碎分布参数与磨机直径无关，具体的破碎率参数随磨机直径变化为D ^γ，并且磨机直径指数 γ 与粒径无关。然而，在工业研磨操作中，我们对研磨介质和磨机的颗粒含量都有非常宽的粒度分布。因此，在这些条件下产生的实验数据取自文献并进行了分析。这些数据与石灰石、石英以及钒和烧绿石矿石的干湿分批研磨有关。我们对数据的分析表明，与早期研究人员的发现相反，破碎分布参数与磨机直径无关，并且在多组分矿石的情况下，特定破碎率参数的 γ 值随粒度变化. 由于这些复杂性，单个参数，比指定尺寸更细的材料的特定生产速率被用作放大的基础。结果表明，磨机直径放大系数的值随材料的破碎特性、磨机颗粒含量的尺寸分布、所需产品的尺寸和研磨方式（干磨）而显着变化。 /弄湿）。因此，目前可用的球磨机放大模型需要根据这些新发现进行修改。