基于球磨机放大数学模型的钢球与钢锻磨矿效率对比研究——以某钨矿石为例

Comparative Study of Grinding Efficiency of Steel Balls and Steel Cylpebs Based on Ball Mill Scale-up Mathematical Model:Taking Tungsten Ores as Example

钢球与钢锻作为磨矿介质在磨矿效率上的差异长期存在争议,基于实验室试验和磨矿流程模拟,对钢球和钢锻在实验室球磨机和工业磨矿回路的表现进行了对比。对云南某钨矿石进行了增强型邦德球磨功指数试验,并采用理想混合模型对2种磨矿介质在实验室试验中的破碎率参数(r/d)进行了计算。根据实验室试验获得的破碎率参数,采用球磨机放大数学模型预测了工业规模球磨磨矿回路的循环倍率和产品粒度。结果表明,尽管2种介质可以在实验室试验中获得相近的邦德球磨功指数,但在粗粒端钢锻产生的破碎率参数比钢球更大,在细粒端则相反。在工业规模球磨磨矿回路中,当循环倍率接近时,2种介质产生的旋流器溢流产品粒度分布总体较接近,但相比于钢球介质,钢锻的产品粒度分布更均匀,粗颗粒含量和细颗粒含量均少于对应的钢球产品。由于最终产品粒度分布曲线形状上的差异,对钢球与钢锻磨矿效率进行比较时,可能会受到所选磨矿细度衡量指标(P80或-0.075 mm含量)的影响。因此,应当结合矿石的实际解离特征和浮选作业的具体需求,来决定采用哪种磨矿细度衡量指标进行评估。

There is long-standing controversy over the difference in grinding efficiency between steel balls and steel cylpebs as grinding media.This paper compares the performance of steel balls and steel cylpebs in laboratory ball mill and industrial grinding circuit based on laboratory experiments and grinding process simulations.An enhanced Bond Ball Mill Work Index test was conducted on a tungsten ore from Yunnan province,and the Perfect Mixing Model was used to calculate the breakage rate parameter(r/d)of the two grinding media in laboratory experiments.The circulation ratio and product particle size of industrial-scale ball mill grinding circuits were predicted using a ball mill scaling-up model,based on the breakage rate parameter obtained from laboratory experiments.The results show that,although the two media can achieve similar Bond Ball Mill Work Indices in laboratory experiments,the breakage rate parameter of steel cylpebs is greater at the coarse end than that of steel balls,while the opposite is true at the fine end.In industrial-scale ball mill grinding circuit,when the circulation ratio is similar,the particle size distribution of overflow products from cyclone separators produced by the two media is relatively similar.However,compared with steel ball media,the product particle size distribution of steel cylpebs is more uniform,with less coarse and fine particles than steel ball products.Due to the differences in the shape of the final product particle size distribution curve,the comparison of grinding efficiency between steel balls and steel cylpebs may be influenced by the selection of grinding fineness measurement indicators(P80 or-0.075 mm content).Therefore,the decision as to which grind fineness measure to use for evaluation should be made in the context of the actual liberation characteristics of the ore and the specific requirements of the flotation operation.