Grinding Medium Optimization Based on Grinding Kinetics and Discrete Element Analysis
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摘要:
采用磨矿动力学与离散元法（DEM）模拟仿真分别研究了钢球与钢段作为磨矿介质对多粒级矿石破碎效果及能量利用率的影响，并以此为基础在大红山铁矿三选厂细磨作业开展了工业实验研究。实验结果表明：与钢段相比，钢球作为磨矿介质时，对粗粒级破碎速率更大，磨矿产品中+0.15 mm含量降低了0.98百分点，−0.074 mm含量提高了5.66百分点；DEM模拟仿真分析发现钢球的运动状态较钢段更为活跃，钢球方案中用于矿石破碎能量的占比为65.41%，钢段方案为61.29%，钢球方案用于矿石破碎的能量占比较钢段方案高4.12百分点，钢球方案用于破碎矿石的有效能量利用率更高；将钢球作为磨矿介质用于大红山铁矿三选厂后，旋流器溢流−0.074 mm含量由74.00%增加至81.71%，提升了7.71百分点，单位钢耗由0.63 kg/t降为0.57 kg/t，降低了9.52%，单位电耗从11.46 kW·h/t降至 10.13 kW·h/t，下降了11.61%。通过磨矿动力学得出钢球、钢段级配方案，并通过DEM软件模拟仿真验证了钢球方案的磨矿效果要优于钢段，工业实验验证了模拟仿真结果的可靠性。
Abstract:In this study, the effects of steel balls and steel cylpebs as the grinding media on the crushing behavior and energy utilization of multi−grain ores were investigated using grinding dynamics and discrete element method (DEM) simulation, and industrial experimental research was carried out based on the results. The results of grinding kinetics show that the effect of steel balls on the crushing rate of the coarse grain fraction was better than that of steel cylpebs. The content of +0.15 mm in the grinding product is reduced by 0.98% and −0.074 mm increased by 5.66% in the case of steel ball compared with that of steel cylpebs as the grinding medium. DEM analysis showed that the motion state of steel balls was more active than that of steel cylpebs. The percentage of energy used for ore crushing using steel balls and steel cylpebs as the grinding medium was 65.41% and 61.29%, respectively, with the former being 4.12% higher than the latter so that the effective energy utilization of steel balls for crushing the ore is higher. Based on the above results, after using steel balls as grinding media in the Dahongshan Iron Mine, the overflow −0.074 mm content of the cyclone increased from 74.00% to 81.71%, an increase of 7.71%, the unit steel consumption decreased by 9.52%, from 0.63 kg/t to 0.57 kg/t, and the unit power consumption decreased by 11.61%, from 11.46 kW·h/t to 10.13 kW·h/t. This study verified the validity of the steel ball scheme through grinding dynamics and discrete element analysis experiments and verified its accuracy through industrial tests.
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Key words:
- grinding kinetics /
- discrete element simulation /
- grinding medium /
- Dahongshan iron mine /
- steel ball /
- steel cylpebs
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图 5 不同尺寸钢段对不同粒级铁矿石的破碎行为（a—D×L 45 mm×50 mm；b—D×L 35 mm×40 mm；c—D×L 30 mm×35 mm；d—D×L 20 mm×25 mm）
Figure 5.
图 6 不同尺寸钢段下给矿尺寸对特定粒级破碎率的影响（a—D×L 45 mm×50 mm；b—D×L 35 mm×40 mm；c—D×L 30 mm×35 mm；d—D×L 20 mm×25 mm）
Figure 6.
表 1 DEM 模拟中使用的材料参数
Table 1. Material parameters used in the DEM simulations
名称 钢球 矿石 密度/( kg·m−3) 7800 3100 泊松比 0.3 0.38 剪切模量/Pa 7.00×1010 4.60×1010 
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表 2 离散元仿真接触参数
Table 2. Contact parameters in discrete element simulation
颗粒模型 恢复系数 静摩擦系数 滚动摩擦系数 钢−钢（钢球、衬板） 0.7 0.4 0.01 矿石−钢（钢球、衬板） 0.5 0.5 0.01 矿石−矿石 0.3 0.8 0.01
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表 3 球磨机介质级配
Table 3. Ball mill media gradation
粒级/mm 给矿
产率/%扣除−0.2 mm后
待磨产率γ待/%钢球
尺寸/mm钢段
尺寸/mm比例/% +2 4.33 12.85 50 45×50 15 −2+0.45 9.06 26.88 40 35×40 25 −0.45+0.3 15.78 46.82 30 30×35 45 −0.3+0.15 4.54 13.45 20 20×25 15 −0.15 66.30 —— —— —— —— 合计 100.00 100.00 —— —— 100
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表 4 球磨机钢球方案及钢段方案磨矿效果综合指标对比
Table 4. Comprehensive index of grinding effect of ball mill steel ball scheme and steel cylpebs scheme
/% 名称 钢球 钢段 粗级别γ+0.15 mm 0.47 1.45 可选级γ−0.15+0.019 mm 74.91 76.85 过细级γ−0.019 mm 24.62 21.70 γ−0.074 mm 86.09 80.43
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表 5 不同介质类型碰撞能量统计
Table 5. Collision energy statistics
碰撞类型 介质−矿石 介质−衬板 矿石−矿石 介质−介质 矿石−衬板 碰撞总能量 钢球/J 3913.38 168.14 281.29 1689.71 360.71 6413.23 占比/% 61.02 2.62 4.39 26.35 5.62 100.00 钢段/J 2454.63 101.25 203.34 1317.87 259.56 4336.65 占比/% 56.60 2.33 4.69 30.39 5.99 100.00
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表 6 溢流细度统计
Table 6. Overflow fineness statistics
时间 质量浓度/% 溢流细度/% 处理量/(t·h−1) 实验前 —— 74.00 330.00 2021.07 38.54 81.95 325.50 2021.08 40.09 81.69 343.97 2021.09 39.00 82.22 336.43 2021.10 39.07 82.24 337.95 2021.11 43.47 79.06 341.12 2021.12 42.70 81.03 342.87 2022.01 39.20 83.57 332.87 2022.02 39.41 81.91 341.01 平均 40.19 81.71 337.72
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