Modification and Industrial Application of Liners of Semi−autogenous Grinding Mill Based on Orthogonal Design and Discrete Element Method
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摘要:
针对新疆某选厂Φ5.5 m×1.8 m半自磨机筒体衬板易磨损、断裂等问题，首先基于正交试验确定其筒体衬板的最优结构参数，其次运用离散元法模拟现场半自磨机的运行过程，对比研究在不同衬板结构参数下（提升条高度、宽度与面角）半自磨机内颗粒运动及内部碰撞能量的变化规律，最后通过工业试验验证优化方案的可行性。研究结果表明：适宜的提升条参数组合可有效优化磨机内颗粒的运动状态，增加钢球—矿石、矿石—矿石的有用碰撞，减少因无用碰撞引起的衬板或磨矿介质的损耗，进而改善半自磨机的运行参数。经正交试验确定最优的衬板提升条参数组合为高度190 mm、宽度140 mm和面角60°。由工业试验验证，优化后的衬板使用寿命、磨机运转率与台效较优化前分别提高了51 d、16.36百分点、15.55 t/h，磨机电耗较优化前降低了6.07 kW·h/t。试验结果证明了正交设计法和离散元法的联合应用在半自磨机筒体衬板形状优化过程的可靠性及优越性。
Abstract:In order to solve the problem that the liners of Φ5.5 m×1.8 m SAG mill were easy to wear and fracture in a concentrator in Xinjiang. Firstly, the optimum structural parameters of cylinder liners were determined by the orthogonal test. Secondly, The discrete element method (DEM) was used to simulate the real operation of SAG mills. Based on the different structural parameters of cylinder liners (height, width and angle of lifter bars), the motion of particles and the change of collision energy in SAG mills were studied. Finally, the feasibility of the optimization scheme was verified by industrial tests. The results showed that a suitable parameters of the liners can effectively optimize the motion of particles in the mill, increase the effective collision of ball to ore and ore to ore, reduce the wear of liners or grinding media caused by invalid collision, and thus improve the operating parameters of the semi-autogenous mill. The optimum parameters of the lifter bars were determined by orthogonal experiment to be 190 mm in height, 140 mm in width and 60 ° in angle. The optimum parameters of liners were used to carry out industrial tests. The results showed that the optimized liner service life, mill operation rate and efficiency were increased by 51 days, 16.36% and 15.55 t/h, and the mill power consumption decreased by 6.07 kW·h/t. The results verified the reliability and superiority of the discrete element method and the orthogonal design method in the modification of the cylinder liners.
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表 2 正交设计试验方案
Table 2. Orthogonal design experimental scheme
方案 参数 A B C 1 3 1 3 2 2 3 1 3 1 3 3 4 3 2 1 5 3 3 2 6 2 2 3 7 2 1 2 8 1 2 2 9 1 1 1 
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表 3 仿真试验矿石颗粒参数
Table 3. Simulation experiment ore particle parameters
颗粒尺寸/mm 填充质量/kg 单个颗粒质量/kg 单个颗粒体积/m3 颗粒数量/个 250 400.99 28.64 0.00818 14 200 319.28 14.51 0.00418 22 150 373.88 6.03 0.00176 62 100 266.12 1.76 0.00052 151 80 459.57 0.90 0.00026 510 45 233.94 0.16 0.00005 1459 35 307.71 0.075 0.00002 4079 25 117.88 0.027 0.000008 4288 20 1136.45 0.014 0.000004 80746 总计 3615.82 — — 91331
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表 4 衬板与矿石本征参数
Table 4. Intrinsic parameters of liner and ore
名称 衬板 矿石 容重 /(kg·m-3) 7800 3360 静弹性模量 /Pa 1.82×1011 3.31×1010 泊松比 0.30 0.26
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表 5 材料的基本接触参数
Table 5. Coefficient of restitution of the materials
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） 0.70 0.20 0.01 矿石−钢（钢球、衬板） 0.41 0.50 0.25 矿石−矿石 0.35 0.56 0.05
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表 6 试验结果
Table 6. Experiment results
方案 参数 高度A /mm 宽度B /mm 面角C /(°) 衬板受撞
能量占比/%1 3（220） 1（120） 3（70） 3.85 2 2（190） 3（160） 1（50） 3.62 3 1（160） 3（160） 3（70） 3.87 4 3（220） 2（140） 1（50） 3.77 5 3（220） 3（160） 2（60） 3.20 6 2（190） 2（140） 3（70） 3.38 7 2（190） 1（120） 2（60） 2.83 8 1（160） 2（140） 2（60） 3.07 9 1（160） 1（120） 1（50） 4.12
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表 7 方差分析
Table 7. Analysis of variance
变量 离差平方和 自由度 均方差 F 显著性P 修正模型 1.455 6 0.243 52.343 0.019 截距 111.725 1 111.725 24113.288 0.000 高度A 0.283 2 0.142 30.583 0.032 宽度B 0.063 2 0.032 6.827 0.128 面角C 1.108 2 0.554 119.619 0.008 误差 0.009 2 0.005 — — 总计 113.189 8 — — —
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表 8 极差分析
Table 8. Range analysis
数值 参数 高度 A /mm 宽度B /mm 面角C /(°) K1 11.06 10.8 11.51 K2 9.83 10.22 9.1 K3 10.82 10.69 11.1 
3.69 3.6 3.84 
3.28 3.41 3.03 
3.61 3.56 3.7 R 0.41 0.19 0.81
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表 9 工业试验中筒体衬板使用寿命统计
Table 9. Statistics on the service life of liners in industrial experiments
方案 开始时间 整体更换时间 使用时间/d 年使用量/套 年成本/万元 现场方案 2019年4月6日 2019年7月22日 108 3.60 403.20 优化方案 2019年7月24日 2019年12月29日 159 2.26 325.44 优化方案与现场方案差值 — — +51 −1.34 −77.76
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