Investigations of autogenous and semi-autogenous grinding in tumbling mills

A model based on the specific rates of breakage of each size in a mill as affected by balls and large lumps has been developed. Three mechanisms of breakage are recognized: ‘normal’ fracture of smaller sizes by balls and larger pebbles, ‘chipping’ of raw feed to give rounded pebbles and ‘abrasion’ from the surfaces of pebbles. A tracing technique was developed to distinguish these contributions to autogenous breakage in batch grinding tests. It was found that the accumulation of finer material strongly cushions the impact between pebbles and pebbles and pebbles and balls. Empirical relations were developed to describe this cushioning effect. It was also found that chipping breakage is first order for short times of grinding. The mathematical model lumps fracture and chipping in a single contribution and considers the material as if it were a mixture of fast- and slow-breaking components. Breakage rates and primary breakage distributions measured on an ore in batch tests were used to predict the performance of a 1.8-m diameter pilot-scale mill, and predictions compared to the pilot-scale data on the same ore.     

Modeling of a grinding circuit with a swing-hammer mill and a twin-cone classifier

A model was formulated for a continuous, air-swept milling system, assuming the mill to be fully mixed, with all particles leaving the mill in the air stream. The air-sweeping effect was treated as an internal classification which allows fine particles to leave and returns coarse particles for regrinding. The kinetic parameters for the continuous model were estimated using experimental data from a continuous pilot-plant air-swept swing-hammer mill. Functional forms that provide information regarding the power, the internal classification action of the mill, and the action of the external classifier, were deduced for different plant conditions. It was found that the specific rates of breakage could be assumed to vary with particle size according to S_i = a(x_i/x_o)^α, where the value of α was 1.3 for the coal used in the tests. The values of a varied with mill hold-up W, giving a maximum of aW as W became large. The primary breakage distribution values were assumed to be normalized, giving a value of characteristic slope of γ = 0.60.     

Kinetics of fine wet grinding in a laboratory ball mill

The kinetics of batch wet grinding of quartz from a feed of 600×425 μm to a product of 80% less than 8 μm have been determined using sieving and laser diffractometer sizing for size analysis. A dispersing agent was added while proceeding to longer grinding times to prevent particle agglomeration in the mill. The specific rates of breakage (S_i) values obtained were higher than those of dry grinding of quartz at the same experimental conditions, but the primary breakage distribution (B_i,j) values were the same. Non-first order grinding was observed with continued decrease of the specific rates of breakage for finer grinding. The simulations of the product size distributions were in good agreement with the experimental data, providing the decrease in rates was included.     

The axial mixing model applied to ball mills

The unsteady-state, one-dimensional convective mixing equation was solved with finite end boundary conditions for a pulse of tracer admitted into a steady flow, assuming a constant dimensionless mixing factor D*. Radiotracer tests were performed on two continuous wet overflow ball mills, a laboratory mill of 0.3 m i.d. and a pilot-scale mill of 0.91 m i.d. Counting through the mill case enabled the tracer concentration to be measured at L/3, 2L/3 and L for the small mill, and L/2 and L for the pilot-scale mill. The results were consistent with the mixing model with D* = 0.5 and 0.3, respectively, with D* constant along the mill. The mean residence time of water was about 0.85 that of the solid, showing the slurry density in a mill to be higher than that of the feed and product streams.     

搅拌磨微粉碎氧化铝数学模型的反求

研究了搅拌磨微粉碎Al2O3的动力学数模，及粉磨条件对数参数的影响。实验是在窖为2L的实验搅拌磨中进行的，根据粒度分布数据利用非线性最优化方可以方便地反求数模参数。在一定粒级范围内，这些参数可以较好地描述搅拌磨中Al2O3微粉碎过程的粒度变化规律，预测粉碎产品粒度分布以及判断粉碎条件的影响。     

筒辊磨粉磨冶炼钢渣技术开发应用

首条采用国产化筒辊磨粉磨冶炼钢渣项目在河北某钢厂建成投产,其核心工艺技术与装备采用中国第一重型机械股份公司开发研制的筒辊磨技术与装备。详细介绍了采用筒辊磨钢渣微粉生产系统主要设备技术特点、运行状况和达到的技术指标。性能考核数据显示,筒辊磨钢渣粉磨系统技术及其装备各项技术经济指标已经到达业内先进水平,竞争优势凸显。     

A comparison of the Bond method for sizing wet tumbling ball mills with a size—mass balance simulation model

A comparison is made of the results from a ball mill model simulation with those of the conventional Bond ball mill design method, for a material whose breakage characteristics and Work Index have been determined. In order to perform the simulation, ‘normal’ values were chosen for make-up feed size distribution, mill residence time distribution, ball mix, classifier behaviour, etc. At high flow rates through a mill (low reduction ratio), it is necessary to allow for the reduction in breakage rates caused by over-filling of the mill, using an empirical mass transfer relation: filling

. By suitable choice of the constant in this relation, it was found possible to duplicate the variation of mill capacity with feed size and product size (in wet closed-circuit grinding) predicted by the Bond method. The simulation model is then used to predict the variation of performance with design variables not included in the Bond method.     

Empirical and scale-up modeling in stirred ball mills

Stirred ball mills are frequently used for ultrafine- and nanogrinding in food, pharmaceutical and chemical industry, but only few investigations have been published on empirical or scale-up modeling of stirred ball mills. Experiments have been carried out with a laboratory scale stirred ball mill. During the experiments the main technical parameters such as stirrer speed, grinding media, filling ratio, grinding time and the solid mass concentration have been systematically adjusted. The particle size distribution of mill products can be well estimated by empirical functions, so an empirical model has been prepared for the laboratory mill. The relation between the grinding fineness, grinding time and specific grinding work was represented for several materials such as pumice, andesite, limestone and tailings of ore mining industry. The power consumption of the stirred ball mill for scale-up was determined by a method based on the dimensional analysis. A new scale-up model has been presented as well by with industrial size stirred ball mills can be designed on the basis of the laboratory measurements.     

Modeling and simulation of a fully air swept ball mill in a raw material grinding circuit

A raw material grinding circuit was modeled using plant data. Samples were collected from around the circuit and, following a crash stop, from inside the mill. The size distributions of the samples were determined down to a few microns. Using the data from inside the mill a modeling approach, based on perfect mixing, was developed. The modelling approach implicitly assumes that the mixture of feed materials broken is homogenous from the breakage point of view. The air classification around the circuit was modeled using the efficiency curve approach. In order to measure the success of the method the circuit performance was predicted by simulation studies while it was operating at different conditions. The results were then compared with the measured data. It is concluded that modeling gives a useful quantitative indication of what may occur in fully air swept mills.     

Reduction of the porcelain firing temperature by preparation of the raw materials

An innovative way of reduction of firing temperature of porcelain tableware is reached by preparation of raw materials down to submicron- and nanoscaled powder for higher reactivity. In this study a common slurry was ground in an agitator ball mill from d₅₀ = 5.0 μm to 0.9 μm, green bodies were prepared, and glost firing was simulated in a dilatometer. The sintering temperature has been decreased by approximately 180 °C. A reflection between ball mill and agitator ball mill regarding the grinding cost shows no difference which means that the ball mill could be replaced. The energy consumption during the grinding process will be discussed regarding to energy savings resulting from reduced firing temperature. Furthermore a comparison between experimental and literature data will be done. The effect of grinding of raw material is finally evaluated concerning sintering behaviour and material properties.     

A Comparative Study on a Vertical Stirred Mill Agitator Design for Fine Grinding

Comminution is an energy intensive process. A small change in efficiency can lead to substantial benefits in an overall economy of the process plant. This study focused on the comparison of vertical stirred mill agitator designs. A double helical screw agitator was designed for this purpose. A series of stirred mill experiments were performed with two types of agitator designs a standard pin type and CSIRO’s designed double helical screw stirrers. The effects of operating parameters such as grinding time, stirrer speed, and pulp density on grinding performance was investigated using a magnetite concentrate. Grinding performance was analyzed by considering the product fineness and the energy consumption. The test results show that the grinding time and stirrer speed played a significant role; however, the pulp density had little impact on grinding performance in both cases of agitator designs. The 80% passing target product size of 38 μm was obtained with double helical screw agitator in 20 min of grinding with an expend of 10.53 kWh/t specific energy, whereas, the target product size of 38 μm was achieved with the pin type stirrer at the rate of 21.73 kWh/t. It is evident that grinding in a vertical stirred mill with a double helical screw is more efficient than that using a pin type stirrer in terms of the product size distribution and the specific energy consumption. It is concluded that the double helical screw design provides better energy efficiency compared to the pin type stirrer design. The models were developed for the responses P₈₀ and E_cs. Both models show high regression coefficients thus ensuring a satisfactory of models with experimental data. The model equations developed were then optimized using a quadratic programming to minimize the P₈₀ size at minimum specific energy.     

An analysis of ball-and-race milling part II. The babcock E 1.7 mill

A mathematical model was developed for a ball-and-race mill based on specific rates of breakage and primary fragment distributions. The model includes internal classification of particles falling back into the race and external classification due to the built-on classifier. It was demonstrated that the normalized primary fragment distribution produced in a pilot-scale Babcock E-type mill of 17 in. race diameter was the same as in the Hardgrove laboratory test mill and that the specific rates of breakage varied with particle size in the same manner. Steady-state continuous tests on the pilot-scale mill showed that breakage rates depended on the rate of feed, since the mill pulled less power at low feed rates. This effect plus the residence time effect gave coarser product size distributions at low and high feed rates than at a medium feed rate. Model simulations based on parameters measured in the Hardgrove mill correctly predicted the product size distribution from the E-type mill.     

Rapid extraction of canola oil

The simultaneous size reduction and solvent extraction of canola seeds were studied using a laboratory blender and a small, pilot-scale Szego mill. The laboratory tests established that over 95% of the oil may be removed from the seed in a single contact stage. The effects of contact time and solvent-to-seed ratio were investigated. The extraction equilibrium favored the extraction of the oil at higher solvent-to-seed ratios. In all cases the extraction reached some 90% of the equilibrium value after 3 min. Runs in the Szego mill, which is a unique orbitalmill developed by one of us (O. Trass), confirmed that solvent grinding is an efficient extraction technique. In this equipment, contact times as short as 30 sec give significant extraction, with the system approaching equilibrium in one minute. The Szego mill appears to be suitable for the rapid extraction of edible oil seeds such as rapeseed.     

高石灰石掺量水泥专用助磨剂试验研究

通过试验室模块试验和小磨试验,研究了高石灰石掺量水泥专用助磨剂对水泥的增强和助磨效果。结果表明,高石灰石掺量水泥专用助磨剂在9个新型干法水泥厂10个水泥样品的模块试验中28d抗压强度平均增加7.3MPa;小磨试验水泥45μm筛余减少3.8%～6.0%,3～32μm颗粒含量增加3.11%,28d抗压强度增加5.7～6.8MPa。高石灰石掺量水泥专用助磨剂同时具有显著的后期强度增强作用和助磨作用。     

Using the discrete element method to analyze the breakage rate in a centrifugal/vibration mill

The grinding characteristics of a centrifugal mill with varying G/D (gyration/mill diameter) ratios were investigated using the population balance model and the discrete element method (DEM). A series of grinding tests were conducted on illite samples using a centrifugal mill under various conditions, and the breakage parameters were calculated. Three-dimensional DEM simulations were also conducted. It was found that the specific rates of breakage estimated for various grinding conditions correlated well with the impact energy calculated from DEM simulations. This information was used to develop scale-up functions for the centrifugal mill in terms of G/D ratio, rotational speed, mill diameter, grinding media diameter, and ball loading.     

Application of grinding kinetics analysis of inorganic powders by a stirred ball mill

The need for ultra fine particles has been increasing in the preparation field of raw powders such as fine ceramics and high functional products. A series of wet grinding experiments were carried out on inorganic powders such as calcite, pyrophyllite and talc by a stirred ball mill. The grinding rate constant K’ in the equation of grinding kinetics was examined based on the grinding kinetics analysis as the same type of function of a previous paper on a vertical type planetary ball mill. The experimental particle size distribution of the ground products was obtained in various grinding conditions. The grinding rate constants K and K’ were expressed by empirical equation involving experimental conditions by a stirred ball mill. The empirical equation on the grinding rate constant was expressed in terms of a function involving the ball diameter of grinding balls, the median diameter of feed material, and Bond’s work index of material, in the experimental conditions. The values of empirical constants C1 and C₂ were 21.13 and 0.0109 on K, while C₁ and C₂ were 120.99 and 0.0192 on K′, respectively. And the particle size distribution of ground products of each test material for a given grinding time was found to be expressing the selection function (the specific rate of breakage) which was obtained from the grinding kinetics analysis. In this study, the grinding rate change on calcite and pyrophyllite was similar at the same experimental operation condition. However, in the case of talc, it was observed that the grinding rate was not increased compared with other samples.     

The investigation of grinding kinetics of power plant solid fossil fuel in ball mill

The kinetics of batch dry grinding of power plant solid fossil fuel, from the feeds of sieve sizes −3.350 + 2.360, −2.360 + 1.700, −1.180 + 0.850, −0.425 + 0.300 and −0.212 + 0.150 mm have been determined using a Bond ball mill with a mixture of five ball sizes. The mill used has a diameter of 30.5 cm, length of 30.5 cm, providing a total mill volume of 22.272 cm³ with a total mass of 20.125 g steel ball mixtures of 38.10, 31.75, 25.40, 19.05 and 12.70 mm diameters. The balls occupied 22% of mill volume. The speed of rotation of the mill was chosen as 70 rpm. The specific rates of breakage (S_i) and primary breakage distribution (B_i,j) values, called as grinding breakage parameters, were determined for those feed size fractions to simulate the product size distributions for comparison to the experimentally obtained data. As the feed sizes increase, the S_i values also increase, that is, faster breakage values from higher to lower values were in the order of solid fossil fuel by comparing to its α values. Breakage distribution functions were found non-normalizable. It is dependent upon the initial feed particle sizes. In other words, the simulations of product size distributions for fossil fuels were in good agreement with the experimental data using a ball mill simulation program, called JKSimMet.     

The effect of ball and mill diameters on grinding rate parameters in dry grinding operation

For dry ball mill grinding operation, the effect of ball and mill diameters on grinding rate parameters of the size-discretized population balance model has been investigated for quartz, limestone, a soft cement clinker and a hard cement clinker. Experiments were performed in three mills of 29.2, 40.6 and 61.0 cm diameter. The diameter of the balls used ranged from 1.27 to 3.81 cm. The particle size range covered was $\text{8}\text{10}$ to $\text{100}\text{150}$ mesh. The rate parameter values were determined very accurately using a special technique. It has been shown that the particle size exponent α in equation S_i = Ax_i^α is independent of ball and mill diameters. Based on this fact, a new correlation has been developed to describe the effect of ball and mill diameters on the rate parameters. The various constants in this correlation are strongly material dependent.     

石英原料粉碎过程动力学研究与分析

通过石英原料在间歇球磨机中的粉碎实验研究,测出不同粒级物料质量分数随时间的变化数据,并以此为依据进行粉碎过程动力学解析及回归,获得了该过程的动力学方程,目的在于预测产品达到粒度要求时的时间段以达到节能效果,为工业生产控制及应用打下基础.     

我公司Ф4.2 m×13 m水泥磨综合技术改造升级

洛阳中联水泥有限公司水泥磨（Φ4.2 m×13 m双仓磨）存在有效研磨空间浪费、窜仓、使用钢锻磨机电流高等问题,磨机工况及电耗指标均不理想。为此根据水泥磨实际生产工作情况,对水泥磨进行综合技术改造升级,最终磨机工况及技术经济指标均得到较大幅度的改善和提高。