Trajectories and impact velocities of grinding bodies in planetary ball mills

The motion of grinding bodies in conventional ball mills has been repeatedly investigated, both theoretically and experimentally. It is well-known that, depending on mill filling and speed of rotation, different motion patterns occur and some of these patterns, especially that of cataracting, can be described by simplified theories. This contribution presents such a theory of the cataracting motion of grinding bodies in a planetary ball mill. An analytical method for the evaluation of trajectories is given which permits an iterative calculation of the time and impact location of the grinding bodies on mill shell or mill filling. This leads to the determination of the impact velocity of grinding bodies and its component normal to the mill shell. On the assumption that this component is decisive for the grinding effect, conditions for an optimal design of a planetary ball mill are deduced.     

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.     

Analysis of ball movement for research of grinding mechanism of a stirred ball mill with 3D discrete element method

A simulation of the three-dimensional motion of grinding media in the stirred media mill for the research of grinding mechanism has been carried out by 3-dimensional discrete element method (DEM). The movement of ball assemblies was graphically displayed with some snapshots from start of the milling to 0.20 s. From these simulation results, the grinding zone in the mill was confirmed to be distributed into two regions, which is near the stirrer and the side wall of mill around the stirrer. The power changing the rotation speed of stirrer was examined based on the micro interactive forces at all the contact points between ball-to-ball and between ball-to-stirrer. DEM is a very powerful tool for the microanalysis of movement of balls, which could not have been solved by a conventional experimental method.     

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.     

Scale-up method of planetary ball mill

The objective of this paper is to investigate the scale-up method of the planetary ball mill by the computational simulation based on Discrete Element Method. Firstly, the dry grinding of a gibbsite powder by using four different scales of planetary mill was developed to compare the grinding rate with the specific impact energy of balls calculated from computational simulation. The grinding rate is well correlated with the specific impact energy in all mills; and its relationship is expressed by a linear correlation. It points out that the specific impact energy is very useful for estimation of the grinding rate and optimization for the operational conditions. Secondly, the scale-up method for the planetary mill was established by evaluating the impact energy. The impact energy is proportional to the cube of the diameter of the pot, the depth of the pot and the revolution radius of the disk, respectively. When the planetary mill is scaled-up in geometrical similarity, the impact energy of the balls is proportional to 4.87 power of the scale-up ratio.     

Scale-up of power consumption in agitated ball mills

Previous investigations have shown that the specific energy input is the overall parameter of influence on product size during communition in agitated ball mills, from laboratory up to industrial scale. The specific energy input is the introduced energy related to the amount of comminuted material. This parameter can be used for mill scale-up. Consequently, a method had to be found of introducing power into the mill so as to obtain a given specific energy input. For this purpose, stirring tests with purely Newtonian liquids were carried out in absence of solids and hence, without comminution. Mathematical models are presented which describe the power consumption in agitated ball mills in absence of grinding beads. In addition, tests with grinding beads filling were also performed, leading to scale-up guidelines with respect to power consumption. Finally, the influence of size and material of grinding beads was investigated.     

A comparative study of comminution in rotary and vibratory ball mills

A comparative study of the comminution in rotary and vibratory ball mills using sodium chloride is presented. The many advantages of vibratory over rotary ball milling are outlined and it is shown experimentally that the rate and extent of grinding is higher for the vibratory ball mill. It is further shown that fine particles re-aggregate in the rotary ball mill and ‘cake’ irreversibly. This phenomenon, exclusive to the rotary ball mill, is explained in terms of consolidation and high stress relaxation of the crystals occurring during prolonged grinding.     

Study of the process of stirred ball milling of poorly water soluble organic products using factorial design

The objective of this work was to investigate the mechanism of very fine grinding in a wet ball mill as a function of process parameters, i.e. rotation speed of the mill and grinding medium bead size. The ball mill used was a Dynomill and the grinding medium consisted of zirconium oxide beads. The product is a poorly water-soluble organic compound. Laser diffraction was used to analyze the particle size distribution.During grinding the average particle diameter of the product was reduced to a minimum size, which was constant within the range of tested operating conditions.The grinding parameters were studied to control the grinding process with respect to the required grinding time for reaching the minimum particle size and wear of the set-up.The grinding time was strongly dependent on the grinding medium bead size and on the rotation speed. The grinding process became faster when the rotation speed increased and the grinding medium bead size decreased. The wear of the set-up, and therefore the contamination of the final product with heavy metals, strongly increased with the rotation speed. A similar trend was observed with an increase of grinding medium bead size. The degradation rate of the product was not significant in the range of grinding parameters studied.     

Further studies of ball and powder filling effects in ball milling

The specific rates of breakage of quartz have been studied in three tumbling ball mills, two of 195 mm i.d. and one of 0.6 m i. d., as a function of fractional ball and powder loading. It was found that power results from a small mill with small lifters were anomalous, probably due to slippage, so that results reported previously from tests in this mill were not correct as a function of ball load. New results are presented for both wet and dry grinding.     

Effect of mill diameter on the rate of initial grinding in vibration ball mills

Vibration ball milling was carried out using three kinds of mills with the same internal volume but different diameters. The variations of specific surface area produced with time were investigated at a constant vibration intensity using feldspar with an initial size range of 74 – 149 μm. As a result, it was found that the specific surface area of product was markedly influenced by the difference in mill diameter even at the same vibrating conditions. According to an empirical equation proposed in a previous paper, the rate of initial grinding was also found to vary by a factor of 1.4 to 2.0, depending upon the mill used. The dependence of the rate of grinding on mill diameter can be explained by considering an effective area of mill shell capable of colliding with balls and a motion of balls in each mill. An available suggestion for designing a mill pot was obtained from this work.     

球磨机研磨体级配设计与计算

球磨机研磨体合理的级配,对提高磨机产量和产品质量、降低粉磨电耗,具有重大的作用。在总结几百家水泥厂磨机工艺技术员工作经验的基础上,根据笔者长期从事物料粉磨研究和实践的心得体会,综合考虑研磨体总装载量、各仓填充率、平均球径、物料水分、物料流动性、物料粒度、隔仓板形式、隔仓板篦缝大小、各仓长度、粉磨流程等因素,详细介绍了球磨机研磨体级配计算的方法、原理和步骤,并编制成“球磨机研磨体级配及补球计算程序”软件。     

A simulation model for an air-swept ball mill grinding coal

The conventional model for grinding in tumbling ball mills was modified to allow for air-sweeping, for the case where all the material is carried out of the mill in the air stream. It was shown that this type of mill can be treated as a single fully mixed reactor. The values of the internal classification numbers given by the air-sweeping were determined for a 1 m by 1.5 m pilot-scale mill grinding coal. The results showed that only 1 to 2% of the mill charge are exposed to the sweeping action per mill revolution. S and B values determined in a laboratory mill were scaled-up for use in the continuous mill model and the simulations gave product size distributions and mill capacities which agreed with the pilot-scale mill data within the experimental accuracy of the pilot-scale data.     

Flow of particulate solids through tumbling mills

The transport behavior of particulate solids flowing through tumbling mills depends strongly on the mill operating conditions. This paper presents the results of a detailed study to delineate the effect of the important operating variables on the hold-up, mean residence time and residence time distribution of particulate solids flowing through ball mills and rod mills. The effects of feed rate, media load, and mill speed on these transport parameters are discussed, emphasizing the fundamental differences between particulate transport in ball mills and rod mills. Under identical dimensionless operating conditions over the range of the investigation, the material hold-up and the Peclet number of the flow regime in the rod mill were always higher than those in the ball mill. Mechanistic interpretations of the observed transport phenomena are presented, and their implications in the context of tumbling mill analysis and design pointed out.     

Optimization of variables in grinding brass particles for paint and pigment industry

Flaky metal powders commonly used as paint and pigments, are generally produced by grinding in ball mills or vibration mills. The key to good quality powder production is to optimize the processing parameters. In the present work grinding of brass particles is studied in detail in a laboratory size ball mill to determine the optimal levels of the ball to material ratio, type and amount of additives, mill speed, ball load, etc. The quality of the powder is assessed on the basis of water coverage, degree of flattening and luster by visual inspection. Preliminary results in a 35 cm diameter ball mill with 30% ball load show that a material to ball ratio of 0.067 with a 0.1% dosage of stearic acid is required for good quality powder. For determining optimal mill speed and ball size a 2² factorial design of experiment has been followed. It has been determined that to achieve best powder quality the mill must run at 70% critical speed and the ball size must not exceed 20 mm. The quality of the powder assessed through SEM study for surface morphology and particle size analysis compares very well with the industrial samples.     

Naßmahlung in Rührwerksmühlen

Wet grinding in agitated ball mills. To ensure certain product qualities it is necessary to have very fine particles or a narrow particle size distribution. For this process agitated ball mill grinding can be used as well as crystallisation and precipitation. Cost effective grinding of very fine products to a narrow particle size distribution requires that the effects of variation of strain intensity, frequency of impacts, residence time distribution, size of grinding media, viscosity of liquid and concentration of feed material should be known. The most important parameters and their effects on the grinding result are demonstrated, as well as explained by a model, and the consequences for the operating conditions of agitated ball mills are presented. By using small grinding media in agitated ball mills the production rate can be increased, or at the same energy level smaller particles can be obtained by grinding or deagglomeration. At high flow rates and a narrow residence time distribution the feed material becomes more homogeneous. These facts require the development of new or modified types of agitated ball mills.     

Axial mixing of particles in batch ball mills

An experimental study of the axial mixing of dry, powders in batch ball mills has been carried out. For a system of silicon carbide and garnet particles in a laboratory mill containing small plastic balls, the observed mixing is in good agreement with a simple diffusion model. Empirical expressions are presented which relate the diffusion coefficient to the ball and particle loading in the mill. The expressions seem to be valid over most of the practical range of operating conditions except when the filing of either particles or balls is very low. Under these conditions, segregation of balls and particles occurs, apparently leading to anomalous values of the diffusion coefficient.     

Effect of media size in stirred ball mill grinding of coal

As a prerequisite to producing super-clean coal with any physical coal-cleaning process, such as microbubble flotation, the feed coal must be micronized to liberate finely disseminated mineral matter. The stirred ball mill is regarded as one of the most efficient devices for micronizing coal. Using a 13.4 cm batch mill, the optimum operating conditions have been determined in terms of media size, feed size and media type. The rate of breakage determined with monosized feeds are compared on the basis of specific energy consumption. It has been found that a 20:1 ball size/particle size ratio gives optimum grinding conditions.     

球磨法制备超细镍粉及其表征

为了获得在自然条件下稳定存在的超细镍粉,通过控制行星式高能球磨机的转速、研磨时间、磨球数、运转时间、暂停间隔、转动方向等参数对镍粉进行了研磨实验,并对不同参数下的研磨结果进行了测试表征。结果表明,在转速260 r/min、研磨时间19 h、运行时间3 min、暂停时间30 s、磨球数为10个、原料5 g且晴朗天气下实验,可以制备出亚微米级超细镍粉,并在空气中稳定存在。     

Radial mixing of particles in a dry batch ball mill

Poor mixing in dry ball mills can lead to insufficient presentation of fine particles to the classifying air, overgrinding of particles and wastage of energy in a ball mill. A video capture method has been used to study radial mixing kinetics in a dry batch ball mill. Experiments were conducted in a ball mill with PVC plastic powders being used as particles so that the effect of size reduction could be neglected. Radial mixing in ball mills was studied at typical industrial speeds of 75%, 80% and 90% of critical. The rate of particle mixing was observed to increase with increasing mill speed. A simplified mathematical model is presented that can be used to predict the radial mixing of particles in a ball mill. A parameter, k, was used to quantify the kinetics of mixing as affected by the mill's speed.     

基于MEEMD-多尺度分形盒维数和ELM的球磨机负荷识别方法

针对球磨机在磨矿过程中负荷(充填率、料球比)靠经验难以准确判断的问题,提出基于改进的集总平均经验模态分解算法(modified ensemble empirical mode decomposition, MEEMD)-多尺度分形盒维数盒和极限学习机(extreme learning machine,ELM)的负荷识别方法。该方法首先利用MEEMD算法对不同负荷状态下的磨音信号进行分解得到本征模态分量,然后,采用相关系数法选取敏感模态分量进行重构得到降噪后信号;通过分析重构信号的多尺度分形盒维数,结果表明,欠负荷、正常负荷和过负荷状态下的多尺度分形盒维数存在明显的差异,能够很好地区分磨机的不同负荷状态。将重构磨音信号的多尺度分形盒维数作为极限学习机(ELM)的输入,磨机负荷状态为输出,建立磨机负荷识别模型;通过磨矿实验验证了该方法的有效性,整体识别率高达94.8%,模型能够准确识别磨机负荷状态。