Analysis of grinding kinetics in a laboratory ball mill using population-balance-model and discrete-element-method

Grinding processing consumes a lot of energy in mineral processing, but it is a low-efficiency process in which only approximately 1% of the total energy is used to reduce the actual particle size. Therefore, an efficient operation in the grinding process increases the competitiveness of the production and is an essential for enhancing the energy efficiency of the entire mineral processing procedure.Therefore, the study will focus on to finding a different method to predicting the particle size distribution of the ball mill, by using the PBM which reflects the actual size distributions of ground product and the DEM which can understand the internal particle behavior in the mill chamber. First, the grinding parameters were calculated by applying size distributions of ground product under various conditions to PBM and the behaviors of the particles inside the ball mill obtained through DEM were analyzed to predict the distribution of the impact energy used for grinding. Next, the relational expression between the grinding rate parameter and the normal force applied to the grinding materials was derived. Using the relational expression derived from this study, it was confirmed that the size distributions in other conditions can be predicted.     

Dry grinding in planetary ball mills: Evaluation of a stressing model

Planetary ball mills at laboratory scale are widely used for grinding and alloying processes. However, in contrast to other mill types, no applicable mechanistic model exists to describe the stressing conditions and their effect on particle breakage, so that processes are empirically evaluated so far. Within this study, the stressing conditions are determined by simulations based on the discrete element method including the contact model of Hertz and Mindlin. The contact model parameters are carefully calibrated by a series of experiments, so that it is finally possible to validate the simulation results by comparison of measured and calculated power values. The correlation of stressing conditions and breakage rates of alumina powder demonstrates the effect of stressing on breakage kinetics and breakage mechanism. It allows calculating the active mass in dependence on process parameters by an extension of Schönert’s active mass model.Altogether, the presented stressing model features analytical functions for the mill-related stressing conditions and highlights the importance of stressing intensity as process determining parameter, which defines the required number of material-related stressing events and the specific energy.     

The effects of friction characteristic of particle on milling process in a horizontal rice mill

The physical and mechanical properties of rice are of significant change during milling from brown rice to white rice, especially the friction characteristics. In order to clarify the effects of roughness of rice surface on the milling process and mechanism, in this work, motion of spherical particle in a horizontal rice mill under different static friction coefficients (i.e., between particle and cylinder sieve wall μ_s,pt and between particles μ_s,pp) was simulated using the discrete element method. The uniformity of axial motion and circular motion were qualitatively and quantitatively analyzed, which are characterized by introducing the axial dispersion coefficient and uniformity index, respectively. Then, the effects of static fiction coefficients on residence time and collision energy among particles were discussed. The results indicated that the μ_s,pt mainly affects the axial motion while the μ_s,pp primarily influences on the circular motion. The residence time is strongly affected by the uniformity of axial motion while the collision energy is significantly influenced by the uniformity of circular motion. Finally, the relationship between friction characteristics and milling performance can be described based on the method of polynomial fitting. This work is useful for providing essential references to control the quality of milled rice.     

DEM study on effects of particle size and grinding media properties on energy transitions in a horizontal agitator

Thermal-mechanical cuttings cleaner, utilizing the energy dissipation of dense particle flow in the mill, is a type of low-temperature method for drying drill cuttings. In this paper, the energy dissipations of particle flow at the particle scale are simulated via discrete element method in a horizontal agitator. The effect of the particle diameter of sample particle and grinding media properties are considered in the simulation. The velocity distributions, contact force, input torque of the mill, and power dissipation of each component are employed to assess energy transitions. The results reveal that the contact force network in the bed is the main factor affecting the momentum transfer, and the motion and power dissipation are sharply promoted by the presence of grinding beads. The density of grinding beads has a significant effect on the permeability of grinding beads in sample particles and the consequent energy dissipation.     

The influence of the rotation frequency of a planetary ball mill on the limiting value of the specific surface area of the WC and Co nanopowders

An increase in the hardness and wear resistance of WC-Co alloys with a decrease in the grain diameter of WC and Co makes it relevant to search for methods for producing powders with a maximum specific surface area (SSA). SSA growth is limited even when milling powders of WC and Co in the most high-energy mills. Effect of increasing the rotation speed of a planetary ball mill on the limiting value of the SSA of obtained nano sized WC and Co powders is studied. According to the developed model, an increase in the rotational speed of the mill leads to an increase in the limiting value of SSA if the cause is particle hardening. If the cause is coalescence, an increase in frequency leads to a decrease in the limiting value of the SSA. It was determined that the limiting value of SSA of WC particles increases from 1.0⋅10⁸ m²/m³ to 2.2⋅10⁸ m²/m³ (Sauter average diameter decreases from 60 to 27 nm) with increase of mill rotation frequencies from 2.5 to 4.2 rps due to a decrease in the volume of “indestructible” particles. And the limiting value of SSA of WC particles decreases from 2.2⋅10⁸ m²/m³ to 1.1⋅10⁸ m²/m³ (Sauter average diameter increases from 26 to 55 nm) with increase of mill rotation frequencies from 5 to 6.7 rps due to the increase of the coalescence rate. The experiment showed that the limiting value of SSA for Co powder decreases from 1.0⋅10⁸ m²/m³ to 1.1⋅10⁶ m²/m³ with increasing of the rotational speed of the mill from 2.5 rps to 6.7 rps (Sauter average diameter increases from 60 to 5450 nm) due to the increase of the coalescence rate. Studies have shown that the growth of SSA of WC grains is limited by a certain value (11.5 nm).     

Studying the effect of different operation parameters on the grinding energy efficiency in laboratory stirred mill

In this study, considering different operational parameters for stirred media mill, change in specific energy was compared to the change in R_x values, i.e. the cumulative weight of the material undersized to a specific sieve. R values, namely R₃₈, R₇₅, R₁₀₆, were measured before and after grinding in stirred mill. The change in R_x (ΔR_x, %) values were calculated and they were used to evaluate the certain unit of effectual energy (Ecb). This abovementioned calculation is performed by proportioning the Specific Energy (SE) to ΔR_x values. The effectual part of SE is considered to be the ratio of the energy needed only for size reduction in grinding and it should be related to the ΔR_x. The relative Ecb ratios of different grinding conditions give the relative specific energy efficiency ratio (SEe). The relative specific energy efficiency ratio is inversely proportional to specific grinding parameters and ground product particle sizes. The relative specific energy efficiency can be considered as the relative amount of energy for various grinding conditions. The variation between relative energy amount and the previously specified particle size provides a realistic comparison of different grinding parameters. The abovementioned variation could be employed to understand the resistance particle size which is a new concept to describe the particle size at which the maximum effectual SE is directly used. In the context of this study, it was aimed to figure out the interrelation between specific energy efficiency and PSD variation along with the resistance particle size.     

Influence of dry and wet grinding conditions on fineness and shape of particle size distribution of product in a ball mill

The influence of grinding conditions on the production of fine particles and the width of the particle size distribution produced during ball mill grinding was investigated. The grinding experiments were carried out varying the grinding ball diameter under dry and wet conditions. The relation between the weight passing size observed in an arbitrary cumulative undersize fraction and the grinding time was expressed by modifying Tanaka’s semi-theoretical equation for the grinding limit. The fineness of the product was evaluated by the median particle size in undersize distribution, and the shape of the particle size distributions by three different size ratios calculated using 10%, 20%, 50%, 80% and 90% cumulative weight passing sizes, that showed the width of the particle size distribution. The median particle sizes of product obtained for the grinding limit in wet and dry conditions were around 0.5–0.6 μm and 2 μm, respectively. The width of the particle size distribution in wet grinding decreased with decreasing median particle size of the ground product, and the size distribution in dry grinding became nearly constant. The particle size distribution width was lowered by using smaller grinding balls in wet condition and larger grinding balls in dry condition.     

Effect of particle size distribution on hydrodynamics of pneumatic conveying system based on CPFD simulation

The effect of particle size distribution on the hydrodynamics of dilute-phase pneumatic conveying system was analyzed using computational particle fluid dynamics (CPFD) simulation. The influence of a simulation parameter, i.e., correction factor of drag coefficient (k), on the hydrodynamics of pneumatic conveying system was determined via CPFD simulation. When results of simulation were compared with experimental data of previous studies, the average error of pressure drop per length predicted by the CPFD approach with the correction factor was below 4.4%. Saltation velocity and the pressure drop per unit length declined as the drag force coefficient increased. Simulation results also revealed that the pressure drop per length and the saltation velocity were decreased when the fine powder fraction in the particle size distribution was increased, although the width of particle size distribution was widened, and the standard deviation was increased. Finally, the Relative Standard Deviation (RSD) of pressure drop per length was measured and compared with median diameter (d₅₀), Sauter mean diameter, geometric mean diameter, and arithmetic mean diameter. The RSD of the Sauter mean diameter was 5.8%, approximately twice less than the RSD value of d₅₀ commonly used in pneumatic conveying.     

A statistical analysis of void size distribution in a simulated narrowly graded packing of spheres

The void microstructure of a simulated packing of polydisperse spheres has been investigated by means of a radical Delaunay tessellation. We have focused on creating sphere packings by mimicking processes involved in the construction of embankment dams: the polydisperse spheres are collectively released under gravity and denser states are mainly obtained by means of shearing cycles. This study has been performed on a narrowly graded material for four porosities ranging from 0.42 to 0.36. The void structure is quantified in terms of probability density functions of pore and constriction sizes, cumulative distributions and connectivity functions. We emphasize the implications of the sample construction technique on the geometric packing arrangements, among them a well disordered medium where tetrahedra remain the most represented unit void structure. We point out that when porosity decreases, void distributions become narrower but the initial structure is never destroyed. Nevertheless, the densification modifies significantly the computed mean void quantities. In this study, usual geometric arrangements obtained for very dense materials are not encountered.     

Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts

In this article, the Coefficient of Restitution (COR) and Energy Loss Percentage (ELP) of one-dimensional impacts are determined experimentally for different ball sizes using a drop test apparatus. Ball diameters range from 6 to 12 mm, made of steel and aluminum dropped on steel and aluminum sheets.     

Effect of lognormal particle size distributions on particle spreading in additive manufacturing

Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.     

超声法纳米颗粒悬浮液粒径测量中温度影响的实验研究

针对医药、化工领域高浓度纳米悬浮液颗粒粒径超声检测中温度影响,采用超声衰减谱法(UAS)对体积浓度30%的纳米铟锡金属氧化物(ITO)水性悬浮液在循环流速800 r/min,温度298～358 K时颗粒粒径分布进行实验。结果表明:温度升高,超声幅值A减小,超声衰减系数增大,颗粒中位径D50增大,颗粒系分布曲线整体朝大颗粒方向偏移,但是分布宽度保持稳定的趋势。同时,将室温(298K)测量结果与CPS离心沉降颗粒测量仪对比,结果较吻合。通过线性回归的方法修正温度对测量结果的影响,超声衰减法能够应用于358K的高温下高浓度纳米颗粒检测。     

Scale-up and flow behavior of cohesive granular material in a four-bladed mixer: effect of system and particle size

Flow of cohesive granular materials with different moisture contents was examined in a four-bladed mixer via the discrete element method (DEM). Firstly, the mixer diameter (D) was increased while keeping the particle diameter (d) constant. It was observed that when the mixer diameter to the particle diameter ratio (D/d) was larger than a certain critical size (D/d ≥ 75), granular flow behaviors and mixing kinetics followed simple scaling relations. For D/d ≥ 75, flow patterns and mixing kinetics were found to be independent of system size, and velocities of particles scaled linearly with the tip speed of the impeller blades and particle diffusivities scaled with the tip speed of the blades and mixer diameter. These results suggest that past a certain system size the flow and mixing of cohesive particles in large-scale units can be predicted from smaller systems. Secondly, system size was kept constant and particle diameter was changed and it was observed that by keeping the Bond number constant (by changing the level of cohesion) the flow behavior and mixing patterns did not change, showing that larger particles can be used to simulate flow of smaller cohesive particles in a bladed mixer by matching the Bond numbers.