A multiscale method for including fine particle effects in DEM models of grinding mills

A multiscale model for including interstitial powder or fine particles in DEM simulations of grinding mills is proposed. This consists of a traditional DEM model at the macroscale which includes only grinding media and potential coarser fractions of feed and product. Microscale models are embedded within this macroscale model. These can be sufficiently small that the fine powder can be included in a computationally affordable manner. The direct inclusion of the fine particles in the model allows predictions to be made of the effect of the local grinding environment on these fine particles. A shear cell is a good choice for the microscale model as it can well represent the local flow conditions at different points within the mill macroscale model. Averaging the macroscale flow allows the local collisional environments to be characterised and provides estimates of the shear rate and normal stress at each of the microscale locations which then controls the configuration of each microscale shear cell. A 1-way coupled implementation of this multiscale model is demonstrated for a simple cement ball mill. The relative importance of each region of the flow is determined with the toe region being the dominant contributor to the grinding. The grinding action produced by the shearing of thin layers of powder between adjacent layers of media flowing over each other is clearly demonstrated by the behaviour predicted in the microscale models. Methods for calculating power draw that include the effect of powder and for constructing collision energy spectra for the powder are described. Finally, the importance of the cushioning effect of high powder loads on the flow behaviour of the media is demonstrated.     

Estimating energy in grinding using DEM modelling

The latest state of the art on Discrete Element Method (DEM) and the increased computational power are capable of incorporating and resolving complex physics in comminution devices such as tumbling mills. A full 3D simulation providing a comprehensive prediction of bulk particle dynamics in a grinding mill is now possible using the latest DEM software tools.This paper explores the breakage environment in mills using DEM techniques, and how these techniques may be expanded to provide more useful data for mill and comminution device modelling. A campaign of DEM simulations were performed by varying the mill size and charge particle size distribution to explore and understand the breakage environment in mills using DEM techniques. Analysis of each mill was conducted through consideration of the total energy dissipation and the nature of the collision environment that leads to comminution.The DEM simulations show that the mill charge particle size distribution has a strong influence on the mill input power and on the way the energy is distributed across the charge. The smaller particles experience higher energies while the larger experience less, but this variation is strongly dependent on the mill size. The results also showed that the average particle collision energy increases with increasing mill size, whereas its distribution over particle size is strongly influenced by the mill content particle size distribution. The simulations also captured the energy distribution within different regions of the tumbling charge, with the toe impact region having higher impact energies and the bulk shear region having higher tangential energies. Regardless of the mill size most of the energy is consumed by the particles in the mid-size range, which has the highest percentage mass of the total charge distribution.     

Using DEM to compare the energy efficiency of pilot scale ball and tower mills

Tower mills are considered to be appreciably more energy efficient than ball mills. Why this should be so is a question which can be explored by using DEM to simulate one machine of each type with similar breakage capabilities. This paper reports on a comparison between a pilot scale tower mill and a small ball mill in terms of the power required to produce reasonably similar distributions of normal and tangential impacts. While the tower mill produces quite a narrow spectrum of normal energies, the ball mill produces a wide distribution. Hence, the ball mill can be expected to be much more “forgiving” of variable feed conditions but much less efficient in terms of utilization of the energy from media interactions.     

基于检测球的球磨机磨矿介质运动试验分析

针对球磨机磨矿介质运动信息很难测量的问题,以Φ520mm×260mm试验球磨机为研究对象,基于设计的检测球装置分析了不同转速率工况下磨矿介质运动参数的变化规律,并提出了一种试验验证离散元仿真的方法。研究结果表明,检测球加速度主要介于0-3.3g,球磨机的转速率越大,加速度的波动范围越大,磨矿介质的冲击碰撞越明显;检测球角速度主要介于0-31rad/s,球磨机的转速率越大,角速度的波动范围越大,磨矿介质的研磨作用越明显;检测球试验与离散元仿真的单位质量转动动能累积分布基本一致,说明检测球试验验证离散元仿真是有效的。     

Applying discrete element modelling to vertical and horizontal shaft impact crushers

The PFC3D (particle flow code) that models the movement and interaction of particles by the DEM techniques was employed to simulate the particle movement and to calculate the velocity and energy distribution of collision in two types of impact crusher: the Canica vertical shaft crusher and the BJD horizontal shaft swing hammer mill. The distribution of collision energies was then converted into a product size distribution for a particular ore type using JKMRC impact breakage test data. Experimental data of the Canica VSI crusher treating quarry and the BJD hammer mill treating coal were used to verify the DEM simulation results.Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle breakage behaviour.     

Modeling breakage rates in mills with impact energy spectra and ultra fast load cell data

A new era in modeling particle size distribution in grinding mills started at the beginning of 2000s. A direct estimation of breakage parameters became possible via computation of collision energy by discrete element method (DEM) and material breakage data.The material breakage data can be obtained for primary modes of breakage. In this study, impact and abrasion are assumed to be the primary modes of particle breakage, which are readily studied in the laboratory. The impact breakage mode is studied in a drop-weight apparatus and in a specialized device known as the ultra fast load cell. The abrasion mode of breakage is studied in a laboratory scale ball mill. Next, the particle breakage versus energy data is converted into breakage rates via impact energy spectra of the grinding mill computed by a DEM code. The fundamental material breakage information is converted into energy based breakage distribution function.The verification of the modeling concepts is shown for a 90 cm laboratory scale ball mill. In the batch mill, approximately a 10 kg mass of limestone in the 30 mm size is ground with around 100 kg of 50 mm steel ball charge. The breakage rate and the breakage distribution functions constitute the parameters of the energy based batch population balance model. It is shown that accurate particle size distribution predictions are possible with this modeling approach for different grinding regimes.     

Effects of media shape on milling kinetics

Spherical balls are the dominant grinding media used in ball mills. However, balls which are initially spherical, wear into non-spherical fragments. The proportion of worn, non-spherical balls in the charge of a mill fed with 50 mm balls is dominant in ball sizes less than 30 mm. Their effects on mill performance in terms of material breakage are not yet established.The variations of specific rate of breakage with single size feed and fractional filling U, were studied for the two media shapes (spherical and worn balls). Higher breakage rates were noted with spherical media than worn balls but the differences narrow with decreasing feed size and increasing material fractional filling, U.     

不同转速率下球磨机介质运动状态分布行为研究

针对球磨机介质运动分布问题,本文以Φ520 mm×260 mm球磨机建立离散元仿真模型,开展不同转速率下球磨机介质运动状态分布行为研究。研究结果表明：介质运动过程中,不同尺寸的介质会出现分层现象,相同尺寸的介质会聚集在一起;球磨机筒体端面对介质运动状态有影响,不可以忽略;介质运动循环中心径向半径受转速率的影响较小,介质质量中心径向半径受转速率的影响较大;球磨机内矿石颗粒的破碎是多次累积冲击破碎,且发生一次冲击碰撞破碎的概率很小。     

Vertical Agitated Media Mill scale-up and simulation

Vertical Agitated Media Mill modeling has become subject of a research project due to its potential application as a secondary grinding mill as well as regrind and pellet feed preparation projects. A test campaign with a pilot scale vertical mill was carried out with five different ore samples to elaborate a simple and robust methodology to scale-up vertical mills and perform simulations. The methodology proposed considers breakage parameters determined from tests in a conventional batch ball mill and population balance model for simulations. The tests can be performed very quickly in any process laboratory with a small quantity of sample. Two different models can be used for scale-up purposes: the first is based on the specific grinding energy and the corresponding tests were carried out on samples with natural size distribution. The second is based on particle residence time distribution and the tests carried out with narrow sized particles. Breakage and selection function parameters were estimated from each test procedure. The results indicate that it is possible to perform vertical mill scale-up and simulations with acceptable accuracy using the results from laboratory ball mill tests. The data analysis showed that the ratio of grinding net powers between ball and vertical mills is approximately 1.35 for all samples tested.     

Ball motion,axial segregation and power consumption in a full scale two chamber cement mill

Grinding of clinker for cement production is often performed in a two chamber ball mill. In the first shorter chamber, raw feed is ground using media consisting of large balls. The ground product of the first chamber exits through a discharge grate and enters the second longer chamber. Here smaller balls are used to grind the product material even finer. In this paper we analyse the charge motion, short term ball segregation processes and energy utilisation in a 4 m diameter cement ball mill using DEM. The power draw predicted is consistent with the rated power of the mill. The energy dissipation in the mill is dominated by shear interaction. The gentle liner profiles ensure that few balls move on cataracting trajectories. The distribution of energy utilisation between the different size media fractions is explored as are differences in the collisional environment between the two mill chambers.     

Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge.In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored.     

Experimental and simulated instrumented ball in a tumbling mill—A comparison

Tumbling mills play an essential role in modern mineral processing. Because of the nature of the mill, the internal forces make instrumentation of the mill interior difficult. One solution to this problem is the use of an instrumented ball. An instrumented ball, equipped with an accelerometer, rotation rate sensors and a temperature sensor has been built. The instrumented ball and a camera system are used to measure the state of the charge within a laboratory mill. In parallel, a discrete element model (DEM) of the laboratory mill is developed. Using the distributions and moments of the energy terms of the charge, the simulation and experimental results are analyzed and compared. The moments are used to tune the DEM, such that the simulation results are in agreement with the experimental results. The comparison also identifies which aspects require further improvement.     

Comparing three DEM charge motion models

In comminution research, recent trends have been made to describe internal dynamics of mills using the discrete element method (DEM). In this work, three modelling approaches to DEM implementation to charge motion modelling are compared these being single ball trajectories, system of individual balls describing the mill charge and charge balls grouped together using an arbitrary discretization scheme. After presenting some charge motion fundamentals as well as a presentation of the three approaches to DEM implementation, charge profile results are presented for a 12 m mill. Further power predictions for a number of ball mills are presented along with a brief internal charge dynamics comparison. A discussion focuses on the needed future research to improving these approaches.     

Modeling breakage rates of coarse particles in ball mills

Breakage rates of coarse particles in ball mills generally follow non-first-order kinetics and the distribution products from batch milling are often characterized by significant contributions of abrasion besides breakage by impact, which are not well described using traditional size–mass balance formulations. Under such conditions, particles are often subject to impacts of insufficient magnitude to produce breakage in each stressing event, so that they are broken by a combination of abrasion and impact and also particles undergo weakening due to unsuccessful stressing events. The paper presents a mathematical model of batch grinding which takes into account the distribution of stressing energies in the mill, the distribution of fracture energies of particles contained in the charge, describing breakage by impacts from grinding media producing catastrophic breakage, abrasion and weakening from repeated impacts. The model has been applied to describe the rate of disappearance of two materials in batch grinding with good results.     

The effect of particle breakage mechanisms during regrinding on the subsequent cleaner flotation

Stirred mills have been widely used for regrinding, and are acknowledged to be more energy efficient than tumbling mills. These two types of mills present different particle breakage mechanisms during grinding. In this study, the effect of regrinding by both mills on surface properties and subsequent mineral flotation was studied, using chalcocite as the mineral example. A rod mill and a stirred mill with the same stainless steel media were used to regrind rougher flotation concentrates. Different chalcocite flotation recovery was achieved in the cleaner stage after regrinding in tumbling and stirred mills. The factors contributing to the different recovery included particle size, the amount of created fresh surfaces, surface oxidation and the redistribution of collector carried from rougher flotation. All the factors were examined. It was determined that the predominating factor was the different distribution of collector resulting from different particle breakage mechanisms in the stirred and tumbling mills, in line with ToF-SIMS analysis. In the tumbling mill, the impact particle breakage mechanism predominates, causing the collector to remain on the surface of newly produced particles. In the stirred mill, the attrition breakage removes collector from the surface, and decreases particle floatability. Furthermore, the type of grinding media in the stirred mill also influences the subsequent flotation, again due to the change of particle breakage mechanisms. The results of this study demonstrate that the selection of regrinding mills and grinding media should not only depend on the required energy efficiency, but also on the properties of the surfaces produced for subsequent flotation.     

Modeling breakage of monodispersed particles in unconfined beds

Mathematical models of grinding mills and crushers are undergoing significant advances in recent years, demanding ever more detailed information characterizing ore response to the mechanical environment. In a mechanistic model of a comminution machine, the type of characterization data used should cover, as much as possible, the conditions found inside the size reduction machines. This applies to the particle size, the stressing energy and rates that particles are subject to, the breakage mechanism and the level of interaction of the particles during stressing, which all must be described appropriately. Whereas, a very large number of experimental techniques and published data exist that allows understanding and quantitatively describing the response of single particles to stressing, comparatively little information exists on the breakage of particles contained in beds. The present work investigates breakage of particle beds impacted by a falling steel ball in unconstrained conditions, such as those that are likely to be found in tumbling mills. The influences of particle size, impact energy, ball size and bed configuration are investigated for selected materials and a mathematical model is proposed that describes the influence of all these variables. The key element of this model is that it allows predicting breakage in monolayer unconfined particle beds with a combination of single-particle breakage data and functions that describe energy partition and volume of material captured in the bed. This model has been calibrated and validated using data from quartz, granulite, limestone and a copper ore, with good agreement.     

Modelling comminution patterns within a pilot scale AG/SAG mill

The patterns of rock comminution within tumbling mills, as well as the nature of forces, are of significant practical importance. Discrete element modelling (DEM) has been used to analyse the pattern of specific energy applied to rock, in terms of spatial distribution within a pilot AG/SAG mill. We also analysed in some detail the nature of the forces, which may result in rock comminution.In order to examine the distribution of energy applied within the mill, the DEM models were compared with measured particle mass losses, in small scale AG and SAG mill experiments. The intensity of contact stresses was estimated using the Hertz theory of elastic contacts. The results indicate that in the case of the AG mill, the highest intensity stresses and strains are likely to occur deep within the charge, and close to the base. This effect is probably more pronounced for large AG mills. In the SAG mill case, the impacts of the steel balls on the surface of the charge are likely to be the most potent. In both cases, the spatial pattern of medium-to-high energy collisions is affected by the rotational speed of the mill.Based on an assumed damage threshold for rock, in terms of specific energy introduced per single collision, the spatial pattern of productive collisions within each charge was estimated and compared with rates of mass loss. We also investigated the nature of the comminution process within AG vs. SAG mill, in order to explain the observed differences in energy utilisation efficiency, between two types of milling. All experiments were performed using a laboratory scale mill of 1.19 m diameter and 0.31 m length, equipped with 14 square section lifters of height 40 mm.     

Use of the attainable region method to simulate a full-scale ball mill with a realistic transport model

Optimisation and better control of milling circuits require extensive modelling of milling data. This paper extends the enquiry to the use of the attainable region (AR) technique to determine the optimal residence time of ore in a ball mill. It also evaluates the energy requirements of the mill at the set residence time to maximise the production of the desired size range which enables maximum recovery of platinum group minerals (PGM) during the flotation stage.With these purposes in mind, the breakage function and the scaled-up selection function parameters were used to simulate the operating conditions required by an industrial ball mill and the power requirements were predicted using the Morrell power model. This allowed the application of the AR methodology to be extended to a full-scale ball mill. Then a link was established between residence time to mill product specifications for a given feed size.The findings showed that the residence time required by a full-scale mill falls between those at which the fully mixed and the plug flow mills operate. The results also showed that operating the ball mill at a lower mill speed and a higher ball filling saves energy. Mill speed was again found to be a key operational factor for controlling the retention time of particles inside the mill. This yielded valuable insight for the importance of optimally controlling both the residence time of the material inside the mill and the amount of energy required to maximise the desired size range, in this case −75 + 9 μm.     

The effect of the design of a secondary grinding circuit on platinum flotation from a UG-2 ore

Platinum concentrator plants experience significant losses in their overall Platinum Group Elements (PGE) recoveries due to the inefficiencies of their secondary grinding circuits. This study involves an investigation of selective grinding of the platinum-bearing silicate particles present in UG-2 platinum ores found in the Bushveld Igneous Complex (BIC).Batch-scale laboratory test work was done to investigate the effect of a secondary milling circuit configuration, using a hydrocyclone underflow sample from a UG-2 concentrator plant as feed material. The envisaged secondary milling circuit consists of a conventional hydrocyclone to de-slime the feed followed by density separation with a spiral concentrator to separate the ore into lights (silicates-rich) and heavies (chromite-rich) fractions, followed by separate milling of the two fractions in parallel ball mills, and combined rougher flotation. A full-scale spiral was run in batch mode, followed by separate milling of samples in a 200 mm diameter mill and combined flotation in a 4.2 l cell. The milling energy inputs were re-distributed between the lights and heavies mills to determine the effect on the platinum mineral rougher flotation recovery and the Cr entrainment.The most promising results were found with 88% of the energy input to the lights mill and 12% to the heavies mill. The results indicated that under batch conditions, the secondary rougher flotation recovery (69% 4E) was similar to the conventional mill-float circuit (70%) however the Cr entrainment was significantly reduced by approximately 40% (2.3–1.4% Cr).This test work has confirmed the benefit of separate milling in the secondary milling circuit for a UG-2 ore. Spiral concentrators have shown potential as an effective density separating device to produce a silicate-rich and chromite-rich fraction for milling; further test work will be conducted to confirm its viability on an industrial scale.     

Is media shape important for grinding performance in stirred mills?

Models for understanding the basic concepts of fine grinding and how they apply to the design of stirred media mills have not yet matured. While spherical media in tower mills has previously been studied, real grinding media shape in stirred mills can range from spherical (steel/ceramic balls) to highly non-spherical (sand or slag) resulting in very different media and grinding dynamics. Handling the contact mechanics of non-spherical particles is a challenge for numerical models, and very few studies dealing with non-spherical particle shape exist in the literature. Discrete Element Method (DEM) simulations of dry media flow in a pilot-scale tower mill are performed for four cases with different shaped grinding media, in order to understand how flow and energy utilisation within a stirred mill depend on media shape. Differences in media transport, stress distribution, energy dissipation, and liner wear were observed in the tower mill for the spherical and non-spherical cases. A significant departure from sphericity of the media leads to strong dilation of the bed, reduced bulk density, and a reduction in active volume and collisional power levels leading to a reduction in power draw for the mill. In addition, highly non-spherical media tend to pack tightly near the mill walls forming a near solid layer around the inside of the mill shell which results in poorer transport and mixing, as well as increased wear rates on the screw impeller. Grinding performance in stirred mills appears to deteriorate strongly when using highly non-spherical media.