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.     

Understanding fine ore breakage in a laboratory scale ball mill using DEM

DEM models of fine grinding in ball and stirred mills have to date almost entirely focused on the motion of the media and their interaction with the mill configuration. For SAG mills, a large fraction of the feed material can now be accurately represented in DEM models. However, for other mill types with much finer feed materials, such as the second chamber of a cement ball mill, the vast numbers of feed particles makes their explicit inclusion in the models prohibitive. However, it is now feasible to model a periodic section of a laboratory scale ball mill and include the coarser end of the ore size distribution directly in the DEM model. This provides the opportunity to better understand the effect of media on the interstitial bed of powder and of the effect of the powder on the media. The effect of the powder fill level, which is varied between 0% and 150% of the pore space in the media charge, is explored. The distribution of the powder, its effect on power draw and the way in which it contributes to the pattern of energy utilisation is assessed. The simulation results are compared with experimental results from a test at similar ball loading and rotation rate and for several size fractions of ore at a range of powder fill fractions. Tracking the collision histories of specific ore particles within the charge allows estimates of the probability (per unit time) of collision between media and ore particles (the “Selection” function) and of the intensity of each collision which can be used to estimate the severity of breakage using the JKMRC breakage model (the “Breakage” function). The energy spectra indicate that for a typical ore, only very few collisions are large enough to cause damage to the body of each particle. This provides an estimate of the energy efficiency which is less than 10% at even the best operating conditions.     

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.     

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.     

What is required from DEM simulations to model breakage in mills?

It is quite common to encounter discrete element method (DEM) simulations of mills that present images of the motion of grinding media, summaries of tangential and normal forces, and mill power. The usefulness of this data is questioned, with respect to modelling breakage. This work presents hypotheses of how the DEM simulations can be used as input to comminution modelling, and this guides the data logging and analysis requirements. Techniques are proposed for collecting and using this data in a manner useful for predicting breakage in a comminution device. Individual particle impact histories of contact angle, force, and impulse are required to realistically model breakage. It is argued that the majority of breakage results from cumulative damage, thus it is essential to track individual particle histories to realistically predict the breakage product from a mill.     

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.     

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.     

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.     

Using DEM to understand scale-up for a HICOM® mill

Scale-up is a process of developing a larger version of a processing machine based on the performance of a smaller machine. For mills, scale-up is made difficult by the different rates at which different physical processes occurring within the machine change with the increasing size. Discrete Element Method (DEM) modelling can now be performed at a range of scales and can be used to help understand scale-up issues for mills. This paper explores the ways in which DEM can be used to assist in the scale-up process for a mill using the HICOM mill as a case study. By choosing speeds at each mill size that have the same charge distribution and structure a scale-up relationship is developed which allows prediction of the power draw with increasing mill size. Similar scale-up relationships are developed for the specific power intensity and the most common collision energy occurring within the charge. The peak loads on the liner and at the nutation point of the mill are key inputs to mechanical design. Their variation with increasing physical size is also explored. Finally, the change in wear behaviour with increasing scale is also determined. This scale-up process can be applied to any form of mill.     

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.     

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.     

Characterising porosity of multi-component mixtures in rotary mills

The measurement of porosity presents a significant challenge in modelling of slurry transport in rotary mills. This is due to the aggressive environment within rotary mills. In this paper, a method of measuring the porosity of mill charge, using the positron emission particle tracking (PEPT) technique, is presented. In this work, multiple particles are tracked, in turn. The packing density of each size component is proportional to the residence time distribution of its representative tracer particle, based on the ergodicity of the system. The charge porosity is a linear combination of the packing densities of individual components. The porosity is modelled as a function of mill geometric and operating parameters—mill speed and filling fraction. The results show correlations between porosity distribution and operating parameters.     

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.     

The effect of regrind mills on the separation of chalcopyrite from pyrite in cleaner flotation

Stirred mills have been widely used for regrinding and are more energy efficient than tumbling mills. These two types of mills present different particle breakage mechanisms and redox environments during grinding. In this study, the effect of regrinding with these two types of mills on the separation of chalcopyrite from pyrite in the cleaner stage was studied. A laboratory rod mill and a laboratory stirred mill were used to regrind rougher flotation concentrates. It was found that chalcopyrite and pyrite exhibited different flotation behavior after regrinding with the rod mill and the stirred mill, resulting in different separability of chalcopyrite from pyrite. The mechanism underpinning this phenomenon was investigated by a range of techniques including dissolved oxygen demand measurements, X-ray photoelectron spectroscopy (XPS) and Time of flight secondary ion mass spectrometry (ToF-SIMS). It was found that the two mills produced different surface oxidation and pyrite activation by copper ions which determined the separation of chalcopyrite from pyrite. This study demonstrates that the selection of a regrind mill should not only depend on its energy efficiency but also the property of surfaces produced for subsequent flotation.     

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.     

Discrete element modelling of the influence of lifters on power draw of tumbling mills

Crushing and grinding are the most energy intensive part of the mineral recovery process. A major part of rock size reduction occurs in tumbling mills. Empirical models for the power draw of tumbling mills do not consider the effect of lifters. Discrete element modelling was used to investigate the effect of lifter condition on the power draw of tumbling mill. Results obtained with PFC3D code show that lifter condition will have a significant influence on the power draw and on the mode of energy consumption in the mill. Relatively high lifters will consume less power than low lifters, under otherwise identical conditions. The fraction of the power that will be consumed as friction will increase as the height of the lifters decreases. This will result in less power being used for high intensity comminution caused by the impacts. The fraction of the power that will be used to overcome frictional resistance is determined by the material’s coefficient of friction. Based on the modelled results, it appears that the effective coefficient of friction for in situ mill is close to 0.1.     

Acoustic emissions simulation of tumbling mills using charge dynamics

Knowledge of the internal variables of a mill is of importance in design and performance optimization of the mill, notwithstanding the difficulty in measuring these variables within the harsh mill environment. To overcome this problem, the research has focused on measuring the internal parameters through non-invasive measurement methods such as the use of the vibration/acoustic signal obtained from the mill. Alternatively, virtual instruments, such as discrete element methods (DEM), are employed. Here, a methodology is developed to simulate on-the-shell acoustic signal emitted from tumbling mills using the information extracted from a DEM simulator. The transfer function which links the forces exerted on the internal surface of the mill and the acoustic signal measured on the outer surface is measured experimentally. Given this transfer function and the force distribution obtained from the DEM simulation, and assuming a linear time-invariant response, the on-the-shell acoustic of a laboratory scale ball mill has been simulated. Comparison of this simulated signal with the signal measured experimentally can be used as a criterion to judge the validity of the DEM simulations, and as a tool for enhancing our understanding of both DEM simulations and the use of acoustics within the context of mineral processing. The results derived from preliminary experiments on a laboratory scale mill shows satisfactory agreement between the actual measurement and the simulated acoustic signal.     

Discrete element method simulation of bed comminution

This paper evaluates fragmentation behaviour, particle size distribution and liberation degree during bed comminution of particles. Three different cases of bed comminution are modelled through discrete element simulations. The role of stressing velocities on breakage, effects of crushing walls on fragmentation and influence of crushing gaps on liberation and particle size distribution are considered. The discrete element sample is modelled to represent the concrete specimens of B35 strength category.It has been observed that the particles around the stressing walls fail differently than the inner particles during bed comminution. The stressing velocity and the crushing walls have been found to affect the cracking mechanism of the particles. The liberation degree in bed comminution is less as compared to single particle crushing. The results presented in this paper can be used to model the liberation and recycling of valuable aggregates from cheaper matrixes.     

The energy distribution theory of comminution specific surface energy,mill efficiency and distribution mode

The present paper is a partial theoretical approach to the comminution process. A general theory of comminution should consist of two parts, one that deals with the energy required to break mineral particles and another that examines how this energy is distributed to the particles generated after breakage. The present approach deals with the second part that examines how the energy invested for comminution is distributed to the mill product. It uses the generally accepted concept, which assumes that the useful part of comminution energy is consumed to create new surfaces and finds the relationship between a characteristic particle size of the mill product and the energy consumed for grinding. The paper introduces the concept of potential energy and provides the means to give a value to the energy state of a material produced by a specific type of equipment. The energy efficiency is also taken into consideration and is used to calculate the energy actually invested for comminution. The main conclusion is that the specific surface energy is a physical property of materials and can be used as a universal index characterizing their grindability, regardless of the mill type or the mill efficiency. The physical dimensions of this index are energy per unit surface area (J/m²) compared to energy per unit volume or unit mass, which are the dimensions of the indices proposed so far.