Discrete element method modelling of forces and wear on mill lifters in dry ball mining

Since the beginning of the last century, many studies have been performed in order to improve our understanding on the milling process. Recently, Mishra and Rajamani (1992) applied the Discrete Element Method (DEM) to solve the milling problem. Since then, this method gained considerable success due to its ability to predict load motion and power draw by tumbling mills as affected by operating conditions. The application of this method at an industrial stage requires a more rigorous validation in order to produce realistic output. Lifter profiles play a key role in the performance of tumbling mills since they influence the motion of mill charge. Since lifters change profiles during their useful life due to wear, the performance of tumbling mills will correspondingly vary as a function of time. There is therefore a need to predict forces and wear on mill lifters in order not only to chose or design an initial lifter profile which optimizes tumbling mills performance over the lifters’ useful life but also to evaluate lifter replacement time and type and also modifications which can be performed on lifters and/or operating mill conditions in order to extend the lifters’ useful life. Despite the importance related to this subject, few works has been done in this field. In this thesis, we firstly assess the ability of the Discrete Element Method to model the tangential and normal forces exerted by the mill charge on lifters. Data from an experimental two-dimensional mill designed in order to record the normal and tangential forces exerted on an instrumented lifter were available. The measured results obtained at different speeds and percentages of filling have been compared to the Discrete Element Method simulated results in the same conditions. A good agreement has been found between the experimental and the simulated results in terms of toe, shoulder positions and amplitude of forces. After this validation of the DEM, we secondly assess the ability of this method to predict the wear of lifters in dry milling conditions. We derived a mathematical wear equation describing the removal of materials from lifters which takes into account all types of wear occurring in dry milling environment. We introduce a new approach to implement this equation in the DEM code in order to produce realistic simulated profiles. Our new method developed has been tested against laboratory and industrial data of evolving lifter profiles due to wear. Good agreement has been found between the simulated and the measured profiles. The variation of the load behaviour as a function of lifter wear in industrial tumbling mills studied was also investigated in this thesis. The objectives were to improve the understanding of the grinding process and quantify the variation of load behaviour as a function of lifter wear. Lifter modifications were also explored in order to extend lifters useful life. An attempt was also made in this thesis to derive, from the description of the load behaviour, equations in order to predict the wear of lifters without using the Discrete Element Method. Equations derived show the difficulty to use this approach. Success in this case was achieved only in a particular case where no significant changes occur in the load behaviour as a function of lifters wear. This finding confirms the DEM as the adequate tool to model forces and wear of tumbling mill lifters. The results obtained are of great economical significance since they can improve the profitability of mineral processing plants. A step forward in the use of the DEM not only to design milling equipments but also to improve the understanding, optimise and quantify the change occurring as a function of lifters wear was achieved

Circulation rate modelling of tumbling mill charge using positron emission particle tracking (PEPT)

Includes abstract.Includes bibliographical references.This research is focused on developing theoretical understandings of charge circulation trends as observed in tumbling mills at different operating conditions. Of particular interest is the underlying assumptions being made by many mill models that a particle imparts energy for potential breakage only once per revolution of the mill to the charge body – that is, that the circulation rate of mill charge can be assumed to be constant irrespective of the speed at which the mill is run. The trajectory data used in this thesis is derived from positron emission particle tracking (PEPT) experiments conducted at the University of Birmingham positron imaging centre and further experiments were conducted at the iThemba LABS in Cape Town. The experimental approach is highly suited to allow the effective examination of the assumption that the grinding charge in these mills circulates at a constant rate of unity

Effects of grinding media shapes on ball mill performance

Student number : 0318567G School of Chemical and Metallurgical Engineering Faculty of EngineeringComminution is an important process in mineral processing, power plants, cement production and pharmaceutical industries. It is costly and an inefficient process in terms of energy requirements and steel consumption related to grinding media and liners. Spherical grinding media are predominantly used in final stages of ore grinding. The spherical balls change shape through breakage and wear. Though this is universal in milling, its contribution and effect on milling kinetics, load behaviour and mill power is not fully established. One area that is usually ignored is the relationship between media shape and mill power. The objective of this dissertation was to investigate how media shape affects grinding. Ball size distribution inside an industrial mill was analysed in terms of shapes and sizes. Load behaviour, mill power and breakage as affected by media shapes were studied in a pilot laboratory mill. An inductive proximity probe, light emitting diode, phototransistor and video photographs were used to determine the load orientation in terms of toe and shoulder positions. A load beam was used to measure the torque exerted by the charge. The variation in load orientation and mill power with speed among different media shapes was observed. Higher shoulder positions were noted with cylpebs than with worn and spherical balls. The power increased to a maximum with increasing mill speed for all media shapes reaching its peak at different mill speeds for the three shapes studied. Variations of breakage rates with media shapes were found; higher breakage rates were noted with spherical media but the differences narrows with decreasing feed size and increasing material fractional filling U. Considering that worn balls in an industrial mill charge constitute about 15 to 40 percent and that the highest difference in breakage rate observed being nine percent for purely one shape charge; it is very doubtful whether it is worthwhile in attempting to develop techniques for removing worn balls from the mill

Assessing the influence of lifter profiles on the velocity profile and the charge toe and shoulder using data from the PEPT system

Includes bibliographical references.The research focus of this thesis is lifter height effect on different charge characteristics. Thecharge characteristics identified were shoulder and toe angle, charge size and toe height. Anattempt was made to develop a model for the velocity profile incorporating lifter height.Therefore the objectives of the study are to: •Determine the effect of lifter height on the velocity profile using the particle tracking data. •Determine the effect the lifter height on the charge shoulder and toe. •Develop a velocity profile model including lifter height using granular flow theory and to compare the model to experimental data. The motivation for the study is that lifters are one of the most important design variables in a mill. Without lifters the mill’s energy efficiency would decrease. In Meaders & MacPherson, (1964) the effect of lifters on energy was quantified to be between 20% and 30%. The lifters control the height and angle of departure from the charge at the mill shell and therefore control the impact area and magnitude. The area and magnitude of the charge impact will affect the grind of the mill and energy utilization in the mill. The thesis was also aimed at generating data that can be used to model the velocity profile that can be incorporated in power models. Most of the power models do not account for the effect of lifters. The experiments involved collecting data from three dimensional particle tracking of selected particles in the charge. using the PEPT system. The PEPT experiments were conducted at IThemba Labs in Cape Town South Africa using a 300 mm x 285 mm experimental mill. The charge used for the experiments were glass beads with an approximate specific gravity (SG) of 2.7. The PEPT system operates by tracking the x, y and z coordinates with respect to time of an irradiated particle (tracer). The experiments were run under different conditions to evaluate the effect of the lifter height. The experiments were operated by varying mill speed (55%, 70% and 85%), mill fill (20%, 30% and 40%) and lifter heights (1.5 mm, 3 mm, 6 mm and 10 mm)

Effects of pool volume on wet milling efficiency

The volume of slurry in a rotary mill has a bearing on the presence of a pool of slurry and therefore on milling efficiency. Load behaviour was investigated at different volumes of slurry. The insight gained was then used to evaluate the implications of slurry pooling on milling. First, the effects of viscosity on mill charge behaviour were measured using photographic techniques applied to a Perspex mill. A model of the angular location of the free surface of the slurry pool, as affected by slurry filling was proposed. Next, a real ore was used and the load behaviour was measured using non-invasive sensors fitted to a pilot mill. At this point, the angular position of the pool and the net power draw were correlated to the volume of slurry for mill speeds ranging from 65 to 85 % of critical. An additional series of tests was carried out on a mill filled with grinding media only, for speeds spanning from approximately 24 to 110 % of critical. The aim here was to isolate and study the media charge. Lastly, a laboratory mill was used to run batch grinding tests on a Platinum ore for slurry fillings U between 1.0 and 3.0 and at 65 % solids content. Two ball fillings were considered for identical slurry volumes: J = 20 % and 30 %. Results showed that not only did the proposed pool model work well using an artificial slurry in the Perspex mill, but it also worked for the Platinum ore tested in the Wits pilot mill. The behaviour of the media charge was not substantially affected by slurry viscosity and slurry filling. The net power drawn by the ‘dry mill’ compared well with DEM prediction for non-centrifuging speeds. The effect of slurry pooling on net power draw, on the other hand, was best accounted for using a Torque-arm model and an empirical model developed to this end. As for milling kinetics, results suggested that the slurry pool should be avoided because milling efficiency deteriorated as a result. However, the production of fines was not largely altered

Development of a model for temperature in a grinding mill

Abstract Grinding mills are generally very inefficient, difficult to control and costly, in terms of both power and steel consumption. Improved understanding of temperature behaviour in milling circuits can be used in the model-based control of milling circuits. The loss of energy to the environment from the grinding mill is significant hence the need for adequate modeling. The main objectives of this work are to quantify the various rates of energy loss from the grinding mill so that a reliable model for temperature behaviour in a mill could be developed. Firstly models of temperature behaviour in a grinding mill are developed followed by the development of a model for the overall heat transfer coefficient for the grinding mill as a function of the load volume, mill speed and the design of the liners and mill shell using the energy balances in order to model energy loss from the mill. The energy loss via convection through the mill shell is accounted for by quantifying the overall heat transfer coefficient of the shell. Batch tests with balls only were conducted. The practical aspect of the work involved the measurement of the temperatures of the mill load, air above the load, the liners, mill shell and the environmental temperature. Other measurements were: mill power and sound energy from the mill. Energy balances are performed around the entire mill. A model that can predict the overall heat transfer coefficient over a broad range of operating conditions was obtained. It was found that the overall heat transfer coefficient for the grinding mill is a function of the individual heat transfer coefficients inside the mill and outside the mill shell as well as the design of the liners and shell. It was also found that inside heat transfer coefficients are affected by the load volume and mill speed. The external heat transfer coefficient is affected by the speed of the mill. The values for the overall heat transfer coefficient obtained in this work ranged from 14.4 – 21W/m2K. iv List of Publications The author has published the following papers based on the contents of this dissertation as follows: Published conference abstract Kapakyulu, E., and Moys, M.H., 2005. Modelling of energy loss to the environment from the grinding mill, Proceedings of the Mineral Processing 2005’ Conference, SAIMM, Cape Town, South Africa, 4-5 Aug. pp 65-66 - SP03 Research Papers: Accepted for publication and currently in press in Minerals Engineering: Kapakyulu, E., and Moys, M.H., 2006. Modelling of energy loss to the environment from a grinding mill, Part I: Motivation, Literature Survey and Pilot Plant Measurements, (Currently in press in Minerals Engineering) Kapakyulu, E., and Moys, M.H., 2006. Modelling of energy loss to the environment from a grinding mill, Part II: Modeling the overall heat transfer coefficient, (Currently in press in Minerals Engineering

Measuring, characterisation and modelling of load dynamic behaviour in a wet overflow-discharge ball mill.

Overflow ball mills have found popular application in the ore dressing process for post-primary grinding firstly owing to their ability to produce finer grinds, necessary for efficient mineral liberation and better flotation recovery and secondly due to lower initial capital outlay. However they are inefficient and intensive energy consumers. This trend has been exacerbated in the wake of increased installation of large diameter ball mills to benefit from economies of scale, coupled with diminishing ore quality currently being experienced by mines worldwide. To fully utilise the available mill capacity and achieve optimal performance whilst maintaining energy efficiency for these large devices, closer and more effective control is needed. Satisfaction of this need would result in stability of the entire mineral processing circuit, thereby reducing the overall cost in mineral extraction. Clear and deeper understanding of the in-mill behaviour is fundamental to the realisation of the above objective. This thesis explores several experimental and modelling techniques to obtain deeper understanding of the internal behaviour of an overflow ball mill. A direct load sensor comprising an inductive proximity probe and a conductivity probe installed through the mill shell has been utilised to collect information of the media and slurry dynamic positions inside a laboratory ball mill while a commercial on-line ball and pulp sensor was employed to collect similar information on an industrial overflow ball mill. Useful insights were acquired that can help the design of control strategies for optimal mill performance. Four feature variables, i.e. dynamic media angle, slurry pool angle, conductivity signal amplitude and the slurry pool depth, derived from the sensor signals data were characteristically influenced by changes in mill operational conditions. Therefore the possibility of using these features to predict the associated mill operational variables is feasible. In view of the findings, two multivariate models, one based on the concept of data projection to latent space (PLS) and the other combining PLS and radial basis functions neural networks (RBF) were built and applied to predict the in-mill slurry density and ball load volume. Both models yielded adequate predictions, albeit the hybrid PLS-RBF model displayed marginally better prediction performance. The results are indicative of the available potential for mill on-line monitoring and control by multivariate techniques based on relevant features contained in the media and slurry sensor signals data. In another endeavour, a gamma camera was successfully employed to study the flow and mixing behaviour of slurry inside a laboratory mill using Technetium-Tc99m radiotracer as a flow follower. The effects of slurry viscosity and mill rotational speed on slurry mixing rate within the ball charge and slurry exchange rate between the pool and the ball charge were assessed, yielding insightful data. However, the results remain inconclusive as only qualitative information could be obtained owing to the radiation attenuation effects by the steel ball charge. In the quest to improve the understanding of material transport inside the mill, the data acquired on an industrial mill through salt tracer tests was adequately analysed to assess the variation of slurry residence time distribution (RTD) and volumetric holdup inside the mill as affected by changes in slurry concentration and ball load volume. A model based on the concept of serial stirred mixers with a plug flow component produced fairly accurate predictions of the RTD data. Also, equations derived from a mathematical description of the dynamic load profile produced good estimates of the in-mill slurry volumetric holdup. Further, an improved mixing-cell model was developed and applied to characterise the in-mill slurry hydrodynamic transport based on the measured RTD data. The model was able to account for the effects of non-ideal flow conditions such as slurry back-mixing, slurry exchange between the pool and ball charge and bypass flows on the main flow of slurry thus giving correct description of the inherent in-mill slurry transport dynamics. Note that failure to tune the mill appropriately to achieve desirable in-mill slurry transport behaviour may result in poor milling performance and corresponding high energy expenditure. Thus, the results obtained in this thesis clearly demonstrate that, a combination of experimental techniques and mathematical models is a viable route to enhance understanding of mill internal behaviour, which in turn enables development of better control schemes for optimal mill performance

An investigation into the parameters effecting the performance of tube mills : the behaviour of a single particle on the inside of a rotating cylinder

This thesis is the first stage of a project to investigate the parameters effecting the performance of tube mills. The main topics that the project will cover are the motion of mill charge and the wear characteristics of the balls and the mill liners. A literature survey highlighted that no examination had been performed that investigated the motion of a particle with specific emphasis on the response to changes in the coefficient of friction between the particle and the liner. This thesis concentrates on the motion of a single particle moving on the inside of a smooth rotating cylinder. Three formulations are presented that model the motion of the particle. The first model assumes that the particle slides along the cylinder. To ensure that it slides, and does not roll, a block shaped particle is modelled. The second motion type assumes that a spherical shaped particle rolls along the cylinder. The assumption that is made, is that the point of contact between the ball and the cylinder does not slip or skid. This mode of rolling has been defined as Pure Rolling. A third model is proposed that is a combination of the sliding and rolling models. The formulation attempts to incorporate both actions, rolling and sliding. In this way the motion of the particle.is dependent on both the rolling and sliding interactions. The governing equations for the Sliding and Rolling models are solved numerically, using an Euler Forward Approximation. Both models are solved by a computer implementation of the resulting numerical equations. The Sliding program has been extended to animate the response of the block on the inside of the cylinder. The theoretical predictions from the two numerical solutions are presented and discussed

A study of the charge structure and energy utilisation in a Stirred Media Detritor using DEM-SPH

The Stirred Media Detritor, (SMD), is a grinding device used for fine and ultra-fine grinding applications in mineral processing. The SMD has a vertically orientated shell that supports a shaft, with protruding impeller arms for agitating the charge. There is currently limited understanding of charge structure and motion in the SMD, particularly the interaction of the media and the slurry. Additionally, the number of arms and their arrangement on the shaft, are important aspects of the impeller that determine flow, energy consumption and grinding efficiency. Impeller geometry choices affect these characteristics of the process. This work focuses on studying the flow of grinding media and slurry for the industrial scale SMD 1100- E. This information is used to explore charge dynamics and energy utilisation in the SMD. To investigate the effect of impeller arm configuration on the operational behaviour of the SMD, the commercially available impeller configuration of the industrial scale SMD 335-E is used as the base case. Mill charge dynamics, transport and mixing, patterns of energy absorption on the mill surfaces are examined for the base case and compared to three different impeller arm arrangements. A two-way transient coupled Discrete Element Method (DEM) and Smoothed Particle Hydrodynamics model is used to achieve this. The ceramic grinding media is represented by the DEM component of the model, which is fully resolved, while the slurry (water and fine particles) is represented by the Smoothed Particle Hydrodynamics (SPH) model. The focus is on steady state operation therefore discharge from and feed into the mill are omitted. A nominal media size of 8 mm is used. The rotational action of the impeller forces the charge to the mill wall creating vortex centred on the mill shaft. The vortex is conical with a large diameter at the bottom, which decrease towards the bottom of the mill. Abrasion is found to be the dominant breakage mechanism in the SMD. Mixing behaviour is complex with media transfer past layers of impeller arms being influenced by the fall distance of media between impeller arm encounters