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Effect of ball size and percentage of solids on grinding efficiency. Dry data is the average of duplicate cases (J=30%, U=100% and í µí½ í µí² =75%).
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Ball mills have large applicability in the mining industry. At the same time, ball mills
are considered as low efficient equipment. Laboratory tests using tumbling mills for
batch grinding have been crucial to a better understanding of the variables that affect
their development. These tests, when allied to adequate analysis tools, are able to
eluc...
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Please cite this article as: R. Panjipour, K. Barani, The effect of ball size distribution on power draw, charge motion and breakage mechanism of tumbling ball mill by discrete element method (DEM) simulation. Physicochemical Problems of Mineral Processing, http://dx. Abstract In this research, the effect of ball size distribution on the mill power...
Citations
... The milling media fill one third of the total volume of the drum. Rotary speed was set to 60 rpm in order to induce a cataracting regime for the balls [17,27]. The vibratory ball mill (VBM, Sweco, Belgium) consists of a 36 L-capacity grinding chamber made of an abrasion-resistant elastomer, put in vibrating motion by high-tensile steel springs [28]. ...
Plant biomass as a substitute for fossil oil is one of the most promising pathways to reducing the environmental impact of human activities. Ultrafine comminution of plant materials can produce ultrafine powders suitable for direct use in advanced-technology applications as an engine, becoming a sustainable powdered biofuel. However, comminution is an extremely energy-intensive process, making it vital for industry to select the most efficient milling device for the biomass. Here we comprehensively compared the efficiencies of three batch ball mills employable for ultra-fine comminution of plant materials. First we led a ball motion study to estimate the predominant mechanical stresses generated by each device. Two biomasses with contrasted physical properties were milled using three devices to achieve a target particle size of 20 μm. Milling times and process energy consumption were recorded, and the particle size distributions and specific surface areas of the ground powders were measured. The balls mills were then compared based on several indicators of energy efficiency, productivity and processing speed. The results show that the energy input is better utilized in mills that work by attrition or by combined impact and attrition.
... Based on particle breakage research in other industries, agglomerated particle breakage can be classified into surface breakage and body breakage (Francioli, 2015;King, 2012). Surface breakage is generally associated with limited particle damage, while body breakage can change drastically the particle morphology. ...
Dairy powder breakage occurs in many processes and causes deterioration in powder properties but there is currently no research presented in the literature on dairy powder breakage behaviour. The breakage behaviour and the effect of powder properties of an infant milk formula and its sieved size fractions were investigated during three processing methods (powder venturi feeder, lab-scale dilute phase pneumatic conveyor, and laboratory high-speed mixer) based on the changes of particle size distributions (PSD) before and after breakage. Particle size influenced other properties and the breakage behaviour of powders. Four breakage mechanisms were found, dispersion, chipping, disintegration, and splitting, corresponding to the increasing degree of breakage. More intense processing conditions were needed to cause the same breakage mechanism for smaller-sized particles because of their higher powder strength. The breakage of samples with wide PSD often displayed a combination of breakage mechanisms due to the influence of particle size on breakage behaviour.
... Regarding the rotation speed ball mills operation is based on two distinct regimes namely, cataract and cascade. While cataract favors collisions hence, body breakage, cascade leads to breakage by attrition [19]. In fact, the breakage motion of rod milling nearly resembles to ball milling. ...
Shape of particles made by grinding is one of the important measures for determining the utilizations of industrial minerals namely barite, calcite, and talc particles, particularly at production (like coating pigments, paints, rubber and paper) and processing stages (beneficiation by flotation). Therefore, measurement of particle characteristics is a critical issue in the development and control of industrial mineral products in most of the industries for some demanding applications. Ball and rod mills are commonly used as conventional grinding mills to produce a controlled grind size for the flotation circuit in the beneficiation of industrial minerals. Dynamic Image Analysis (DIA) offers reproducible results of a huge number of particles for some industrial minerals namely, barite [1], calcite [2] and talc [3] particles, whose shapes are crucial for some industries utilized as fillers. Thus, this review is about the comparison of shape values in terms of circularity (C) and bounding rectangle aspect ratio (BRAR) determined by the real time DIA. It was found that the shape results of the previous studies for the same samples by SEM measurement [4] were in good agreement with DIA results. It was concluded that the more rounded particles were encountered in the rod milled products for calcite and barite minerals. On the other hand, the more elongated particles were found in the ball milled products for talc mineral. It was attributed to the material type since the same mills were used for all tests. Hence, DIA can be used as a useful tool, which is easy, fast and highly accurate to control the particle shape distributions whether the required powder is fit for use
... It was found that the longer the grinding time, the retained mass fraction decreases. Where Si = material selection function based on size i, t = milling operation time, wi (t) = mass fraction with initial size in mill at time t, bi.j = another mass fraction at size of mill j [11]. ...
... The size of the grinding media (ball) is a variable that affects the level of damage from the raw material to be milled. The use of larger balls will result in more efficient damage and reduce the required power consumption [11]. ...
Ball mill is an operating unit used to grind various types of solid materials into finer particle sizes. The purpose of this study was to determine the best variation of operating conditions of mung bean milling in a ball mill by varying the grinding time, weight of raw materials and the number of balls used. In this study, the raw material used is mung bean. After grinding, the beans are then sifted through sieves 70, 140 and 200 mesh where the fraction of green beans that passes each sieve was obtained. From the studies, it can be concluded that the best operating conditions of mung bean milling in the ball mill are at 60 minutes grinding time, the weight of the raw material is 45 grams and the number of balls size is 8 medium balls and 6 small balls.
... It is to be expected that there is a relationship between the energy required to break the material and the new surface produced in the process, but this relationship can only be made evident if the energy consumed in creating new surfaces can be separately measured (Wills and Napier-Munn 2006). Over the history, semi-empirical energy-size reduction relationships were proposed by Rittinger, Kick, and Bond, known as comminution laws (Francioli 2015). Nevertheless, none of these three laws is applicable over a wide range of sizes (Rao 2011). ...
... The probability of breakage in comminution is high for large particles, and rapidly diminishes for fine sizes. He shows that Kick's law is reasonably accurate in the crushing range above about 1 cm in diameter; Bond's theory applies reasonably in the range of conventional rod-mill and ball-mill grinding, and Rittinger's law applies fairly well in the fine grinding range of 10-1000 microns (Francioli 2015). Although Bond was successful at theoretically proving his assumption, it is known nowadays that Bond's law is an empirical relation that provides acceptable fit to results from grinding experiments. ...
... Moreover, Bond's theory is still commonly used as a tool for sizing crushing and grinding equipment in the industry. It is also recognized that this methodology may present discrepancies around 20% in respect to the actual energy consumption for ball mills and even higher in for crushers (Francioli 2015). ...
Buzwagi Gold Mine (BGM) is operated by Acacia Mining and located in the Lake Victoria Goldfields of central Tanzania. The mine commenced its operation since April 2009 and treats a sulphide copper-gold ore to produce gold in form of doré bars and a concentrate containing gold, copper and silver. The BGM comminution circuit includes a primary crushing stage with a gyratory crusher and a two grinding circuits using a Semi-Autogenous Grinding (SAG) mill and a ball mill. The SAG mill circuit also includes a single-deck screen and a cone crusher while the ball mill circuit utilizes hydrocyclones. Currently, the grinding circuits are inefficient in achieving the aspired product fineness of xP,80 = 125 μm even at low to normal throughputs (450-600 t/h). An evaluation and optimization study of the circuit performance was conducted to improve the product fineness through circuit surveys, experimental lab work and simulations. In three full scale sampling campaigns, size distributions and solids contents of the samples were determined at selected points in the circuit. Further, several types of breakage tests were conducted; standard Bond tests to determine ore grindability and work indices, batch grinding tests to determine parameters for breakage and selection functions , and standard ball mill tests for mineral liberation characterization by an automated mineral liberation analyzer (MLA).The tests were conducted in a size range from 0.063 to 2 mm. Then, mass balance of the circuit was calculated and the models for mills, screens and hydrocyclones were employed in MODSIM (version 3.6.24). Firstly, simulations were conducted to optimize the existing plant. Several options were evaluated such as reduction of SAG screen aperture, adjustment of cyclone feed solids content and reduction of vortex finder and apex diameters. Moreover, simulations were also evaluated for a possible modification of the existing circuit and include; partial splitting of the cyclone underflow back to SAG mill, introduction of a second classification stage as well as introduction of a second ball mill. The evaluation of breakage tests and survey data revealed the following; the Bond work index obtained for the current ore ranges between 17.20 - 18.70 kWh/t compared to 14.50 - 16.50 kWh/t which was estimated during plant design.This indicates a change in hardness of the ore during the last 7 years. Harder ore means more energy requirement for an efficient operation, the consequence of which is increased costs.
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Thus, a periodic review of the ore hardness for ongoing mining operation is recommended. This will help in establishing better blends as well as prediction of appropriate tonnages for the existing ore types, so as to be efficiently treated by the available plant design. The work indices of the ore blends treated during survey were correlated with their quartz content and showed a strong linear relationship (R2= 0.95). Therefore, the work index for the BGM ore could be predicted based on known quartz content of the material. Further, the model could be used as a control tool for monitoring hardness variation of the SAG mill feed. The mineral liberation studies indicated that the valuable phase (pyrite-pyrrhotite) could be liberated at relatively coarser particle sizes (200-400 µm). This implies that, there could be no problem with the efficiency of the gravity circuit for the BGM operation, where the gold contained in pyrite-pyrrhotite could be easily concentrated. However, the efficiency of flotation and cyanidation processes will still require finer feed. In overall, the liberation characteristics of the ore blends treated during survey showed minor differences. The Bond efficiency factors of 48-61 % were obtained for the BGM grinding circuit, indicating an inefficient operation. This suggests that the operation could achieve targets by lowering the throughput. Further, the SAG mill circuit was characterized by fluctuating feed size of between xF,80 =102 to 185 mm. A need for control of the feed size as well as blending ratios was recommended for an efficient operation in terms of throughput and final product size. This could be achieved through closer monitoring of the primary crusher performance and proper control of the ratios for the SAG mill feeders drawing the ore from the stockpile. The ball mill grinding efficiency was poor and could be indicated by the fraction < 125 µm of only 5-9 % or xP, 80 : >400 µm in the mill discharge. This was deemed due to poor hydrocyclone performance which was characterized by higher feed solids content, coarser overflow xP,80: >200 µm as well as cut sizes, xT : > 200 µm. An improvement of product fineness up to 327 µm could be achieved during the simulation and optimization of the existing design. This could be achieved by modification of the operating conditions such as reduction of SAG screen aperture from 12 mm to 10 mm, reduction of vortex finder from 280 mm to 270.3 mm, reduction of apex diameter from 150 mm to 145.6 mm as well as adjustment of the cyclone feed solids content from 66.7 to 67.1 %. Based on this result, it was concluded that the current equipment could not achieve the target product quality (i.e. xP,80 = 125 µm ).
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Further simulations based on flowsheet modification options showed that a second ball mill (series configuration) can help to achieve the desired product fineness as well as an increase of throughput from 618 t/h to 780 t/h. Although the circulating load increases to approximately 500 % in this configuration, it is outweighed by the benefits. Importantly, this option is cost intensive and hence may be considered as a long term solution and especially after cost-benefit analysis. Finally, the results based on optimization of the existing design is recommended as short term solution for improvement of the BGM operation. Although the fineness achieved is still low (i.e. xP,80 = 327 µm) compared to the target (i.e. xP,80 = 125 µm), this gives additional advantage in the sense that, also better hydrocyclone performance is achieved in terms of overflow product (xP,80 = 105 µm vs. > 240 µm) , cut size (xT =133.1 µm vs. > 220 µm) and circulating load (CL =350 %). The improved overflow fineness will contribute to improved efficiency for the downstream processes.
... Extensive studies have been reported on the performance of ball mills with respect to the choice of operational parameters, material properties, and milling conditions. Commonly, properties such as the particle size distribution, powder specific surface, powder density, breakage rate, collision energy and collision frequency are compared among different systems in order to evaluate the grinding energy efficiency and the particle size reduction properties [6,7,8,9]. However, in many experimental studies of ball milling, the range of tested parameters is limited, and therefore inconclusive results are found. ...
By means of Discrete-Element simulations with Bonded-Cell method for particle breakage, we investigate the evolution of crushable granular materials in a 2D rotating drum partially filled with heavy balls and powder grains. The grinding process with balls of different sizes or numbers is analyzed in terms of grain size and specific surface. The grinding rate is an increasing function of the number of balls, but, as a result of increasing energy dissipation by inelastic collisions between the balls, the process becomes energetically less efficient for larger number of balls. When the total volume of balls is kept constant, the ball size has generally little influence on particle breakage. We also introduce a model for the evolution of three size classes by accounting for the cushioning effect and transition rates between the classes. This model predicts an exponential decrease of the volume of large particles at the beginning of the process.
... An important advantage of using numerical simulations is to allow us to isolate the effect of each operational parameter (e.g. drum and particle size, rotation speed, filling degree, drum width) on the grinding and ii Introduction Figure 1 -Image of a ball mill [88]. ...
... Extensive studies have been reported on the performance of ball mills with respect to the choice of operational parameters, material properties, and milling conditions. Commonly, properties such as the particle size distribution, powder specific surface, powder density, breakage rate, collision energy and collision frequency are compared among different systems in order to evaluate the grinding energy efficiency and the particle size reduction properties [82,158,88,100]. However, in many experimental studies of ball milling, the range of tested parameters is limited, and therefore inconclusive results are found. ...
... Images of a ball mill with lifters filled with the product and steel balls of two different sizes[88]. ...
A crucial step of nuclear fuel manufacture is the co-milling of uranium and plutonium oxides to obtain a targeted particle size and excellent mixing. However, the scale-up from the laboratory to plant production is still mainly empirical. The goal of this doctoral thesis is to model and characterize granular flows in rotating drums and to elucidate the mechanisms of particle grinding across scales. By means of particle dynamics simulations and a particle breaking model involving the tessellation of breakable particles into cells and a dynamic debonding criterion based on fracture mechanics, we investigate single-particle impacts, the properties of granular flows in the cascading regime in a rotating drum as a function of system parameters, the effect of the size and amount of grinding media on the grinding process, and the evolution of particle breakage in granular flows of breakable particles. Our simulations reveal several well-defined relationships between flow variables such as surface profile, flowing thickness, force fluctuations and wall slip, as well as with system parameters such as rotation speed, drum size and filling degree, and with particle fracture during flow. We identify two dimensionless parameters for the scale-up of flow characteristics and particle breakage in rotating drums.
... An important advantage of using numerical simulations is to allow us to isolate the effect of each operational parameter (e.g. drum and particle size, rotation speed, filling degree, drum width) on the grinding and ii Introduction Figure 1 -Image of a ball mill [88]. ...
... Extensive studies have been reported on the performance of ball mills with respect to the choice of operational parameters, material properties, and milling conditions. Commonly, properties such as the particle size distribution, powder specific surface, powder density, breakage rate, collision energy and collision frequency are compared among different systems in order to evaluate the grinding energy efficiency and the particle size reduction properties [82,158,88,100]. However, in many experimental studies of ball milling, the range of tested parameters is limited, and therefore inconclusive results are found. ...
... Images of a ball mill with lifters filled with the product and steel balls of two different sizes[88]. ...
Une étape cruciale de la fabrication des combustibles nucléaires est le co-broyage des oxydes d’uranium et de plutonium pour obtenir une taille ciblée et un mélange homogène de particules. Cependant, le changement de l’échelle du laboratoire à celle de la production reste essentiellement empirique. Le but de cette thèse de doctorat est de modéliser et caractériser les écoulements granulaires dans des tambours rotatifs et d’élucider les mécanismes de broyage de l’échelle des particules à celle du procédé. A l’aide de simulations granulaires, et d’un critère de décohésion dynamique basé sur la mécanique de la rupture, on étudie la fragmentation de partic- ules sous impact. La dissociation de ces particules se fait au niveau d’une tessellation en cellules sous-jacentes fragmentables. Les analyses développées portent notamment sur : les propriétés d’écoulements granulaires dans le régime de cascade en fonction des paramètres du système; l’effet de la taille et du nombre de corps broyants sur le processus de broyage; l’évolution de la frag- mentation dans les écoulements en tambour rotatif. Nos simulations révèlent plusieurs relations bien définies entre différentes variables caractérisant l’écoulement (profil de surface, épaisseur d’écoulement, fluctuations de force, glissement aux parois), l’évolution de la taille des particules et les paramètres du système (vitesse de rotation, taille du tambour, taux de remplissage). Ces travaux conduisent à la définition d’un paramètre sans dimension qui peut être utilisé pour la mise à l’échelle des écoulements dans les tambours tournants et les broyeurs à boulets.
... At 175MPa, the particle size distribution of the analysed clinker was finest among the four clinkers and vice versa. (Francioli 2015) stated that semi-empirical energy-size reduction relationships were previously proposed by Bond, Rittinger and Kick. However, these laws are not applicable over a wide range of sample sizes (Rao 2011). ...
... However, this law is mainly used as a tool for sizing crushing and grinding equipment. (Francioli 2015) recognized that this methodology could have up to 20% discrepancies in respect to the actual energy consumption for ball mills and much higher in crushers. "The probability of breakage in comminution is high for large particles, and rapidly diminishes for fine sizes (Wikedzi 2018;Francioli 2015;Bye 1999). ...
... (Francioli 2015) recognized that this methodology could have up to 20% discrepancies in respect to the actual energy consumption for ball mills and much higher in crushers. "The probability of breakage in comminution is high for large particles, and rapidly diminishes for fine sizes (Wikedzi 2018;Francioli 2015;Bye 1999). (Mohan and Glasser 1977). ...
The aim of this study is to investigate the different factors that influence the chemical and mineralogical composition of cement clinker and their effects on the required energy potential during cement grindability and comminution. Analyses of the different mineral phases were achieved using SEM, XRD, and MLA, while the comminution and grindability tests were determined using a piston-die press and ball milling, according to Zeisel. Though several empirical formulars according to Ziesselmar and Polycom Process Guidelines from Thyssenkrupp Industrial Solutions AG were adopted and considered, this simplified the scale-up for large cement industries. The results obtained from the grindability test are assumed for the scale-up of the real machine (HPGR). The primary goal of this work is to compare the results obtained from a piston-die press and a ball mill while taking into account the influence of mineral phases on energy consumption. Additionally, several other factors such as clinker grains, selection function, breakage function, Blaine (fineness), porosity (void volume), and particle contact points all played a significant role in the outcome of the energy potential for the investigated cement clinkers. Investigation on the influence of the chemical-mineralogical composition on the grindability showed that the tricalcium silicate mineral phase is the main mineral phase in K1 while dicalcium silicate is the dominant mineral phase in K4. Both the mineral grain sizes and clinker grains of tricalcium silicate (Alite) are larger than dicalcium silicate (Belite), based on the results obtained from X-ray diffraction and MLA. The following reasons contributed to the energy consumption of K1: unfavorable hard belite mineral phase, large clinker grains, high porosity (void volume), compression, and fewer contact points in K1 compared to K4. The high energy potential required for grinding K1 owes to the fact that the clinkers are not from the same location, therefore their properties differ. In addition, the coarse clinker grains and unfavorable hard clustered belite present in K1 are the major factors that contribute to the high energy potential as compared to K4.
... Some studies have been performed in order to evaluate the performance of ball mills regarding the choice of operational parameters, material properties and milling conditions. Commonly, properties such as the particle size distribution, powder specific surface, powder density, breakage rate, collision energy and collision frequency are compared among different systems in order to evaluate the grinding energy efficiency and the effectivity of particle size reduction [2,3,4]. In many experimental studies of ball milling, the amount/range of the parameters tested is limited, and therefore inconclusive results are found. ...
In this paper, the grinding of powder inside a ball mill is studied using the Bonded Cell Method (BCM) implemented in the framework of Contact Dynamics. In BCM the parent particles are divided into cells that are glued to one another until, under the action of external loading, both a cohesion threshold and a certain distance threshold are reached. Numerical simulations of a rotating hollow cylinder filled with a mixture of heavy balls and powder crushable particles were carried out. Systems with balls of different sizes and/or numbers are compared in terms of the evolution of the powder particle size and specific surface. We find that, in general, the milling process is increasingly faster as the ball size increases. But energy dissipation due to increased collisions between balls slows down the grinding process and makes it energetically less efficient. On the other hand, when the total volume of balls is kept constant, the ball size is not relevant for the evolution of particle breakage except in the limit cases of very small and very large ball sizes.
