Comminution Process Research Articles

Insights into phthalocyanine blue pigment dispersion: Modeling particle size distribution and grinding rate constants

The study presents an advanced mathematical model aimed at enhancing the understanding of pigment dispersion processes, with a particular focus on analyzing the dynamics of particle size distribution and determining grinding rate constants. Pigmented dispersions are crucial in various industries, including paints, coatings, and inks, where achieving optimal particle size distribution is vital for product quality. This investigates the relationship between grinding duration and pigment dispersion, aiming to establish empirical equations for the grinding rate constant as a function of particle size distribution and feed rate. Through experimental validation, the developed kinetic model provides insights into the dynamics of pigment dispersion and offers predictive capabilities for optimizing dispersion processes. Understanding the underlying mechanisms of pigment dispersion through mathematical modeling contributes to enhancing the performance and quality of final products in diverse industrial applications. The development of a new kinetic model, effective mathematical model is proposed to accurately simulate the evolution was applicable for the particle size from 32.67 to 122.4 nm distribution of pigment during comminution processes. In addition, it was observed that the kinetic model was not applicable for the particle size from 166.2 to 190.1 nm and also confirmed that the grinding was completed within 40 min, which was possible for uniform particle size distribution.

Field evidence and indicators of rockfall fragmentation and implications for mobility

Rockfall fragmentation can play an important role in hazard studies and the design of protective measures. However, the current lack of modeling tools that incorporate rock fragmentation mechanics is a limitation to enhancing studies and design. This research investigates the fragmentation patterns of rockfalls and analyzes the resulting distribution of fragment sizes within corresponding rockfall deposits. We focus on small rock fragments, which provide insights into the dynamics of the rockfall event and can be used as input for numerical modeling. We analyzed multiple rockfall events from locations worldwide, each exhibiting different degrees of fragmentation. Using image analysis techniques, we mapped all visible blocks, determined their volumes, and measured the distances they travelled from the initial point of impact. A key finding is the identification of three indicators of fragmentation. First, in cases where fragmentation was largely absent, we observed a trend of increasing block size with distance from the impact point or source area, which aligns with previously published findings. However, for energetic rockfall events characterized by intense fragmentation, we observed that small fragments exhibited longer travel distances compared to larger fragments. This distinction allowed us to differentiate blocks primarily resulting from the disaggregation process from those primarily resulting from dynamic fragmentation, with implications for rockfall mobility. Second, although the size distribution of rockfall deposits exhibits a power-law scaling for volumes larger than a minimum size threshold corresponding to a rollover of the distribution, in some case studies a deviation from power-law scaling is observed, indicating a process of larger block comminution due to fragmentation. Third, we found that rockfalls with fragmentation experience reduced mobility, indicated by higher reach angles, and higher lateral dispersion showing a wider distribution of trajectories. We interpret these findings as being directly related to the energy-consuming nature of fragmentation, which prevents farther deposition of fragmented rock blocks.

Discrete Element Modeling of the Breakage of Single Polyhedral Particles in the Rotary Offset Crusher

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (<50 kg/h). The ROC operated with a stationary disc is not recommended for hard rock applications due to expected excessive wear of crushing surfaces and higher energy consumption. The freewheeling discs are recommended, but there is scope to optimize the crusher performance in terms of the power draw, size reduction, and throughput by manipulating the difference between the speeds of the discs. There is also scope to optimize the crusher performance when it is simulated with many particles. Once the full performance potential of the ROC is established, it will then be important to benchmark it against the existing crushers in the minerals industry as well as other industries where crushers are used.

Daten und Modellierung von Zerkleinerungsvorgängen

ZusammenfassungQualitativ hochwertige Daten sind für die Entwicklung von Berechnungsmodellen von Zerkleinerungsvorgängen von großer Bedeutung. Moderne Anlagen sind mit einer Vielzahl von Sensoren ausgestattet, die eine kontinuierliche Überwachung vieler Systeme ermöglichen. Die Speicherung in Datenbanken bietet unter anderem ein großes Potenzial für Prozessanalysen und -optimierungen. Am Lehrstuhl für Aufbereitung und Veredlung wurde im Jahr 2021 in Zusammenarbeit mit der Firma CEMTEC – Cement and Mining Technology GmbH und der Linz Center of Mechatronics GmbH ein Forschungsprojekt initiiert. Dessen Ziel ist die Entwicklung eines Mahlmodells für Rührwerkskugelmühlen, das den realen Prozess bestmöglich abbildet. Dadurch soll ein besseres Verständnis für den Mahlprozess und die relevanten Einflussfaktoren erlangt werden, um ein Tool zur Prognose des Mahlergebnisses zu schaffen. Dieses Modell soll nicht nur das Mühlen-Upscaling ermöglichen, sondern auch beim Design von Anlagen mit optimaler Energieeffizienz unterstützen. Dafür werden gezielte Mahlversuche mit der containerbasierten Rührwerkskugelmühle des Lehrstuhls für Aufbereitung und Veredlung durchgeführt. Neben einer Anlagenbeschreibung werden erste Auswertungen der Mahldaten gezeigt und erläutert, welche Optimierungsarbeiten nötig waren, um zuverlässige Daten zu erhalten. Zur Modellierung wurde vorab das Population Balance Modell gewählt, dessen Grundlagen erläutert werden.

Virtual reassembling of 3D fragments for the data-driven analysis of fracture mechanisms in multi-component materials

This paper introduces a novel method for characterizing fracture mechanisms in multi-component materials using 3D image data gained by X-ray computed tomography (CT) measurements. In mineral liberation, the understanding of these mechanisms is crucial, particularly whether fractures occur along the boundaries of mineral phases (intergranular fracture) and/or within mineral phases (transgranular fracture). Conventional techniques for analyzing fracture mechanisms are focused on globally comparing the surface exposure of mineral phases extracted from image measurements before and after fracture. Instead, we present a virtual reassembling algorithm based on image registration techniques, which is applied to 3D data of multi-component materials before and after fracture in order to determine and characterize the individual fracture surfaces. This enables us to conduct a local quantitative analysis of fracture mechanisms by voxelwise comparing adjacent regions at fracture surfaces. A quantitative analysis of fracture mechanisms is especially important in the context of recycling processes. As primary deposits are decreasing worldwide and the focus is shifting on reducing wast, the interest in secondary raw materials has increased. However, lower-concentrated, but valuable materials are often overlooked in recycling routes designed for higher-concentration materials and dissipate. Therefore, efforts are being made to enrich valuable elements, such as lithium, as engineered artificial minerals through pyrometallurgical processes. The subsequent liberation through comminution processes, such as crushing, is essential for the recovery of valuable minerals. A better understanding of crushing processes, especially fracture mechanisms in slags, is crucial for the success of recycling. The reassembling algorithm presented in this paper is evaluated through a simulation study, followed by an application to a naturally occurring ore and a slag resulting from a recycling process.

The Comminution of Chert Gravel by Microwave Irradiation

Chert, a by-product rock of sand quarrying, has historically posed economic challenges for aggregate production, resulting in significant “waste” accumulation in quarries. Our study investigates the effect of microwave irradiation on the mechanical properties of chert gravel, a mineralogically homogenous material composed of fine quartz grains. The results, which demonstrate that increased irradiation time leads to a substantial decrease in chert gravel strength (by a factor of 4–6 for 2.5 min of irradiation), underscore the potential impact of this research on comminution processes. With quenching altering the fractional content of the samples after the crushing test, reducing the Gravel-to-Sand ratio, this study is driven by the promising potential of crushed chert gravel as a pivotal aggregate within the concrete and asphalt industries, offering a practical solution to their material needs. The urgent need to rehabilitate previously utilized quarry areas, offering an environmentally beneficial solution for which we all should be responsible, motivated the present study.

Multi-head neural networks for simulating particle breakage dynamics

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation. In this paper, the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics. Unlike conventional methods, the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size, predicting values on arbitrarily fine grids without the need for model retraining. The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes. The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill. The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

Surface stress can initiate environment-assisted fracture in metals.

Controlling environmental effects in surface plasticity/fracture of metals is of interest for areas as diverse as manufacturing processes, product performance, and structural safety. The key to controlling these effects is understanding the effect of adsorbates on surface energy (γ) and surface stress (f). While γ has been well studied, the role of surface stress has received much less attention. We characterize surface stress induced in metals by adsorption of organic monolayers. Linear alkanoic acids of varying chain length (3-18) are deposited by molecular self-assembly onto one side of an aluminum cantilever, several centimeters in length. The surface stress is estimated from in situ measurement of the cantilever deflection. We find that the organic adsorbates induce large surface stress of -4 to +30N/m. Furthermore, we show that f may be tuned by varying adsorbate-molecule chain length. The stress data explain beneficial embrittlement of metal surfaces by organic adsorbates in cutting and comminution processes, and point to a critical role, hitherto ignored, for f in environment assisted cracking (EAC) phenomena. Our results suggest opportunities for utilizing controlled environment-assisted fracture as an aid-fracture as a friend-to enhance material removal processes, apart from using surface stress itself as an experimental probe to explore various manifestations of EAC.

Concepts of entropy for raw materials

In recent years, several definitions of entropy have been proposed and used in the literature to assess the efficiency of processes in the field of raw materials, including waste management, the circular economy and mineral separation. However, these definitions lack a common framework, making it difficult to compare them and assess their similarities, connections, and complementarities. In this contribution, we propose a common framework which describes the calculation of the entropy of particulate systems. This framework extends existing definitions and introduces new insights into their combination. Our approach focuses on describing disperse particulate systems in comminution, separation, and classification processes, with potential extensions to evaluate other processes of particle technology, such as mixing, sampling, and agglomeration.

Influence of mechanical comminution of raw materials and PEF treatment on the aqueous extraction of phenolic compounds from artichoke wastes

In this study the combined effect of mechanical comminution and pulsed electric fields (PEF) treatments on both cell disintegration and extractability of phenolic compounds during aqueous extraction from artichoke external bracts, was investigated. Different-sized bract discs were treated with varying PEF conditions, namely 0.5–5 kV/cm of electric field strength (E), and 1–20 kJ/kg of total specific energy input (WT). The cell disintegration index (Zp) of bract tissues, as well as the total phenolic content (TPC) and antioxidant activity (FRAP) of the extracts, were assessed.The results showed that increasing the comminution process intensity led to greater cell disintegration, resulting in a peak extraction yield of phenolic compounds (17.61 ± 1.24 mgGAE/100 g FW) achieved with the smallest sample size. Moreover, the application of PEF treatment further increased the Zp value of the bract tissues in a size-dependent manner. The greater the sample size, the stronger the PEF efficiency. Coherently, under optimized PEF conditions (E = 3 kV/cm, WT = 5 kJ/kg), the extracts exhibited higher TPC (+112–361%) and FRAP values (+83–836 %) as compared to the control samples after 120 min of diffusion. The extraction rate of phenolic compounds increased when the comminution degree was increased for both untreated and PEF-treated samples, and this was successfully predicted using Peleg's model.These findings suggest that PEF can be a viable alternative to energy-intensive comminution pretreatment, thus enhancing the extraction of phenolic compounds without requiring finely ground raw material handling.

Quantitative Estimation and Comparative Assessment of Particle Morphological Features and Energy Requirement During Hammer Milling of Softwood Chips and Wheat Straw

Highlights Quantified particle size and shapes generated during hammer milling of softwood and wheat straw. Size reductions in length and width correlated with milling energy requirement. Assessed the validity of existing comminution laws for predicting milling energy requirement. Improved milling energy requirement prediction for softwood based on size reductions. Abstract. The valorization of agricultural and woody residues into higher quality fuels is an attractive pathway and can contribute to decarbonizing the energy system. One essential step for the conversion of these residues to fuels is comminution through commercial mills. This study aimed to investigate the effects of feedstock, input feed size, and milling screen size on particle size and shape, as well as to validate the reliability of existing comminution laws for predicting energy requirements during hammer milling of agricultural and wood biomass. Additionally, the study proposed a new empirical correlation for comminution energy prediction, taking two-dimensional size reduction descriptors into consideration. A machine vision-based image processing method was used to estimate particle size, particle size distribution (PSD), and particle shape factors. The aspect ratio of wheat straw particles was 1.3 to 1.5 times larger than softwood particles, suggesting they are more fibrous. The shapes generated during hammer milling were estimated, with rectangular shapes being predominant. The specific energy requirement (SER) estimated for the hammer milling of softwood chips and wheat straw at different mill screen sizes (4, 8, and 12 mm) was found to be in the range of 153.2–25.5 kJ kg-1 and 38.5–16.1 kJ kg-1, respectively. The validity of existing comminution laws to predict the SER during hammer milling of softwood and wheat straw was tested at a fixed feed rate of 45 kg hr-1, and an improvement in SER prediction for softwood was achieved by formulating a new empirical correlation factoring size reductions in length and width. Further, the correlation developed for the SER for wheat straw was found to lack statistical significance. The findings of this study can be applied to improve the effectiveness of the comminution process, a critical precursor to numerous thermochemical conversion methods used for transforming biomass residues into valuable fuels. Keywords: Bioenergy, Biomass comminution, Machine-vision image analysis, Particle shape, Particle size distribution, Specific energy consumption.

Evaluation the Effectiveness of the Comminution Process in a New Rotary Vibration Mill Using the Finite Element Method

With the rapid development of nanotechnology the urgency of the issue of increasing the efficiency of fine and ultrafine comminution of materials has increased. Nowadays, one of the most popular issues is to obtain a grinding product with a size of less than 20 μm for various technological processes. The purpose of the investigations presented in this paper is an increasing in the effectiveness of fine and ultrafine grinding process. To achieve this purpose, the authors of the article have analyzed new technical solutions to improve the efficiency of fine and ultrafine comminution. Based on the existing principles for improving the design of stirred mills, a new design of the so-called «rotor-vibratory mill» has been proposed. Using the finite element method, the efficiency of the proposed design of the mill with the support of computer simulation of the grinding process has been evaluated. The results of the investigations showed that the new design of the mill allows to increase the product fineness by 69...75% and decrease the time of the grinding process by 60...74% in comparison with existing analogues.

Soft Computing Application in Mining, Mineral Processing and Metallurgy with an Approach to Using It in Mineral Waste Disposal

In the past two decades, the mining sector has increasingly embraced simulation and modelling techniques for decision-making processes. This adoption has facilitated enhanced process control and optimisation, enabling access to valuable data such as precise granulometry measurements, improved recovery rates, and the ability to forecast outcomes. Soft computing techniques, such as artificial neural networks and fuzzy algorithms, have emerged as viable alternatives to traditional statistical approaches, where the complex and non-linear nature of the mineral processing stages requires careful selection. This research examines the up-to-date use of soft computing techniques within the mining sector, with a specific emphasis on comminution, flotation, and pyrometallurgical and hydrometallurgical processes, and the selection of soft computing techniques and strategies for identifying key variables. From this, a soft computing approach is presented to enhance the monitoring and prediction accuracy for mineral waste disposal, specifically focusing on tailings and spent heap leaching spoils database treatment. However, the accessibility and quality of data are crucial for the long-term application of soft computing technology in the mining industry. Further research is needed to explore the full potential of soft computing techniques and to address specific challenges in mining and mineral processing.

Valorization of Air-Cooled EAF Manganese Slag in Comminution Processes: an Investigation into the Breakage Characterization

In recent years, slag, a residue from pyrometallurgical processes, has become more attractive in circular economy frameworks to increase the efficient use of resources throughout the life cycle of steel products and help in the reduction of carbon emissions. Its applicability is strongly dependent on the particle size, and therefore, the optimization of breaking processes should be approached by increasing the knowledge of the dynamics of slag to promote fracture. Increasing the knowledge on the mechanical response of manganese slag opens up the potential for the development of cost-effective numerical models, e.g., constitutive models based on inverse engineering calibration frameworks or digital twins. In this study, rate-dependent tests of manganese slag have been performed using a split Hopkinson pressure bar device for testing its dynamic mechanical response. In order to obtain information about the crack initiation and fracture process, 2D ultra-high speed imaging was implemented with a sampling frequency of 663,200 fps for diametrically loaded specimens. Full-field deformation measurements using digital image correlation (DIC) techniques showed a staggered fracture process where failure points on mechanical response curves vary due to the internal events happening in the material. Localized frictional occurrences and inertial effects acting inside the pre-cracked matrix have a strong effect on the global mechanical response, and therefore, a great variability of strengths was obtained.

Deposit comminution in a weak variably-cemented breccia rock avalanche

Rock avalanches display a distinct and complicated behavior that is not yet completely understood. Analyzing the deposit characteristics is crucial for studying the comminution mechanism during its emplacement. Combining field investigation, image processing, and numerical modeling, we explore the deposit characteristics and comminution process of the Wangjiapo rock avalanche triggered by the Mw6.2 Ludian earthquake. First, we use UAV photogrammetry to obtain a three-dimensional point cloud model and a digital orthophoto, from which we semi-automatically extract the geometry and position of 80,602 blocks by adopting a new block photo-analytical procedure, in addition to a further 4388 coarse blocks that were mapped from manual procedure. We analyze the longitudinal and transversal variation of the block distribution within the deposit. Large boulder content was more abundant in the middle part, while the fine blocks were distributed more evenly. Blocks were prevalently equant-sphere (ES) shaped with no dependence on volume and location, but the roundness increased significantly with runout. Additionally, we find fractal dimensions ranging from 1.42 to 1.83, lower with respect to other rock avalanches, probably due to the high weakness of materials. Furthermore, we propose two comminution models based on the significant differences observed between the eastern deposit II and western deposit III, which were caused by variably-cemented breccias. Finally, numerical modeling indicates that the large amount of fine material damped the grain-grain velocity during runout, leading to a limited spread of the rock avalanche and so explaining the short displacement of the front observed.

Fracture behavior and energy efficiency of silica under a tensile load using molecular dynamics

Existing theories on the energy consumption of comminution are mainly applicable at the macroscopic and mesoscopic scales, and there is a lack of studies on the fracture behavior and energy efficiency at the microscopic scale. To reveal the energy evolution of the comminution process at the atomic scale, silica was subjected to a tensile load test using a molecular dynamics simulation. The crack propagation behavior, mechanical properties, major energy changes, and energy efficiency were analyzed for the comminution process of silica. The results showed that the mineral morphology and load direction affected the number and propagation path of cracks and that the crack propagation direction was generally perpendicular to the load direction. With an increase in the pre-crack length, the breaking strength, Young's modulus, elastic energy, input energy, and new surface energy of the specimens decreased to varying degrees. The energy efficiency can be significantly improved by creating pre-cracks, changing the morphology of silica to an amorphous state, and applying a load perpendicular to the crack direction. The maximum energy efficiency was 6.69 times the minimum value. This study explains the influence of pre-cracking, mineral morphology, and load direction on energy efficiency at the atomic scale and reveals the fracture mechanism and energy evolution of silica during comminution. This is of positive significance for reducing energy consumption by improving the energy efficiency of comminution processes.

Numerical modelling of microwave irradiated rock fracture

Rock fracturing through microwave irradiation has received significant attention recently as a viable pretreatment for improving the energy efficiency of comminution processes. This study presents a numerical analysis on the effects of microwave heating on the mechanical properties of hard rock. In particular, the reduction of the uniaxial compressive and tensile strength of granite-like rock due to microwave irradiation induced damage is numerically assessed.Rock fracture is modelled by a damage-viscoplasticity model, with separate damage variables for tension and compression types of failure. A global solution strategy is developed where first the electromagnetic problem is solved in COMSOL multiphysics software, then its solution is used as an input for the thermo-mechanical problem, which is finally solved by means of a staggered explicit solution method. Due to the preeminence of the thermal radiation, the thermal and the mechanical parts of the problem are considered as uncoupled.The model behaviour is tested in 3D finite element simulations of three-mineral numerical rock specimens, with mesostructures explicitly defined, pretreated first in a microwave oven and then subjected to uniaxial compression and tension tests. The results show that the compressive and tensile strength of rock can be considerably reduced by the microwave irradiation pretreatment.

Quality Evaluation of Buffalo Meatballs Produced at Different Comminution Process Temperatures

Buffalo meatballs were formulated and the effects of different comminution temperatures on the quality (cooking yield, water holding capacity (WHC), protein, texture, colour, and sensory) were evaluated. During the mixing of ingredients, the comminution temperature was adjusted using different types of water which were ice (0°C), ice water (4°C), cold water (10°C), room temperature water (22°C), and warm water (32°C). Following comminution for 3 minutes, the temperatures of the batters were recorded at 14, 25, 25, 29, and 27°C, respectively. The comminution took a total of 15 minutes had produced batters with similar final temperatures (ranging from 36 to 38°C), except ice temperature mixing (28°C). Cold water meatballs produced the highest cooking yield but significantly the lowest (P<0.05) water-holding capacity. The colour of the cold water meatball shows significantly (P<0.05) the highest L* (lightness), significantly (P>0.05) the lowest a* (redness), and the lowest b* (yellowness) values. While the textures (hardness, cohesiveness, gumminess, chewiness, and springiness) of all meatballs were similar (P>0.05). All meatball samples had nearly similar soluble protein concentrations (0.97 to 1.06 ug/ml) but ice water meatballs had the highest (P<0.05). The panellists gave all the meatballs a score ranging from 6.32 to 6.98, with ice meatballs receiving the highest mean score (6.98) acceptability score (P>0.05). In conclusion, comminuted buffalo meatballs can be produced using either ice, ice water, cold water, room temperature water, or warm water without affecting their quality. However, ice is suggested for safety purposes against microbial growth during processing.

A breakage model for DEM based on a probabilistic particle replacement with Voronoi fragments

Due to mechanical stress, bulk material is crushed and fines are produced. This can either be desired in comminution processes or undesired in conveying and storage processes. In this work a novel breakage model for the Discrete Element Method is presented to allow a prediction of the resulting particle size distribution after damaging events. The breakage model is based on a probabilistic particle replacement strategy. Depending on the load, the initial particle is replaced by a breakage pattern tessellated with the Voronoi algorithm. Replacement probabilities and breakage patterns follow results from breakage tests. In contrast to other replacement models, mass and volume remain constant. Initial particles are polyhedral and can be of any shape. Crushing processes with multiple breakage can be simulated. The computational scheme is described in detail. The model was verified and validated with trials of shatter tests and two conveying processes with blast furnace sinter from two different industrial partners.

ОПРЕДЕЛЕНИЕ КОЭФФИЦИЕНТА ЗАГРУЗКИ МАТЕРИАЛА В КАМЕРЕ ПОМОЛА ШАРОВОЙ БАРАБАННОЙ МЕЛЬНИЦЫ

The predominant application of ball drum mills in industrial enterprises for the comminution process of various materials, which is one of the most energy-intensive basic technological processes, is demonstrated in this scientific article. As one of the parameters that can enhance the efficiency of the comminution process, the rational quantitative ratio of grinding bodies to the material being ground is noted. To calculate the material loading coefficient in the grinding chamber, the feasibility of developing a mathematical description is shown. This allows to determine the change in the area of gaps between grinding bodies in a cross-sectional plane perpendicular to the longitudinal axis of the mill's body, as the rotational frequency changes. A mathematical description is obtained to determine the area of the ball-material load in the cross-sectional plane of the grinding chamber during the static state of the mill's body and at different rotational frequencies. Using this mathematical description, research on the change in the area occupied by the ball-material load in the transverse section of the grinding chamber during the transition of the mill's body from the static state to the operating state is conducted. Regularities of its changes for an industrial-sized mill are determined. At different values of the filling coefficient of grinding bodies, it is established that the transition of the mill's body from static to operating state leads to an increase in the area of the transverse section of the ball-material load by an amount close to 17 %. An expression is proposed to determine the material loading coefficient in the grinding chamber corresponding to its operating rotational frequency.