Grinding Product Research Articles

Pimozide and Adipic Acid: A New Multicomponent Crystalline Entity for Improved Pharmaceutical Behavior

Pimozide is a first-generation antipsychotic used in the treatment of schizophrenia, Gilles de la Tourette syndrome, and other chronic psychoses. Its in vivo efficacy is limited by poor solubility and consequent poor bioavailability. Therefore, adipic acid was used as a coformer for the preparation of a binary product with improved pharmaceutical properties. The thermal behavior of the liquid-assisted grinding products of compositions included in the range 0.1 < XPMZ < 0.9 has been interpreted using a thermo-dynamic model according to which the two components originate a new crystalline entity in molar ratio pimozide:adipic acid 0.66:0.33, which forms an eutectic system with adipic acid. The model was confirmed using the quantitative analysis of the melting peaks and using the X-ray diffraction measurements from powders and single crystals. In particular, the latter have demonstrated that the new entity resulting from the pimozide:adipic acid 0.66:0.33 composition is actually salt [PMZH]2[adipate]. The crystalline product was characterized, from a pharmaceutical perspective, in terms of solubility and wettability (contact angle). Then, a tablet formulation was developed, and its dissolution behavior was compared to a commercial product considered as a reference. The new entity showed improved pharmaceutical properties in terms of solubility and wettability compared to the pure drug in both deionized water and bio-relevant fluids simulating oral administration in fed and fasted conditions. The tablets containing the new crystalline form can make this virtually insoluble drug available for absorption within minutes regardless of the variability in gastric conditions.

Исследование параметров системы аспирации рельсошлифовального поезда

The rail-grinding technology is used for the railway network of the JSC RZhD to eliminate rail defects and extend the lifecycle of the railway track. In order to implement the rail-grinding technology, currently, rail-grinding trains RShP-48 are used. Rails are ground with special grinding wheels made of zirconium electro-corundum manufactured based on aluminum oxide and zirconium oxide, with bakelite organic bond as a binder. In addition, the abrasive wheel composition includes various chemical components. When an abrasive tool is destructed, grinding waste in the form of suspensions is generated during its mechanic work. The suspensions spread over long distances and negatively affect both the environment and the working conditions of the rail-grinding train maintenance personnel. Today, the company «Sinara — Transport Machines» is developing a new rail-grinding train RShP 2.0 with a pre-installed aspiration system to collect grinding wastes for further utilization. When developing the technical design of RShP 2.0, the main characteristics of the aspiration system have been determined. In order to confirm the efficiency of the obtained parameters of the aspiration system, laboratory tests have been conducted on a special rail-grinding unit. According to the results, the aspiration system with the stated technical characteristics absorbs the fine fraction of grinding products which is about 50 % of the total lost mass of the grinding wheel. Considering a large abrasive that sticks to the spark arrestors together with metal chips, the aspiration system RShP 2.0 will enable removing up to 90 % of grinding waste.

The effects of processing parameters on the shape of particle size distribution and grinding rate in a stirred mill

The study of particle size distribution (PSD) of materials is a crucial aspect of mineral processing. It not only determines the appropriate beneficiation process and equipment but also has a significant impact on the grade and recovery of concentrate. This study utilizes a pin-stirred mill for the wet fine grinding of limonite to examine four different widths of PSD functions and compares their quantitative descriptions of the PSD. Skewness is a parameter introduced to quantitatively describe the asymmetry of the PSD. This study aims to investigate the effect of the stirrer speed, the density and the size of the grinding media on the shape of the PSD and on the grinding rate. The results show that a lower stirrer speed and a lower density of the grinding media result in a narrower and a more symmetrical PSD of the grinding products. Moreover, the time-dependent approach succeeds in simulating and proving the evolution behavior of the median particle size. It was found that the optimum mixing ratio of the grinding media can effectively adjust the shape of the PSD and improve the grinding efficiency.

Photocatalytic persulfate activation by silica microsphere-supported g-C3N4 for efficient carbamazepine degradation

A silica-loaded g-C3N4 composite photocatalyst (M-SiO2/g-C3N4) was prepared by grinding amorphous SiO2 microspheres (M − SiO2) with melamine and calcining the resulting grinding products. This composite was used for photocatalytic persulfate (PMS) activation to degrade carbamazepine (CBZ). The results showed that the degradation efficiencies of CBZ by M-SiO2/g-C3N4-2.5 (39.16 % of g-C3N4)-activated PMS were 78.92 % and 100 % after simulated sunlight irradiation for 60 and 120 min, respectively. These values were significantly greater than those of the system with pure g-C3N4 (29.15 % and 42.4 %). In particular, the degradation efficiency of CBZ with M-SiO2/g-C3N4-2.5 decreased by only 9.47 % after 4 cycles of recycling. In the catalytic process, h+, SO4•− and O2•− were the main reactive species contributing to CBZ degradation. Compared with g-C3N4, loading g-C3N4 on the surface of M − SiO2 resulted in a decrease in g-C3N4 lamellar stacking, which increased the number of active surface sites and improved the separation and migration of photogenerated carriers, improving the degradation performance.

Effect of temperature and particle size on dielectric property of vanadium-titanium magnetite

The current body of research on microwave-assisted grinding of vanadium-titanium magnetite (VTM) predominantly focuses on the analysis of changes in particle size and dissociation degree of the grinding products. Nonetheless, the microwave heating mechanism of the ore remains inadequately explored. In this study, the dielectric property of VTM with different particle sizes were measured at a frequency of 2.45 GHz and temperatures ranging from ambient to 800 °C. The results indicate that the dielectric constants (ε′) and dielectric loss factors (ε″) of VTM increase with temperature. The loss tangent coefficients (tan δ) initially increase and then decrease, reaching a maximum value of 0.44 at approximately 500 °C. The values of dielectric property parameters increase as the particle size decreases. By calculating the penetration depth equation, it can be determined that the optimal particle size for uniform heating in microwave of VTM is approximately 15 ∼ 30 mm. The heating rate of the ore in the microwave field is divided into two stages. Initially, the heating rate is very fast due to the ore being a strong magnetic mineral. However, when the ore temperature reaches 500 °C, the tan δ of the ore decreases, leading to a decrease in the heating rate.

Study on the Population Balance Dynamics Simulation of Grinding under Impact Crushing

During the grinding process, the crushing of minerals mainly depends on the impact action of the grinding medium. Based on the JK drop weight test data of quartz and pyrrhotite and the research results of their impact crushing characteristic parameters, this paper calculates the specific crushing energy (Ecs) of mineral samples subjected to impact in a ball mill using the grinding medium motion theory and then calculates the cumulative particle size distribution under screening under any mesh size using the JK drop weight test method. On this basis, the breakage distribution function of mineral samples is calculated, and a selection function is obtained based on grinding experiments. Finally, using Matlab programming and function-fitting mathematical methods, as well as a particle size population balance dynamics simulation of grinding, the particle size distribution characteristics of the grinding products of the two mineral samples in the mill that are only subjected to impact action are calculated. The results show that the selection function of quartz and pyrrhotite decreases overall with the prolongation of the grinding time, and the selection function of the coarse particle size changes more significantly than that of the fine particle size. At the same time, the selection function decreases with the decrease in feed particle size, and the smaller the feed particle size, the lower the probability of impact crushing. The Ecs values of quartz and pyrrhotite at each particle level in the mill are different, and the degree of mineral crushing is closely related to the impact energy, feed particle size, and mineral properties.

Preparation of TiO2 composite photocatalyst using amorphous SiO2 microspheres loaded with spent SCR catalysts

The products of S-SCR grinding and alkali treatment (S-SCR-T, primarily consisting of anatase TiO2 with a size less than 20 nm) were utilized as photocatalysts, while SiO2 microspheres (MS-SiO2) were used as carriers. A TiO2 composite photocatalyst (M-Si/SR-Ti) was prepared by wet mechanical grinding. The results demonstrate that in M-Si/SR-Ti, S-SCR-T was uniformly loaded on the MS-SiO2 surface in a well-dispersed state and firmly bonded at the interface with Si–O–Ti bonds. M-Si/SR-Ti prepared under optimized conditions exhibited excellent photocatalytic degradation and recycling properties for methyl orange. The degradation rate of methyl orange solution at 10 ppm for 60 min under UV irradiation was 97%, which was comparable to that of S-SCR-T, and remained unchanged after four cycles of recycling. Compared with S-SCR-T, M-Si/SR-Ti exhibited significantly improved settlement recovery performance in water. The loading of S-SCR-T on the MS-SiO2 surface, which increased the exposure of the nano-TiO2 active site and decreased the energy gap, was the mechanism responsible for improving the photocatalytic performance of M-Si/SR-Ti. This study positively impacted the effort to efficiently utilize and increase the value of S-SCR and reduce the cost of the photocatalyst.

Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

The object of this study is the grinding process in a tumbling mill when the mechanism of destruction by abrasion is implemented, which is caused by the mechanism of shear loading. The abrasive effect due to the impulse interaction during the mutual chaotic movement of granular particles in the shear layer of loading, characterized by the granular temperature, is taken into account. The task solved was determining the parameters of the shear interaction, which is caused by the difficulties of modeling and complexity of the hardware analysis of behavior of the internal loading in the mill. A mathematical model was built based on data visualization for the abrasion grinding mechanism. The power of the shear interaction forces was taken as an analog of the grinding performance. The initial shear characteristic was considered to be the average value of the shear velocity gradient in the central averaged normal section of the shear layer. The impact on productivity of the granular temperature and mass fraction of the shear layer and loading turnover was taken into account. The effect of rotation speed on performance was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative particle size of 0.0104. The maximum value of the energy and productivity of grinding by abrasion was established at the relative speed of rotation ψω=0.55–0.6. The results have made it possible to establish a rational speed when grinding by abrasion, ψω=0.5–0.6. This value is smaller in comparison with grinding by crushing ψω=0.55–0.65 and breaking ψω=0.75–0.9. The established effect is explained by the detected activation of the chaotic quasi-thermodynamic movement of particles of the shear layer at slow rotation. The model built makes it possible to predict rational technological parameters of the energy-saving process of fine grinding in a tumbling mill by abrasion

Grinding optimization using nondestructive testing (NDT) and empirical models

Proper choice of grinding parameters is important because productivity is limited by the possibility of grinding burns. Nondestructive testing (NDT), as Barkhausen noise (BN), can provide a tool for determining parameter limits. However, BN requires a threshold value for approval and requires multiple experiments to provide grinding parameters corresponding to high productivity. Other limiting process outputs, such as surface roughness, need to be fulfilled. In this study, process modeling, experiments and NDT are combined to produce optimized grinding parameters that fulfill the process output requirements and reduces the number of experiments for a new component. Design of experiments (DOE) grinding tests were performed with cutting power measurements. The outcome was verified with BN and surface roughness outputs. Then, using polynomial fitting, regression models were fitted into the BN, surface roughness and cutting power data. Malkin’s temperature model was utilized to analyze the temperature rise in the grinding zone. Combining all models, a grinding productivity optimization problem was defined from a specific material removal rate perspective. The polynomial fits of BN results and cutting power showed good prediction capability, as expressed by their R2 values. The study provides a novel method to choose grinding parameters to produce quality parts with minimal loss of productivity.

Comparative study on grinding kinetics behavior of vanadium-titanium magnetite ore before and after microwave pretreatment

Vanadium-titanium magnetite underwent closed circuit crushing before and after microwave pretreatment. Subsequently, batch grinding tests were conducted on the crushed products, with varying grinding times. Ultimately, the m-order grinding kinetics model of the ore was established both before and after microwave pretreatment. The results show that microwave pretreatment causes a significant increase in the number of micro-cracks on the ore's surface. Moreover, the specific surface area and pore volume of the ore increase by 17.29% and 40.98% respectively. These changes result in a reduction in the mechanical properties of the ore. During the grinding tests, the number of micro-cracks is found to be the primary factor influencing the grinding speed in the initial stage. However, as the grinding progresses, the grinding probability becomes the main factor affecting the grinding speed. The coarse particle size of the microwave-treated ore exhibits a significantly higher grinding speed than the untreated ore. Conversely, the grinding speed of fine particle size ore change slightly. The application of microwave-assisted grinding for vanadium-titanium magnetite proves advantageous in improving the particle size composition of the grinding product. Consequently, this can lead to enhanced separation efficiency and concentrate quality.

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.

An innovatory approach for determining grinding media system to optimize fraction compositions of grinding products based on grinding dynamics principle

An innovatory approach for determining grinding media ratio and sizes to optimize fraction compositions of grinding products was created based on the principle of grinding dynamics by the single fraction tests, which were conducted with the ore from Yongping Copper mine (China) in a discontinuous conical ball mill (D × L 360 × 160 mm, China), and the results show that the optimal ball size for +8 mm fraction, −8 + 5 mm fraction, −5 + 0.45 mm fraction and −0.3 + 0.2 mm fraction are Φ70 mm, Φ60 mm, Φ50 mm and Φ30 mm, respectively. Furthermore this approach was supported from the point of view of collision energy between ore and media by discrete element method (DEM), wtih results illustrating that the materials are more active with the highest tangential collision energy with 2.23 J. In addition, the comparable tests of the full fraction feed were conducted with media system determined by this method, with the grinding technical efficiency 71.71%, being 7.61 and 1.63 percentage points higher than that under the scheme on site and the other scheme. Furthermore, applicability and feasibility were proved to be tremendously positive through the industrial tests, and results of industrial tests show that unit media consumption and unit energy consumption are reduced by 0.56 kW·h and 0.072 kg/t, respectively, what's more, not only the production capacity is promoted by 1.04 t/h, but also concentrate indexes are also improved with grade and recovery being increased by 1.01 and 2.61 percentage points compared with that before the test. This method is extremely promising and novel and could be used in most beneficiation plants to optimize the media system of ball mill to elevate indexes and promote production in all probability.

Effect of Size-Distribution Environment on Breakage Parameters Using Closed-Cycle Grinding Tests.

The so-called population balance model (PBM) is the most widely used approach to describe the grinding process. The analysis of the grinding data is carried out using-among others-the one-size fraction BII method. According to the BII method, the breakage parameters can be determined when a narrow particle size fraction is used as feed material to the mill. However, it is commonly accepted that these parameters are influenced by changing the particle size distribution in the mill. Thus, this study examines the breakage parameters through kinetic testing in different natural-size distribution environments generated by closed-cycle grinding tests that simulate industrial milling conditions. The differentiation of the milling environments was accomplished using various reference sieves in the closed-cycle tests. The experimentally determined breakage parameters were back-calculated and then used to simulate the closed-cycle tests using the MODSIMTM software. Additionally, the energy efficiency was evaluated based on the specific surface area of the grinding products and the energy consumption. The results of the kinetic tests showed that the breakage rate of the coarse particles increases as the aperture size of the reference sieve decreases, and consequently, the content of fines in the mill increases. The back-calculated breakage parameters can be reliably used to simulate closed-cycle circuits, thus helping control industrial milling operations.

Kostenki 4 ground stone tools in the collection of Kunstkamera museum (MAE RAS)

Tools made of soft rock materials at the Upper Paleolithic sites are usually represented by pebbles that were used for various domestic purposes without intentional modification of their shape. In the Neolithic period, the anisotropic stone raw materials were processed for manufacturing tools (such as axes, adzes, chisels, etc.) by abrasion — grinding, cutting edge sharpening, surface polishing. During the Upper Paleolithic, the occurrences of this technology use are rare due to the lesser role of woodworking in the life of glacial hunters. An exception is a series of ground tools from the Pavlovian sites in Central Europe, as well as from a few Gravettian sites similar to them by culture in the Kostenki-Borshchevo locality on the river Don. The largest assemblage of the ground tools originating from the site Kostenki 4 (excavations by A.N. Rogachev in 1937–1938) is housed in MAE RAS. Among these items there are rounded biconvex and plano-convex items (discs), rod-shaped and bullet-shaped items, as well as objects and fragments with polished surfaces and edges. The site comprises materials of a full cycle of manufacturing polished products, including a set of raw materials — quartzite abrasive tiles, pebbles and pieces of slate, dolomite, marl. The major part of collection consist of a series of bifacially treated blanks and amorphous items with the localized grindings. Polished discs and rods stand out for their peculiarity even against the background of the Holocene Stone Age ground tools, remaining beyond typological analogies. The traces of utilization such as short scratches and dints have surface localization instead of cutting edges or tips. The function of these objects as retouchers was determined through a traceological examination by S.A. Semenov. However, the presence of commonly used pebble and flint retouchers in the collection, combined with labor costs during grinding and mass production of such items, leaves the question of their usage open. The article presents a description of polished items from the collection of Kostenki 4, stored in the MAE (Kunstkamera) of the Russian Academy of Sciences, as well as the results of studying the issues of their manufacture and functioning.

CREATION OF ENVIRONMENTALLY SAFE TECHNOLOGIES OF DIAMOND GRINDING OF PRODUCTS FROM HEAVILY PROCESSED MATERIALS

The paper shows that the most effective diamond grinding technology for improving the ecology and culture of production is grinding with diamond wheels on high-strength metal bonds using their electro-erosion dressing to restore cutting properties and improve the quality and productivity of processing. This technology makes it possible to exclude the use of harmful electrolytes from the technological process of straightening a diamond wheel. Therefore, practical recommendations have been developed in the work on the creation of environmentally friendly and safe for health working technologies for grinding with diamond-abrasive tools (diamond wheels) on metal bonds based on the use of electroerosive dressing. Products made from various metal and non-metal hard-to-cut materials are processed, including grinding products made of hard alloys with welded high-strength materials, cutting high-hard rocks, cutting edges on the surfaces of crystal products, cutting natural diamonds into diamonds, processing products from hard-to-cut ceramics and ferrites etc. As a result of the practical application of these technologies, it became possible to produce environmentally friendly and safe for the life of workers mechanical processing by grinding products from materials of high hardness at industrial enterprises of Ukraine with high quality and productivity.

Mechanical activation mechanism of cassiterite based on copper-based grinding media

During grinding, the abrasion and corrosion of the grinding media generate metal ions, thereby affecting mineral flotation separation. In this study, the mechanical activation mechanism of cassiterite by copper-based media was investigated via grinding and micro-flotation experiments, inductively coupled plasma optical emission spectroscopy (ICP-OES), solution chemistry calculations, X-ray photoelectron spectroscopy (XPS) and Density functional theory (DFT). Compared with ceramic medium, copper-based medium enhanced the grinding technical efficiency of cassiterite and improved the flotation recovery. Mechanism study revealed that the increase Cu ions content in the pulp of cassiterite grinding products was the main contributor to the mechanical activation of cassiterite by copper-based grinding media, and the main forms of Cu in the solution were Cu2+, Cu(OH)+ and Cu(OH)2. XPS results demonstrated that the Cu components adsorbed on the surface of cassiterite as Cu(II) and Cu–O groups. Meanwhile, DFT calculation results shown that the Cu components were spontaneously adsorbed on the surface of cassiterite (110) in the following order: CuOH+ < Cu(OH)2 < Cu2+. Therefore, the adsorption capacity of BHA increased. These results indicate an improvement in the flotation behavior of cassiterite mechanically activated by copper-based grinding media.

ANALYSIS OF LOGISTIC RISKS OF TRANSPORTATION OF GRAIN GROUP LOADS TO EUROPEAN PORTS USING PIGGYBACK TECHNOLOGY

Purpose. Since the beginning of russia's full-scale aggression against Ukraine, our state has lost the existing established routes for the export of grain cargoes. The export of grain and grinding products was based on the delivery of grain by land transport and, in small volumes, by river transport to seaports with subsequent transshipment to sea transport. The traditional sales markets for Ukrainian grain and grinding products are Asia, Africa and the Middle East. The limitation of the European grain market requires the search for new ways of delivering grain cargoes to sales markets. The Polish ports of Gdansk, Gdynia, Szczecin and the Romanian port of Constanta are being considered as alternative seaports for the transshipment of grain cargoes. Against the background of the problems of crossing the border by rail and road transport and the need to minimize transport and logistic costs, the task of finding alternative transportation options with the minimum duration of border crossing arises, and one of the options is the use of piggyback transportation technology. The purpose of the study is the estimation of the logistic risks of using piggyback technology to improve the efficiency of the multimodal process of grain cargo transportation. Methods. A comprehensive analysis of the technical equipment and work technology of railway transport in interaction with road transport, the infrastructure of border crossings and the technology of crossing them during cargo transportation, statistical analysis. The results. On the basis of the analysis of the main schemes of crossing the border during the transportation of grain cargoes and the logistic risks that arise, the following scheme was chosen. Grain is delivered by road to the Khyriv railway station, which is connected by a combined track of 1435-1520 mm, and there are also tracks with a width of 1435 mm, and where road trains are loaded onto the platforms of the Ro-La system piggyback train. Further transportation is carried out by rail transport to the port without overloading and changing carts. The time of transportation of road trains can be combined with the driver's rest in accordance with the working mode of the tachograph. Practical significance. The organization of a loading point for road trains on railway platforms of the Ro-La system at the Khyriv station of regional branch of «Lviv Railway» will allow to speed up the delivery of grain cargoes from Ukraine to one of the ports of the Black or Baltic Seas and reduce the overall logistic costs.

Assessment of the effect of iron magnetic concentrate desulfurization by flotation method on the quality of green and cooked pellets: A laboratory and pilot-scale study

The effect of flotation for desulfurizing the iron pelletizing feed has been investigated. The flotation method can reduce the emission of harmful environmental gases during the pelletization process by reducing the concentrate's sulfur content. On the other hand, flotation causes a change in the Blaine of the iron concentrate and wastes some magnetite particles. In this research, the samples were collected from the iron concentrate grinding circuit product in the Golgohar pelletizing plant. They were subjected to flotation tests on a laboratory and industrial scale. In addition, the properties of pellets produced before and after desulfurization by flotation were investigated. The results showed that using flotation, iron and sulfur grades changed from 66.08% and 1.12%, to 68.3% and 0.33%, respectively. Although flotation reduces the Blaine number of the pelletizing feed from 1800 to 1512 cm2/g, this reduction is mainly due to the removal of fine clay particles and did not harm pellet oxidation. Decreasing the sulfur content of the iron concentrate feeding to the pelletizing process led to an increase in the quality of raw and cooked pellets in terms of increasing the cooking speed (5%), increasing the compressive strength (13%), and reducing the residual FeO (2%), together with less emission of SO2 to the environment.

Study on preparation of pillararene cocrystals by liquid-assisted grinding

Liquid-assisted grinding (LAG) has received wide attention in chemical synthesis field. Here, we reported that LAG provides a smart strategy to build macrocyclic cocrystal (MCC), achieving quick modification. The macrocyclic cocrystal has been assembled by electronegative permethylated pillar[5]arenes (EtP5) and electropositive ligands. We select three ligands with strong electron-deficient groups for cocrystal preparation with EtP5 by LAG and judge whether the grinding products are cocrystals by color change, Infrared (IR), Ultraviolet-visible (UV-vis) absorption, and X-ray diffraction (XRD). We demonstrated that the same structure as solvent cocrystal can be obtained by LAG. We obtained the single crystal structure of the EtP5 cocrystal with the promising ligand, confirming the formation of cocrystals and the reliability of the liquid-assisted grinding method.

Reliability of the Non-linear Modeling in Predicting the Size Distribution of the Grinding Products Under Different Operating Conditions

During the modeling of grinding systems, population balance modeling (PBM) which considers a constant breakage rate has been widely used over the past years. However, in some cases, PBM exhibited some limitations, and time-dependent approaches have been developed. Recently, a non-linear framework which considers the traditional linear theory of the PBM as a partial case was introduced, thus allowing the estimation of product particle size distribution in relation to grinding time or the specific energy input to the mill. In the proposed model the simplified form of the fundamental batch grinding equation was transformed into the well-known Rosin–Rammler (RR) distribution. Besides, the adaptability and reliability of the prediction model are among others dependent upon the operating conditions of the mill and the adjustment of the RR distribution to the experimental data. In this study, a series of grinding tests were performed using marble as test material, and the adaptability of the non-linear model was investigated using three loads of single size media, i.e., 40, 25.4, and 12.7 mm. The results indicate that the proposed model enables a more accurate analysis of grinding, compared to PBM, for different operating conditions.