The insufficient substantiation of phase equilibrium analysis results in the underutilization of the extensive thermodynamic information contained in phase diagrams. Using the iron–silicon system as an example, the applicability of the developed methodology for calculating phase equilibrium lines to evaluate the melt structure through the degree of dissociation or association of congruently melting chemical compounds is demonstrated. It is shown that when dissociation of a congruently melting compound occurs in the melt, the newly obtained values of the Bjerrum–Guggenheim osmotic coefficient, accounting for the degree of dissociation or association of this compound in the melt, exhibit a linear dependence. A characteristic feature of the crystallization line of the FeSi compound is the formation of associates, as evidenced by the initially concave shape of the Φᵢ curves. The aim of this study is to identify the regular features of silicon behavior along the crystallization line from the standpoint of the Bjerrum–Guggenheim osmotic coefficient and to derive a universal mathematical expression for predicting the phase composition of alloys at various silicon concentrations through the degree of dissociation (association) of the congruently melting FeSi compound. For the first time, a mathematical expression for the silicon crystallization line in the iron–silicon system is proposed in the form of a semi-empirical Schröder–Le Chatelier equation relating the liquidus temperature to the silicon concentration. Based on the iron–silicon system, a justified selection of the functional form for the analytical description of the silicon crystallization surface is carried out using the Bjerrum–Guggenheim coefficient. Experimental data from the Fe–Si phase diagram are approximated, and the accuracy and applicability range of the obtained model are evaluated. Characteristic features of the silicon crystallization line behavior associated with changes in crystallization mechanisms and component interactions are identified. The obtained results can be used for numerical modeling of crystallization processes and for predicting the properties of iron–silicon alloys. Key words: phase diagram; degree of association (dissociation); phase equilibrium lines; Gibbs energy; Bjerrum–Guggenheim coefficient; phase crystallization fields.

10.48081/BGQF1926

2026

Issue 1

This paper examines the physicochemical and mineralogical properties of pellets produced from secondary aluminum slags with the addition of silica-enriched aspiration dust from ferroalloy production. To incorporate finely dispersed industrial waste into metallurgical processing, a pelletizing method was applied in a disk granulator using an aqueous lignosulfonate solution as a binder. The resulting pellets were subjected to high-temperature firing at temperatures of 600, 800, and 1000 °C. The phase and mineralogical composition were studied using X-ray diffraction and petrographic analysis, and the microstructure was analyzed using electron microscopy. It was found that increasing the firing temperature intensifies solid-phase interactions and forms calcium silicate and aluminosilicate phases, such as wollastonite, dicalcium silicate, and mullite. The introduction of aspiration dust with a high SiO₂ content helps reduce the sintering onset temperature and strengthen the pellet structure by forming a binding silicate matrix. It has been shown that optimizing the composition and firing temperature allows for the production of heat-resistant and mechanically strong pellets, promising for use in processes for producing ferrosilicon with increased aluminum content.

10.48081/BGQF1923

2026

Issue 1

The article presents the results of successful industrial trials of an environmentally safe technology for stabilizing refined ferrochrome slags aimed at solving the urgent problem of their spontaneous disintegration. This phenomenon, caused by the polymorphic transformation of β-2CaO•SiO₂ into γ-2CaO•SiO₂, leads to the conversion of slag into a powdery material, which makes its further use impossible and creates significant environmental risks. Unlike the traditional chemical stabilization method using boron-containing materials, which ensures only a metastable state of the slag, the authors propose a fundamentally different physico-chemical approach. The key idea of the technology is to regulate the basicity of the slag (CaO/SiO₂ ratio) by introducing an additive—expanded clay (keramzite)—into the melt, which shifts the phase composition into a thermodynamically stable region where the formation of unstable dicalcium silicate is excluded. The paper provides a detailed description of the theoretical justification of the method, including equilibrium phase composition calculations, as well as the stages of laboratory studies and full-scale industrial trials. The highest technological efficiency was demonstrated by an out-of-furnace treatment method, which involves feeding expanded clay through a tapping tube directly into the stream of liquid slag during tapping from the furnace. This method ensures intensive mixing and rapid dissolution of the additive (within 3–5 minutes) without any adverse impact on the reduction processes occurring inside the furnace. The implemented technology makes it possible to produce a stable, non-disintegrating lump product with a basicity below 1.4, suitable for commercial use in the construction industry as an aggregate. Thus, the technology not only solves a significant environmental problem related to the utilization of industrial waste but also provides an economic benefit, transforming waste into a marketable product and contributing to the creation of a closed production cycle at ferroalloy plants.

10.48081/BGQF1922

2026

Issue 1

The article presents the results of the development and testing of a conical rotor centrifuge for the primary purification of vegetable oils, specifically safflower oil, using flax fibers as a filter material. The design of the installation is described, combining centrifugal separation with barrier filtration through a layer of fibrous material. Experimental studies were conducted to determine the optimal operating parameters: oil temperature (35°C), mass fraction of impurities (0,1%), and separation factor (1300). It has been established that the proposed technology allows achieving an oil purification degree of up to 93% and reducing the sludge content to 0,02%. Using experimental design methods, a regression equation was obtained, describing the influence of the main factors on the process efficiency. The developed centrifuge is an economically efficient solution for small and medium-sized processing enterprises, promotes the implementation of resource-saving technologies and the utilization of secondary raw materials. Furthermore, it demonstrates significant potential for adaptation to other types of oils and production conditions.

10.48081/BGQF1915

2026

Issue 1

This article presents a scientific and technical justification for the use of a sand-polymer composite material (SPC) as an alternative to steel for the manufacture of key load-bearing components (shells and barrels) of belt conveyor rollers, particularly those used in the mining industry. To confirm the feasibility of the concept, computer strength modeling of an LKR-1000 roller with SPC elements was conducted, followed by a comparative analysis of the stress-strain state (SSS) with a similar steel structure (S35 steel). For the modeling, the composite shell thickness was assumed to be 10 mm, while the steel shell thickness was 3.5 mm. Calculations were performed with loads varying from 200 to 600 kPa. The results showed that, despite the fact that SPC is a less rigid material and exhibits greater stresses (70 MPa versus 55 MPa for steel at 400 kPa) and displacements (0.64 mm versus 0.097 mm at 400 kPa), its factor of safety (FOS) remains at an acceptable level (FOS ≥ 1.5) for loads up to 600 kPa. At a maximum load of 600 kPa, the FOS for SPC is 1.6. A key advantage is the 37% reduction in the weight of the roller with composite elements compared to its steel counterpart, which contributes to reduced energy consumption and increased conveyor drive efficiency. The study scientifically substantiates the feasibility of using SPC in conveyor rollers, offering a lighter and more efficient solution for the mining industry. Key words: stress, deformation, displacement, shell, roller.

10.48081/BGQF1908

2026

Issue 1

This paper investigates the impact of stochastic permission-transfer delays on the capacity of a railway section. The study focuses on a single-track section equipped with semi-automatic blocking, which is characterized by a high variability of time intervals caused by operator involvement and the interaction of technical systems. An additional parameter accounting for the stochastic component of permission-transfer delays is introduced into the existing capacity calculation formula. This parameter is evaluated using normal, exponential, and empirical distributions constructed from an observation sample. A comparative analysis is performed to assess the influence of different delay modeling approaches on the actual capacity of the railway section. The results demonstrate that accounting for stochastic delays leads to a reduction in the calculated capacity compared to deterministic estimates and provides a more realistic representation of operational train movement conditions. Particular attention is given to the tail behavior of delay distributions, which has the most significant impact on timetable stability and operational performance. The proposed approach ensures the reproducibility of capacity calculations and can be adapted to various railway line configurations and train interval control systems. The findings confirm the relevance of applying a stochastic approach in railway capacity assessment.

10.48081/BGQF1933

2026

Issue 1

This paper examines the characteristics of fine grinding processes under different directions and types of mechanical impact. A theoretical analysis was conducted for four representative cases of loading a spherical particle by grinding media: one-sided, two-sided, and combined impacts with mutually perpendicular force directions. To determine the theoretical fineness of grinding, a mathematical model based on the Hertz–Shtaerman contact problem and previously developed dependencies was applied. The calculation results showed that two-sided impact provides a higher degree of grinding compared to one-sided impact at the same collision velocities. This effect is explained by the formation of a more uniform stress–strain state within the particle and by more complete utilization of impact energy. In multivector loading cases, where the directions of forces are mutually perpendicular, the calculations were performed using the resultant velocity, which allowed for an adequate assessment of the combined influence of differently oriented forces. The obtained theoretical relationships can be used in the design of energy-efficient fine grinding methods and the development of new mill designs that implement multivector loading modes. The results contribute to the advancement of the scientific foundations of energy saving in solid material disintegration processes and provide prospects for optimizing industrial grinding technologies.

10.48081/BGQF1907

2026

Issue 1

The paper presents a mathematical model of a dual-loop steering mechanism for a mobile robot, based on Ackermann geometry and enhanced with a corrective PD loop compensating for position error. The aim of the study is to improve trajectory tracking accuracy by combining a precise geometric model of the inner loop with adaptive feedback from the outer loop. The work develops kinematic equations of motion, derives relations for curvature and steering angles, and performs a formal stability analysis of the corrective PD controller. The research methodology includes numerical simulation in MATLAB, allowing evaluation of platform dynamics, trajectory tracking performance, position error, and the influence of noise on control stability. To verify the proposed approach, single-loop and dual-loop steering control systems were compared. Simulation results show a significant reduction in the root-mean-square trajectory tracking error when using the dual-loop mechanism. It is demonstrated that the external PD correction ensures control stability and robustness even under Gaussian noise conditions. The obtained results confirm the effectiveness of the proposed dual-loop architecture and its applicability for control systems of mobile robots, autonomous transport platforms, and other mechatronic devices requiring high motion accuracy. The model is computationally simple and can be used both for educational purposes and for implementation in real robotic platforms.

10.48081/BGQF1904

2026

Issue 1

The article presents an analysis and program of stability of a closed nonlinear system "FC-BLDC" by the method of phase trajectories. The analysis of nonlinear systems has its own peculiarities in contrast to the analysis of linear systems. First of all, this is due to the fact that the stability of a nonlinear system depends on the initial conditions and external influences: with some input signals, the system will be stable, and with others it loses the property of stability. Since several equilibrium positions may exist for a nonlinear system, stability should be analyzed in the vicinity of each of them. Which complicates the task of research. System stability analysis is the process of determining whether a system will return to its initial state after a change in its parameters or whether it will deviate from it and eventually become unmanageable. System stability is an important property for dynamic control systems because unstable dynamic systems can lead to undesirable or even dangerous consequences. The root criterion determines the stability of the system by the type of transfer function. The dynamic characteristic of the system, which describes the basic behavioral properties, is a characteristic polynomial located in the denominator of the transfer function. By equating the denominator to zero, the characteristic equation can be obtained, the roots of which determine the stability. The most important task in analyzing dynamic control systems is to solve the problem of their stability. The technical concept of stability of automatic control systems refers not only to the stable operation of the technical system in normal modes, but also to the property of “not getting out of control”.

10.48081/BGQF1905

2026

Issue 1

This article systematically analyzes the factors that determine the sustainability of intermodal transportation of agricultural products in Kazakhstan. The study proposes a three-dimensional conceptual framework (economic, operational, and external – geopolitical/ecological), while the evaluation indicators are defined as timeliness, damage rate, total cost (USD/t), share of empty return, delay frequency, carbon footprint (CO₂, kg/t), and integrated risk level (1–5). Geographic specifics (lack of direct sea access, long routes, climate), route complexity, modal combinations, digital solutions (Astana-1, CIM/SMGS, KTZ Express, IoT/AI/WMS), regulatory and legal environment (TIR, COTIF/OTIF, EAEU), and operational “bottlenecks” (shortage of wagons/containers, port/ferry capacity, border procedures, workforce/automation, container turnover) are considered comprehensively. Case studies (KTZ Express – Xi’an Dry Port; DHL Rail Connected; Astana Agro – India; “Transco” – Afghanistan; KTZ Express – Turkey, LCL) are comparatively analyzed; based on the international benchmark (Germany, China, Finland, Poland, Singapore), a roadmap and a KPI dashboard for policy and management have been proposed. The analysis demonstrates that intermodal sustainability depends not only on infrastructure but also on legal-institutional and digital interoperability. The developed indicators and KPI dashboard are tailored for practical monitoring. The 2025–2027 roadmap provides conditions for measurable enhancement of the sustainability profile.

10.48081/BGQF1927

2026

Issue 1