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

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

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

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

Finding optimal methods for processing accumulated chromium-containing waste is a pressing issue in the metallurgical industry. Considering the growing demand for ferrochrome, recycling chromium-containing wastes to produce commercial chromium concentrate is considered the most feasible approach. Existing processing methods demonstrate the possibility of using an inexpensive and widely available reagent – sulfuric acid. Chromium-containing waste also includes dust collected by the wet method from the exhaust gases of ore-smelting furnaces during the smelting of carbon ferrochrome. The accumulation of this dust poses a serious environmental problem, as it contains significant amounts of chromium and other components that can negatively impact the environment. This article presents the results of a study of the chemical and phase composition of chromium-containing dust and presents laboratory experiments on its sulfuric acid leaching. The research was conducted in two areas: sulfatizing roasting followed by sinter leaching and direct leaching of dust with sulfuric acid solutions. Experimental data confirmed the high efficiency of sulfuric acid, which ensures the conversion of a significant portion of the chromium into solution and the subsequent recovery of chromium concentrate. The use of an inexpensive reagent reduces the cost of the process and makes it possible to recycle large volumes of waste generated during ferrochrome production. Implementing this approach will not only yield secondary raw materials for metallurgical production but also significantly reduce the environmental impact associated with the storage and accumulation of dust in landfills, thereby improving the environmental safety of enterprises.

10.48081/BGQF1924

2026

Issue 1

The results of modeling and experimental studies focused on improving the technological process for producing low-alloy steels with an enhanced level of performance properties and environmental sustainability are presented. An increased level of consumer properties was achieved by reducing non-metallic inclusions in the steel during secondary metallurgy (out-of-furnace treatment). Environmental sustainability was ensured through the use of a flux-forming additive based on waste refractory materials containing Al2O3. This material enabled the stabilization of refining slags, reduced steel production costs, and served as a substitute for fluorspar CaF2. To investigate the feasibility of using this flux-forming additive in secondary treatment units, slag samples from several metallurgical enterprises were analyzed. Samples were taken during the metal processing stages in the ladle furnace (LF) unit. The refining and physicochemical properties of the selected slag samples were evaluated through calculations using a polymer model of slag structure. The possibility of stabilizing refining slags using an Al2O3-based additive derived from refractory waste has been confirmed. It is shown that the introduction of Al2O3 into the slags—allowing for operations with highly basic slags—improves the surface properties of the slags, increases refractory lining durability, and reduces metal losses in the form of droplets (beads) as well as the quantity of non-metallic inclusions. Using experimental data from literature and thermodynamic calculations, it was determined that the maximum permissible Al2O3 content in the slag, from the perspective of ladle furnace processing technology, is no more than 30%. The results of experiments on stabilizing model slag with the studied additive showed that, in this case, a primarily chemical stabilization method is implemented.

10.48081/BGQF1921

2026

Issue 1

This article presents the mathematical modeling of thermo-frictional milling with pulse cooling of HARDOX 450 steel using ANSYS Workbench software. The model enables dynamic investigation of the thermal and physical processes occurring within the cutting zone. The developed methodology is focused on analyzing heat distribution during the cutting process and determining optimal parameters for thermo-frictional milling with pulse cooling for high-strength, wear-resistant steels, specifically exemplified by HARDOX 450. To perform the study from a variety of existing models of fracture during cutting, a criterion was used that was first proposed by Professor V.L. Kolmogorov and adapted to conditions of large plastic deformations and high temperatures. In order to increase computational efficiency, a simplified mathematical model was proposed, including two objects: a parallelepiped-shaped workpiece made of HARDOX 450 steel and the cutting edge of a friction milling cutter in the form of a plate. The model took into account the friction coefficient between the cutting edge of the friction cutter (plate) and the workpiece, assumed to be μ = 0.4. To analyze the temperature field in the subcontact layer of the workpiece, the coordinates of nine characteristic points were entered at uniform intervals in the local coordinate system. As a result of modeling, the contact temperature values at these points were obtained at different friction cutter rotation frequencies. The results of the study showed the possibility of effective thermal process control during thermo-friction milling with pulse cooling of HARDOX 450 steel.

10.48081/BGQF1911

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 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