The present study aims to establish the effect of loading conditions on the shaping mechanics and stress-strain state of a surface microprofile for machine parts under the initial roughness impact. The used calculation model of microroughness includes physical and mechanical characteristics of a soft copper-simulating material. A numerical model of microsettlements on the surfaces of machine parts is developed for various loading conditions. The transition from free to restrained loading of the microroughness model increases the angle at the base of the deformed microprofile from 35 to 58°, relative length of the smoothed section from 0.46 to 0.8, and vertical rise of the microprofile depression point from 0.012 to 0.21. For one unfastened pair of side microprofile surfaces, orthogonal pair is deformed to a greater extent relative to the corresponding freely fastened surface. The maximum elongation of the sample in the direction of oX and oZ axes is 7 and 13%, respectively. Depending on loading conditions and location of microprotrusions, the full-settlement stress under the microroughness peaks ranges from 1050 to 1370 MPa exceeding the ultimate strength of the samples by 5–7 times. The stress of depressions on rigidly fastened samples reaches a maximum value of 1190 MPa, which exceeds the values for other fastening options and ultimate strength of the samples by 4–12 and 0.5–6 times, respectively. The lowest stress homogeneity across the microprofile cross-section has been found in freely fastened samples; rigidly fastened samples have the highest stress homogeneity. The optimal microprofile smoothing is typical for rigid fastening loading with a more uniform stress across the microprofile cross-section. The studies are relevant for assigning the conditions of workpiece processing using local deformation methods under the varying degree of restrained loading within the boundaries of the processed surfaces.

This study aims to optimize cutting conditions by controlling the working angles of cutting tools when machining shaped surfaces and changing operating parameters of the cutting process for technological reasons. The study object includes cutting conditions for machining shaped surfaces, their influence on the operating parameters of the cutting process, the working angles of cutting tools (rake angle and lead angle), and cutting edge inclination. When developing mathematical models, we used methods of the theory of cutting, analytical mechanics, and thermodynamics. Static and kinematic geometry analysis of a blade in a cutting tool showed that changes in the angular coordinates of the front surface of a blade require the introduction of controlled rotation axes when conducting technological operations under different cutting conditions. These axes should control the main blade angles, i.e., lead angle, rake angle, and cutting edge inclination. With more than 85% of the tool penetration, the working angles considerably change even when its installation errors are relatively small. It is proposed to introduce controlled rotation axes of the front surface of a blade in a cutting tool by its main angles, i.e., lead angle, rake angle, and cutting edge inclination. It is shown that working angles considerably change even when its installation errors are relatively small. The study revealed that these angles constructively limit the regulation range of the rake angle of a cutting tool due to the impermissible reduction of the back relief angle; these angles should be taken into account when calculating the power characteristics of the cutting process. Thus, in order to solve the problem of stabilizing the working angles of cutting tools, new methods and technologies should be developed, which would make it possible to control kinematic parameters in the cutting process more accurately. It is important to take into account the influence of various factors such as workpiece material, cutting tool type, and cutting conditions.

The study aims to analyze the skin effect as applied to the active resistance of aluminum wires using a mathematical model based on the theory of electromagnetic fields. The study uses the Elcut finite element simulation software. The simulated object includes round aluminum and cylindrical steel-aluminum wires with a cross-section of 339 mm² each, as well as AS 300/39 wire. The nonuniformity of a real power transmission line with steel-aluminum wires is considered. Calculations were verified in the Elcut software by dividing the aluminum wire into two components: a circle with a cross-section of 39 mm² and an outer ring with a cross-section of 300 mm². The results of aluminum wire simulation at different harmonics have established a coincidence of the obtained skin effect coefficients with the mathematical model. This coefficient reflects an increase in the active resistance of the wire at the highest harmonic in relation to direct current resistance. For an aluminum wire with a cross-section of 339 mm², the active resistance at the 5th, 7th,11th, and 13th harmonic has increased by 24, 40, 71, and 84%, respectively. This circumstance confirmed the need to consider the skin effect in the assessment of power losses in power transmission lines at higher harmonics. We propose to simulate the AS wire as a cylindrical nonuniform wire consisting of a steel circle inside an aluminum ring. For AS 300/39 wire, the error of determining the skin effect coefficient using this method is below 5% in the studied harmonic range. Thus, the proposed research method considering AS wires as round cylindrical shows the possibility of refining their mathematical model.

This study aims to develop and carry out numerical analysis of a methodology for determining the temperature of conductors of insulated wires, which implies measuring electric current and insulation surface temperature as well as using Smart Grid technology. We used a mathematical model of thermal conditions for conductors in the form of an algebraic fourth-degree equation and the Ferrari method to solve this equation. Simulation of temperature fields providing comparison results was carried out using the finite element method in the COMSOL Multiphysics. The temperature of conductors was measured taking into account measurement errors and using the least squares method together with the golden-section search. The finite element method made it possible to study temperature distribution in the section of SIP-3 shielded wire as well as in its insulation surface. The dependencies of changes in the maximum and minimal temperatures of the wire insulation surface were obtained as a result of simulation; these dependencies were influenced by wind speed changes at the maximum permissible temperature of conductors. The difference between the maximum and minimum surface temperatures was shown to reach approximately 25°C at wind speeds of 3–4 m/s. Our study resulted in function, the minimization of which makes it possible to find the temperature of current-carrying conductors of shielded wires by values of the insulation surface temperature. Comparative analysis of the developed method for determining the temperature of conductors and the finite element method provided the calculation error of 0.44°C given accurate settings of electric current value. The study results substantiate the need to take into account the nonuniformity in temperature distribution on the insulation surface of shielded conductors when monitoring power lines. The developed methodology for calculating the temperature of conductors by measurement data provides high accuracy at almost any nonuniformity in the surface temperature provided that the current measurement error equals 5% or less.

This study aims to thoroughly examine the potential of the Kolmogorov-Arnold Network (KAN) and its application to improving energy management efficiency, particularly in lithium-ion batteries. The study employs a novel method that utilizes one-dimensional adaptive activation functions parameterized by splines, in contrast to traditional neural networks, where activation functions are fixed. Traditional methods for activation function selection are based on empirical approaches and do not guarantee accurate approximation, potentially leading to suboptimal results. This approach enables the KAN to flexibly adapt to complex data structures, ensuring precise state-of-charge estimation. To objectively evaluate the algorithm's effectiveness, experiments were conducted on real datasets, focusing on analyzing the accuracy of state-of-charge estimation at confidence intervals of 95%, 90%, and 85%. The test results for various charge-discharge cycles demonstrated that the proposed method achieves high accuracy and maintains stability throughout the operation. The proposed method reduces the maximum error by at least 4.26% and significantly improves key performance metrics such as Mean Absolute Error, Root Mean Square Error. Thus, the obtained results confirm the efficiency and innovative nature of the KAN in energy management. This method holds great potential for energy management and can be effectively implemented in areas requiring precise time-series forecasting, including smart home systems, electric vehicles, and industrial devices. Future research will optimize the network architecture and expand its practical applications. Signifi-cantly, this method can be flexibly adapted to different types of batteries and energy systems, broadening its applicability in real-world conditions.

The present paper focuses on I-V curves for localizing possible defects in a photovoltaic module. The study considers the response of a photovoltaic module to changes in external and internal factors of the urban environment in Chelyabinsk, Russian Federation. To carry out measurements and control the module condition, we use the IV Swinger 2 software package reading data from the module to plot I-V curves and determine the maximum power point in real time. Changes in the internal parameters of the module are simulated by connecting additional resistances of different values to the external terminals of the experimental module. The conducted research has demonstrated additional resistance changing the shape of the I-V curve of the photovoltaic module regardless the type of connection and electrical circuit section of the module. This resistance simulates the main faults according to the given classification. Additional resistance in the cell circuit makes the shunt diode a conductor in the range of values from 0.71 to 1.06 Ohm. If additional resistance is installed between modules, the resistance can increase in a wide range of values without the diode transition to the conducting state. Additional resistance can reduce the power generation of a photovoltaic module. Therefore, we have assessed the impact of different cell shading levels on the module power generation. Given the resulting shunt resistance for all cells of one module, the slope of the I-V curve is inversely proportional to resistance due to the increased current leakage. Thus, the data of the I-V curve and the slope angle near the maximum power points is appropriate to identify and analyze the emerging faults of the photovoltaic module by evaluating its resistance.

This study aims to develop models for defining harmonic distortions in electromagnetic modeling of artificial railroad structures, taking into account high harmonic generation of electric locomotives. The research objects included tunnels and galleries, as well as through-type and deck-type truss bridges. Calculations of sites having a flat relief were carried out for comparison. When developing digital models, an approach representing power supply systems in phase coordinates in the Fazonord software package (5.3.7.0-2024 version) was used. Sets of conductors grounded on both sides were used for constructions. Electromagnetic fields were defined by simulation of five down trains weighing 3192 tons and moving at intervals of 22 minutes. For several constructions, the maximum working values of electric field intensity at the studied sites exceeded the permissible value of 5 kV/m, i.e., 9.8 kV/m for the deck-type truss bridge and 5.9 kV/m for that of the tunnel type. Due to extended train intervals, magnetic field intensity had never exceeded the specified limit of 80 A/m. Our study revealed that high harmonics of electric locomotives provoke severe distortions in the hodographs of magnetic fields, while artificial structures significantly change field distribution in the section of the electric traction network. Thus, digital models of traction-energy systems were developed. These models make it possible to accurately define the dynamics of changes in electromagnetic field intensity in a space surrounding the electric traction network of 25 kV inside artificial structures consisting of many metal parts. The computer technology developed by the authors can be effectively used in the development of measures to ensure electromagnetic safety in artificial structures of electrified railway transport.

The creation of a reversible AC electric machine with rotary motion based on a four-circuit power module of an electromagnetic exciter of low-frequency mechanical oscillations, i.e., an electric machine of reciprocating (oscillatory) motion, represents a relevant research task. The research object includes a three-phase electromagnetic exciter of low-frequency mechanical oscillations, whose power module consists of four paired identical resonant circuits. The circuits include an inductor and a capacitor connected in series in the power supply circuit. The design of this electric machine was carried out using the COMSOL MULTIPHYSICS software environment. In order to convert the frequency of the supply voltage (50 Hz) in the input circuit to the low-frequency range of mechanical oscillations at the output of each power module, the parameters of the series-connected inductance of the coil and capacitor were adjusted to achieve voltage resonance. In order to generate an increased torque, the paired circuits of the power modules alternately acted on the anchor located in the center by analogy with electric machines of rotary motion. The animations depicting the processes of beating of the input high-frequency signals inside a slowly changing sinusoid of the traction force obtained as a result of computer simulation demonstrate the possibility of their smooth modulation in the low-frequency region at the output. The obtained data also demonstrate the possibility of creating a reversible rotary motion of the electromagnet anchor when changing the polarity (direction of movement of electric currents) of the corresponding pairs in the resonant circuits, performed taking into account the assumption of conditioned linearity of passive elements in the resonant circuits of the alternating current electric circuit and the linearization of the dependence of active parameters on passive ones. The following areas of application of electromagnetic exciters of low-frequency mechanical vibrations can be recommended: (1) in the motor mode of operation, as an actuator in technological processes of mixing and preparing liquid products to a homogeneous consistency; (2) in the generator mode, as a converter of energy from renewable sources into electrical energy.

The aim is to develop a procedure for gold analysis of carbonaceous ore cyanidation tailings bearing gold in an adsorbed form. The proposed procedure includes high-temperature washing of the solid phase of tailings using a filter followed by transferring the adsorbed gold to the washing solution. The filtrate is analyzed separately, the solid phase undergoes standard fire assay, and the total gold grade is calculated by summing the gold in the solution and that in the solid phase. Using the proposed procedure, the proportion of adsorbed gold not detected by standard fire assay decreased by 4.1 times, from 38.2% to 9.3%. The studies were conducted using additions of gold solutions with a gold balance estimation. This additionally allowed gold adsorption isotherms to be studied by natural carbonaceous matter under cyanidation conditions. It was shown that at a gold concentration of 0.01–0.05 mg/dm³ typical of industrial cyanidation tailings, the adsorbed gold value was significant at the level of 0.1–1.1 g/t. These gold losses are directly determined by the preg-robbing activity of the raw material. The K constant of Freundlich isotherms plotted as the Au loading of organic carbon, g/t vs Au concentration, mg/dm³ was 303–3037 g/t, which is only an order of magnitude lower than that for commercial activated carbons. However, the greater mass of natural carbonaceous matter and its extended surface result in substantial gold losses with cyanidation tailings. The developed analytical procedure can be used to refine the actual gold losses with cyanidation tailings of carbonaceous raw materials.

The present paper aims to study the efficiency of using sodium lignosulfonate surfactant for hydrothermal treatment of zinc sulfide with copper sulfate solutions. The solutions were analyzed by the optical emission spectral method; an ARL ADVANT’X wave X-ray fluorescence spectrometer was used to study cakes. MS Excel, OriginPro, and Statgraphics software packages were used for data processing. Particle size was determined using a Bettersize ST laser diffraction particle size analyzer. We have studied the effect of sodium lignosulfonate on the hydrothermal extraction of zinc from sphalerite. The addition of this surfactant enhances the precipitation of copper on the sphalerite surface, thus increasing the degree of zinc extraction into the solution. Effects of temperature (180–220°C) and concentration of lignosulfonate (0–1 g/dm³), sulfuric acid (10–30 g/dm³), and copper (6–24 g/dm³) has been studied; optimal conditions for the maximum zinc extraction of 55–71% into the pregnant solution and copper cake precipitation of 45–83% were identified. Elevated temperatures increase the reaction rate and solubility of metals. Changes in the concentrations of sulfuric acid and copper affect the equilibrium of reactions and the efficiency of copper precipitation and zinc extraction into the solution. The performed experiments have resulted in the optimal parameters of hydrothermal treatment: 0.25 g/dm³ lignosulfonate concentration, 220°C temperature, 10 g/dm³ sulfuric acid concentration, and 15 g/dm³ initial copper concentration. For these parameters, 74% of zinc is extracted into the solution in 120 min and 83% of copper is deposited on the cake. Thus, the effect of sodium lignosulfonate on the hydrothermal treatment of sphalerite can be stated as positive: the concentration of this additive below 0.25 g/dm³ accelerates sphalerite treatment by 1.5–2 times.