Introduction. The technology of centrifugal bimetallization using an independent axisymmetric electric arc is becoming increasingly important due to the high need to improve the quality of bimetallic compositions used in the manufacture of plain bearings, cylinder barrels for hydraulic units, and friction pair elements in internal combustion engines. The existing research in this area emphasizes the need for a more in-depth study of the features of thermal processes associated with this technology. In modern scientific literature, issues related to temperature control at the interface of materials are not fully disclosed, and the existing gap in the concept of the behavior of bimetallic compounds under heating conditions hinders the implementation of this technology in industrial production. The objective of this study is to conduct analytical modeling of a heat source in the form of an axisymmetric electric arc to determine the heat concentration coefficient and reduce the proportion of experimental data in the thermal process model, which will increase its versatility. The tasks arising from the stated goal are comparison of the results of calculating the effective heat flux density from two different expressions (using trigonometric and exponential functions), as well as evaluation of the distribution of the heat flux of an axisymmetric arc along the inner surface of the sleeves (this is required to establish the relationship between the temperature of the outer surface of the welded sleeve and the temperature at the interface between the materials).

Materials and Methods. Direct control of the temperature at the interface between the base material and the deposited layer is difficult, but it is possible to carry out indirect control using the temperature of the outer surface. To determine the relationship between the temperature of the outer surface of the deposited sleeve (billet) and the temperature on its inner surface, i.e., at the interface between the base material and the deposited layer, a heat source was modeled, the heat flux distribution of an axisymmetric electric arc along the inner surface of the sleeve was estimated, and an analytical expression was obtained to determine the heat concentration coefficient.

Results. In the course of the work, an analytical expression was obtained for determining the coefficient of heat concentration, k = 0.945 / R₁². It was required for calculating the electric arc parameters considering the distribution of the effective thermal power in the hot spot according to an exponential dependence. To simulate the heat source of the facing process (bimetallization) of the inner surface of steel sleeves with heating by an independent axisymmetric electric arc, the results of calculating the effective heat flux density were compared using two expressions: q = q₀ ∙ cos³φ and q = q₀ ∙ e^{–k· r²п}. This comparison showed that for calculating temperature fields during facing of the inner surface of steel sleeves (billets) with metal alloys under heating by an independent axisymmetric arc, it was possible to use the analytical exponential form of representation of the heat source.

Discussion and Conclusion. Modeling thermal processes of the centrifugal bimetallization using simplified schemes of uniform distribution of heat flow q = const on the entire free surface of the deposited layer, which simulates the spread of heat of an electric arc, requires the introduction of correction factors and a series of experiments to determine them. In this case, the description of the thermal process in the thermal process model contains a high proportion of experimental data and correction factors. Therefore, in order to exclude most of the experimental components when modeling the heat source and heat flow distribution of the facing process (bimetallization) of the inner surface of steel sleeves under heating by an independent axisymmetric electric arc, the author in this paper proposes an analytical solution for calculating the effective heat flow density in the form of an exponential function. This function allows determining the heat concentration coefficient of an independent axisymmetric electric arc during the facing process, which is required to increase the accuracy of calculating the temperature field of the bimetallized sleeve and improve the temperature control of the thermal parameters of the technological process.

Introduction. Modern research aimed at reducing emissions of harmful substances resulting from the operation of diesel engines using alternative fuels emphasizes their importance and relevance. This topic is becoming increasingly significant in the context of global environmental changes. The development and implementation of alternative energy sources not only contribute to improving air quality, but also help reduce dependence on fossil fuels. Therefore, it is important to continue investing in research and new technologies that will provide for cleaner and more efficient use of resources. There are numerous such studies, specifically, theoretical ones, conducted in European and Asian countries. However, there are practically no experimental works devoted to hemispherical combustion chambers of Russian diesel engines, whose rotation speed, compression ratio and other design parameters differ significantly from similar characteristics described in known studies. In addition, there are practically no experiments devoted to the combustion process of Russian diesel engines with an undivided hemispherical combustion chamber in the piston, which determines the complexity of the volumetric-film mixing process. The research objective is an experimental study of the power and economic indicators, parameters of the combustion process of a diesel engine with an undivided hemispherical combustion chamber in the piston, running on ethanol and rapeseed oil (RO). The study is aimed at establishing dependences showing the effect of various engine operating modes on the specified indicators in order to determine their numerical characteristics.

Materials and Methods. The diesel engine was started using rapeseed oil, after which the ethanol supply was switched on, replacing the rapeseed oil until the set optimum value was reached. The increase in the operating load mode was provided through regulating the ethanol supply. An additional high-pressure fuel pump (HPFP) 2UTNM was installed to supply rapeseed oil, and ethanol was supplied through the standard fuel supply system.

Results. The indicators of the combustion process of a diesel engine running on ethanol and rapeseed oil differ from its regular diesel engine. When working with ethanol and rapeseed oil, an increase in the ignition delay period is noted, which affects the “rigidity” of the combustion process and results in a growth of P_z value. These factors are most likely the main limitations for the use of ethanol by direct injection. One of the solutions to this problem, proposed in this paper, is the use of ignition (pilot) rapeseed oil, which makes it possible to adjust parameters of the combustion process through controlling the amount of ignition fuel supply.

Discussion and Conclusion. The results of the conducted experimental study confirm the possibility of complete replacement of petroleum motor fuel in a diesel engine with an undivided hemispherical combustion chamber in the piston with an alternative (renewable) fuel. This undoubtedly solves important issues of environmental safety of diesel engines. The research results may be useful both to scientists working on this topic, and to engineers and technicians in the machine-building industry.

Introduction. Electrolytic plasma technologies used for dimensional and finishing processing of metal surfaces attract attention due to their high efficiency and precision. The key factor that determines the quality of processing is the temperature of the electrolytic-plasma discharge (EPD), which affects the ionization of the electrolyte and the properties of the surface. The lack of comprehensive studies of the temperature characteristics of jet EPD limits the optimization of processes. The research objective is to determine the distribution of temperatures and heat flows in the system “jet electrolytic cathode — metal anode” under various processing conditions.

Materials and Methods. The study was conducted using an electrolyte jet with a diameter of 3 mm and a mass flow rate of 0.25–3.75 g/s at a voltage of 20–500 V. KhVG and 08Kh18N9T steels were used as anodes, and the electrolytes were aqueous solutions of NaCl, (NH₄)₂SO₄, C₆H₈O₇, with a concentration of 4–50 g/l. The temperature was measured with a chromel-alumel thermocouple, an infrared pyrometer, and a thermal imager.

Results. A heat balance equation was developed, describing heat distribution among the metallic anode (MA), jet cathode, electrolyte, vapor, and radiation. The analysis of the volt-ampere characteristics (VAC) showed an increase in current at low electrolyte flow rates (0.75–1.2 g/s) followed by a decrease at 300–500 V, and a parabolic dependence with a maximum of 2.6 A at a flow rate of 2.37 g/s. The maximum MA temperature reached 100°С (NaCl, 4–35 g/L), decreasing to 82°С at 150 g/L, while the hollow cathode reached 158°С at an initial electrolyte temperature of 90°С. Vapor temperatures ranged from 67.3°С (high flow rates) to 87.5°С (low flow rates). Electrolyte loss due to evaporation reached 5,8 g at 300–340 The temperature at the periphery of the anode was 15–20% higher than in the center.

Discussion and Conclusion. The main source of heat was the Joule-Lenz law, with the contribution of exothermic reactions of carbon oxidation up to 260 V. The maximum heat release was observed in the EPD zone, forming an ellipsoid. The data obtained and the heat balance equation create the basis for optimizing jet electrolytic-plasma polishing in mechanical engineering, medicine, and microelectronics.

Introduction. Under designing, a large safety margin of components and units is included at the calculation stage, which does not exclude premature failures that occur at random. The consequences of such failures are not only economic losses, but also threats to the safety of people and the environment. In modern literature, the topic of assessing the reliability of machines, considered as complex probabilistic systems that take into account not only the dynamic parameters under operation, but also the processes of manufacturing the components of the system, is not sufficiently covered. Therefore, to provide for the targeted management of the reliability of machines as complex technical systems, it is required to apply the principles of cybernetics. The research objective is to study the method of monitoring the reliability of technical systems by identifying the entropy of the causes of their failures.

Materials and Methods. The materials for the study were statistical data on machine part failures obtained through long-term observation of the working condition of basic parts of lifting-and-shifting machines, as well as road and construction machines. The paper used mathematical statistics and probability theory — a parametric method for assessing reliability with a simplified approach, which assumes the deterministic behavior of the machine as a system with a predetermined functioning that does not depend on external circumstances. The value of the safety margin is taken at a level greater than one.

Results. The degree of impact of the uncertainty of the reference values of the operating process, design features, manufacturing technique of machine parts and the malfunctions that occur in them, on the final probability of failure-free operation and reliability of machines is determined.

Discussion and Conclusion. The analysis of the theory of verification calculations of machines confirmed the compliance of the obtained results with regulatory requirements. The conducted studies have proven that machines are deterministic systems, whose behavior is specified in advance by the calculation. Therefore, it can be argued that the developed method of monitoring the reliability of technical systems, based on identifying the entropy of the causes of failures, will allow establishing a quantitative and qualitative relationship between the design, material, size, manufacturing technique of machine parts, and failures that occur in them.

Introduction. Trade development requires the implementation of artificial intelligence and machine learning technologies to improve the accuracy of delivery forecasts. The scientific research published to date in this area appears insufficient for two reasons. First, it focuses primarily on global supply chains, although the issue is relevant for local businesses as well. Second, forecasting typically requires large amounts of data for machine learning and significant computing resources that are not available to the majority of companies. The presented study aims to fill these gaps and demonstrate the efficiency of using open, accessible data and known algorithms. The research objective is to describe a pattern of appropriate selection of the least resource-intensive delivery forecasting model based on the analysis of machine learning algorithms.

Materials and Methods. The open data set DataCo Smart supply chain for big data analysis on deliveries in online trade was used. To process and analyze the information, methods of data cleaning, eliminating multicollinearity, normalization and coding of categorical features were applied. The following algorithms were used with the cleaned data: Decision tree, Random Forest, k-nearest neighbors, Naïve Bayes, Linear discriminant analysis, XGBoost, CatBoost, LightGBM, AdaBoost, and Perceptron.

Results. The basic algorithm for the delivery forecasting model was the Decision Tree algorithm. This choice was due to its high accuracy, ease of use, and low risk of overfitting. The model evaluation showed a high determination coefficient close to one (0.986). Low values of the mean square error (0.0367) and mean absolute error (0.0324) were recorded. The model showed satisfactory results in terms of time spent on training (3.3087 s) and forecasting (0.0051 s). Actual and predicted values almost perfectly matched. Deviations from actual values were minimal.

Discussion and Conclusion. The proposed model is efficient and has a high predictive ability. High-quality forecasting of delivery time is possible without the use of extensive databases and powerful computing resources. The study opens up the prospect of high-quality organization of logistics operations for small and medium enterprises. In further research, it is advisable to integrate weather data, traffic conditions and other indicators into the model. Using such information in real time will increase the adaptability and accuracy of forecasting.

Introduction. Compounds with lanthanum and neodymium (La₂Zr₂O₇ and Nd₂Zr₂O₇) have low thermal conductivity, high permittivity and melting point, stability and resistance to defects. They can be used for thermal insulation of metal components in turbines and air engines. Also, these compounds are widely studied from the point of view of the development of materials science, particularly, for the improvement of laser technology and optics. However, the physical properties of La₂Zr₂O₇ and Nd₂Zr₂O₇ have not been sufficiently studied experimentally. This gap is intended to be filled by the presented study. The research objective includes model calculations of the electronic structure and optical properties of La₂Zr₂O₇ and Nd₂Zr₂O₇.

Materials and Methods. Based on model calculations within the framework of the density functional theory, the electron-energy structure of pyrozirconates La₂Zr₂O₇ and Nd₂Zr₂O₇, containing Zr and having the crystal structure of pyrochlore was investigated. The parameters of the crystal lattice of La₂Zr₂O₇ taken from the literature were used in the calculations. Due to the lack of experimental data, the parameters for Nd₂Zr₂O₇ were calculated by minimizing the forces acting on the atoms of the compound. A combined exchange-correlation potential was used, taking into account the strong interactions of d- and f-electrons of La and Nd atoms with a correction in the form of a modified Becke-Johnson meta-potential. Wien2K software package was used for the calculations.

Results. The densities of electron states of all atoms of the studied compounds were obtained. The calculated densities of valence electron states of the compounds were compared to the experimental X-ray photoelectron spectra. At zero energy, the optical characteristics of La₂Zr₂O₇ and Nd₂Zr₂O₇ were calculated. Firstly, it was the permittivity: for La₂Zr₂O₇ — 8.4334, for Nd₂Zr₂O₇ — 8.501; secondly, refraction: for La₂Zr₂O₇ — 2.904, for Nd₂Zr₂O₇ — 2.916; thirdly, reflection: for La₂Zr₂O₇ — 23.786%, for Nd₂Zr₂O₇ — 23.935%. High optical absorption coefficient (˃10⁵ cm⁻¹) was recorded in the ranges: from 5 to 14 eV, from 14 to 28 eV, and from 28 to 40 eV. Peak extinction values were in the ranges from 5 to 13 eV, from 14 to 28 eV, and from 28 to 40 eV. La₂Zr₂O₇ and Nd₂Zr₂O₇ crystals could absorb photons in a wide energy range (4–10 eV).

Discussion and Conclusion. The study supplemented the concept of the properties of La₂Zr₂O₇ and Nd₂Zr₂O₇ with new experimental data. The densities of electron states and optical spectra of La₂Zr₂O₇ and Nd₂Zr₂O₇ compounds were calculated. This made it possible to explain features of the experimental X-ray photoelectron spectra of the compounds. In the approximation of the modified Becke-Johnson potential, the values ​​of the widths of the forbidden bands of the compounds corresponding to the experimental ones were obtained. The research is fundamental and can open up prospects for creating more efficient, reliable and functional materials, laser and optical devices.

Introduction. Control of underwater robotic complexes (URC) is complicated by factors, such as inertia, stochastic disturbances, and lack of navigation infrastructure. Existing approaches to modeling and predicting URS behavior are known for their weak or absent integration of data from real sensors in real time. By eliminating this gap in integrated solutions, it is possible to combine physical models, digital twins, and visualization. A promising tool for overcoming the above limitations is a digital twin (DT), which provides an accurate digital representation of an object through the integration of data from physical sensors and mathematical models. The objective of the presented study is to develop a method for predicting the dynamics of the URC using a digital twin to improve the efficiency of autonomous control.

Materials and Methods. The basis of the study was the development of a mathematical model of the motion of an underwater robotic complex. It included differential kinematics, modeling of environmental resistance, and rotation dynamics. The following sensors were used to collect and process data: incremental encoders, a three-axis accelerometer, and a gyroscope. A proportional-integral differentiating (PID) controller was applied to control the motion along each axis. The Unity Game Environment was used to visualize and test the model. It created a digital twin module with the ability to display the system state in real time. The Arduino IDE platform was used as software for low-level programming, as well as MATLAB and Python for data analysis and graphing.

Results. To verify the model, experiments were conducted on a physical model. They were compared to the simulation of the object's behavior in a virtual environment. Graphs of discrepancies between physical and simulated trajectories were presented. Statistical metrics characterizing the accuracy of the digital twin were calculated. The maximum deviation in coordinates did not exceed 5.3 mm, the average angular deviation was 3.5°. This confirmed the reliability and practical applicability of the proposed model in autonomous control of a robotic complex. It was also found that the average error along X — 3.11 mm, along Y — 2.92 mm. The average error in angle Z — 1.8°. The response time was less than 10 ms. The stability of the digital twin to minor fluctuations in the data was provided by smoothing the input data, the stability of the system regulator, and adaptation of the model to the calibration values at the start of each cycle.

Discussion and Conclusion. Digital twins are suitable for predictive control and monitoring of an object under uncertainty. The proposed approach can be scaled for various types of robotic systems operating in aggressive and poorly predictable environments. Further research in this area may involve the introduction of adaptive and neural network control methods.

Introduction. Problems and methods of finding Н_∞ – control are the basis of modern control theory. They are actively used to develop robust controllers, especially in aircraft control systems under limited external actions. These methods allow for adapting control systems to changing environmental conditions, which is critically important for providing the reliability and safety of aircraft operation. Current research is aimed at improving approaches to the synthesis of controllers covering both linear and nonlinear dynamic systems. In this context, special attention is paid to the integration of new mathematical methods, such as linear matrix inequalities and frequency analysis, which allows for optimizing the system response to various external actions and providing protection against unexpected conditions. It is important to note that, despite the progress made in this area, significant problems remain unsolved regarding the analysis and synthesis of controllers for nonlinear systems. This necessitates further research and development in this promising area. In this paper, in order to fill the existing gap, sufficient conditions for the existence of control for one of the frequently encountered classes of nonlinear systems are formulated and proven, which will then be used as a theoretical basis for developing approximate algorithms for finding it.

Materials and Methods. The basic research tool was the Н_∞ – control synthesis methods based on the minimax approach, which consisted in finding the control law under the worst external action. In this context, it was proposed to prove sufficient conditions for the existence of control using the extension principle. However, due to the computational difficulties that might arise when applying those conditions, it was decided to simplify the initial formulation of the problem. The simplification process was performed by approximate replacing the nonlinear system with another nonlinear system, which was similar in structure to the linear one, using the factorization procedure. This approach made it possible to use the solution of the Riccati equation, whose coefficients depended on the state vector, for the synthesis of controllers. To solve model examples and applied problems, a software package was developed using the MATLAB mathematical package.

Results. The article solved the problem of synthesis of Н_∞ – control of the state of nonlinear continuous dynamic systems, linear in control and disturbance. Sufficient conditions for the existence of Н_∞ – control were formulated and proved on the basis of the extension principle. An approximate method was proposed that provided solving the problem of finding control laws for dynamic systems that were nonlinear in state, similar to the methods used for linear systems. Analytical solutions were found for two model examples, which were illustrated by graphs of transient processes to demonstrate the results of numerical modeling of the considered nonlinear dynamic systems in the presence of external actions.

Discussion and Conclusion. The proposed approximate algorithm for synthesizing state and output controllers guarantees the required quality of transient processes and asymptotic stability of closed nonlinear control systems. This significantly expands the class of dynamic systems for which it is possible to synthesize controllers capable of resisting various external actions. The methods presented in this paper can be effectively applied to solve a variety of control problems, including the design of autopilots and automatic navigation systems for aircraft, even under conditions of limited external actions.