K. L. Panchuk, T. M. Myasoedova, E. V. Lyubchinov
Construction of a PH-curve of space by orthogonal projections of its hodograph
DOI: 10.25206/1813-8225-2025-196-5-11
In modern geometric modeling, a class of plane and spatial PH-curves (рythagorean hodograph curves) is known, which were theoretically substantiated by mathematician Rida T. Farouki in 2007. PH-curves have a unique property that is important in solving many different practical problems, namely: the "parametric speed" of these curves, i.e. the derivative of the arc length with respect to the curve parameter, is a polynomial (or rational) function of the parameter. This property is due to the fact that the coordinate components of the hodograph of the PH–curve are elements of the Pythagorean (n+1)-tuple of coordinate polynomials.  Due to this property, PH-curves are in demand in solving various practical problems: generating trajectories for UAVs (unmanned aerial vehicles), optimizing the path of mobile robots, calculating segments of the axis of a road that are optimal in shape and length, etc. etc. In the theory of spatial PH-curves, algorithms for their analytical construction have been developed. In this paper, an approach to constructing these curves is proposed, based on the theory of plane PH-curves and implemented by sequentially constructing imagesprojections of spatial PH-curves on two coordinate planes. That is, solving the spatial construction problem is reduced to solving two problems of sequential construction on coordinate planes. Numerical examples are given that demonstrate the efficiency of the proposed approach. At the same time, the calculation algorithms are simpler than in the case of the known spatial analytical approach. In the direction of developing the proposed approach, numerical examples of constructing a spatial composite PH-curve by smoothness C1 are given. 

Keywords: PH-curves, рythagorean hodographs, polynomials, orthogonal projection, composite curve, smoothness of connection.

V. Yu. Yurkov, M. A. Chizhik, I. A. Sheveleva
Structural geometric model of associated sets of curves
DOI: 10.25206/1813-8225-2025-196-12-17
The paper is devoted to an iterative algorithm for constructing a one-parameter family of sets of mutually connected curves. Mutual connection means existence some one-to-one and continuous correspondence between the points of the curves. Each set of curves in the family satisfies its own set of boundary conditions that leave one parameter free for each curve of the set. This parameter allows us to organize an iterative process of approaching for each curve to the set of boundary conditions set for it. A special case of the described approach is considered in detail. The structural geometric model for predicting the shape of three-layer fabric package is proposed. Deformation of the package occurs through the action of an external force. The structural geometric model of normal cross-sectional image of such package is a one-parameter family of interconnected parabolas of higher degrees. Only one free parameter is connected functionally with the total stiffness of the package. The total stiffness of the package and its function can only be determined experimentally. In the paper, we consider this function as a linear one. One of the conditions for constructing one-parameter family is constancy of the lengths of arcs of mutually connected curves. Proposed approach may be applied to solving a number of theoretical and applied problems of engineering geometry in the field of designing multilayer fabric packages. 

Keywords: geometric shape, parameterization, forecasting, mutually connected curves, one-parameter set, multilayer fabric package, deformation.

A. Kh. Shamutdinov, I. Yu. Lesnyak
Methodology for calculating the kinematics of the piston rod of a translational motion engine of a lever manipulator moving in a rectilinear guide
DOI: 10.25206/1813-8225-2025-196-18-25
The article deals with the analysis of the kinematics of the upper end of the hydraulic cylinder rod (pneumatic cylinder, ball screw pair, etc.), which is part of the circuit solution of a lever manipulator, the end of the leading rod of which moves along a given rectilinear guide. Analytical dependencies of the analogs of angular velocities and angular accelerations of the mechanism rods are determined. A technique for determining the kinematic characteristics of the considered lever manipulator using a graphical method is developed. Using a dimensionless coefficient of change in angular velocities (the ratio of the areas of triangles), angular velocities and accelerations of the driven rods of the mechanism are determined based on its geometric parameters and a given linear velocity of the leading rod, which significantly reduces the time of calculating its kinematics in the technological process of operating the mechanism. 

Keywords: lever manipulator, translational motion engine, hydraulic-pneumatic cylinder, ball screw pair, straightening mechanism, generalized coordinate, speed.

Yu. D. Markina
Impact of the location of technological equipment on the calculation results of the digital cell tower
DOI: 10.25206/1813-8225-2025-196-26-34
Modern antenna-mast structures, used for housing wireless communication equipment, are characterized by high sensitivity to wind load effects. The geometric features, shape, and spatial arrangement of antennas significantly influence the stress-strain state of the load-bearing metal structures. The study presents the calculation results of a digital model of a cell tower, taking into account the actual placement of antennas and various wind flow directions. The conducted numerical analysis shows that applying a limited number of wind load calculation directions, based solely on the norms of SP 20.13330.2016, does not provide the required calculation accuracy. The authors prove the necessity of an individual approach in selecting the directions of action and constructing computational models with varying structural orientations relative to the wind. The obtained results are relevant for the design and reconstruction of antenna-mast structures, as well as for their subsequent retrofitting. 

Keywords: antenna-mast structures, wind load, lattice metal structures, panel antennas, digital modeling, stress-strain state, aerodynamic resistance, engineering calculation.

M. O. Shalnev, Ya. V. Denisova
Application of digital tools in the sphere of lean production at industrial enterprises
DOI: 10.25206/1813-8225-2025-196-35-42
The article examines the application of digital tools in the sphere of lean production in industrial enterprises, which fundamentally changes the approach to enterprise development. The study covers the basic concepts of lean manufacturing and their integration with digital technologies in the context of Industry 4.0. The paper provides examples of the main digital tools of lean manufacturing, develops a process for implementing a lean manufacturing system using digital tools into the production process, provides a stepby-step description of the process of implementing a BP system using digital tools, presents examples of successful application of digital tools, and shows their impact on the efficiency of production processes and the quality of manufactured products. 

Keywords: digital lean manufacturing, Industry 4.0, digital tools, production system, industrial enterprise, production process, operating system.  

A. B. Yarov, A. V. Tolok, A. E. Pankova, A. E. Chentsov
Functional-voxel method for geometric description of a radar detection zone 

DOI: 10.25206/1813-8225-2025-196-43-50
The study presents an improved methodology for constructing precise geometric models of detection zones for ground-based radar stations. The primary focus is on integrating a functional-voxel approach. The analytical description of the radiation pattern is defined via piecewise functions with angles µmin = 0.1°; µ0 = 1.7°; µmax = 4°. The transformation between polar and Cartesian coordinate systems is accounted for, and R-functions are applied to combine the analytical equations used. The modeling incorporates the Pattern Propagation Factor of the Earth using the following computational methods: decomposition of  5Ч5 matrices into 4Ч4 submatrices via Laplace’s method and construction of local approximating planes with coefficient normalization. The study develops 2D-models with a maximum detection range of 125.5 km, as well as 3D-models. Since the functional-voxel method is employed, base M-shapes of local characteristics are constructed. The simulation accuracy aligns with functional-voxel method readings, meaning the model’s values are calculated at each point while maintaining continuity, depending on the scale used. 

Keywords: functional-voxel method, M-shape, R-functions, homogeneous vector, local geometric characteristics, radiation pattern, radar simulation.

N. D. Prokopenko, M. S. Morozova, M. Yu. Chubukov
Expertise in applying lean manufacturing tools to reduce costs of the pipe chemical processing
DOI: 10.25206/1813-8225-2025-196-51-57
This article presents results of the use of lean production methods and tools to ensure improvement of efficiency of the pipes chemical processing process at JSC “Volga Pipe Plant”. The paper presents practical experience in applying lean production tools, particularly the Lean Six Sigma process management methodology, to optimize the use of acids in the chemical processing of pipes and improve labor productivity. To achieve this goal, the DMAIC lean manufacturing concept is used. The use of lean production tools provides determination of the most optimum process conditions of the chemical processing of pipes. The study demonstrates the feasibility of applying lean production methods and tools at a metallurgical enterprise. 

Keywords: lean production, DMAIC, pipes chemical processing, acid regeneration, etching acids, metallurgy, stainless steel pipes.

D. V. Polovinka, Yu. V. Rubleva, M. N. Ivlev
Moisture content control system for transformer oil using measured Q-factor
DOI: 10.25206/1813-8225-2025-196-58-64
This paper discusses the issues of determining the moisture content in transformer oil. A system for the rapid determination of the moisture content in transformer oil during its operation is proposed. Recurrent analytical relationships for the capacitance and active resistance of a measuring transducer with transformer oil as a function of the integral charge and discharge voltage have been derived. The task of calculating the capacitance and active resistance using these recurrent formulas is assigned to a microcontroller within the voltage recording device. 

Keywords: transformer oil, quality, testing method, equipment, liquid dielectric, quality factor, Lambert function, microprocessor.

B. D. Tabarov
Evaluation of the expansion of the functionality of a reactor-thyristor voltage regulator with wide voltage regulation ranges
DOI: 10.25206/1813-8225-2025-196-73-81
The paper considers the effect of a reactor-thyristor voltage regulator during voltage stabilization on the sinusoidal current and voltage of electrical complexes and systems with a stepwise increase in supply voltage to +16 % and a decrease in load current to –70 % of the nominal level. This study is conducted in the Matlab environment on a simulation model of electrical complexes and systems using measuring modules to evaluate the expansion of the functionality of the proposed voltage regulator when voltage is stabilized in electrical complexes and systems with high energy performance. The study is conducted when the supply voltage is increased to +16 % in steps of +2.5 %, and when the load current is reduced to –70 % in steps of –10 % of the nominal value. The obtained research results confirm that the claimed device does not distort the sinusoidal voltage of the supply network and currents of electrical complexes and systems when regulating voltage in wide aisles and sub-ranges. The results of numerical experiments also showed that the new technical solution creates a maximum voltage distortion in the power transformer and in electricity consumers by 3.75 % when the voltage in the supply network increases by +10 % and by 1.63 % when the load current decreases by –40% of the nominal level, which does not exceed the normally permissible standards established by domestic and foreign GOST standards. The most appropriate area of application of the claimed technical solution is electrical engineering complexes and systems wh ere it becomes necessary to maintain the voltage at a given level in the event of a positive deviation and voltage fluctuations in the supply network and negative deviations, and current fluctuations on the load in wide ranges with high efficiency.

Keywords: electrical engineering complexes and systems, thyristor switch, reactor, non-sinusoidal voltage coefficient, current sinusoidal distortion coefficient, angle control, wide range voltage regulation.

V. A. Dyshlevskiy, I. S. Kudryavtseva, A. P. Naumenko, V. A. Rol’geyzer
Methods of decision theory as a way to increase the reliability of assessment of the technical systems state
DOI: 10.25206/1813-8225-2025-196-82-91
The article discusses various approaches to technical diagnostics based on decision-making methods. Particular attention is paid to probabilistic and statistical methods that help to make informed decisions, taking into account the likelihood of certain functions being performed. The study shows that the choice of a specific technique depends on the specific problem being considered. Bayesian methods are efficient and easy to calculate, which makes them popular for industrial applications in assessing technical condition. For high-risk systems the article recommends to apply the Wald method. 

Keywords: assessment of technical condition, methods of decision theory, probabilistic and statistical methods, monitoring and diagnostic system, Bayes method, Wald method.