Статьи журнала - Siberian Aerospace Journal
Все статьи: 341
Статья научная
In the conditions of continuous financing of the programs of the Ministry of defense of the Russian Federation, the question of finding the most effective ways to modernize weapons and military (special) equipment, the developments in which are maximum and the processes of their improvement can take no more than a few years, is particularly acute. Such products, in particular, include aviation artillery weapons (AAO), the prospects for the use of which remain for the entire period of the army's existence with conventional weapons. The main factor influencing the quality of the AAO functioning is considered to be the thermophysical loading of a small-caliber artillery barrel (hereinafter referred to as the barrel) during firing. The problem of increasing the accuracy of determining the temperature field of the barrel is again updated by tightening the conditions for striking targets. Issues closely related to the intensification of AAO application regimes have come to the fore. These are issues of heating, cooling, thermal strength, wear, barrel survivability, issues of safety and firing efficiency. Despite the methodological evidence of analytical and numerical approaches to formalizing heat transfer in the wellbore, their practical implementation is rather complicated. The physical and mathematical meaning of this reason is as follows: possible instability of solutions; manifestation of oscillations in areas of large gradients; simultaneous presence in the solution regions of supersonic, sonic and subsonic zones; the existence of laminar, turbulent flows and other non-linear formations; non-triviality of setting boundary conditions; the presence of thermal resistance of surfaces, etc. However, the practical needs of ensuring safety and increasing the efficiency of fire operation of AAO dictate the need to obtain a close approximation of the problem under consideration to its possibly existing exact analytical solution. The aim of the work is to improve the mathematical apparatus that simulates the temperature field of the shaft based on a combination of heat transfer methods and mathematical physics. By verifying the reliability of the developed mathematical model (hereinafter referred to as the model, if from the context of the presentation of the material it is clear that we are talking about the proposed tools), the facts of the absence of methodological errors in the formation of the constituent blocks of the model and the increase in the accuracy of determining the thermal loading of the wellbore by 9.4 % were established. Based on the accents of the stated problem, the directions for improving the model are argued.
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Mathematical modeling of autocompensation devices
Статья научная
The article studies the order of developing and describing mathematical models of automatic compensation devices of all-round radar stations. The development of algorithms for spatial processing of signals in radar systems with phased antenna arrays is an important stage in the design of radar stations. This article considers the procedure to create mathematical models of automatic compensation devices that differ in implementation methods, namely: the number of compensation channels, the position of the main and compensation (additional) channels of the radar station (stationary or dynamic), the amplitude-phase distribution of the main and additional antennas, the representation phased antenna array, algorithms for finding the weight vector. The method of computational experiment verifies the adequacy of the operation of the models and the results are comparable with the implemented automatic compensation devices in radar stations. Presented in the form of graphs of the signal at the output of the automatic compensation device as well as the passage of the matched filter, the results of the computational experiment show effectiveness of the algorithm to calculate the weight vector; they permit to visually, quickly and economically compare the efficiency of the automatic compensation devices, depending on the method of their implementation. The article discusses the algorithm for the direct formation of the weight vector and the algorithm for the formation of the weight vector through the inverse correlation whitening matrix. Mathematical models of automatic compensation devices and the results of a computational experiment can be used to train future specialists who develop and operate radar stations.
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Mathematical modeling of the flat ingot casting process for solving automation problems
Статья научная
Aluminum alloys are widely used in the production of aircraft due to their strength, lightness, corrosion resistance, and necessary electrical conductivity. At the same time, aluminum ingots used in further processing of the space industry must be of high quality. Technological problems and defects arise when temperature, speed, and other technological parameters of casting are not observed, or when modes change. At the same time, foundry processes are partially automated; the human factor significantly affects product quality and work safety. Therefore, automation of these complex processes using mathematical models to predict casting parameters is an urgent task. The goal of the work is to create mathematical models available for use in automated process control systems (APCS), as well as for the development of a digital twin. The work presents simplified formulas for modeling the temperature distribution of an aluminum ingot during the casting process, cooling the metal when moving along a metal path, and test calculations of the temperature distribution inside the ingot when the ingot reaches a fixed length. The results of this work can be used to improve the efficiency and accuracy of controlling the process of casting aluminum ingots, to eliminate emergency situations.
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Статья научная
In this scientific work, a method of controlling high-frequency products from polymeric composite materials is considered. The authors of the work present the rationale for choosing a method of high-frequency diagnostics as the most suitable for non-destructive testing of products from polymeric materials of machine-building and rocket-space purposes. In the presented article, the primary task of creating and studying a mathematical model of the effect of highfrequency radiation on a polymer product, including those with a “metallic inclusion” defect, has been stated and solved. In addition, the work presents the calculations of diagnostic parameters using the mathematical model developed during the study. The calculation of the dynamics of heating the product and the temperature distribution during the control process is presented. The results of the calculation of specific power are described, the dependence of the instantaneous power consumption on the warm-up time is found. In the study based on a mathematical model, the Aleo- Diagnost software package was developed and registered, which is directly intended to ensure the functioning of the diagnostic devices and the investigation of the monitoring process. In addition, the developed complex allows solving a number of such practical problems as the calculation of the operating voltage depending on the geometrical parameters of the product and the determination of the value of energy consumed for monitoring the product for a specified period of time. This stage was necessary, as the consumed energy is the main output parameter of the diagnosis. In addition, the value of energy consumed is taken as the basis for the organization of the process of non-destructive testing in the automated mode. The solution of the tasks in this work has significantly reduced the cost of preparation of diagnostic operations, as well as improve the quality of control of products on an industrial scale at the stages of manufacture, operation and during repair work. The article also presents practical results, conclusions.
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Measurement of temperature distribution using a three-wire system of sensors based on thermistors
Статья научная
Improving the reliability and increasing the avionics resource is associated with possibility of continuous control of temperature fields of printed circuit boards. This problem can be solved only with the use of a large number of temperature sensors. It raises the problem of connecting the measuring elements and recording equipment. Several methods with their own advantages and disadvantages are proposed. One of the implemented and patented methods is using a set of resistive diode sensors installed in series on a threewire line. The temperature sensors are pairs of counter - connected diodes with a sequential survey when applying sawtooth voltage. The system is simple and easy to implement, but its main drawback is the method of determining the temperature by measuring the amplitude of the total reverse currents of diode pairs. It determines the large measurement errors, especially in the temperature range less than 20°C. The article deals with a similar design of a three-wire circuit, but with a fundamentally different approach to temperature measurement. The temperature sensor here is not diode pairs, but thermistors with a well-known dependence of resistance on temperature and high accuracy, and diode pairs record only the moment of coincidence of the sawtooth voltage with the voltage on the thermistors. This approach allows using mathematical methods of signal processing to accurately determine the voltage drop on the thermistor, and this ensures the accuracy of the resistance/temperature and the expansion of the temperature range. Given the fact that thermistors are increasingly used to measure temperature, simplifying their inclusion in a large number will allow to register the temperature field of electronic units, which is extremely important for spacecraft. The proposed version of a three-wire circuit for connecting temperature sensors at several points was tested experimentally, including at negative temperatures.
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Статья научная
Based on the previously compiled physical and mathematical model of the vortex ejector workflow, its solution was made. The solution of this model made it possible to compile two calculation methods: a method for calculating the optimal geometry of a vortex ejector for given thermodynamic characteristics and a method for calculating the thermodynamic characteristics of a vortex ejector with known geometric dimensions [1; 2]. Vortex ejectors are used in many areas of aerospace engineering. The compiled development of a method for calculating the thermodynamic characteristics of a vortex ejector with known geometric dimensions will make it possible to use vortex ejectors more widely in the aerospace industry. The calculation method is based on the concepts of tangential stresses arising in a viscous medium when two flows moving at different speeds interact. The mechanism of kinetic energy transfer from a high-energy gas to a low-energy one is shown.
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Статья научная
The construction of detailed accounting that allows to generate complex analytical reporting is an in-dispensable requirement of a modern financial system. For enterprises of the State Space Corporation “Roskosmos” with custom-made and small-scale production, operating in the conditions of Federal Law No. 275, characterized by a large amount of R&D and a high degree of uncertainty in the process of creat-ing products, this task is a system-forming one. The reporting should contain consistent data in any area of management and accounting at any given time. Along with this, system must provide the flexibility, reliabil-ity and performance inherent in transactional databases. To build information support that satisfies the specified conditions, it is required either to separate OLTP and OLAP data schemes, or to apply special-ized solutions based on the use of structures and techniques optimized for performing OLAP operations in traditional RDBMSs. This article considers the approach to form the multidimensional data in an automat-ed management system for economic tasks, as an effective alternative to complex and expensive BI solu-tions. Unlike many commercial systems, the ASU FEZ does not store redundant data (for example, opera-tional accounting registers in the 1C: Enterprise platform) required to build analytical accounting. The underlying data structures and methods of their processing allow for all types of accounting and have pow-erful tools for constructing analytical reporting. The article proposes algorithms for the operation of the system using the example of building simple OLAP cubes used in real tasks of automating financial and economic activities in ISS JSC for one of the Purchase subsystems. The formalization of these problems is carried out, the mathematical apparatus for constructing multidimensional data models based on infor-mation from a fixed set of normalized tables of a relational database is considered.The examples of SQL queries and outputs are provided. The advantages of using the system in operational management and accounting at the enterprise increasing its operational efficiency are summarized.
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Статья научная
When designing rocket engines, the problem of providing the specified basic design parameters is solved. In connection with the increase in requirements for products of rocket and space technology, the requirements for ensuring the energy efficiency of all its constituent elements are also increasing. As a rule, the task of increasing the energy characteristics of a rocket engine is carried out by increasing the pressure in the combustion chamber and the rotational speed of the turbopump shaft. An increase in the rotational speed of the shaft of a turbopump unit requires the provision of a cavitation-free operation of the pump with the absence of cavitation breakdown. This problem can be solved in various ways: by constructive improvement of the pump or by increasing the pressure parameter at the pump inlet. However, too much increase in inlet pressure is not possible, as this will increase the thickness of the walls of the rocket's fuel tanks and a corresponding increase in the mass of the entire rocket. Turning on the screw, although it does not guarantee cavitation-free operation at any inlet pressure, is the most preferred method. The geometry of the bore part of both the screw prepump and the pump blades is designed to ensure non-cavitational operation. When designing, at the stage of experimental testing of pump modes, it is pos-sible to use the methods of computational fluid dynamics (Computational Fluid Dynamics, CFD). These methods are used in various areas of general engineering and have proven themselves well. However, the rocket motor pump has a high pressure drop with relatively small dimensions. The question arises of adapt-ing CFD methods to modeling cavitation tests. This work is aimed at deriving a function approximating the TPU test data set with a view to its further adaptation for CFD methods.
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Статья научная
Plates, beams and shells with a non-uniform and micro-uniform regular structure are widely used in aviation and rocket and space technology. In calculating the strength of elastic composite structures using the finite element method (FEM) it is important to know the error of the approximate solution for finding where you need to build a sequence of approximate solutions that is connected with the procedure of crushing discrete models. Implementation of the procedure for grinding (within the micro-pass) discrete models of composite structures (bodies) requires large computer resources, especially for discrete models with a microinhomogeneous structure. In this paper, we propose a method of equivalent strength conditions (MESC) for calculating elastic bodies static strength with inhomogeneous and microinhomogeneous regular structures, which is implemented via FEM using multigrid finite elements. The calculation of composite bodies’ strength according to MESC is limited to the calculation of elastic isotropic homogeneous bodies strength using equivalent strength conditions, which are determined based on the strength conditions set for composite bodies. The MESC is based on the following statement. For all composite bodies V0 , which are such a homogeneous isotropic body V b and the number of p , if the safety factor nb of the body Vb satisfies the equivalent conditions of strength 2 pn1(1 ) nb (1 ) pn2 (1 ) , the safety factor n0 of the body V0 meets the defined criteria for strength n1 n0 n2 , where n1 , n2 specified, the safety factor n0 ( nb ) complies with the accurate (approximate) solution of elasticity theory problem is built for body V0 (body Vb ); (n2 n1) / (n2 n1) ; is the upper b error estimation of the maximum equivalent body stress V b , corresponding to approximate solution. When constructing equivalent strength conditions, i. e when finding the equivalence p coefficient, a system of discrete models is used, dimensions of which are smaller than the dimensions of the basic composite bodies models. The implementation of MESC requires small computer resources and does not use procedures for grinding composite discrete models. Strength calculations for bodies with a microinhomogeneous structure using MESC show its high efficiency. The main procedures for implementing the MESC are briefly described.
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Статья научная
This article formulates the topical problem of formalizing the methodological principles of the search for a compromise between properties repeatability and modification (novelty) for the new models of space technology – communication satellites. The main methodological principles of development continuity are the unification of products and their component parts, means of technological equipment and technological processes, which allows to reduce their diversity and nomenclature. The order of the nomenclature of the articles and their component parts is achieved by developing parametric and type-size series with rationally chosen intervals between the adjacent members of the series according to a complex criterion, a link to the target product performance with the cost of creating the product. The research develops a project model and defines criteria for selecting the size type of a universal space platform. In designing a new spacecraft on the basis of a unified space platform (USP), there is a need to refine it to meet the resource requirements of the new payload (mass and energy consumption). The article sets out the methodological principles for assessing the range of effective applications of the universal space platform for the two most extreme cases of resource requirements (by mass and energy consumption) of the payload: the resources of the platform are excessive or insufficient. Methodological principles have been developed to form a number of unified space platforms. Using the methodological principles for the formation of a series of unified space platforms, the effectiveness ranges of USP were evaluated and the completeness of a number of geostationary communication satellites developed by “ISS” was assessed.
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Methodological principles of space vehicle design for the maximum energy supply of the payload
Статья научная
The design of spacecraft at the initial stages is carried out in the presence of uncertainties in terms of parameters and conditions. The determination of design parameters is performed step by step: determination of the nominal values of design parameters, normalization of resource reserves (mass, volume, energy consumption) according to the design parameters to parry uncertainties, designing spacecraft for marginal resources. The operation of spacecraft with an electrical load switched on includes several stages: launching into the target orbit, putting into regular operation, regular operation for the intended purpose, decommissioning from the intended use in case of emergencies. The power supply system is designed to provide uninterrupted autonomous power supply to the onboard equipment in all modes and at all stages during the period of active existence of spacecraft, taking into account the presence of shadow zones of the orbit from the Earth and the Moon. In this article, the methodological principles for designing spacecraft for the maximum power supply of payload in the presence of uncertainties in parameters and conditions are developed. The mathematical models for calculating the parameters of the energy balance of spacecraft have been developed for various options for realizing the power of the session load, depending on the level of illumination of the orbit and the period of operation of spacecraft. The effectiveness of using the methodological principles of designing spacecraft for the maximum power supply of the payload, depending on the level of illumination of the orbit and the period of operation of spacecraft, has been evaluated. A technique has been developed for rationing reserves by spacecraft energy resources to parry uncertainties in terms of parameters and conditions, as well as the principles of its application when designing spacecraft for maximum payload power supply.
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Methodology for assessing reliability of stand-bed systems in testing liquid throat engines
Статья научная
In the process of design processing of low thrust rocket engines great attention is paid to special bench test methodologies, technical use of benches, simulation measurements of the physical conditions of outer space, as well as the use of diagnostic studies and equipment for various physical studies and measurements. The efficiency of ground (bench) testing is ensured by simulating the conditions of full-scale tests and taking into account the influence of all operational factors affecting the reliability of the assessment of reliability indicators during design testing in ground conditions. A special place in the issues of achieving test efficiency is occupied by the requirements to ensure the accuracy and reliability of test results. A significant amount of testing during the development of engines should be carried out under the required vacuum conditions on test benches equipped with pressure chambers with vacuum systems. As a result of failures of some elements of a complex bench system, the quality of functioning deteriorates and the probability of successful performance of the functions that determine the output effect of the system decreases. Therefore, the task of evaluating the reliability of the systems of the stand for firing tests of rocket engines is reduced to elucidating the effect of element failures on the quality of operation and the output effect of each system. When testing, the given conditions must unambiguously determine the technical characteristics of the test stand, including the pressure chamber and vacuum equipment. Tests must be carried out with a sufficient degree of certainty. When assessing the dynamic characteristics in pulsed modes, significant errors are introduced by inertial forces. Methods for ensuring the dynamic similarity of the characteristics of the engine supply systems with fuel components on the stand and as part of the propulsion system of the spacecraft, including the correspondence of the hydraulic, inertial and wave characteristics of the mains, are considered. An analysis of the errors in the test results was carried out. The tasks of the methodology for calculating instrumental errors are formulated. An assessment of the frequency characteristics of bench hydraulic lines was carried out. Recommendations have been developed to improve the accuracy of measuring parameters during bench firing tests of low-thrust rocket engines.
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Статья научная
This paper considers the methodology for calculating the de-weighting system of spacecraft elements for ground tests, taking into account the deployment options, de-weighting conditions, types and options of de-weighting systems. An example of calculation for a 3-section solar battery without a beam with incomplete de-weighting and with minimization of moments in the hinges is given. Genetic algorithms are used as an algorithm for determining the parameters of the de-weighting system, which allows obtaining the minimum moments in the hinges. The moments and forces acting in the system were checked by plotting diagrams in the expanded state. In addition, a check for compliance with the specified distance, based on design constraints, between the points of application of the weighting forces was made.
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Статья научная
At present visualization of graph models is an inherent part of the processing of complex information about the structure of objects, systems and processes in many applications in science and technology, and at the market there are widely presented science-intensive software products, using the information visualization on the basis of graph models. Since the information to visualize is constantly growing and becoming more complex, more and more situations are arising, where classical graph models cease to be adequate. More powerful graph-theoretic formalisms are required and appear to represent information models with a hierarchical structure, since hierarchy is the basis of numerous methods for visual processing of complex big data in various fields of application. One of these formalisms is the so-called hierarchical graphs. This formalism allows to select a set of such its parts (so-called fragments) in the given classical graph that all elements of each selected fragment deserve a separate joint consideration, and all fragments of the selected set form a nesting hierarchy. At the A. P. Ershov Institute of Informatics Systems, the Visual Graph visualization system was constructed, which is based on hierarchical graphs and allows to explore complex structured big data through their visual representations. In many applications, objects modeled by graph vertices are complex and contain non-intersecting logical parts (so-called ports) through which these objects are in a relationship modeled by arcs. In the paper, the formalism of attributed hierarchical graphs with ports is introduced and new possibilities of the Visual Graph system for visualization of large structured data based on attributed hierarchical graphs with ports are considered.
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Methods for constructing routes outside urban areas based on GPS data
Статья научная
Route constructing methods include the task of finding the shortest trajectory between two or more ob-jects, which may vary depending on weather conditions, altitude coordinates, and other parameters. The methods discussed in the article allow constructing routes using GPS tracks for various fields of knowledge: designing routes within a city, region, country, or with remote sensing of the earth. The consid-ered algorithms are used in the field of environmental monitoring in emergency situations, to search for optimal data transmission routes in satellite systems and their validation, as well as in organizational and economic systems. The most widely used approaches for constructing routes are graph theory and search in the state space, where any trajectory between objects is given its own weight. However, there is still no system that allows to make a tourist route over rough terrain. The article discusses such methods as the Dijkstra, Levit, Floyd-Warshell algorithm, and it also compares their effectiveness in terms of running time and complexity. The aim of the work is to develop an algorithm for finding the shortest path and building a tourist route from a given point A to point B. This development will open up new opportunities for citizens to independently visit new interesting areas, actively spend their free time and get to know the surroundings of the city. The system has been tested on the territory of the Torgashinsky ridge, includes more than 38 route points located at a distance of more than 25 kilometers, and allows to build the desired routes within less than 15 milliseconds. At the same time, the system enters person’s coordinates, which are considered when constructing routes.
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Статья научная
It is a fact that during data transmission, inter-symbol interference can occur, caused by the presence of multipath propagation and frequency-selective fading in the radio channel, which can significantly reduce the energy efficiency of communication systems. One of the methods to combat such effects, relevant today, is the use of OFDM modulation (OFDM – Orthogonal Frequency Division Multiplexing), which allows to flexibly change the data rate, reduce the frequency resource by improving the spectral efficiency, and also deal with frequency – selective fading and selective interference. However, there are channels that are particularly susceptible to inter-symbol interference, such as, for example, the tropospheric channel. Also, the problem of selective interference is particularly acute in near-field magnetic induction communication systems. For such channels, the use of OFDM modulation itself is not a panacea; the task of increasing the energy efficiency of an OFDM signal is an urgent one. This paper presents the key features of the OFDM mode of operation, which make it possible to increase the energy potential of the radio link in channels subject to intersymbol distortion. The results of modeling methods for PAPR reduction and digital predistortion for the linearization of the transmission path are presented. The practical significance of the work lies in the fact that the use of transmission path linearization methods will increase the maximum bandwidth of communication systems, primarily those using tropo-spheric, radio relay and near-field magnetic induction communication channels. At present, this issue is particularly acute, since there are no high-speed tropospheric stations with a data transfer rate of 50 Mbps in Russia. Increasing the throughput in tropospheric communication will provide communication to hard-to-reach settlements with difficult terrain. Also, the use of high-speed tropospheric communication is a cost-effective alternative to satellite communication, since its use does not require the lease of a satellite channel.
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Methods of removing unwanted objects from aerial photography images using iterative approach
Статья научная
Removing objects from images refers both to the tasks of improving the quality of the image, for example, in the field of recovering damaged photographs, and the tasks of increasing safety when removing people or cars from aerial photography images with remote sensing of the earth. At the same time, methods for removing unwanted objects usually include two stages: selecting objects for removal and restoring texture in areas of the image. The first stage can be performed manually by users, if it is necessary to select specific objects, or automatically by training the model on different classes of objects. The problem of image restoration in the course of research was solved by various methods, the main one of which involves using of the values of neighboring pixels for rendering in distant areas. In recent years, methods using deep learning based on convolutional and generative neural networks have shown good results. The aim of the work is to develop a method for removing objects from aerial photography images with manually selecting objects and drawing textures in the processed area. The paper reviews modern methods of image restoration, among which the most promising are the use of deep learning networks, as well as texture analysis in the restored area. The proposed algorithm is based on an iterative approach when analyzing neighboring areas and gradually painting the restored area with a texture from neighboring pixels, taking into account the weight and contours of the boundaries. The article evaluates the effectiveness of the proposed method using the base of video sequences obtained from quadcopters and containing people and natural objects. At the same time, both an expert assessment was carried out, which showed good visual results, and a comparison of the quality of the algorithm with known approaches according to the PSNR metric, which showed the best results in the presence of a complex texture in the scene.
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Mobile device to collect heat and power parameters of the refrigerator
Статья научная
The article deals with the system used to reduce the amount of time to carry out the refrigeration tests; it was developed to cut the acceptance testing time of each refrigerator up to 6-9 minutes. The main parts of the system , considering each piece of equipment separately and its role in the system as a whole, the way all devices connected to a single unit, communication protocol, cloud storage method to access data from any mobile device are described in the article. The main purpose of the system is to measure the temperature at certain points of the refrigerator capacitor when it is connected to the power grid. The analysis of the thermal energy properties of the refrigerator, combined with the analysis of the cooling speed of the refrigeration chambers (as well as the heating of the capacitor) makes it possible to understand whether each refrigerator corresponds to certain characteristics established by GOST. The article also presents the characteristics of the devices being used (temperature meter-regulator TRM 138, the ME110-224-1M electrical network measurement module).
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Статья научная
The main requirements for LRE gas generators are high stability of operation, ease of workflow management, as well as high efficiency of the generator gas. A particularly difficult task is to ensure the sustainability of the workflow. In addition to the probability of transverse vibrations in the in-chamber volume, due to the presence of additional volumes of various configurations and lengths attached to the reaction chamber, acoustic vibrations of complex longitudinal modes may occur. Most of the existing methods of testing a gas generator are criterion-empirical in nature and are based on the processing of experimental results, which does not always provide the required accuracy of calculating dynamic and thermal characteristics. The need for experimental and theoretical refinement of the calculation methods of thermodynamic processes of gas generators is an urgent task that will significantly reduce the material and time costs for preliminary design, testing and fine-tuning of modern models of engines and power plants of aircraft. Therefore, the calculation and analysis of the LRE gas generator is an important stage in the design and development of modern engine designs. Using the finite element method of the SOLID WORKS software package, a model of a two-zone gas generator for supercharging fuel tanks of the LRE was built. A study was conducted on modeling the workflow in a gas generator, visualization of thermodynamic processes in the product was built, numerical characteristics were obtained. The method of autonomous bench (firing) tests of fuel tank supercharger gas generators, the method of verification of numerical methods are considered.
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Статья научная
The problem of weightlessness simulation of beam systems suspended on inextensible cables is considered. Imitation of weightlessness means zeroing or reducing any selected force factor (for example, the reaction of the support or the moment in the support or joint), and the kinematic factor (deflection or angle of rotation). It is required to select the forces in the cables such that the sum of the squares of the deflections at the points of the elastic line of the beam is minimal. The problem is formulated as a nonlinear programming problem; the search for the minimum of the objective function with constraints, in the form of equilibrium equations, is carried out. In general, all equations written out for a geometrically variable system are linearly dependent. Parameters are selected from the system of equations, the vectors at which are entered into the basis, and the remaining parameters are considered free and are the coordinates of the objective function. The problem was reduced to the problem of quadratic programming without restrictions. Partial derivatives of coordinates give a system of linear algebraic equations that allows you to determine the coordinates taken as free parameters, and then calculate the coordinates entered into the basis. The reference plan of nonlinear optimization problems can have local minima; it is shown that for any initial basis, the optimal plan is the only one. To calculate the deflections of the beam, the method of initial parameters is used. Deflection, angle of rotation, additional angles of rotation in articulated joints are considered as initial parameters; as well as the reaction and bending moment. The continuum problem is transformed into a discrete one by limiting the number of points at which deflections are calculated. The objective function has a finite number of variables. It is determined which number of selected points on the elastic line of the beams is sufficient to ensure the convergence of the functions of deflections, angles of rotation, bending moments and transverse forces for the purpose of application to practical calculations. Optimization of deflections of a beam pivotally fixed, suspended on two cables with verification of solutions, change of basic variables and convergence study depending on the choice of the number of points at which deflections are calculated is performed. The deformation of systems of I-beams connected by hinges to each other, having linear weight in gravity conditions, is analyzed. To simulate weightlessness, the system is supported by six cables. The boundary conditions are considered: – rigid pinching; – hinge-fixed support, – sliding sealing; – free edge. Models of three-beam systems in the simulation of weightlessness, to a certain extent equivalent. The type of boundary condition affects the first beam to a greater extent; the tension forces of the cables equalize the deformed and stressed state in subsequent beams. Any of the considered systems with the presented boundary conditions can be converted into an equivalent one by changing the boundary force factors, setting torques or installing a spring with a given stiffness and adjusting the tension of the cables.
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