Статьи журнала - Siberian Aerospace Journal
Все статьи: 374
Статья научная
Failures of elements during the operation of technical and many other systems are, as a rule, random in nature. This leads to various models of the recovery process, studied in probability theory and mathematical reliability theory. During the restoration process, failed elements are restored or replaced with new ones, and there is often a change in the costs and quality of the restored elements (time-to-failure distribution functions). The work examines the cost function (average cost of restoration) in the process of restoration of order k1, k2 , in which, according to a certain rule, the costs of each restoration and the distribution functions of operating time change. Considering, that the recovery function (average number of failures) is well studied in reliability theory, a solution to the integral equation for the cost function is obtained through the recovery function of the model under consideration. For the order restoration process 1 2 k , k , a formula is obtained for calculating the cost function through the restoration function of a simple process formed by the convolution of all distribution functions of the periodic part. For practical application, explicit formulas are obtained for the cost function during the restoration process, in which the periodic part is distributed according to an exponential law or an Erlang law of order m with the same exponent α. The resulting formulas can be used to study the properties of the cost function and solve optimization problems in strategies for carrying out the restoration process in terms of price, quality, risk, if, for example, the average number of failures is taken as quality, the average cost of restorations as price, the dispersion of the number of failures as the risk, or cost of restoration.
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Solution to the first boundary value problem of plane elasticity theory using conservation laws
Статья научная
A huge number of works are devoted to solving boundary value problems for the equations of plane elasticity theory. The largest number of studies in this area are based on the formula found by G. V. Kolosov. He was the first to express the general solution to the problem of plane elastic deforma-tion by finding two independent functions of a complex variable. This made it possible to apply a welldeveloped theory of analytic functions to solving problems of elasticity theory. Later, the solution method based on Kolosov's formula was developed by his student N. I. Muskhelishvili. But the described method also has significant limitations. It is applicable only to those areas that can be conformally mapped onto a circle. Therefore, other methods for solving elasticity theory problems are also needed, since a large number of practically important problems are solved for areas that do not satisfy this condition. The method developed in the work is based on the use of conservation laws that are constructed for equations describing a plane deformable state. The assumptions made in the work make it possible to construct a solution to the first boundary value problem for arbitrary plane areas bounded by a piecewise smooth contour. In this case, finding the components of the stress tensor is reduced to calculating contour integrals along the boundary of the region under consideration. As in the case considered by G. V. Kolosov, the solution to the problem is based on two exact solutions of the Cauchy – Riemann equations, which have singularities at an arbitrary point in the region under consideration.
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Статья научная
The plane problem for elasticity equations is well studied. It can be explained by its importance for applications and by the fact that the equations can be reduced to the Cauchy-Riemann system. In spite of this importance, exact solutions that would describe the stress-strain state of bodies of finite dimensions are not numerous. Conservation laws for differential equations have been appeared more than a hundred years ago, but, as a rule, they were not used to solve specific problems, but were of purely academic interest. The situation changed with the development of the technique of construction of conservation laws for arbitrary systems of differential equations, and then with the use of conservation laws to solve boundary value problems of the theory of plasticity and elastic-plasticity. In this article, new conservation laws are constructed for the equations of the plane theory of elasticity in the stationary case. These laws form an infinite series, which is closely related to the elasticity equations solving. This fact made possible to reduce solving of boundary value problems, in terms of displacements, to the calculation of contour integrals along the boundary of a domain bounded by the studying elastic body. As it follows from the proposed technique, the studied area can be multiply connected, and the considered boundary can be piecewise-smooth.
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Solving the problem of stretching an elastic-plastic strip weakened by cuts and holes
Статья научная
In this paper, the boundary between elastic and plastic regions in a stretchable strip is con-structed. The band is weakened by side slits and holes. Such tasks are still relevant, since its solution allows us to make an assessment of the limiting state of the structure under consideration. Cuts can have an arbitrary shape, their number is not limited. For simplicity, only sections with rectilinear boundaries are considered in the article. The holes may have an arbitrary shape and be located anywhere in the strip. In operation, only circular holes are considered for simplicity. Numerical methods are currently very often used to solve such a problem, unfortunately, often without much justification. Therefore, analytical methods for solving such problems are becoming more and more relevant. In this paper, the conservation laws of differential equations are used. The conserved current is linear in the first derivatives. The task is solved in two stages. At the first stage, Dirichlet is solved for the Laplace equation, and at the second stage, the technique of conservation laws is used. Their use makes it possible to reduce the finding of the components of the stress tensor at each point to a contour integral along the boundaries of the region un-der consideration. And this makes it possible to build an elastic-plastic boundary.
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Spacecraft motion in a low circular orbit in establishing intersatellite link
Статья научная
The article investigates the problem of inter-satellite linking in the constellation of spacecraft in a low circular orbit. A specific problem of establishing intersatellite link (IL) in that orbit – cross-pointing of the antennae – is also studied. To support cross-tracking, it is important to place spacecraft (SC) in the orbital plane so that they are constantly in the zone of mutual visibility. The line-of-sight range is analyzed both in one orbital plane and between adjacent planes. IL is treated in terms of the orbital constellation (OC) ballistic formation. Several typical modes of motion of SC with IL in adjacent planes are determined – parallel, orthogonal, oncoming. The parameter values of IL antenna pointing are also assessed. The obtained results of OC formation and antenna pointing parameters’ calculations may be relevant for establishing a modified system.
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Specialized LED assembly for out-atmospheric solar simulator
Статья научная
Traditional solar simulators for thermal vacuum tests of spacecraft are based on gas-discharge lamps. Due to the characteristics of such lamps, they can only be installed outside the thermal vacuum chamber. High-efficiency LEDs can be installed directly in the thermal vacuum chamber, which can significantly improve the luminous and operational characteristics of solar simulators. Obtaining a spectrum close to the spectrum of the extraterrestrial Sun (AM0) is one of the primary and most difficult tasks in ensuring that the luminous characteristics of the solar simulator meet the requirements. The article considers a pre-viously proposed model of a combined emitter consisting of halogen lamps and assemblies of high-performance LEDs of various wavelengths. We have proposed a method for determining the spectral match for AM0 solar simulators and determined the requirements for LED assemblies intended for use in the combined emitter. Simulation with a sample of the most suitable commercially available LED assembly, at the nominal power level of halogen lamps, showed a good spectral match, which deteriorates significantly with decreasing lamp power. At the same time, many programs and methods of thermal vacuum tests re-quire simulation of different irradiance levels. Taking this into account, the authors developed an experi-mental LED assembly. Simulation of the combined emitter with this LED assembly showed the best results. The required spectral match is maintained at various irradiance levels. The achieved characteristics of the developed LED assembly are not limiting and can be improved by further optimization.
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Статья научная
According to the specific energy consumption, the shaping processes are arranged in three energy levels. Electrophysical and electrochemical methods of metal processing are at the third level, where the specific energy consumption is more than 6·104 J/cm3. The analysis of the literature data showed the inconsistency of the specific costs of some authors. The specific energy consumption of electrical contact processing cannot be commensurate with the costs of electrochemical processing due to the different sizes of the particles removed from the surface of the workpiece. There are no literature data on the specific energy consumption of electro-contact-chemical treatment of metals with a vibrating instrument in the electrolyte, therefore, experiments have been carried out with the fixation of current, voltage and interelectrode gap oscillograms. The method of calculation of specific energy consumption according to the oscillograms of the process is given. The energy costs for vibration of the electrode-tool are calculated, which are an order of magnitude less for electro-contact-chemical treatment. When the vibration amplitude decreases or the voltage on the electrodes increases, the process in the interelectrode gap turns into dimensional arc processing. When electro-contact-chemical treatment of metals with a vibrating tool in water, the specific energy consumption is equal to (3.5–3.8) · 105 J/cm3, which corresponds to electrocontact treatment. It is assumed that the use of aqueous solutions of neutral salts will lead to a reduction in energy costs.
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Статья научная
Active development of science-intensive technologies in the aerospace industry requires consideration of the operation of devices and instruments under extreme conditions; it is important to study the degradation of materials during rapid heating and cooling. On the basis of the theoretical and experimental work performed, the authors of the paper consider the degradation of cadmium telluride detectors caused by the development and evolution of a network of point defects resulting from pulsed exposure with a heat dose of about 1,000º С for no more than 10 s, simulating an extreme situation of a short circuit near the detector or direct heating by light pulses. The study showed that the crystalline material quickly degrades under such extreme conditions due to the rapid evolution of the defect network. The phenomenological model of the formation and distribution of defects during short-term exposure of the detector to thermal radiation has been improved. Electron microscopic studies of samples exposed to pulsed infrared radiation showed the development of a dense defect network, vacancy and interstitial defects, their clusters and other damage in all samples.
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Spraying plasmatron coatings with powder supply to plasma flow
Статья научная
The efficiency of using plasma energy when applying coatings is largely determined by the design of a plasma-tron. The main difference of the developed plasmatron PM-1 is the supply of transporting gas with powder to the plaza flow, which allows us to ensure more efficient and uniform heating of the material being sprayed. This paper presents the results of measuring a material usage factor (MUF), which is an important and indicative characteristic of plasmatrons, showing their economy and productivity. The authors calculated the cost of electricity and con-ducted studies of the sprayed samples for thermal shock.
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Статья научная
The article presents the problem of optimizing the structure of information processing computer appli-ances for real-time control systems used, among other things, in the rocket and space industry. In addition, the features of this problem that affect the choice of optimization methods are studied. It’s concluded that this problem can be effectively solved using evolutionary optimization methods. Existing performance models allow you to determine the minimum hardware configuration of a multi-processor computing system. The approach proposed in this article allows us to find configurations that have hardware redundancy (compared to the minimum configuration), but, due to this, have a greater probability of being in states that provide performance sufficient to achieve the goals of functioning of the designed real-time control system. The described approach is more flexible than simply duplicating all hardware components of the minimum configuration, which can be used to reduce the cost of creating and operating the designed control system. The proposed model can be used to optimize the performance of multiprocessor hardware and software complexes of real-time control systems. At the same time, it should be taken into account that the resources allocated for the creation and operation of the hardware and software complex are always limited. There-fore, it is advisable to consider the problem of performance optimization as a multi-criterion: one criterion will be performance, and the other-the cost of creating a hardware and software complex.
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Статья научная
The S-box is the most important component of modern cryptographic algorithms which largely determines the quality of cryptographic transformation. The modern method of estimating the S-boxes quality employs their representation as component Boolean functions to which cryptographic quality criteria are applied. Such criteria include: nonlinearity, correlation immunity, an error propagation criterion, and a strict avalanche criterion. Nevertheless, it is obvious that a cryptanalyst is not constrained in the ways of representing the cipher components, in particular, using the functions of many-valued logic. The design features of modern cryptographic algorithms allow their representation in the form of 4-logic functions, which determines the need to research cryptographic properties of the S-boxes represented as component 4-functions. In the literature today there are methods for measuring the nonlinearity of 4-functions; nevertheless, there are no similar methods for researching the differential properties of 4-functions, in particular, involving their compliance with the strict avalanche criterion. In this paper the strict avalanche criterion is generalized to the case of 4-functions and the compliance of the S-boxes component 4-functions of the “Magma” cryptoalgorithm to the strict avalanche criterion has been researched. All balanced 4-functions of length N = 16 satisfying the strict avalanche criterion were synthesized using the restricted brute-force method. The basic properties of the constructed class of 4-functions are determined, and bijective S-boxes based on them are constructed. It has been established that S-boxes of length N = 16 satisfying the strict avalanche criterion, both in terms of component Boolean functions and in terms of 4-functions, also possess optimal nonlinear properties. This circumstance allows us to recommend S-boxes satisfying the strict avalanche criterion of component 4-functions for use in modern cryptographic algorithms.
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Structural-phase state and properties of hypereutectic silumin treated with a pulsed electron beam
Статья научная
Hypereutectic silumin composition are promising modern materials of wide application (mechanical engineering, aviation, instrumentation, medicine, etc.). Disadvantages of hypereutectic silumin, significantly limiting their scope of application, are pores and cavities, large (about 100 µm) inclusions of lamellar and needle-shaped second phases. As a result of the studies carried out in this work, the possibility of forming structural-phase states in the surface layer of silumin, the size and morphology of which can purposefully change in the range from tens of micrometers to tens of nanometers, is demonstrated. The irradiation modes that allow more than 5 times to increase the microhardness (15 J/cm2, 150 µs, 0.3 s–1, 5 imp.) and more than 3 times to increase the wear resistance (50 J/cm2, 150 µs, 0.3 s–1, 5 imp.) of silumin were revealed.
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Статья научная
The purpose of this work is to reveal the patterns of formation of the structure of the surface layer of high-chromium steel subjected to nitriding in a low-pressure gas discharge plasma using a plasma genera-tor with a hot cathode "PINK". Heating of the samples to the nitriding temperature was carried out by the ionic component of the plasma, as well as by the electron and ionic components of the plasma (elion mode). The object of the study was heat-resistant corrosion-resistant steel of the austenitic class grade 20X23H18 (foreign analogue is AISI 310S). The relevance of research is due to the relatively low level of hardness and wear resistance of steels of this class. Nitriding of steel was carried out on the TRIO installation, retro-fitted with a switching unit for implementing the aelion (electronic and ionic) processing mode. It has been established that the thickness of the hardened layer is (55–60) μm and weakly depends on the method of nitriding, temperature (in the range of 793–873 K), and duration (3–5 hours) of the process. A nitriding regime has been revealed that makes it possible to form a surface layer with a microhardness of 13.7 GPa (ionic heating mode) and 10.8 GPa (elion heating mode). It has been revealed that the high strength and tribological properties of nitrided steel are due to the formation of a nanocrystalline structure in the surface layer, the main phases of which are iron nitrides Fe4N and chromium nitrides CrN. It is shown that heating the samples to the nitriding temperature in the aelion mode, which uses the electron and ion components of the plasma, leads to a significantly lower level of material roughness compared to the samples heated during nitriding by the ion component of the plasma.
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Structure, network protocols of the internet of things for quality production control
Статья научная
The subject of research is the model and structure of the Internet of things (IoT) network for product quality control in industry and agriculture. The purpose of the article is to analyze communication protocols and structures of IoT networks. The method of analysis and structural design of IoT networks is applied. The field of application is automation of monitoring products of enterprises of the aerospace industry. The article provides an overview and analysis of existing IoT technology; it considers the protocols and composition of IoT networks, and provides variations in the structures of building such networks. 4 levels of IoT architecture are described, as well as the communication protocols are used. The directions of building the Internet of things network for product quality control are defined. A multi-agent model of such system is presented, for the implementation of which the structure of the IoT network is given. The structure of a multi-agent system (MAS) for monitoring product quality in industry and agriculture includes many agents, such as product quality agents, communication agents, database agents, agents for analyzing information received from sensor agents, and decision-making agents. This MAS implements functions to ensure the required class of product quality and it is based on building a local network of the Internet of things. The research proposes an algorithm for processing information in such an IoT network. Analyzers (sensors) product qualities will be periodically polled and their values will be recorded in the server database. The decision-making subsystem sends data on product quality compliance to the enterprise administrator on a mobile device. The server structure is implemented using cloud IoT platforms, for which a brief overview is provided. The one IoT network implementation is developed using LTE NBIoT technology. This approach can be used in the aerospace industry for product quality control within automation 4.0.
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Статья научная
This paper discusses and estimates the effect of some design parameters on the value of axial thrust appearing during functioning of the core component of a spacecraft’s (SC) thermal control subsystem – electric pump unit (EPU). The major causes of axial forces in centrifugal pumps of in-line arrangement are described and analysed. Design parameters having an effect of axial thrust value are: impeller position relatively to EPU diffuser (position was chosen based on dimension chain calculation), presence and size of discharging holes in the impeller, number and shape of impeller vanes (numbers of 14 & 16 were considered). EPU impellers with different number and shape of vanes were designed and manufactured. A series of experiments was carried out in order to research the effects of all aforementioned parameters: measurements of head vs flow curves and axial thrust values at given flow values. Each parameter’s contribution in the value of axial thrust appearing during EPU functioning is evaluated. Vibration measurements were obtained and analysed for electric motor DBE 63-25-6.3 fitted with different impellers. In this study, a DLP additive process was used for impellers manufacturing, which significantly sped up the tests. Obtained results will extend knowledge of processes taking place in EPU impellers, enable choice of the aforementioned parameters at design phase so to minimise axial thrust appearing during functioning of a centrifugal EPU of a spacecraft’s thermal control subsystem. Outcomes of this study are capable of improving SC reliability at all phases of its life because EPU axial thrust causes its premature loss of operability.
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Study of structural properties of bismuth pyrostannate by Raman and IR spectroscopy
Статья научная
Chromium-substituted bismuth pyrostannates with a pyrochlore structure were synthesized by the solid-phase reaction method. The X-ray structural analysis performed at room temperature showed that the samples Bi2(Sn1-xCrx)2O7, x = 0; 0.05, 0.1 are single-phase and belong to the Pc monoclinic structure. Polymorphic transformations of the synthesized samples were studied by Raman and IR spectroscopy. IR spectra were obtained at the temperature range 110–525 K and frequencies 350–1100 cm–1. Raman spectra were measured at room temperature at frequencies of 100–3000 cm–1. Heterovalent substitution of Sn4+ for Cr3+ modifies the spectra of pure Bi2Sn2O7. The crystal structure of Bi2Sn2O7 consists of two oxygen sublattices: SnO6 and Bi2O'. Chromium ions substituted tin ions in the SnO6 oxygen octahedra, distorting the local structure in the vicinity of bismuth ions. Phonon modes are softening in the vicinity of phase transitions. А shift of the phase boundaries of polymorphic transitions is observed for Bi2(Sn1-хCrх)2O7, x = 0.05, 0.1. The frequencies of stretching vibration modes were determined from IR and Raman spectra. The substitution of chromium for tin ions resulted in the appearance of two new modes at frequencies of 581 and 822 cm–1 in the Raman spectra. The absence of an inversion center in the crystal structure of Bi2(Sn1-xCrx)2O7 is confirmed by Raman spectroscopy. IR spectra of chromium-substituted samples consist of complex lines, which decompose into 2 and 3 Lorentzian lines. The softening and broadening of optical absorption modes are associated with the electronic contribution. Impurity states of electrons form polarons.
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Статья научная
The article contains the results of a study of the influence of abrasive flow machining on the structure of the surface layer of the Al2O3 ceramic coating of the inner cylindrical surface. The experience of finishing the surface of ceramic coatings by grinding, hydro abrasive machining and abrasive flow machining is considered. Taking into account the high hardness of the aluminum oxide coating, black silicon carbide was used as a filler for the medium. The abrasive flow machining was carried out in seven stages. Each stage included 50 cycles of reciprocating flow of the medium through the machining channel. After each stage, a qualitative assessment of the coating surface structure was carried out with recording of a visual image of the surface on a microscope. A quantitative assessment of the change in structure was carried out by measuring the surface roughness. As a result of abrasive flow machining, it was possible to reduce the roughness of the surface layer from Ra = 16.9–18.5 µm to Ra = 3.6–3.68 µm. It is assumed that during machining, due to the removal of most of the microprotrusion peaks and smoothing of the surface layer, the contact area of the surface – the grain of the medium becomes significantly smaller. This leads to a significant decrease in the cutting depth and the transition of the machining mode from brittle to plastic. Based on the dynamics of change and structure of the surface layer of the ceramic coating, for complete removal of the original structure of the surface layer, 100–150 additional machining cycles will be required after 400 main cycles. The obtained results confirm the practical possibility of using this type of machining to improve the structure of the ceramic coating.
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Study of the influence of alphanizing on the structure and properties of the alloy BT6
Статья научная
The paper considers the influence of two technologies of alphanizing (oxidation) on the structure and properties of the deformable titanium alloy BT6, which is used, in particular, in the aviation and space industries. The application of oxide coating by methods of chemical-thermal treatment (CTO) allows to compensate for the main drawback of the alloy – low wear resistance of the surface. The initial set of properties increases. The objects of research are titanium alloy BT6 and its oxide coatings. Two samples of the part with oxide coatings obtained by different technologies were compared. The first technology is alphanizing in finegrained graphite, the second one is alphanizing in a vacuum. The aim of the work is to find out the influence of two technologies of alphanizing on the structure and properties of the BT6 alloy. Alphanizing was carried out: 1) in fine-grained graphite at a temperature of 800 ± 10 ° C with exposure for 8 hours; 2) in an electric furnace at a temperature of 760–780 ° C in a vacuum of 10-1 – 10-3 mm Hg. for 1.5–2 hours. A study of the microstructure (light and electron microscopy) was performed. We used a microscope type Carl Zeiss Axio Observer A1m using a digital camera, adapter devices for converting an optical signal, a computer. Statistical processing was carried out according to the SIAMS700 program. Electron microscopic studies were performed using a scanning electron microscope (SEM) EVO 50 with an energy-dispersive microanalyzer INCA Energ 350. X-ray phase analysis was carried out using an X-ray diffractometer Shimadzu XRD7000, Japan (CuKa radiation, monochromator), in the following mode: range from 5 to 70 ° on a scale of 2θ, increments of 0.03°, scanning speed of 1.5 ° / min. Powders obtained from two types of coatings were investigated. The microhardness of the samples was measured on the DM8 microhardometer according to GOST 9450–76. The wear resistance of the alloy was assessed at a special laboratory installation. The phase composition and structure of the BT6 alloy after alphanizing were clarified. In the diffusion layer, the following points were detected: after alphanizing in graphite – TiO2 phases; Ti3O; TiN. After carbonation in vacuum – TiO2; Ti6O11. In the alphad layer, after processing in graphite, grains of α – solid solution, intermetallics Ti–Al-V, Ti–V and Ti–Al were detected; the alphanized layer contains more titanium after treatment in vacuum, and areas with 100% (at.) titanium have also been identified; the region of solid solution (α) and the intermetallics Ti–Al-V, Ti–V and Ti–Al are visible. The thickness of the oxidized layer is on average 103.6 μm (graphite), and in a vacuum – 66.8 μm. The average grain size in the layer is 17.2 μm (graphite); 6.0 μm (vacuum). It has been established that chemical-thermal treatment (alphanizing) contributes to a significant increase in microhardness in the diffusion layer. The hardness of HV580 (vacuum) and HV724 (graphite) was obtained on the surface. Alphanizing in graphite and in vacuum ensures the wear resistance of the product, but the best result is obtained after alphanizing in a vacuum. Both technologies improve the properties, but it is more profitable to carry out alphanizing in a vacuum, since in this case the process is carried out within 2 hours instead of 8 hours in graphite. Alphanizing (oxidation) provides wear resistance of the BT6 alloy, which contributes to the reliable operation of the product during operation.
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Study of the influence of hybrid filler on the strain sensitivity of a nanocomposite material
Статья научная
The reflector of spacecraft is in operation in the unfolded and folded position, thus an urgent task is to develop strain gauges that determine the position of the reflector. The paper presents a study of the influence of hybrid filler on the value of the strain resistance coefficient of a flexible strain-resistive element made of a nanocomposite material and describes the technological process of its manufacture using the vacuum infusion method. As hybrid filler, a composition containing an electrically conductive component (carbon nanotubes) and a solid component (silicon carbide), which promotes uniform distribution of the filler in the polymer matrix, were used. Using a rotational rheometer, the content of the carbon nanotubes (CNTs), at which the limiting level of viscosity for impregnation of glass fiber with a binder is achieved, was determined. The distribution features of the filler in the nanocomposite material were studied using a scanning electron microscope at the Krasnoyarsk Regional Centre for Collective Use of the Federal Research Centre KSC SB RAS. In the course of the work, the influence of the content of hybrid filler on the strain-resistive properties of the nanocomposite material was determined. The maximum values of the strain resistance coefficient were observed at the initial stage of the study (0.05 % tension): at 0.1 mm tension at a total length of 200 mm for the samples of a nanocomposite material with SiC hybrid filler of 1, 5 and 10 % and is 38, 40 and 40. The strain resistance coefficient of the nanocomposite material samples containing 1, 5 and 10 % SiC hybrid filler at maximum tensile (1 %) is approximately 19, 21 and 22 respectively.
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Study of the payload extraction trajectory heavy class carrier rocket
Статья научная
As the weight and complexity of the payload that needs to be launched into orbit increases, the relevance of rational trajectory selection to ensure maximum efficiency and minimum costs for delivering the payload to a given orbit increases. Rational choice of the trajectory of a heavy-class launch vehicle has a number of important practical applications. Firstly, it allows you to increase the payload capacity of the launch vehicle and reduce the cost of delivering payload to the target orbit. This is especially important in the context of the development of the space industry, when more and more companies and organizations are showing interest in launching their own satellites and other spacecraft in conditions of fierce economic competition. Choosing a rational trajectory for launching a payload into orbit will significantly reduce the cost of launches and make them available to a wider range of potential customers. Secondly, the choice of launch vehicle trajectory parameters is important for ensuring safety and minimizing risks during spacecraft launches. Thanks to the rational choice of trajectory, it is possible to reduce adverse impacts on the environment and eliminate the possibility of emergency situations associated with loss of control over the flight of the launch vehicle. Rational selection of launch vehicle trajectory parameters is a complex task that requires comprehensive research and consideration of various factors, such as aerodynamic parameters of the atmosphere, mass and characteristics of the payload (spacecraft), engine operating parameters, characteristics of the target orbit, features of the launch of the launch vehicle and many other factors. A more thorough and systematic study of the influence of these parameters will significantly improve the efficiency and reliability of launching spacecraft into orbit. Thus, the choice of rational parameters for the launch vehicle trajectory is a relevant and important topic for scientific research. Increasing the rocket's payload capacity, reducing the cost of delivering a spacecraft to a given orbit, and ensuring launch safety are tasks that depend on the chosen shape and parameters of the rocket's trajectory. Such research has important practical significance and can become the basis for the development of new technologies and methods in the space industry. The purpose of the study is to study and select rational parameters for the trajectory of a heavy-class launch vehicle when launching a payload. The main task is to determine the flight path parameters that will allow achieving maximum efficiency and accuracy in delivering the payload to a given orbit. To achieve the goal of the study, the analysis of various factors influencing the launch parameters of the spacecraft is required, such as structural and aerodynamic characteristics of the rocket, the influence of aerodynamic factors and the Earth’s gravitational field on the flight path. Taking these factors into account, numerical calculations were carried out on the basis of a system of differential equations of motion using a computer program created in the MAPLE software package. Based on the calculations, modeling of the shape and parameters of the launch vehicle flight path was carried out. Research results. During the study, the rational parameters of the trajectory of a heavy-class launch vehicle were selected. The calculations were carried out using numerical modeling of the parameters of payload launch trajectories, and the analysis of the resulting trajectories was carried out. Minimizing the rocket's flight time was identified as the main criterion for the rational choice of a trajectory, which allows increasing launch efficiency and saving energy resources. An increase in payload mass and minimization of fuel consumption were adopted as additional criteria. Conclusion. The procedure for choosing rational parameters for the trajectory of a heavy-class launch vehicle proposed in this work will improve the delivery accuracy and reliability of spacecraft launches at the stage of ballistic analysis when designing rockets. The results of the study have practical significance for the development of future heavy-lift launch vehicle missions and improving the efficiency of space launches.
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