Vol 24, No 3 (2023)

The purpose of this work is to create a method for solving the problem of optimal traffic distribution in a network using the contour data analysis method. In the first section of the work, the principle of converting any available network to a contour form is explained, and the case is considered both for networks without loss and for networks with losses. The second section shows in a general way the method of bringing the network in contour form to a system of non-linear inequalities, by solving which one can obtain a certain distribution of traffic in the system. In the final section, using the M/M/1/N queuing system as an example, the solution of the problem of optimal traffic distribution according to the loss minimization criterion is shown. The initial data for the task were the incidence matrix, service intensity and buffer dimension for communication channels. A feature of the proposed algorithm is the search for a contour matrix, for the compilation of which it is proposed to use loss edges as elements of the spanning tree of the graph, which allows you to immediately determine the contour matrix using the concept of a fundamental cycle of a graph. This approach to optimal traffic distribution reduces the number of variables used compared to the known methods based on loopless routes, and also does not require their preliminary search, since they are determined from the dimension of the incidence matrix of the simulated network graph.

In the present paper the method for the numerical solution of Poisson kinematic equations system that determine the evolution of the spacecraft position is proposed. The system of Poisson kinematic equations is used to determine the transition matrix from the coordinate system associated with the spacecraft at the selected time t₁ to the coordinate system associated with the spacecraft at the current time t₂. This matrix is used in the process of solving problems of determining a three-axis orientation of the spacecraft from the readings of the magnetometer using information about its angular velocities. The proposed method is based on replacing the derivatives of the desired functions in the Poisson kinematic equations by partial sums of series in the scaled Haar system. The partial sums of these series are generalized polynomials in the scaled Haar system. Hence these sums are step (piecewise constant) functions. The estimates of the proposed method error are derived, which reveal that in the case of the coefficients of the equations which are functions matching the Lipschitz condition, the absolute error in calculating each of the elements of the transition matrix from one coordinate system to another is the value O(N^–1) at N ® ¥, where N is the number of partitions of the segment [t₁, t₂] when constructing a grid of nodes involved in this method. It is proved that the complexity of constructing an algorithm for approximating the system of Poisson kinematic properties insignificantly exceeds the complexity of solving this system by Euler method, which has the first order of accuracy. The results of numerical experiments are presented, showing that in certain cases the Haar sums method gives an error that is much smaller than the Euler method, and is almost identical to the errors of the Euler – Cauchy and Runge – Kutta methods of the 2nd order, the complexity of which is approximately two times greater than the complexity of the Haar sums method.

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 equivalents. 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.

This article presents some of the main parameters of the netfold that affect the radio-reflective properties of the reflector and the technology for achieving these parameters by controlling the tension force of the netfold at various stages of manufacturing the radio-reflective surface of the reflector. The article also includes a brief overview of the existing and applied methods of measuring and controlling the tension force of the reticular reflectors of spacecraft at the RESHETNEV JSC enterprise and an analysis of their shortcomings as a result of their development is presented. A new method for monitoring and measuring the tension force is proposed, based on the local deformation of the mesh by the force of the pressure of the drawn air through its surface. The results of the development and testing of the method and prototype of a device for monitoring the tension force of the net are presented. The purpose of the study was to determine the operability of the device and the possibility of its further use to control the tension of the grid on working reflectors.

The developed method and the prototype of the device that implements it, allow you to quickly monitor the tension force of the net pole at any of its spatial position.

The prospects of possible use of the method in the rocket and space industry in the manufacture of radio-reflecting surfaces of spacecraft antennas are proposed and analyzed. According to the results of the conducted research, the dependence of the tension force of the mesh on the force of the pressure of the drawn air through the mesh is established. The need for further refinement of the developed device to improve the accuracy of obtaining measurement data has been identified.

Upon successful testing of the modified device for measuring and controlling the tension force of the net in the laboratory, further tests will be carried out at the stage of cutting the net and on the net in the reflector.

This article presents an analysis of the possibility of applying an alternative approach to testing the mechanical effects of the design of a small spacecraft for remote sensing of the Earth, which has an analog product that has passed a full cycle of ground experimental testing. However, despite the similar power scheme and the maximum borrowing of onboard equipment with minimal modifications, the spacecraft planned for testing has a number of significant differences. The application of the main alternative strategies in foreign and domestic practice in the ground-based experimental development of space technology is considered, their advantages and disadvantages are described. Some criteria for decision-making on the rejection of the use of traditional methods of ground-based experimental testing of space technology for mechanical effects are given.

The analysis of the normative and technical documentation adopted in the domestic industry in terms of clarifying the list of development tests of spacecraft, the assumptions of applying the computational and experimental method to the development of dynamic (vibration) strength and the analysis of the design of the spacecraft planned for testing in comparison with an analog product showed that the most preferred method of testing dynamic (vibration) strength is the strategy “protocol qualifications”. In accordance with the chosen strategy, a list of tasks was defined that will clarify the nomenclature of the development tests of the research object.

The article discusses the prospects of utilization of aerodynamic control to maintain the formation of nanosatellites of the CubeSat class. The purpose of this work is to estimate the limits of the application of active aerodynamic control to stabilize the relative motion of two CubeSat 3U satellites in a sun-synchronous orbit with a height of 570 km. A review of theoretical information about aerodynamic forces acting on artificial Earth satellites is carried out, within the framework of which models of the Earth's upper atmosphere are considered. Aspects of creating a differential drag force for nanosatellites as an active control actuating mechanism are considered. To study the orbital motion of satellites under the action of aerodynamic control using the General Mission Analysis Tool program, a group flight of two spacecraft was simulated taking into account the factors causing orbital disturbances. Based on the results of experiments, the dynamics of the inter-satellite distance was studied, and a conclusion was made about the possibility of using an aerodynamic differential force to achieve a stable relative motion.

With the increase in the number of launched spacecraft, such a direction as automation of spacecraft control processes is gaining popularity. One of these most important processes is the analysis of telemetry data during the operation of the spacecraft. Scientific and educational satellite of the Reshetnev Siberian State University of Science and Technology has been successfully exploitated in orbit and has been performing its scientific tasks for more than six months. The article considers a list of the main parameters analyzed by the operators of the Mission Control Center to assess the state of the ReshUCube-1 satellite. The composition and main functional characteristics of the equipment on the spacecraft are described. Qualitative indicators and quantitative limits for all described parameters are given, as well as their significance and impact on the functioning of devices and the entire spacecraft as a whole.

Complex computational and experimental studies substantiate rational modes of milling of complex contour equiaxed surfaces with high accuracy of shape, dimensions and roughness parameters. Bars made of nanostructured carbide composite (produced by extrusion of WC-Co-Al₂O₃ bimodal powder mixtures) with increased strength, crack resistance and heat resistance were used as a workpiece material for the manufacture of new original tool designs. The combination of these properties is a necessary prerequisite for the effective operation of the developed designs of multi-blade cutters at high cutting speeds and under conditions of variable cyclic loads. A more complex kinematics of the joint rotational movement of the tool during milling dictates the need for new approaches when assigning rational cutting modes. To obtain reliable calculation formulas, numerical experiments were previously carried out, including simulation of the processing process using the VisualStudio integrated development environment, which supports WindowsForms technology. The ability to display graphical 3D objects was implemented using an additional software product in the form of the Open CASCADE geometric core. Numerical experiments using MathCAD software products and based on the analytical provisions proposed in the work made it possible to evaluate the influence of cutting conditions, geometric parameters of the cutting part of the tool (profile and number of teeth), kinematics of relative movement in the “tool – part” system on the shape of surfaces and contour parameters (roughness obtained during milling. A technique, algorithm and program for the automated calculation of cutting conditions has been developed, which has been verified during full-scale experiments and the manufacture of complex profile parts from aluminum alloys for drives of aerospace products (in the form of a RC profile and parts of a pinion transmission of guidance mechanisms). At the same time, on the basis of a 3D model of products, control programs for CNC machines were created using MasterCAM. The practical significance and technical and economic efficiency of the proposed design and technological solutions is to increase productivity and reduce the complexity of processing (in comparison with the basic options) through the use of new multi-edge carbide tools for high-speed milling (including when processing composite materials).

The technology and technological equipment selection have to be substantiating for the modern materials for product the aircraft construction elements from polymer composition. The physical and technical characteristics of the material, ensuring the required accuracy of manufacturing equipment, as well as economic feasibility are the main criteria for choosing the material of technological equipment. The material equipment choosing is depends on the polymer composite construction technology manufacturing. The methodic of rigging materials selection for aircraft constriction elements production from polymer composition by vacuum infusion is considered in that paper. The results of a comparative analysis of typical materials equipment used in production are presented are considered in that paper. It is shown that the main criteria for a comparative analysis are: temperature, resistance to solvents, resistance to mechanical stress; maintainability; the value of the coefficient of linear thermal expansion; the stability of the geometry of the equipment and its tightness. It was showing that the metals and carbon fiber composite are the most appropriate for equipment manufacture that used in high temperature processes manufacturing composite components. The materials equipment algorithm choosing for polymer composite components manufacturing is considered in that paper. It is noted that the same material have to be choosing for equipment manufacturing as the carbon fiber or fiberglass polymer composite component. This allows to ensure the same CLTE, which is important in hot forming of the composite component, and to eliminate warping of the composite component during its cooling on the equipment. However, the equipment gelcoat processing has to be taking into account for specified accuracy achievement. The quantitative assessment of the economic feasibility of material equipment choosing is considered in that paper. It is shown that only a combination of technical, technological and economic factors makes it possible to substantiate the expediency of the rigging material used for the specific production of aircraft construction elements.