# 2017. № 95

## Mechanics

### Theoretical mechanics

Yudintsev V. V.

The article considers the spatial motion of the Yo-Yo mechanism. When employing the Yo-Yo mechanism for an angular velocity damping of an object performing complex spacio movement, the effect of this movement on the operation of this mechanism should be accounted for. As an option of Yo-Yo mechanism implementation, which assumes an object’s complex spatio movement, the author considers implementation of a mechanism as a part of autonomous docking module meant for capturing space debris’ objects. After the docking module separation from the space tow and its docking with a space debris object, it is possible to use the Yo-Yo mechanism for an object’s longitudinal angular velocity damping.

To analyze the spatial motion effect fn the object, on which the Yo-Yo mechanism is installed, on the movement of mechanism’s elements (wire ropes with loads) a mathematical model of the spatio motion was developed. Besides the angular motion of an object the model supposes the location of the plane of the wire ropes reel-out at a distance of an object’s center of masses, as well as the possibility of asynchronous movement of the mechanism’s wire ropes. To form the equations of motion, the Lagrange formalism was used. Equations were set down for each phase of the Yo-Yo mechanism motion.

The performance of the mathematical model is demonstrated by several numerical examples of the of the angular velocity damping of the debris’ object of a prolate and oblate type in terms of the ratio between the principal moments’ of inertia values. It is shown that the determining factor affecting the motion of the wire ropes of the mechanism is the transverse angular velocity of the object. The initial transverse angular velocity of the carrier leads to the exit of the Yo-Yo mechanism wires’ from the plane of the wire ropes reel-out, which can lead to disruption of its operation. The Yo-Yo mechanism can be used as part of an autonomous docking module to decrease the space debris objects’ angular velocity, such as spent orbital stages of carrier rockets with a longitudinal moment of inertia less than transverse moments of inertia.

Keywords: angular velocity, stabilization, tether system, Yo-Yo mechanism, spatial motion, space debris

Sokolov S. V.

The Adler–van Moerbeke integrable case is considered. The case of integrability founded in 1986 by M. Adler and P. van Moerbeke is the most complicated in the rigid body dynamics. It came due to papers A.S. Mishchenko and A. T. Fomenko dedicated to integrability of Euler equations on finite-dimensional Lie groups. As a result a new family of integrable quadratic Hamiltonians with additional integrals of fourth degree on so(4) was appeared. The existence of quartic additional integral is connected with special symmetry so(4) admitting real representation as direct sum of two copies of so(3). Euler equations on Lie algebra so(4) also describe the motion of a rigid body with an ellipsoidal cavity filled by a perfect incompressible vortical fluid around a fixed point in a case of uniform fluid vorticity. These equations as a model of the Earth’s rotation were studied by V. A. Steklov. Modern results for integrable metrics on so(4) and their mechanical interpretation can be found in many reviews.

After Poincare we consider rotations of rigid body with cavity, which contains inviscid incompressible liquid, about fixed axis. Such a case characterizes by additional integral of Lagrange type and corresponds to axially symmetric mass distribution.

We give one of the possible mechanical interpretations for the integrable case under consideration. We explicitly present the most convenient form of additional integral. Put some partial relations between principal values of inertia tensor we reduce our system to Poincare case. Connections with some classical integrable mechanical problems are observed. Conditions of physical realizability for this mechanical model are discussed.

Keywords: integrable hamiltonian systems, mechanical interpretation, Euler equations

### Fluid, gas and plasma mechanics

Kuznetsov M. M., Kuleshova Y. D., Reshetnikova Y. G., Smotrova L. V.

In the previous articles the authors formulated two theorems on the high velocity translational non-equilibrium in a shock wave of a one-component (ordinary) gas. It was noted herewith that the proofs of those theorems in case of shocked gas mixture required overcoming of several significant difficulties. The main difficulty consists in the fact that bimodal distribution of molecules velocities in gas mixtures cannot be used without doubt to determine the structure of a shock-wave, as it was done for the ordinary gas. As a rule, the area of applicability of the classic Tamm – Mott-Smith bimodal distribution with constant approximation of the auxiliary macroscopic velocities and kinetic temperatures for the groups of molecules in the supersonic and subsonic “wings” of such distribution is limited by the small values of concentrations of one of the mixture’s components. Only in this case it is possible to keep all the advantages of the bimodal approximation of partial distribution functions in binary gas mixture to obtain a simple analytical solution for shock wave structure. That is why obtaining necessary and sufficient conditions for high velocity translational non-equlibrium for arbitrary values of gas mixtures’ component concentration becomes much more complex.

The paper presents rigorous formulation and substantiation of these conditions.

These conditions are applicable to the case of variable auxiliary approximation macro parameters of “hot” wing of a binary gas mixture bimodal distribution. At the same time, the values of auxiliary macroscopic velocities and kinetic temperatures for groups of molecules in subsonic «wing» are kept constant. In binary gas mixtures with distribution functions for both the light and heavy components three types of functions of molecules’ pairs distribution throughout their relative velocity module exist. These functions are: G(ll) is the distribution function of pairs inside a light-light component, G(lh) the function of molecules’ pairs of light-heavy component and G(hh) is a function of molecules’ pair inside a heavy component. The numerical calculations of the corresponding “overlap” effect of bimodal distributions for pair of molecules was performed for a special case of small concentration values of heavy component in binary gas mixture (Rayleigh gas). It is known that in Rayleigh gas this effect for function G(hh) is most noticeable. While its computation, the molecules’ rotating degrees of freedom were accounted for.

Keywords: kinetic, equation, non-equilibrium, gas mixture, shock wave

Shchukin A. V., Khabibullin I. I., Il'inkov A. V., Takmovtsev V. V.

This experimental study is aimed at the searching an easy-to-manufacture shape of the previously submitted by the authors highly efficient surface thermal exchange intensifier of a separation type with high functioning intensity of large-scale vortex structures, namely two-cavity diffuser dimple. This dimple, placed in an array of dimples demonstrated a higher level of heat dissipation, exceeding more than three times the heat dissipation while a smooth plate flow-around. It was accepted as reference. The high level of thermal effectiveness of this dimple is associated with implementation of optimal relative height of the rib separating its hollows, the diffuser shape of its hollows for the backflow, as well as with their slope in plan view of the relative direction of the main flow.

Based on visualization of the flows and determination of the pressure coefficient Cp in the bottom part of the studied dimple’s variants the experimental data was obtained on its shape in terms of the self-organizing large-scale vortex structures.

The ways of geometric shape of the two-hollow diffuser dimples’ simplifying were studied, and, hence, its manufacturing technology under condition of preserving the intensity and continuity of large-scale vortex structures functioning.

The authors established that without the hollows’ separating rib, when the entry edge is described by the line of radial contour, two-hollow dimple passes into the class of one-hollow dimples with permanently functioning single large-scale vortex structure. The rarefaction level, however, in the in the dimple’s epicenter decreases compared to the two-hollow diffuser dimples.

The performed comparative studies revealed the existence of the rational geometry of one-hollow diffusor dimple of a separation type ensuring permanent functioning of vortex structures. This dimple allows much simpler manufacturing technology compared to the two-hollow diffuser dimples. However, it is inferior to the latter in the intensity of large-scale vortex structures. Thus, following the two-hollow diffuser dimple structure it is necessary to explore and find such installation angle relative to the main flow that provides maximum vortex intensity. This is essentially the algorithm for further optimization of the easy-to-manufacture one-hollow diffuser dimple of separation-type studied here.

Keywords: visualization, dimple, turbulent flow, pressure coefficient, self-organizing large-scale vortex structure, manufacturability

Pozhalostin A. A., Goncharov D. A.

The authors considered the case of axisymmetric parametric oscillations of an ideal fluid filling the cylindrical vessel. They obtained the differential equation of parametric oscillation damping with account for the main parametric resonance, as well as numerical values of the variables comprising this equation.

It was shown that could initiate small oscillations of the system, with the corresponding values of the modulation index. The value of the modulation index is determined by Van der Pol method. The problem was considered in the linear formulation, with fluid movements were assumed small. The velocity potential satisfies the Laplace equation in a cylindrical domain. On the wetted surface of the vessel the conditions of impermeability were met, while on the free surface of the liquid the linearized boundary condition was met. The velocity potential, in accordance with the Fourier method, was represented as a series of the hyperbolic functions, Bessel functions of 1st order and the time factor.

The equation for the parametric oscillation was obtained for the time factor from the equation for the velocity potential. The kinetic energy of the mechanical system was determined by the gradient of the velocity potential. The reduced inertia coefficient of the system was calculated by the Green’s function method. The viscous resistance force in the fluid was assumed proportional to the first degree of speed. The fluid velocity was defined as the gradient of the velocity potential. Then we compose the Rayleigh dissipative function. Expression for the potential energy was composed. We composed the Lagrange equation of the II-nd order with account for the dissipative forces, due to the presence of viscous friction in the mechanical system under consideration.

The resulting differential equation is a second order differential equation with a small parameter. The damping coefficient implies experimental determination. We indicate references to the papers, which present the numerical values of the damping coefficient. Further, the damping coefficient was assumed as known. The averaging was performed, and the border region of parametric resonance instability was sett. The conclusion on the existence of the small oscillations of the respective values of the modulation index was made.

Keywords: parametric oscillation, fluid, damping, modulation index

Kuli-zade M. E., Skorokhod E. P.

Multi-level physicochemical kinetics at present remains relevant to General theoretical issues of spectroscopy of low temperature plasmas and optical diagnostics in the framework of radiation plasmodynamics, in particular for the device-specific debug modes, where “working fluid” is the Xenon plasma. When composing kinetic equations, multiple radiation constants (Einstein coefficients) are necessary.

Selection of the model itself is predetermined by considering the xenon ion level scheme, recorded in LS-relations. The level scheme composed and supplemented by the quantum-defect approximation allows calculate the transitions that are absent in the reference edition [12].

Six models of probabilities' calculations including the radiation transitions 5d ‒ 6p relating to the lowermost levels are considered. The radial integrals required for calculations of Aki /106 transition probabilities were calculated by the the Bates–Damgaard method using two different values of the effective quantum number: a specific level, and for the entire configuration as a whole. They were also calculated according to the of Hartree–Fock–Slater method. Angular dependencies for these three methods were performed in approximation of the LS–relation and in the framework of intermediate relation.

The article presents the results of the above-mentioned six quantum-mechanical models for 5d ‒ 6p 314 dipole transitions. A comparison with experimentally obtained results of other authors was made [18–21, 24, 16].

The reference data includes also the values of the photo-transition probabilities obtained from the experimental data on the line shifts corresponding to the quadratic Stark effect [22].

The Einstein coefficients differ within a few orders of magnitude. Thus, for the transition 6p 4P5/2 → 5d 4D7/2 with the wavelength of 605.115 nm, the probability calculated by him in Bates‒Damgaard approximation with the use of a relation gives the value of Aki /106 = 0.48 with account for the intermediate relation of 1.5; according to the Hartree-Fock-Sleter method in the framework of the intermediate link ─ 0.041. The other authors give: 20.5 ─ [19]; 52. ─ [20]; 21. ─ [16]. The value obtained from experimental data on the lines' shifts corresponding to the quadratic Stark effect [22] is Aki /106 = 52.9.

The presented Einstein coefficients calculations results from the 5d levels supplement the reference data of the 6s ‒ 6p photo-transitions probabilities [15].

Keywords: Xe plasma, XeII radiation transition's probabilities, Einstein coefficients of XeII ion, optical diagnostics

### Dynamics, strength of machines, instruments and equipment

Blagodyreva O. V.

The article studies the aeroelastic stability of a cruise missile performing longitudinal short-period motion in incompressible airflow. The missile is modeled using a beam structure, including the fuselage, two straight outer wings and flight control surfaces — elevators. The wing of the missile is considered as an elastic beam operating in bending with transverse shear and torsion, while the fuselage and the control surfaces of the missile are considered as rigid. It is assumed, that the elastic vibrations of the wing panels occur according to the hypothesis of flat sections. Control drives with wiring are considered disconnected, and their effect on the structure is replaced with the unknown control forces. Aerodynamic loads are determined based on the quasi-stationary theory of plane-parallel flow cross sections of the wing. The longitudinal compression of the missile body under the effect of thrust force of an engine is also accounted for.
The equations of small vibrations of the system are represented in the form of Lagrange equations of the second kind in generalized coordinates. The generalized coordinates are considered as normal coordinates, representing the movement over the eigenvibration mode of a free structure with fixed operating controls.
Based on the Ritz method the unknown functions of transverse displacements of the axis of the fuselage, the transverse displacements of the axis of the wing and the angle of twist of the wing are presented in the form of expansions along the generalized coordinates.
For a more accurate study of the behavior of a wing’s flexural-torsional oscillations the finite element method (FEM) was used. The wing is separated into a number of compartments — finite elements (FE), within each the geometrical, stiffness and mass properties are assumed to be average and constant.
The article presents a comparative calculation of the flutter of an elastic missile using the Ritz method and the finite element method (FEM). The graphs of the variation of natural frequencies of the missile depending on the changes of the flight speed and engine thrust power are plotted. The critical speed and the stability region of the missile were defined respectively for each method.
All the calculations were performed with the software “Wolfram Mathematica 8”.

Keywords: aeroelastic vibrations, flutter, Ritz method, finite elements method, flying vehicle vibrations modeling

Gnezdilov V. A., Grishanina T. V., Nagornov A. Y.

Long frameworks (lattice beams) are often used in different building structures (cranes, masts, bridges, pylons of electric air-lines, etc.), as well as in space structures deployed or assembled on orbit. In some cases such structures can undergo to large elastic displacements with large angles of the bar turns. At the design it is usually required that there must not be any irreversible deformations and damages (cracks) in the structure at the maximum operational loads. Statically indeterminate frames allow elastic buckling of some compressed bars with moderate finite deflections limited by the relative longitudinal displacements (contaction) and the turn angles at the joints which connect the buckled bars with the others.

In this work the new approach is developed for solution of geometrically nonlinear problem of deformation for a plane frame system with large displacements and turn angles taking into account buckling of some bars with moderate elastic deflection.

Every bar of the system rigidly connected in the movable joints with the other bars and subjected to tension or compression and bending in considered as a beam finite element.

Large displacements and turns of bar in the structure are described by four unknown coordinates of the bar ends (the joints it connects) and by three supplementary generalized coordinates. Two of them represent the relative turn angles of the bar ends and the third — its deflection due to moderate elastic bending. Such representation of describes sufficiently exactly the possible instability of the bar with moderate buckling deflection.

The nonlinear equilibrium equations in displacements for the system loaded by the forces and moments applied in the joints are obtained by use of the virtual work principle. These equations are solved numerically. The example of calculation of the system behavior subjected to the increasing load with the successive buckling of some compressed bars is considered.

Keywords: frame systems, geometrically nonlinear deformation, large displacements, buckling

## Aeronautical and Space-Rocket Engineering

### Aerodynamics and heat-exchange processes in flying vehicles

Garipova L. I., Batrakov A. S., Kusyumov A. N.

The main rotor trimming is one of the important tasks of helicopter aerodynamics. The aim of trimming consists in determining the values of balancing angles (total and cyclic pitch angles) of the main rotor, which allows minimize longitudinal and lateral moments, as well as vibration load. A simple approach to the main rotor's balancing angles determination is based on the Blade Element Momentum Theory (BEMT), based on steady-state aerofoil aerodynamics. However, while straight and level flight the helicopter's blade sections motion bears a complex oscillated character. For this reason, aerofoil performances can differ significantly from its steady-state equivalents.

The aim of this research is numerical simulation of the oscillating NACA 23012 aerofoil flow-around to study the effect of dynamic flow conditions corresponding to a forward flight mode on the values of the main rotor trimming (total and cyclic pitch) angles. Numerical simulation was performed using HMB code (Liverpool and Glasgow universities) based on the Unsteady Reynolds averaged Navier–Stokes equations (URANS) with k‒ω SST turbulence model.

The results of study revealed that the dynamic condition leads to significant changes of the aerofoil aerodynamic characteristics and the main rotor trimming angles compared to the steady state formulation. Based on these results a correction can be employed to improve the simple BEMT approach accuracy.

Keywords: computational aerodynamics (CAD), URANS modeling, rotor trimming angles

### Design, construction and manufacturing of flying vehicles

Klyagin V. A., Petrov I. A., Shkurin M. V.

Avionics’ layout on a modern aircraft is a complex engineering task. A quality solution to this problem currently became potentially possible by using PC. However, at this moment, existing application programs are based on heuristic methods [1, 6, 7] or on analytical solution [4, 5] of the problem. They are still not widely used. One reason for this is the lack of information about the patterns of avionics’ distribution. Statistical analysis will highlight patterns that will become the basis of new methodology. Statistics will clarify the existing methods as well.

The first necessary step for the analysis -is gathering information on the layout diagrams of aircrafts in context of avionics’ placement. Combat aircraft of the second half of the twentieth century were studied. The most common source was the photos of real aircraft, showing the avionics (e. g. open avionics bays).

Next step consisted in calculating the total number of items of avionics with the differentiation of the installation type. This work assumes the following types of installation:

• Single mounting;

• Single racks;

• On the frames or multiple racks.

Thus, the article presents the analysis of the avionics’ placement on combat aircraft of the second half of the XX century according to the installation type for the various classes and the date of the first flight. The results show that for all classes of the aircraft, the vast number of blocks were arranged on the shelves. Single mounted makes approximately 9.5% of the components. Only two out of the 35 types dominated by point installation. Also seen a number of patterns such as on devices with smaller dimension is slightly higher relative number of blocks with a single installation. Based on the work a conclusion was made that for the automated layout method development it is useful to represent the location of the avionics in the planes.

Keywords:

Ngo Q. T., Solenaya O. Y., Ronzhin A. L.

The problem of increasing the operating time of unmanned aerial vehicles in autonomous missions is considered. Approaches to charge or replace on-board batteries on the accompanying robotic platform are analyzed. The key issues remain questions of the autonomous landing of the unmanned aerial vehicle on the platform and the way of servicing battery. The available prototypes of service robotic platforms are differed in the complexity of internal mechanisms, speed of service, algorithms of joint operation of the platform and unmanned aerial vehicle during the landing and maintenance of the battery. Autonomous landing of aerial vehicle in modern studies is considered not only on a fixed platform, but also on a mobile platform that moves in various environments. Landing unmanned aerial vehicle on a service charging station is realized with the help of various systems of navigation and analysis of the surrounding area. A battery-replacement system significantly reduces the preparation time of a multi-copter for a new flight and increases the total number of multicopters that are simultaneously in an autonomous mission. The charging system has a lower cost compared to the battery replacement system by minimizing the mechanical components of the structure. Modern means of navigation and technical vision ensure the landing of UAVs on the ground robotic platform can be performed with high accuracy in indoor environments. In outdoor application, taking into account the influence of weather conditions, the landing error is much higher. To communication the mobile platform to unmanned aerial vehicles, wireless means are mainly used to ensure their coordinated work during landing and take-off, and also to control several vehicles in the queue for charging. The purpose of this study is to develop a multifunctional mechanism for connecting a multi-copter to a ground-based robotic platform that performs the functions of their transportation and maintenance. Based on the results of the analysis, a classification of existing systems installed on robotic platforms for the maintenance of batteries is made. A further study will be devoted to the development of the requirements for the design of a multicopter maintenance system on a projected ground platform, taking into account its functional purpose, as well as the creation of software and hardware for the joint operation of multicopters and a platform.

Keywords: unmanned aerial vehicles, UAV, multicopters, batteries, wireless charging, mobile platform, collaborative robots

Rebrov S. G., Golubev V. A., Golikov A. N.

The article reviews the main results of research aimed at introducing laser ignition for rocket engines using oxygen-kerosene fuel. The purpose of the work was to determine the operational parameters of the laser ignition system and the ranges of the composition and fuel rate of the fuel mixture to ensure reliable ignition in igniters, rocket thrusters and sustainer rocket engines. The method of initiating a spark of optical breakdown in area with favorable ignition characteristics of the mixture was used as a method of ignition. The laser radiation was focused either in the volume of the mixture or near the metallic surface for that.

The tests covered a wide range of changes in the operating parameters of both combustion chambers and ignition systems. Laser ignition was successfully tested on chambers, starting from a small volume of several cm3 for igniters and low-thrust engines to the sustainer chamber of the engines of the first, second stages of the Soyuz launch vehicle with a volume of 65 dm3. The tests were carried out using mixtures of both a reducing composition at a value of oxidizer-to-fuel ratio to 0.1 and an oxidizing composition with a value of oxidizer-to-fuel ratio up to 11. Laser parameters were also ranged for output pulse energy from 1 mJ to 100 mJ and for pulse repetition frequency from 10 Hz to 100 Hz.

The complex of carried out works made it possible to develop the technology of laser ignition of oxygen-kerosene fuel with the determination of the necessary operating parameters of fuel mixtures and the ignition system itself with regard to rocket technology: igniters, thrusters, large combustion chambers for rocket engines with thrust up to 18 tf. Guidelines for introduction of laser ignition for large size rocket engine combustion chambers have been developed on the basis of experience gained. It was also shown the feasibility of laser ignition of large-sized oxygen-kerosene chambers using small-sized lasers mounted directly to the combustion chamber. These results allowed to propose a scheme of laser ignition system to replace the existing pyrotechnic for the first and second stages of the Soyuz launch vehicle, based on the use of micro lasers with fiber radiation delivered to them from a reusable stationary diode pumping station placed on the launch site.

Keywords: laser ignition, optical breakdown, combustion chamber, rocket engine

Dolgushev V. G., Ionov V. A., Kun N. V., Matveenko A. M.

Resiliency is essential for operation of an aircraft during its lifetime. In modern aircraft hydraulic system a specified level of fail-safety in the design process is ensured by the initial selection of the structure and parameters of the system, which cannot be changed during the flight.

The fail-safety can be improved by increasing various safety factors and redundancy of elements. Nevertheless, in its turn, it leads to the system weight increase. However, the increase of fail-safety without weight increase is possible through adjustment of internal parameters by changing operation modes (e.g., unloading in cruising flight and the crossing of the settings at high loads or failure in the system).

The decisive factor is the smaller weight of the system, giving the opportunity to increase the combat effectiveness of the aircraft either due to the smaller mass and therefore greater maneuverability, or to the larger mass of ammunition.

For large passenger aircraft, using forced modes to compensate for failures of pipelines, implementation of titanium alloys and high rated pressure level will allow create a hydraulic system with a significantly smaller mass.

A mixed system, incorporating centralized hydraulic system and stand-alone drives is expedient to be applied on the military-transport aircraft, which due to the extra mass is possible to achieve high survivability.

Keywords:

Borisov A. E., Leont'ev V. A., Novak V. N.

In this paper a new concept of a high-speed main rotor of a single-rotor helicopter is considered. A new concept of a high-speed main rotor is to use the design rotor hub, which allowing to obtain a natural frequency of flap motion blade lower than the rotational speed of the rotor. Reduction of the natural frequency, as well as its increase (screws with positive flapping-hinge offset or rotors with elastic fastening of blades) leads to a phase shift of the flapping motion of the blades. The phase shift of the blades flapping motion leads to an increase the angles of attack on the advancing side of rotor and to a decrease in the retreating side, and thereby detracts from the appearance of a stall at high flight speeds.

The analysis of the effect of its design features on aerodynamic characteristics is carried out. Presented are the equations of the flapping motion of main rotor blades with negative offset of flapping hinges, as well as of the moment on the rotor hub. The paper also considers the method for calculating the coefficients of the first harmonic of the blade flapping motion and the expressions for calculating angles of attack in blade sections. The analysis of the operation of rotors with both negative and positive flapping-hinge offset is carried out, an estimation of the influence of some rotor parameters on angles of attack of blade sections is obtained. Also presented are the results of calculating such rotors that illustrate the possibility of increasing angles of attack on advancing blades and reducing them on retreating blades by means of the swash plate deflection.

Keywords: angles of blade attack, natural frequency of flap motion, flow stall, main rotor hub

### Thermal engines, electric propulsion and power plants for flying vehicles

Minin N. V.

In the report is considered the problem of creation and study of design of the new type of small-sized jet engine with free-piston membrane supercharger of a fuel mix in which the part is used for internal cooling heat-stressed mobile units of the engine and reception of work of compression of the compressor membrane type.

The scheme of the new energy installation is developed. Thermal and thermodynamic calculations by technique of the authors are made. The basic constructive sizes of the engine are calculated and the problem of cooling of piston unit by the charge of a fuel mix of the engine that has led to partial regeneration of heat in a cycle to decrease in the specific charge of fuel and increase in altitude is solved.

The maximum power of the power plant is limited by the working diameters of the piston group, its mass, frequency of operation. Examining the design parameters of the engine raises questions on the solution, for minimum capacities — the task of maximum piston operation speed at a speed of up to 30 m/s, a constructive and technological solution to the problem of avoiding traditional spring-ring sealing methods and switching to a smooth pair, Liquid wedge. And also complete withdrawal from the rotational movements of the crank drive, use in the atmospheric engines of the membrane compression system, with direct massless drive from the reciprocating motion of the lightweight piston group and the group of damper compression in the cycle. And the use of synchronizing mechanisms synchronization of moving pistons, cyclically operating without compression loads.

Based on the developed methodology, the main parameters of the aircraft with a starting mass from 1 to 100 kg have been evaluated and it is shown that the proposed new variant of the combined remote control has a weight efficiency comparable with known developments and deserves further more thorough research. Based on the preliminary technical and economic analysis of the lightweight UAV, it is shown that the proposed version meets all the basic requirements of the current stage of development of launch vehicles.

Keywords: thermal processes, pulsating air jet engine, free piston supercharger

### Control and testing of flying vehicles and their systems

Afanas'ev V. A., Monakhova V. P., Muhina S. D., Versin A. A., Nazyrova O. R., Bolkhovitin M. S.

The article presents the results of the structural components' development of the experimental workbench for calibration of receivers of total and static pressures in the jet of a gas flow. The speed range of the controlled gas flow at the subsonic nozzle edge is regulated from λс = 0.3 to λс = 1.0. The necessity of this workbench development is associated with the fact, that pressure receivers' designs are developed individually for various placement locations along the path of the gas turbine engine compressor.

The basic requirements that had to be met while the development of the stand are as follows

–  The relative velocity of the gas stream λ in the placement of the receiving holes of the comb should be measured with an accuracy of ±0,01;

– The numerical values of the pressures in the pneumatic circuits of the comb should be stay within ± 0,3% of measured values;

– The linear and angular positioning parameters of the receiving holes of the comb under study should be determined with an accuracy of ±1 mm and ±0.5 degrees respectively.

The following calculations were performed in this work:

– Calculation of the subsonic nozzle profile;

– Design of the diffuser.

Calculation of the subsonic nozzle profile allows obtaining a controlled airflow at the outlet with a uniform velocity value in the cutoff of the nozzle. The pointing device allowing the smooth movement of the inlet orifice of the studied receiver with the possibility of speed adjustment, and position it on the geometric axis of the nozzle, as well as change the angle between the flow velocity vector and the axis of the inlet orifice within the limits of ± 45° in the tangential and meridian planes.

The article also presents a calculation of the diffuser design meant for for converting the kinetic energy of the flow into static pressure.

Keywords: calibration workbench, pressures inlets, nozzle, receiver, diffuser, pointing device

### Dynamics, ballistics, movement control of flying vehicles

Konstantinov M. S., Min T.

The spacecraft flight from the low Earth orbit to the geostationary orbit is considered as a typical transport operation. The optimization of the interorbital flight, the control laws for the movement of the spacecraft during the flight and the flight trajectory are carried out. The main goal of the work is to provide the users who analyze the interorbital flight, the possibility of correct and simple estimation of the characteristic velocity for the transport operation in question.

When optimizing the flight from the low Earth orbit to the geostationary orbit, a method based on the Pontryagin maximum principle is used. The problem of optimizing the trajectory reduces to the boundary-value problem. The boundary-value problem is solved using the evolutionary strategy with the adaptation of the covariance matrix.

The characteristic velocity for the operation is considered as a function of the specific impulse of the engine and the initial reactive acceleration. Specific impulse of the engine is considered in the range of 600-900 s. The initial reactive acceleration is considered in the range 1.25-12.5 mm / s2.

The results of the analysis are presented in the tables form of the characteristic velocity reactive as the function of initial reactive acceleration (the range 1.25-12.5 mm/s is considered) and the specific impulse (range 600-900 s). Such a range is typical, for example, a solar thermal rocket engine. Another result of the work is the analysis of the optimal flight, the analysis of the properties of the optimal flight and the optimal control law for the movement of the spacecraft during the interorbital flight.

The results of the work can be used to analyze the space transport systems for interorbital spacecraft flight with the specific impulse of the engine in the range of 600-900 s.

The characteristics of the optimal flight scheme are analyzed. The optimal flight path contains three characteristic sections. On the first of them, the SC engine operates at the perigee section of the multi-revolutions trajectory. In this area, the eccentricity of the orbit increases (the radius of the apogee increases, with a slight increase in the perigee altitude). The inclination of the orbit decreases a little due to a small yaw angle (less than 2 degrees). At the end of the first segment of the flight path, the radius of apogee appears to be substantially larger than the radius of the geostationary orbit. On the second part of the trajectory, the engine operates at the apogee sections of the trajectory. In this case, the radius of the perigee of the trajectory increases actively, the radius of apogee hardly increases. The yaw angle on the flight path provides an effective reduction in the inclination of the orbit. At the beginning of the section, the yaw angle value is large, the optimal yaw angle decreases in each revolution. At the end of the second section of the trajectory, the inclination of the orbit is practically zero. On the third part of the flight path (the duration of the section is approximately two revolutions of the trajectory) the active sections are located in the vicinity of the perigee of the orbit. The engine breaks the spacecraft, providing zero eccentricity of the final orbit.

Keywords: spacecraft, geostationary orbit, optimal trajectory, characteristic velocity

Lunev E. M., Neretin E. S., Budkov A. S.

This work is devoted to the analysis of the existing algorithms of trajectory control and their updating up to the level of 4-D area navigation (4D-RNAV) for further implementation while developing prospective automatic control systems for en-route flight.

With the advent of satellite systems, navigation has changed qualitatively in the direction of increasing accuracy. However, navigation is only one of the constituent parts of the overall process of flight execution. It should be considered thereupon in general concept, namely, communication, navigation, surveying and organization of the air traffic, developed by ICAO in the 1980-s. The navigation concept of the future developed by ICAO is based on the area navigation.

The area navigation principle allows an aircraft to execute a flight on any desired path and thus realize the advantages of navigation of higher accuracy in improving the structure of air area. It leads to simplifying of air traffic servicing, and foremost decrease of aircraft operating costs.

The planned flight path can be specified not only in the horizontal plane in the form of a route, but also in the vertical plane, by specifying the flight heights of the waypoints, angles or gradients of the trajectory inclination. In addition, a space-time trajectory can be set, when for some points the time of their flyby is specified. In accordance with the dimension of the «space» in which the guidance is carried out, the area navigation is subdivided into three types:

– 2D-RNAV ‒ two-dimensional RNAV in the horizontal plane — LNAV (Lateral Navigation). Sometimes, using a literal translation, it is called lateral navigation, since the guidance is provided only by lateral evasion;

– 3D-RNAV ‒ three-dimensional RNAV in the horizontal and vertical planes. For navigation in the vertical plane, the abbreviation VNAV (Vertical Navigation) is used;

– 4D-RNAV is a four-dimensional RNAV in the horizontal and vertical planes plus the solution of the problem of regulating the speed of flight for passing points of the route or arriving at the aerodrome at a given time. Zone navigation by time is abbreviated as TNAV (Time Navigation). [3]

The problem of area navigation implementation consists not barely in ensuring the flight on an arbitrary path, but in ensuring its accuracy according to the requirement set in the given region. In modern aero Thus, the issues of area navigation were closely interleaved with RNP problems. They were so closely interleaved that these two ranges of issues were incorporated into a single ICAO document «RNP Manual» [1].

Today RNP is considered as a tool for flight technical and regulatory control with RNAV application.

Depending on the strictness of requirements to the accuracy of the specified path following, and the type of functional requirements to onboard equipment the following notations are widely used:

– B-RNAV (Basic RNAV) — the main (basic) area navigation;

– P-RNAV (Precision RNAV) — precise area navigation;

RNAV is considered by ICAO as the main type of navigation of the future, since it has a number of undeniable advantages over conventional, traditional navigation.

Keywords: aircraft, Area Navigation (4D-RNAV), trajectory control, modeling, lateral movement stabilization, lengthwise passage control

### Innovative technologies in aerospace activities

Sypalo K. I., Medvedskiy A. L., Babichev O. V., Kazarinov G. G., Kan A. V.

The article presents the methodology for creating demonstrators of technologies in aircraft building, based on the harmonization and use of the existing system of national standards.

As one of the mechanisms of realization of a control system of research works, it is supposed to use a scale of assessment of technology readiness level. The technology readiness level scale is taken as a basis for gradation of development stages of new technologies by many departments and the organizations, both in the USA, and in some other countries. The classification used reflects a condition of research programs depending on the current technologies readiness level that simplifies control for developers and customers control over the course of research works and the choice of the technologies, most ready for industrial introduction.

The scale of technology readiness level represents the formalized assessment of degree of the technologies maturity for practical use when developing from the idea to a prototype of the complete system tested in the conditions close to real.

On the grounds of the system engineering tools which are based on the formalization of measurements of technologies readiness levels, and use of the existing national standards base — state standard specifications — the methodology of creation the technologies demonstrators of technologies in aircraft industry has been offered.

The presented methodology of creation of technologies demonstrators in aircraft industry solves a problem of integration of the existing system of national standards with the world practice of quantitative and quality standard of the developed technologies.

Harmonization of standards on carrying out research and development with world practice and also use of quantitative and high-quality indicators of technology readiness level scale, including methodology for creating of aircraft technology demonstrators, will allow to reduce significantly risks during creation of the aircraft equipment.

Keywords: technology demonstrator, scale of technology readiness level, complex scientific and technological project, problem-oriented project, technological project, technological advance

## Instrument making, metrology, information and measuring equipment and systems

### Instruments and measurement techniques according to measurement types

Kotel'nikov V. A., Kotelnikov M. V., Filippov G. S.

Flat remote and near-wall probes are widely used in probe diagnostics of rarefied plasma (static and dynamic). They are installed on hypersonic aircraft and space satellites in order to study the radiophysical parameters near their surface. Flat probes can be installed both parallel and perpendicular to the flow velocity in the rarefied plasma streams. Nonlinear border and edge effects occur at the edges of a flat probe, which have a significant influence on the probe current. The boundary effect is associated with the thickening of the lines of force of the electric field at the boundary of the active surface of the probe. The final effect arises under the influence of a directed flow velocity if the probe is oriented parallel to the flow velocity. Charged particles enter the space charge layer of the probe. They can fly through the probe line and not contribute to the probe current, depending on the potential of the probe and the velocity of the plasma flow.

The present article is devoted to an analysis of the effect of these nonlinear effects on the probe current. In the literature, there is insufficient information on this issue, the technique for conducting a probe experiment, and processing probe characteristics, taking into account the border and edge effects.

The physical and mathematical models of the problem are formulated. Extensive computational experiments were carried out. Conclusions and recommendations useful for the practice of probe measurements are made.

Consider a probe in the form of an elongated strip of width 2rр and potential φρ. The directional plasma flow rate U is parallel to the probe surface and perpendicular to its short side (fig. 1).

a) the probe is oriented along the flow,

b) the probe is oriented towards the flow;

1 - probe surface,

2, 3 - the surface of the guard electrodes.

If the characteristic size of the probe is 2rр≥103rd, (rd is the Debye radius), then the effect of the border and edge effects can be neglected and the Bohm formula can be used when processing probe characteristics. If 2rр<103rd, then the arising nonlinear effects can be removed by constructing the guard electrodes in the form of strips along the elongated sides of the probe, separating them from the probe by thin insulating layers. In this case, the Bohm formula is also used. The width of the guard electrodes is calculated in numerical experiments and is presented in the work in the form of graphical dependences U, rp and the potential φρ (fig. 2, 3).

If the probe in the form of a strip is directed by its active surface towards the flow, the border effects is absent, and the edge effect is analogous to the case of parallel flow around the probe. If 2rр≥103rd, then the Langmuir formula, which describes the ion current with concentration, flow velocity and probe potential, is valid. If 2rр<103rd, then guard electrodes are placed, which remove the effect of edge effects. Their size is much smaller than with parallel flow around the probe. Recommendations for choosing the width of guard electrodes are given in the work as a function of the characteristic parameters of the problem.

If flat probes of another geometry (square, disk, etc.) are used, it is recommended to take their characteristic size 2rр>103rd. In this case, the role of border and edge effects is small and one can use the recommendations stated above for probes in the form of an elongated rectangle.

Keywords: probe diagnostics, border effect, edge effect, rarefied plasma, dense plasma

### Instruments and measurement techniques

Vernigora L. V., Pichkhadze К. М., Sysoev V. K.

Spacecraft (SC) optical observation is one of the main method of SC tracking and measurement of their parameters.

The successful development of semiconductor emitters' technology allowed gaining the high-efficient laser diodes with high capacity level at low mass and dimensions parameters. This permits to develop optical beacon systems for spacecraft navigation based on these diodes.

Firstly, these are optical beacons installed on planetary landing stations, such as Luna-Glob/Luna-Resource-1 (and in the future – on modules descending to the Martian surface). Installation of such beacons allows high-accuracy location of the landing stations with the help of spacecraft optical TV equipment and ground-based tracking stations. Being connected to the radioisotope power source they can be used as beacons for future lunar missions.

The article describes the developed algorithm for semiconductor light sources' selection necessary to solve the problem of optical beacons design for space expeditions:

1. The beacon's radiation should be reliably registered by the receiving optical system. This requires the following steps:

‒ Determination of the necessary emission power. Selection of the emitter's power is stipulated by sensitivity of the receiving ground-based optical system, distance to the spacecraft, the light source radiation angle and, of course, the time of exposure;

‒ Selection of the semiconductor light source allowing creation of low divergent light beams, which is necessary for transmission of this radiation for long distances;

‒ Determination of necessary emission spectrum of the semiconductor light source (rather wide emission spectrum of the semiconductor light source is allowed for “space-to-space” system). In the case of “Spacecraft‒Earth” system selection of emission spectrum is stipulated by the atmosphere's properties;

‒ Time persistence of the optical beacon should not exceed the frequency response of the receiving equipment, necessary for signal coding.

2. Optical beacon should provide operation in the space flight conditions: diminutive mass and dimension parameters, long lifetime, radiation and vibration resistance, capability to operate at low voltage, high efficiency.

The results of the analysis were used for selection of the optical laser beacon emitters developed within the framework of Luna-Glob and Luna-Resource-1 projects.

### Radio engineering, including TV systems and devices

Zakovryashin A. I.

Estimation of a radio-electronic equipment object’s workability supposes its diagnosis.
Diagnosis of the equipment is performed based on continuous mathematical model.
Measurement and a priori information on an object is being accumulated.
As additional a priori information, the author suggests to employ statistical properties of the object’s parameters.
Studying technical documentation on the equipment objects allowed reveal three types of tolerance ranges.
The article formulated the requirements to the membership functions of parameters with various types of tolerance ranges.
The procedure of construction of membership functions (operability functions) of parameters was developed.
The article presents the examples of constructing of membership functions of parameters based on histograms.
Increasing of a priori information volume used for processing by the described method will allow increase the accuracy of obtaining quantitative estimations of technical states.

Keywords: radio-electronic equipment, types of fields of admissions of parameters, requirements to functions of accessories, creation of functions of accessories of parameters for various types of fields of admissions, examples

### Antennas, SHF-devices and technologies

Kulikov S. V., Gudaev R. A., Mikhalchenkov A. A., Zelenkov A. V., Vikulova Y. M.

The goal of the article consists in improving the methodology of broadband matching units’ synthesis for complex loads, allowing ensure maximum of match strips spacing by employing nonhomogeneous stepped loops.

The set goal is achieved based on Kohn method allowing compute broadband matching units for complex loads on nonhomogeneous loops. The versatility of the suggested method consists in the fact that instead this method any other method, allowing compute a matching unit on homogeneous loops can be used.

This work was supported by the Grant of the President of Russian Federation.

Based on the obtained results of studying of characteristics of the broadband matching unit on nonhomogeneous loops performed using mathematical model the following inferences can be drawn:

Increasing of relative match strip width ω leads to damping reduction in a stop band. Reducing the standing wave ratio in the match strip КСТ leads to a decrease in attenuation in the stop band. Increasing the number of loops of the matching unit contributes to the increase i in the stop band. When placing a heterogeneous loop near the source, the attenuation in odd tuple bands increases, and in even tuple bans decreases. The match strip relative width increase w, stand wave ration in match strip reduction and increasing the number of loops of a broadband matching unit affects the value of match strips’ spacing, which is expressed in its reduction. Employing the five-step loops can significantly improve the characteristics of band rejection, but the characteristics in match strip are degrading.

The simulation results of the synthesized broadband matching unit on nonhomogeneous loops confirmed the principal possibility of developing physically realizable impedance matching units with an increased spacing of the parasitic match strips.

Keywords: matching unit, loop

## Informatics, computation engineering and management

### System analysis, control and data processing

Rybnikov S. I., Nguyen T. S.

The analytical design of the active system of damping of flexural aeroelastic oscillations of the wing, which is optimal according to the extended variational criterion of generalized work.

The first tone of aeroelastic oscillations of wing airliner often have frequencies of the same order with the natural frequency of undamped oscillations of the steering gear. Therefore, the synthesis and analysis of the dynamics of the stabilization systems of the airliner dynamics such the angular position of the wing is expedient to take into account and to ensure high quality in these adjustment systems may be required to build the system damping vibrations of aeroelastic wing independent or internal in relation to systems organized on the basis of the aileron channels. The assumption of the symmetry of the oscillations of the wing considered the synthesis of active system of damping of flexural vibrations of a wing of the airliner. For the synthesis of the damping system uses the method of analytical design of optimal regulators (AKOR) according to the criterion of the generalized work, the extended variable energy members of the penalty function, which takes into account the work of the control forces to move the controlled object. The joint variation in energy of the members of the penalty function is intended for counter control the level of damping wing in the transitional processes of the system, on the one hand, control-related energy consumption.

Damping of flexural vibrations of the wing is constructed using as the executive bodies of external ailerons, or specially imposed limit deflected surfaces mounted on the wing. Steering was adopted with a minor, about 15% excess frequency undamped oscillations over the frequency of the third tone aeroelastic oscillations of the wing that allows you to build a complicated damping system oscillations, which includes the first and third tones. In the mathematical model of the damping system first and the third tone of Flexural vibrations of a semi-wing and working steering aileron are described by differential equations of the second order. The control is constructed as linear, in variants with complete information about the control object and with incomplete information containing signals only of the total velocities and displacements of the console.

Performed parametric synthesis of the system damping with the current settings of the extended control object, it is shown that the choice of coefficients criterion, if sufficient control actions, it is possible to reduce vibration of the object, providing an unambiguous or even its monotonous transition function with its adjustable duration. The change in the coefficient km for the energy the members of the penalty function in the process of designing the system is an effective impact on the nature of the transition process in it. With its growth, the absolute values of the feedback coefficients in the system, its natural frequencies, the level and efficiency of the control action decrease, and the transient process in the system approximates to free fluctuations of the object. With decreasing km, conversely, the moduli of the feedback coefficients in the system and its natural frequencies increase, as well as the values of the control actions and their efficiency, the oscillation of the transient process decreases, then the process becomes single-valued and then goes monotonous. Tightening restrictions on the derivatives of the deviations from the ends of the console from a stable state to be performed in the form of an increase in the coefficients in front of them, with sufficient energy, leads to a decrease in variability transients in the system, in extreme cases , to its complete elimination . The handling qualities transients change in the coefficient km is maintained.

Keywords: analytical design, control, aeroelastic vibrations, tone of aeroelastic, the penalty function

### Automation of technological processes and production control

Smirnov K. K.

Nowadays the quality of modern integrated circuits is considered as a complex indicator, which depends on production operations metrology support and improvement of technological process. The modern development of microelectronics with wide miniaturization solutions complicates control technology, measuring and testing of VLSI integration. Moreover, it requires constant improvement of the technological way of manufacture, technological solutions in the design of the production tools, creation of new instruments of monitoring and evaluation parameters, as well as the tightening of the shop rates and the transition to higher levels of automation of production processes.
The article considers the problem of traceability of subjects of labor in performing functional control of VLSI in terms of production. To solve this problem the author developed special application-dependent software that provides traceability of subjects of labor and carrying out the process, analysis and presentation of results. The author presents examples of the analysis of measurements, and the solution of a number of production targets.
The software developed by the author solves the following tasks of traceability:
— Saving test results on all process stages with reference to serial numbers of products and accompanying documentation;
— Providing the staff of various departments with a uniform access to the measured data;
— Providing opportunities to combine measuring equipment located in different areas in order to form a common information space;
— Providing an opportunity to observe the results of the measuring equipment on a real-time basis;
— Providin a common graphical interface in various process stages;
— Provide the ability to analyze measurement results during various process stages and compare them;
— Providing the opportunity to conduct a correlation analysis of measured parameters on various process stages in order to identify potentially unreliable VLSI.

Keywords: microchips, traceability, microcircuits testing, software, functional control

Astapov V. Y., Khoroshko L. L., Jozdani M. S., Khoroshko A. L.

When designing any components of various aircrafts, it is important that the designer knows the technical capabilities of the preforming and forging production, and focuses on the most advanced technology processes of their manufacture. A large number of components used in an airplane design are composed of parts made of sheet materials, which are used as edge formers. The presence of a web, edging and various elements increasing the stiffness and reducing the weight, is common for such parts. These sheet-metal parts present intricate and mainly closed forms, the manufacturing of which by methods of the plastic deforming requires rather complicated forging outfit and their finishing to the required dimensions following the deforming.

The article is concerned with a topical issue of the determination of optimal conditions of exposure to the deforming force required in the prove-out of an intricate shape forming process of edge former structures by deforming a sheet-metal workpiece with the pulsed magnet field pressure, and the simulation of this process. The process of the magnetic pulse forming makes it possible to concentrate the exposure, deforming a sheet-metal workpiece, within the range of pre-set parameters and within a specified zone, but requires a thorough adjustment of technical regimes. Recommendations are developed for the determination of the required power parameters of the sheet-metal workpiece forming process ensuring the maximum efficiency of the process that reduces the number of technological operations, the complexity and the time of manufacture of the outfit and the equipment operation.

In the theoretical solution, the improved mathematical models of the magnetic pulse deforming of the sheet material were developed with account of actual mechanical characteristics of the workpiece materials. The theoretical dependences obtained were experimentally tested on samples; the assumptions and assertions made were verified. The impact of the magnetic pulse deforming on certain properties of sheet-metal part materials was determined. The proposed new technical solutions for implementing the processes developed in practice were examined. Methods for experimental testing of the high-speed magnetic pulse forming of sheet material were developed and implemented using various moulds of complex geometric surfaces, including the material shift dynamics and the impact of the deforming on the metal characteristics, as well as special aspects of the forming and influence patterns of power parameters, processing factors and tool configuration in operation of magnetic pulse sheet-metal forming were established. The influence of the magnetic pulse deforming on mechanical and process characteristics of materials after their exposure to the pulsed magnet field pressure and forming in a mould was determined. It is found out that when applying the pulsed force action, the metal is compacted, its surface hardness is increased, and micro-fractures and porosity are eliminated, that is the quality of a metal zone deformed by the pulsed magnet field is improved. ANSYS LS-DYNA program, a multipurpose software-based multi-function system of a finite-element complex, was used for the computational investigation and simulation of the magnetic pulse forming process of edge former surfaces. When solving the problems by CAD system, the geometrics of workpieces, material specifications, and energy parameters of the magnetic pulse deforming were variated. The workpiece shift and its deformation in moulds having different profile shapes were simulated. Based on the solutions obtained and in comparison with scales of equivalents, it is possible to determine any timing-wise shift of the sheet-metal workpiece web, the final finite deformation of workpieces, any stresses arising in contact zones with forming tools during the deforming and forming.

Keywords: sheet-metal edge formers of closed shape, intricate transition profiles, magnetic pulse deforming, high-speed plastic forming, computer aided design systems, solid model, three-dimensional simulation

### Mathematical support and software for computers, complexes and networks

Efimov A. I., Il'in V. N.

In this article we will discuss different ways of analysis of objects shape data, received from webcams. Purpose of this research was development of various areas of augmented reality and computer vision.

In the analysis of the video sequence, we can distinguish several steps:

• Pre-processing image. It include decreasing influence of noise effects and light artifacts on data recognition.

• Receiving the camera position. Program try to find special flat marker, placed on image. Depending on received data, we establish relative position of camera in current frame.

• Find stable points. We find set of cue points, using FAST-ER method. After frame data processing we can declare stable points of global coordinate system.

• Getting silhouette. We can resolve image depth and cue points of image drop. By processing of gradient between such points we can produce approximate silhouette of object on current frame.

• Systematization final result to get accurate data about object shape.

In the future we decide to develop halftone recognition to make object shape restore even more accurate. We can also create variation of described algorithms without using of special marker, but it required bunch of sophisticated changes in it.

Described algorithm can be used to get object’s 3D models for create it copy on 3D printer. Next important area for us is augumented reality, because of potential of depth map to resolve problems of real and virtual objects intersections and increased range of objects for tracking. Depth maps also has an ability to create stereographic image from set of frames of video.

Analysis of objects shapes is important way of development of computer vision and recognition.

Keywords: computer vision, analysis 3D shape, augmented reality, object recognition

Krasinsky A. Y., Ilyina A. N., Krasinskaya E. M., Rukavishnikova A. S.

In the paper we provide a method of constructing an accurate mathematical model and solving a steady motion stabilization problem by the example of a simple rover − a four-wheeled mobile single-link manipulator with elastic suspension. It is an actual problem [16] because Lagrange equations of the second kind are not applicable for such systems. Redundant coordinates and equations of motion in M.F. Shul’gin’s form [1-3] are used to model the mechanical part of the manipulator dynamics. Vector-matrix form of the equations is convenient for analysis and control theory and the theory of critical cases [6-8] applying. The algorithm of solving stabilization problem was developed in [10-11].

The manipulator has to move rectilinearly with a constant speed and keep its clamp (with a camera or a scanner, for example) on a specified height. The system has a geometric constraint as the link is connected with a DC motor gear wheel by an inextensible arm AB. As a control action additional tension at the anchor engine is accepted. The wheels are simulated as two springs.

Solving the problem consists of a few steps:

1. Mathematical modeling using F.M. Shul’gin’s equations.

2. Calculating parameters of a steady motion.

3. The first approximation of the disturbed motion equations around the steady motion is found.

4. The linear substitution [10-11] is used for the system to have a special form of the theory of critical cases [6-8].

5. Manipulator controllability [9] is confirmed.

6. Coefficients of the optimal linear control law are determined uniquely by solving linear-quadratic problem using N.N. Krasovsky’s method [9, 15].

7. System stability is analyzed.

Results of numerical computations showed that the control law provides asymptotic stability with respect to all variables. This algorithm was programmed in MATLAB.

Keywords: geometric constraints, redundant coordinates, Shul’gin’s equations, stabilization, steady motion, manipulator

Lisov A. A., Chernova T. A., Gorbunov M. S.

In actual operating conditions of electrical industry’s products the degrading changes of their properties should be accounted for. The object of research is various kinds of electromechanical converters, for which even a slight degradation of the properties leads to the serious technogenic aftermath. Methodological basics for solving such problems were considered and suggested; a number of regularities of degrading changes is established, and mathematical models were developed.

Analysis of the characteristic parameters changes allows the four most typical types of functions for describing these regularities: the entire rational functions or polynomials; fractional rational functions; exponential functions; function describing the saturation processes. For each dependence under consideration, examples of the limiting state attainment forecast and the residual resource calculation are given. Models’ building of degrading changes supposes tabulating the measured values and selection of such approximating function, which will provide the least mean square deviation from the tabular dependence. The best results in solving the problems of this kind is ensured by the method of least squares (OLS).

Analysis of considered functions degradation of processes’ descriptions allows establish the following: all functions have an initial value, known from the nameplate data on the device in service. Thus, it is expedient while the degradation changes analysis to study not the whole function, but only its degradation deviation. The initial value of the deviation function is zero, so its plot passes through the origin. When determining the number of approximating function parameters their number is reduced by one for the deflection function, therefore decreasing the order of normal OLS systems.

A practical tool for predicting the modes of functioning of electrical devices and estimating the residual resource has been developed, and a residual resource has been calculated for the degradation changes described by the dependencies of a different type. Prediction of residual resource is based on the solution of nonlinear equations, in which the degradation deviation function takes normative allowable values. The solution of the equation must be determined by limiting the value of the argument, as the moment of failure. Estimation of the residual resource of the device was performed based on the moment of failure.

Keywords: an imitation-recurrent approach to the degradation processes of electrical devices modeling, method of least squares, types of non-linear functions of degradation change in the characteristic parameters, residual resource, attainment of the limiting state

Deniskin Y. I., Dubrovin A. V., Podkolzin V. G.

The article describes the work on semantic analysis of terms and definitions of national and international standards for quality management. Construction of semantic maps graphically displays the types of information flows within the information system for lifecycle processes quality management.

The trend of increasing the number of applications of digital manufacturing enforces to develop new approaches in the field of quality and competitiveness of products. This kind of manufacturing is a relatively new and isn’t explored yet on domestic enterprises wide enough.

Objective. Providing an integrated life cycle processes quality management of innovative products within digital manufacturing on basis of the computer aided information support.

Subject of research — quality of innovative product lifecycle processes within digital manufacturing.

Research methods. The research was performed using methods of the system analysis, graph theory, the principles of total quality management, expertise of quality control, methods of functional modeling (IDEF0), FMEA methodology, universal CASE-tools.

Practical value of the work is to create an integrated information support tools for the designing and integrated lifecycle process management on the basis of the fundamental requirements of national and international standards in the field of lifecycle support and quality management, in accordance with the specifics of automated enterprise management systems (ERP).

Developed functional and information models may serve as a basis for the rational designing of enterprise process model and for the innovative enterprises structure management.

Designed qualitative methods for evaluating the quality of the life cycle processes within digital manufacturing make it possible to provide information support for quality management system foundation (control, management, maintenance, improvement, planning) within digital manufacturing.

Keywords:

### Mathematica modeling, numerical technique and program complexes

Podaruev V. Y.

The paper enunciates the experience of developing the software based on the Galerkin method with discontinuous basis functions of high accuracy. The purpose of the work consists in describing the specifics of of the program code developing intended for use on a multiprocessor computer system. The methodollogy of the work is based on the modern approach to simulation of complicated 3D flows using Galerkin scheme with discontinuous basis functions. The methodology of this work execution includes theoretical analysis of the method, application of modern approaches to programming, verification and validation of employed ideas and demonstration of the developed code’s suitability for complicated nonlinear calculations. The result of the work are recommendations for the software developing based on modern methods of computational aerodynamics.

To develop a software interface for specific codes, it is convenient to use the Python programming language. Before proceedeing to descring the computational domain topology, the calculated grid type (structured or unstructured) should be defined. It is necessary to determine what types of geometric objects are to be worked with. In the case of “serendipian” elements, the desired order of the problem approximation should be selected and the elements for linear, quadratic, cubic, etc. cases should be identified, with further changing only the sets of shape functions, characteristic to the specified elements. It is convenient herewith to realiize these sshape functions in the form of the so-called “lambda” functions included in the C++ standard.

The results of this work can be applied for educational purposes in technical universities and in practical works on developing new software in scientific institutes and design offices. The main conclusion of the paper is that a high-order scheme allows diminish entropic errors while calculating the flow after stagnant zones, as well as calculate all the flow specifics, which are characteristic for flow around the high-lift wing with released slats and flaps. Modern programming approaches allow ensure the high code scalability. In addition, the main features of the Galerkin method with discontinuous functions, such as reconstruction of conservative variables, the approximation of convective, diffusion and source terms, Gaussian quadratures, with account for the surface curvature, coordinate transformations using “serendipian” elements, are briefly described.

Keywords: discontinuous Galerkin Method, basic functions, high order, supercomputer, verification, validation, high-lift wing