2015. № 79

Mathematics. Physics. Mechanics

Aye M. W., Temnov A. N.

This work is associated with the increasing use of cryogenic liquids in a rocket and space technology. In this work we report the results of the analysis of the stability of rotational motion of a rigid body with ellipsoidal cavity completely filled with stratified (cryogenic) liquid. The problems of the motion of rigid bodies with cavities filled with a homogeneous ideal or viscous fluid are sufficiently studied. However, the development of modern technology and the practice is set for researchers a number of new problems of dynamics of solid bodies with liquid-filled cavities. One of these problems of the motion of solids with cavities filled with a cryogenic liquid. An essential feature of the cryogenic liquid is the heterogeneity of temperature and density, which is observed in all modes of exploitation and storage. In this abstract, assuming no heat exchange with the external environment, we consider the problem of the stability of rotation of a rigid body with an ellipsoidal cavity filled with an ideal stratified fluid. Obtained the characteristic equations are considered some special cases: A) rotation of a rigid body with hardened liquid, B) rotation of a dynamically symmetric rigid body with a homogeneous liquid having a cavity in the form of an ellipsoid of revolution. The regions of instability of motion of a rigid body with a homogeneous fluid in the plane of two parameters, which are coincide with the results of other authors. At the end of the paper the regions of instability of rotation of a rigid body with an ellipsoidal cavity entirely filled with stratified fluid are presented in different cases: a) in case of weightlessness but taking into account the moment of inertia of a rigid body, b) in case of mess weight, when the moment of inertia of a rigid body is equal to zero or not equal to zero. The given investigation of the stability of rotation of a rigid body with a stratified fluid showed that the stable stratified liquid reduces the instability regions. The result also indicate that in case of an ellipsoidal cavity hydrodynamic effects of stratified fluid created a large finite number of partial movements, compared to homogeneous fluid.

Keywords: stratified fluid, the stability of rotation, ellipsoidal cavity, vibrations, cryogenic

Panteleyev A. V., Letova T. А., Pomazueva E. A.

The solution of the PID-controller optimal parameter search problem for a given set of initial states and the set of input signals is obtained. An algorithm and software is suggested.

The novelty of the approach is to add the term with the second derivative of the error and to calculate the integral component not on the whole time interval, but only on an interval defined by a «memory» of the system as well as to apply the criterion of optimality of the controller parameters that characterize the average cumulative error with respect to the set of possible initial system states and the set of input signals. This problem is solved similar to the problem of unconditional minimization of the multivariable function J(Knp , KD1 , KD2 , KI) using the method of simulated annealing and further refining of the result with the help of adaptive random search method.

An example of solving the problem of finding optimal parameters of the PID controller for the longitudinal aircraft motion is given. A comparative analysis of the impact of the controller parameters on the quality of transition process and appropriate recommendations are made.

The suggested technology of solution of the parametric synthesis problem can be used in solving the engineering problems by constructing PID-controllers.

Keywords: PID-controller, optimization criterion, initial states set, set of input signals, simulated annealing method

Pismennaya V. A.

The memetic algorithm for finding the conditional global extremum of functions created by the author based on the concept of meme is considered.

Currently a great attention is paid to solving global optimization problems. Aircraft designing requires the solution of these problems especially when optimizing the characteristic parameters (weight, flight range, aerodynamic characteristics) and developing control systems of individual structural elements and whole object as well.

This article deals with the problem of the orientation of the spacecraft. During the flight the spacecraft orientation maintaining is the most common problem. In the article flat version of the problem when the spacecraft is turning in a single plane due to the rotation of the flywheel, mounted inside the spacecraft, is considered. At start time, the angular velocity of the spacecraft and the orientation angle are zero. It is necessary to bring the spacecraft orientation angle to the target for the finite time due to the rotation of the flywheel, with zero angular velocity.

Application of the algorithm is also advisable for a number of optimization problems such as the problem of stabilization of the satellite (problem of damping rotational motion of the satellite using engines installed on it), the problem of interception (target interception by missile), the problem of stabilization of the height of the aircraft. Application of the described algorithm significantly reduces the time required for solution of such problems.

Usage of existing numerical methods is associated with a number of difficulties: large computational load, the requirements for the task, difficulties in achieving convergence of the method. So there is a need to develop and use the so-called heuristics. These methods have no rigorous justification of convergence, but in most cases they allow to obtain an acceptable solution to the problem.

The term «meme» was introduced and defined by R. Dawkins in 1976 as «the basic unit of cultural transmission, or imitation». The term «Memetic Algorithm» was first introduced by P. Moscato in his report in 1989 as hybrid genetic algorithm coupled with an individual learning procedure for refining the solution of the problem. At the stage of particular learning the solution (individual or its genotype) is replaced with a new one (learned) solution in case if the new solution has a larger adaptation value independent upon the rest part of the population. Thus, there is the so-called cultural development of the individual, which is then transmitted to its descendants during next generations.

At the moment, the term «Memetic Algorithm» is widely used as a designation of the interactions of evolutionary or other approach based on the concept of population, and particular learning of individuals or other local procedure enhancing the solution of the problems of the global extremum search.

In the developed algorithm, the cultural evolutionary component is implemented while solving optimization problem by using either the ant colony method or simulated annealing method. During the cultural evolution information about memes is used to generate in terms of the solving problem better individual.

On the basis of the proposed algorithm the software complex is formed in C# language, allowing to apply the developed algorithm to different functions, as well as to analyze its performance. Effectiveness of the method is demonstrated on several model examples that have both simple and complex structure of level lines.

Keywords: conditional global extremum, meme, memetic algorithm, optimization, hybrid algorithm, simulated annealing method, ant colony algorithm, optimal control, orientation of the spacecraft

Kotel'nikov V. A., Kotelnikov M. V.

Consider a flat wall surface probe in the form of an elongated rectangle, located on a streamlined dense plasma surface. The problem is non-stationary two-dimensional, multi-parameter if the flow velocity is parallel to this surface and perpendicular to the long side of the rectangle.

Mathematical model of the problem includes the equation of continuity for ions and electrons and the Poisson equation for the self-consistent electric field. Total speed of charged particles vector consists of three components: convective, diffusive and a component that is associated with mobility. Convective component is determined from the solution of gas dynamic part of the problem and is considered a given.

Numerical model of the problem is based on the method of successive iterations in time. In particular, the continuity equation is solved by Davydov method of large particles, and the Poisson equation — by spectral methods.

Sets of current-voltage characteristics (CVC), sufficient for practice within limits of geometrical dimensions of the probe and values of directed plasma flow velocity, were obtained in numerical experiments. This set of CVC allows you to refine the results of processing the characteristics of probes installed on the surface of hypersonic aircraft (HA), as well as in plasma jets flowing out of technological plasmatrons in various applications (plasma chemistry, plasma spraying, plasma processing of surfaces, plasma electronics and etc).

In addition to probe characteristics profiles, the self-consistent electric fields, the concentrations of ions and electrons, evolutionary curves for streams of charged particles upon a plane probe and information about the role of nonlinear finite and edge effects are described in article. This information is necessary for analysis of heat, charge, mass flows and momentum flux from plasma upon the surface of HA.

Keywords: electric probe, voltage-current characteristic, flat wall surface probe, continuity equation, Poisson equation, finite effect, edge effect

Bezglasnyi S. P., Krasnov M. V., Mukhametzyanova A. A.

In this note the problem of control of plane motions of a two-mass parametric pendulum is considered. The pendulum is modeled by two equivalent weightless rods with two equivalent point masses. They are fixed on the rods and moving along the circle with the center at the pivot. Pendulum can perform rotational or oscillatory motions in a vertical plane around the point of attachment. Pendulum motion occur in a uniform gravitational field. Two-mass pendulum has two equilibrium positions. Lower position is stable and upper position is instable. Friction forces is neglected.

Possibility of parametric control of pendulum excitation and swing damping in the vicinity of the lower equilibrium position are discussed. The control is realized by varying continuously the angle between two rods. It is a function that depends on the representative point of motion of the gravity center of pendulum. We assume about the restrictions on move of the gravity center of pendulum along the bisectrix of angle between rods.

The aim of this paper is to build new control laws with specified properties that implement processes of excitation and damping pendulum near the lower equilibrium position.

The problem is solved by the method of Lyapunov’s functions of the classical theory of stability.

In this paper the two control law processes of excitation and damping pendulum with the assumption of restrictions on the movement of the gravity center are constructed. The Lyapunov’s functions that prove the asymptotic stability and instability of the pendulum lower position in the respective cases of the pendulum damping and excitation are constructed. It is shown that under controlled movements according to the first law occurs the asymptotic damping oscillation amplitude of pendulum for any initial conditions movements. When control according to the second law is the growth of the amplitude and the transition from oscillatory to rotational motions. The theoretical results are illustrated by graphical representation of the numerical results.

Results of paper can be used in modeling and control of plane pendulum motions of various mechanical systems.

Keywords: two-mass pendulum , management, Lyapunov's function, asymptotical stability

Zveryaev E. M., Olekhova L. V.

A problem of the construction of the composite material beam and plate state equations similar to the classic ones is considered. The construction process is based on the Saint-Venant semi-invers method treated as the iteration one and subjected to the contraction mapping principle. The theory equations are transformed to be applied the simple iteration method. The small parameter is isolated to analyze the convergence process. In accordance with the Saint-Venant semi-inverse method to extract the wishing solution from general equations it is necessary to ask some of the stresses and displacements, and via the rest equations to calculate all the other unknowns. Because of understanding the semi-inverse method as the iterative one the null approximation values are taken the same as these in the classic theory. The first approximation solution gives the possibility to determine all unknowns expressed via the null approximation values. The boundary conditions verification on the face surfaces gives the state body equations with the effective coefficients to determine the first approximation values taking into account the integral composite properties. In general case 16 effective coefficients are obtained for the strip whereas the plate 48. To determine these simple formula are given. All coefficients have to be taken into account to satisfy all boundary conditions at the end faces and determine the stress-strain state in the domain of application of the local load. In the rest body domain the stress-strain state is described by the slowly varying functions calculated from the theory of bending beam and plate classical equations with only effective coefficient of flexural rigidity. The substitution of the found from these equations values into the expression for first approximation unknowns gives the local stresses and displacements. Thus the Banach fixed-point theorem (also known as the contraction mapping theorem or contraction mapping principle) may be considered as the generalization of Saint-Venant semi-inverse method.

Keywords: contraction mapping principle, beam, plate theory, small parameter, composite material

Aviation technics and technology

Dolgov O. S., Bibikov S. Y.

This article describes the approach used by designers in determining fighter aircraft geometric shape. In determining the geometric shape, the boundary conditions are the aircraft squares graphs. The aircraft squares graphs formation takes place on the basis of the classical formula for the body «Sears-Haack.» Further transformation of the aircraft squares graphs is carried out taking into account the changes in statistics. The volume and the squares graphs of bearing surfaces are determined separately.

Designer needs to determine the so-called «Layout area» to form the aircraft geometric shape. At the initial stage of the geometric shape formation «Layout area» is a planned aircraft projection, which determines the airplane carrying capacity, and the squares graphs, defined the sheer aircraft volume and the aerodynamic drag wave increase.

Aircraft planned projection formation traditionally is the first parameter taken in to account for the geometric shape development (after design parameters preliminary determination), is directly related to the aircraft squares graphs and vice versa. Furthermore, the importance of squares graphs defined for the designer illustrates the distribution layout volume in the theoretical layout loop of plane and, thereby, enables the analysis of rational distribution.

Squares graphs (at this stage) is the source of the parameters describing the «necessary» square cross sections. The term «necessary» means that supersonic front aircraft geometric shape formation should follow certain patterns of cross-sectional areas distribution along its length.

In this paper we use two concepts: «aerodynamic» squares graph, and a «full» squares graph.

Under the first refers the cross-sectional and exclude «channels» graph (the volume occupied by the air intakes and engines).

Under the «full» squares graph means aircraft cross-sectional areas graph, built with the contribution of all components, including ducts and nozzles.

After defining the squares graph main parameters, it is necessary to define the parameters of its shape, namely the location of mid-section along the aircraft length. For the Sears-Haack’s body it is characteristically a mid-section location at mid-length, and for modern supersonic aircraft is typical shift back of mid-section. This is due to purely as the layout features, as well as with typical supersonic flight speeds at cruising. That makes it necessary to provide a minimum gain of the wave drag at these flight speeds, and displacement (from the middle of the aircraft length) of mid-section position.

Keywords: shape, jet, volume, midship, layout, designing

Moiseev D. V., Trinh V. M., Mozolev L. A., Moiseeva S. G., Pham X. Q.

The article formulates a number of problems of practical interest, such as detection of a light unmanned aerial vehicle (UAV) flyby route over predetermined points on the earth surface. Routing problem is reduced to different variants of closed and open traveling salesman problem. In particular, we considered variants for the open problem when information about starting and end points of a route is available, or not available. Flight duration over the route herewith is minimized, as far as it provides the rise in operativeness of target function solving. Lightweight UAV is characterized by a relatively small range and short flight time. This allows to assume speed and direction of wind as constant over the entire zone and flight time. Traveling salesman problem matrix elements, representing the flight time between pairs of points, are calculated taking into account the effect of wind. Routing problems under discussion are mathematically formalized as a linear integer programming problem with Boolean variables. Each of the considered arrangements presents its features in limitations and target function records. In terms of computing route preparation is reduced to the successive solution of integer linear programming problems with addition of conditions eliminating sub-loops. Solution algorithmic basis stems from branch-and-bound procedure, realized by MATLAB function bintprog. Thus, the main result of this paper is the development of a unified approach to mathematical formalization and numerical solution of a number of topical and called for in practice light UAV flight routing problems in the fixed wind. We present examples of flight routes. In particular, the calculation of the closed flyby route over 40 uniformly distributed in the flight area points on the computer with Intel ® i3-4160 CPU @ 3.60GHz and 4.00 GB of RAM required 61 seconds.

Keywords: the traveling salesman problem, flight routing problem, unmanned aerial vehicle, Boolean linear programming problem

Rybaulin A. G., Sidorenko A. S.

In load-carrying structures of flight vehicles the connection of details with the help of spot welding is used. Feature of spot welding is the raised stress concentration which can cause decrease in characteristics of the connection fatigue strength. Fatigue cracks arise between welded elements on a contour of a welded point. For an estimation of aviation structure durability the definition of local stress state characteristics in zones of welded points at action of dynamic loadings is necessary.

In the product techniques of numerical simulation and calculated data evaluating of the stress state characteristics of a of flight vehicles structures with dot welded connections at random vibration are presented. Action of random stationary kinematic loading under operating conditions aviation product on an external suspension bracket of the maneuverable carrier is considered.

The load-carrying structures of the product represent the thin-walled cylindrical shell containing filling material simulating weight of a product. On a shell by means of spot welding the X-shaped wing symmetrically relative to a vertical plane is fixed.

For simulation the dynamic deformation of a structure with discrete welded joints the system of solid-state simulation and finite element calculation for complex structure Solid Works is used. Numerical models are developed with the use of solid-state finite elements and allow to estimate the characteristics of the local deformation structures in zones of irregularities. The spot weld model based on experimental data and taking into account the change of mechanical characteristics of the source material in a zone of thermal influence is offered. Improvement of material properties is spent on hardness size in section of welded points.

Welded points are modeled by allocating the related circular areas on the plane and on the shell and specify the conditions of a mutual motion’s absence between them. Each spot weld contains up to 420 finite elements SOLID of the second-order.

The stress state characteristics are determined for a case of loading structure stationary random acceleration with a specified spectral density.

Spectral characteristics and levels of stresses vibration in various points of the product structure are obtained. Zones of the maximum stresses in a structure are defined and dynamic stress state peculiarities in welded connections are revealed. For an estimation of welded connection durability on the basis of the received spectral density and algorithms of statistical modeling time relationships of random process of stress are constructed.

Keywords: aircraft, design, wing box, welded connection, spot welding, finite element method, shell, vibration acceleration, vibration stress, spectral density, durability

Space technics and technology

Malyshev V. V., Starkov A. V., Titkov M. A.

The paper presents a model of the spacecraft with a soft landing, soft landing simulation methods and the expected size of the stand for throwing tests in terrestrial conditions.

For the definition of the critical angles and approaches permissible speed limits applied at planting stands throwing tests. The test stand is designed for the experimental study of the process soft landing spacecraft on the moon, Mars and other planets using polnomassovogo dynamically similar layout.

To solve the problem of the spatial movement of the spacecraft requires two numerical processes:

  1. Calculation of force factors acting on a body in motion;
  2. Solving systems of differential equations in the time interval, starting with the moment of contact of the body and ends when the full stop SC.

On a real stand to ensure perfect accuracy suspension layout of the exhibition on the device and reset the layout giving the desired spatial orientation impossible. It is therefore advisable to choose such options stand that will provide the best simulation of the lunar acceleration with errors show the simulation parameters. Maximum possible accuracy of the point of suspension, the site and removing the device from the equilibrium point is taken decimeter, and the size of the stand taken by analogy with a stand named NGOs Benches, built in 1965.

In an inclined bench throwing tests implemented the most simple scheme unloading. Mock lander suspended on a cable carries contact with an inclined rotating platform simulator and soil lunar surface. This type of discharge best represents the forces acting on the spacecraft at the time of landing on the moon.

The main criterion for choosing the optimal size of the stand taken accuracy simulate lunar acceleration.

Thus, it is proposed to install the suspension point at a height of 27 m, and the pad at a distance 4.1 m to simulate the predetermined velocity in the vertical plane of the layout to be moved at a distance of 4.1 m to 9.3 m and at a distance of 4.2 m to 5.2m, to simulate a horizontal velocity component.

Keywords: spacecraft, spacecraft lander, stand-throwing tests

Kazakov R. R., Mingaliev E. R.

In modern conditions the reduction in funding for space programs, the significant cost of the launch vehicle, cutting production of launch vehicles and spacecraft, the tasks of creating and maintaining a normal part of space-based communications, navigation, missile warning and etc. are connected with difficulties and the risk of non-compliance.

In recent years there is much tension around the issue of environmental safety in restricted zones and areas allocated for receiving separated parts of carrier rockets. It is connected with the fact that after the fall on the Earth’s surface there is a possibility for spill of rocket fuel components, which are currently characterized as highly toxic. One of the most dangerous is the heptyl.

The effect of heptyl on the environment, as well as to the life expectancy, pathology and serious illness of population living close to areas allocated for receiving the separated parts of carrier rockets is analyzed.

The main existing approaches to improving environmental safety based on decontamination, neutralization, as well as localization of straits zones are described.

The basic ways to improve environmental safety are proposed as follows:

  • ensuring the fall of separated parts in a given areas;
  • burning the residues of fuel components in the rocket stages during the passive flight;
  • usage of more ecological fuel for rockets refueling;
  • residues discharge of rocket fuel components from separating parts of rockets.

A comparative analysis of the proposed methods is carried out. Each of the discussed methods has a number of advantages and disadvantages; most of them require some structural improvements of the launch vehicle and its component parts.

Keywords: launch vehicle, spacecraft, separable part, impact area, components of rocket fuel, enviroment

Konstantinov M. S., Nguyen D. N.


The interplanetary trajectory of spacecraft (SC) with electric propulsion


Design of trajectory of spacecraft with electric propulsion (EP) to Jupiter using Earth’s swing-by with the ability to reject disturbances associated with temporary cutoff of the electric propulsion.


  1. Analysis of the ballistic possibilities for rejection of disturbances connected with the temporary contingency cutoff of the electric propulsion.
  2. Development of determination method for a new nominal trajectory, which allows to have the long duration of contingency cutoff of the electric propulsion at any point of the SC trajectory


The trajectory optimization problem is formulated by using the Pontryagin’s maximum principle.

Optimality conditions of gravity assistance are used.

The continuation method along parameter is used to solve the boundary value problem.


The novelty of this study is related to the formulation of the problem as well as to the development of method for finding such a nominal trajectory, at the implementation of which a large duration of contingency cutoff of the EP at any point of the flight trajectory is allowed


Estimates of the permissible duration of abnormal cutoff of electric propulsion for the considered program trajectories are obtained.

A method of the design of an interplanetary trajectory with the need to reject the perturbations caused by temporary cutoff of electric propulsion.

Practical implications

The interplanetary missions of spacecraft with electric propulsion.


In this paper we propose an approach to designing of the interplanetary trajectory of SC with EP with the need to reject the perturbations caused with temporary cutoff of electric propulsion at a point of the transfer trajectory.

Estimates of the permissible duration of the supernumerary cutoff of the EP for the several program trajectories are obtained. The nominal trajectories need to be corrected to increase the allowable time of abnormal cutoff of engine

Two ways to correct the nominal trajectories are proposed. The first way is based on the increase of the duration of the coasting segment of the terminal phase of the heliocentric trajectory. The second way is based on the introduction of one or several additional coasting segments.

For the considered transport problem the determination of a new (corrected) nominal interplanetary spacecraft trajectory gave a possibility to increase the allowable duration of unintended cutoff of electric propulsion up to 2.75 days in any point of the trajectory of flight.

Keywords: spacecraft, Jupiter, optimal trajectory, gravity assist trajectory, temporary cutoff of the electric propulsion

Pikalov R. S.

Within the framework of this work the effect of the climber motion on the nonequatorial space elevator is studied. The dynamics of the payload after separation from the elevator is considered.

Space elevator is a system designed for delivery of a payload into Earth orbit. It consists of a tether, space stations — counterweight and a climber. The tether connects the counterweight located in the geostationary orbit with the Earth. The climber with a payload moves on the tether. A mathematical model describing the spatial motion of the space elevator was developed. A series of numerical simulations was performed to determine the effect of climber’s motion on the space elevator’s dynamics. The motion of the payload after separation of the elevator was studied.

The tether is simulated as a pair of inextensible inelastic bars of variable length and cross-sectional area. Counterweight and climber are considered as material points. The developed model takes into account the effect of the tether bending, but it does not require large computational cost.

Results show that a uniform climbing of payload leads to buildup oscillations of the space elevator. It is shown that the latitude of the point of the tether’s attachment to the Earth affects the oscillations in the elevator. The motion of the payload after its separation from the elevator is researched. The dependence of the apogee and perigee on the payload’s separation altitude is obtained.

Keywords: space elevator, climber, tether, nonequatorial, orbital motion, payload

Aerospace propulsion engineering

Kolmakova D. A., Popov G. M., Baturin O. V.

Comparison of the turbomachinery numerical modeling results with experimental data shows that designers cannot achieve quantitative agreement while having qualitative agreement of the results. Uncertainty of modeling initial data is one of the reasons. The researcher must specify the particular channel geometric dimensions to create computational model. The actual dimension value is unknown — it is known only the range of possible values, defined by measuring instrument error or technological tolerance value

Similarly designer does not have reliable information about the workflow parameters, measured directly or indirectly with error. Also, usually the flow parameters distribution has complex nature, simplifying in the simulation.

Thus, there is only a rough idea of the tested channel actual sizes and flow parameters taken as boundary conditions for the numerical simulation carrying out. This leads to significant calculation quantitative errors.

Currently, there is little number of publications on this subject. And algorithms and software implementation taking into account initial data uncertainty are at early stage.

Therefore, research aimed at quantification of initial data uncertainty impact on turbomachines calculated performances was conducted.

Analysis of industry standards and turbomachinery workshop drawings from various companies was conducted at the preparatory stage. The most important turbomachinery geometric dimensions and bogey value of tolerances for it were identified in the analysis. Error values for the flow physical parameters were taken according to technical literature.

The quantification of geometric and physical variables uncertainty impact on turbomachinery row workflow was conducted using untwisted airfoil cascade of axial turbine nozzle assembly (NA) with uniform cross-section throughout the channel height.

Channel capacity, loss factor and NA outlet flow angle were accepted as controlled performance criteria. The NA base variant calculation results and experimental data comparison demonstrated that created model adequately described the processes occurring in the cascade, but not well predicted the losses numerical value.

The series of computational calculations were carried out for this cascade. The first group of calculations was aimed at the impact of geometric parameters uncertainty on NA parameters identifying. The second group — at identifying the studied parameters depending on the flow parameters changes that are used as boundary conditions in the simulation.

The obtained results showed that initial data uncertainty in CFD calculations has a significant impact on the obtained quantitative estimates. The difference between calculated data modified in accordance with the technological tolerances and accuracy of the measured values of the geometry and process parameters may exceed 5% by value of the considered criteria.

Keywords: turbine, the initial data, characteristic, airfoil, throughput, loss ratio, boundary conditions, finite element mesh, computational model, tolerances, errors

Degtiarev S. A., Kutakov M. N., Leontiev M. K.

Crack in the shaft influences the rotor system during operation. Crack is a reason for parametric oscillations due to presence of local variable stiffness. The aim of the work is to develop the algorithm of consideration of transverse crack influence at mathematical simulation of dynamic behavior of the rotor system.

The article gives the methodology and algorithm of consideration of transverse crack when modeling dynamic rotors behaviour. In the rotor system model crack is substituted for the elastic link dividing the shaft into two sections and described by the stiffness matrix with variable factors. When describing crack, only rotation along lateral axes is taken into account. Displacements at other freedom degrees are neglected. Law of change in stiffness coefficients is obtained by the authors on the basis of the existed crack models and considers opening and closing of crack under external forces.

Calculation results of dynamics behavior of the two-support rotor with crack obtained for the crack’s depth of 30% of the shaft diameter at the acceleration regime from 0 to 4000 rpm and at the stationary regimes1/3х, 1/2х, 1х of the first critical speed are presented. Calculation is hold in the program Dynamics R4 designed to calculate rotordynamic tasks; the algorithm of crack consideration was included there. The obtained results show appearance of parametric resonances at 1/3х, 1/2х and 1х of critical speed; the cascade diagram shows excitation frequencies multiple of 1х, 2х, 3х of the rotor frequency, etc. Orbits of the rotor centre in the crack section are given. Calculation of flexibility of the beam with crack done in Dynamics R4 using the presented crack model showed convergence with similar calculation in the finite-element system with error of less than 1%.

The proposed methodology and the algorithm should be mainly considered as an instrument to train the engineers in the vibrational diagnostics area and to obtain limiting values of diagnostics signs of crack.

Keywords: rotor dynamics, crack, nonlinear model, Dynamics R4

Radio engineering. Electronics. Telecommunication systems

Tikhonov R. S.

One of the crucial issues for modern airborne radar systems is to provide all-aspect low scattering targets detection at maximum range. Currently airborne radar is equipped with two operational modes to meet this challenge: high pulse-repetition frequency for approaching target detection and medium pulse-repetition frequency for receding target detection. Although maximum detection range provided for receding targets is often insufficient because of the terrain clutter.

Significant improvement of radar characteristics could be achieved by using space-time processing. The adoption of space-time processing algorithms became possible due to the introduction of multi-input-multi-output phased array radars and progress of digital signal processing.

Since in practice all the required information about clutter background covariance matrix is unknown, space-time adaptive processing (STAP) is used. Clutter covariance matrix sample estimation is computed using training set composed of range bins that surround the cell under test. With that the surrounding range bins should contain similar interference to achieve STAP performance closed to potential (optimum). Although when the training set considers clutter background closed to altimeter its non-homogeneity increases.

The article contains performance analysis of STAP in multi-input-multi-output phased array radar when the training set composed of range bins considers clutter background closed to altimeter.

According to numerical analysis non-homogeneity of training set has least influence on the suboptimal STAP algorithm based on apriori knowledge of clutter characteristics for different bins. The algorithm significantly reduces (for 15-20 dB) clutter energy losses for low flying receding targets compared to conventional signal processing (at the same radar signal parameters) at sample support about 10-12. The level of the computational complexity of the algorithm allows its real-time hardware implementation.

Keywords: space-time adaptive processing, on board radar, multi-input-multi-output phased array, clutter suppression algorithm

Vovasov V. E., Betanov V. V., Gerko S. A.

The aim of this work is to study the errors of the estimates of the coordinates of the stationary antenna, geodesic bound to the area. The work was carried out secondary processing of information performed by the Kalman filter type (KFT). As measurements are used pseudoranges L1 and L2 obtained double-frequency navigation receiver Javad GNSS TR-G3T. Taking into account the calibration procedures for the specified receiver is defined by the difference of values of the delays in L1 and L2, with zero litter, and changes in latencies per liter, in the same range. It was considered that information from the slot is missing, however, the calibration parameters allowed to obtain measurement values, which is the difference of the frequency-time corrections not accounted for in the ephemeris.

Dimension processing navigation receiver confirmed the hypothesis of linearity of the instrumental delays and the possibility of determining the frequency-time corrections not accounted for in the ephemeris. The estimates of the coordinates of the KFT offset no more than a few meters for a long service life navigation receiver. In general, experimentally confirmed the correctness of the calibration procedures navigation receivers needed for the navigation to obtain unbiased estimates of the coordinates of GLONASS.

Keywords: GLONASS reciever’s, pseudorange, ionosphere delays, frequency response letter, hardware delays, Kalman filter type, SDCM

Material authority

Sokolenko I. V.

The text deals with the development of a new highly effective radiation protective material of space application. We have created a new composition material on the basis of inorganic high-lead glass matrix reinforced by modified nanotubular chryzotile. In the composite production we have used the following components: high-lead glass of special chemical composition; nanotubular chryzotile modified by inclusion of lead tungstate PbWO4; nanocrystalline powder PbWO4. The non-standard matrix material choice is explained by the qualities of the chosen matrix. Due to high density and high lead and boron content it can perform both binding and complex radiation protection functions in the developed composite. The characteristics of initial components and received samples of the material were studied using numerous methods of analysis. Production of the composite samples consists of careful mixing of the initial components taken in the required proportion, subpressing of the received mixture in a compression mould, and the following high-temperature pressing at temperature 430-450oC. Investigation of the mechanic, thermal, radiation-protective and other properties of the received material has proven that it has the range of considerable advantages over its polymeric analogs. In particular, it has density 5,5-6 g/cm3, temperature stability up to 400oC, compressive strength up to 300 MPas, high level of aggressive space factors and radiation resistance. All the aforementioned characteristics definitely surpass those of its polymeric analogs. Radiation-protective properties of the composite are defined both by the high density and high content of a range of heavy and light elements. Furthermore, it is easy to change the chemical composition of the received material and therefore to vary its shielding properties from different radiation types. It is also noteworthy that the material has relatively low prime cost and can be successfully applied not only in space but also in a wide range of fields dealing with ionizing radiation.

Keywords: spacecraft, nuclear power reactor, radiation protection, composite material, efficiency

Economics and management

Vdovenkov V. A.

The principle strategic planning documents — the State program of the aviation industry development until 2025, the Federal target programs — dictate the multiple increase of new technological level aircraft manufacturing, which requires large-scale construction of new production facilities and modernization of existing facilities. They demanded that Russian aviation industry to switch to import substitution for high-tech aircraft component production at a growing rate. At the same time, the major problem of the Russian aviation industry development began the delays of enterprises’ technical re-equipment and modern production facilities creation investment projects’ implementation. The result is shifted delivery of high demand products, the loss of the industry’s competitive position in the market and direct economic loss due to use of outdated technologies.

In this article we propose a simple method for estimating these losses, depending on the duratuion of this delay and technological parameters of production processes. It allows us to estimate what the increase in investment would be justified, if it were possible to avoid delays in the implementation of the investment project. The method relies solely on measurable indicators that can be found in the available statistics. It is shown that the refinement of the investment project parameters requiring delay its implementation for a year, may not be economically justified unless it can reduce the required investment volume by 20-30%. This conclusion should be taken into account in the process of financing for development of the aviation industry companies.

We also systematize the institutional and organizational factors that cause significant delays in the implementation of investment projects in the industry. These factors take place at the level of the enterprises and integrated structures, and at the level of the whole industry. The need for accelerated development of the Russian aviation industry industrial potential and accelerated development of new products requires changes in the procedures of making decisions about allocating financial resources, monitoring their effective and targeted spending.

Keywords: aviation industry, production potential, investment projects, efficiency, losses, time lag, asessment

Spiridonov I. B.

The process of testability control at design stage includes testability modeling, calculation and analysis of indices, comparison of the calculated values with the specified requirements correcting project solutions.

The production system functional model developed for solution to the problem «Testability Analysis» with IDEF (ICAM Definition) methodology to automate testability control at design stages was developed. The model describes processes of system production during the testability with respect to the system quality used for solving the main problem.

Implementation methods of calculation and testability analysis require the introduction of automation in the analysis procedure. It depends of necessity to process with large amount of initial information for production of calculations taking into account a lot of testability criteria evaluations in analysis process.

The proposed approach to the organization of design process allows to:

  1. Process integrated operational schedule of design taking into account tasks of all participants in the design process.
  2. Complexity plan recourse and risks
  3. Develop requirements to ensure, especially for testability analysis software

To realize testability analysis requirements as a part of design process the special software was created.

Software functions are given as follows:

  • basic testability calculation;
  • ranking of testability indices by failure critically level;
  • latent failures detection method;
  • calculated and specified in TRS testability indices comparison;
  • issuance of recommendations for the adjustments to the design decisions to optimize BITE, that perform control function.

Keywords: aircraft equipment, aircraft systems, reliability, safety, maintenance, built in test equipment, design system manufacturing model, diagram, the tree nodes

Malykhina M. A.

Purpose: to analyze the communication system of marketing management and quality management in the modern organization, identify the factors and levels of integration, the potential scope of applying international quality management systems to marketing. A comparative analysis of the marketing role in the international awards in the field of quality management revealed that the requirements to the marketing process in the international quality awards are not spelled out in detail, and the quality of the marketing process is not included in the purposes. Article shows that in the modern version of ISO 9000 requirements to marketing processes that is based on market research and generated on their basis requirements for products or services that meet the consumers’ expectations. Integration requirements for marketing in the quality management system lags behind the real needs of today’s organizations, especially Russian, requiring the use of advanced foreign experience to reduce the time necessary for the modernization of the Russian economy.

The author develops a classification of integration levels of marketing management and quality management and complements this classification based on quality components. Author analyzes the communication of marketing management and quality management in marketing of services. The article shows how marketing management interacts with quality management in the framework of management theory — structurally, in terms of processes and performance, as well as identifies the factors contributing to the integration of marketing management and quality management.

The article discusses the relationship of marketing management and quality management in the light of the modern theory of social systems by Niklas Luhmann. The integration of these management subsystems does not arise automatically, and the author reveals customer satisfaction as the common ground between the two subsystems as the basis of communication between them.

Conclusions of the study are applicable to the development of marketing performance indicators systems in modern organizations, as well as for embedding of marketing into a quality management system to reduce costs and monitor the effectiveness of marketing operations.

Keywords: quality control, quality management, marketing control, marketing management, theory of social systems, quality management system

Kriule E. G.

Subject area of the case. IP management

Importance. The article is discussed the problems of IP management in actual integrated structures, including the creation, registration, state registration and commercialization of intellectual property; discussed the scheme of patent and licensing information exchange in the corporate integrated structures, which could apply in the aerospace industry.

Methods. The analysis of current law in the field of intellectual property, the appliance of the system method, including synthesis of patent and licensing activity experience in the companies of the aerospace industry and experience of payment remuneration to the authors of intellectual property.

Results. Three main stages of IP management are described in integrated structures:

creation of intellectual property, including encouraging creators of intellectual property;

registration of intellectual property, including enterprise registration, agency registration, state registration (receiving protection documents) and registration of protected intellectual activity results to accounting as intangible asset;

commercialization of intellectual property in different directions, including the use of protected intellectual activity results in its own production and stimulating inventive activity through the remuneration payments to authors for intellectual property use;

At the second stage of IP management is proposed the scheme of patent and licensing information exchange between patent departments in the corporate integrated structures. For making high-quality and timely IP management solutions by the main organization of integrated corporate structures suggested use a single database of intellectual property in this scheme. The single database of intellectual property is filled with information about own developments and created by organizations protected intellectual activity results.

Practical implications. The results of the study can be used to create an effective system of IP management in modern integrated corporate structures, including the field of aerospace industry.

Conclusion. The article has practical significance for creation a system of patent and licensing information exchange within creation or modernization IP management system in the corporate integrated structures. The provisions of article can be used in the process of education specialists in the sphere of IP management.

Keywords: management of intellectual property, the integrated structure, industrial property objects, head patent and license department, patent and licensing information exchange, commercialization

Zueva T. I., Khmelevoi V. V.

Development of transport system is one of priority State programs of City of Moscow on 2012-2018. Subprogram «Development of new types of transport» suggests, in particular, development of air transport, as well. The main objectives of this type of transport, in addition to commercial use, are the tasks of public-social nature. The most important step in solving the problems of maintenance of execution of services is the stage of formation of helicopters park, helicopter centers of the city of Moscow based on the volume of demand for services and its quality.

The article considers the problem of building a fleet of helicopters, depending on the volume of demand for services and their quality, and two stages of its solution.

At the first stage, the decision on the purchase on the global and domestic markets such models of helicopters (HM), which, on the one hand, are characterized by high competitiveness and, on the other, cover services of helicopter ports (HP) clients. In addition, the implementation of a successful operation for the purchase HM, is required, in advance, to develop a nomenclature procurement portfolio that meets the requirements of operators and clients — users of the services of the HP.

At the second stage, in accordance with the demand for services is determined quantitative composition HM for every position of the nomenclature of the portfolio, taking into account the quality of services provided specific HM. The quality of the services proposed to be evaluated using a points-based assessment system, which as of scales is invited to consider the rationality of use of a particular HM for specific services (loading of helicopter), and as indicators of the quality of services — runtime services, including fast delivery, tariffs for the basic, additional, related services, professionalism of personnel safety.

The task of forming helicopters of the HP is solved in two versions — as a task of linear programming and more simple algorithmic way. The problem is solved for linear restrictions on the quantity demanded and valid flight resource, and also taking into account limitations on the amount of investment for the purchase of helicopters. In this formulation, investment in the development of ground infrastructure of the HP are not taken into account.

The proposed procedure allows to form the effective operation of a fleet of helicopters, taking into account the interests of operators and consumers that find their expression in terms of HM market competitiveness, operating conditions, in the structure and volume of demand for services.

Keywords: transport system, helicopters, the demand for services, quality of services, integrated market competitiveness, product portfolio, tariff, costs, flight resource, investments

Bazadze N. G.

Subject area of the case. Organization of management

Purpose. This study describes new methods of higher educational programmes in training specialists for enterprises of aviation-industrial complex based on integration of education and practical training at the enterprise — the dual educational programmes.

Design/methodology/approach. The methodological approach is based on the analysis of foreign experience (German dual educational programmes) and application of techniques of lean manufacturing and organization of management.

Practical implications. The article describes fundamental principles and uniqueness of the new format of management studies, as well as the directions of development of a dual educational technologies. The methodological approach can be used in educational programmes in order to improve the quality of preparation experts in branches.

Originality/ Value. Main target of integration process in aircraft corporations and universities is to reduce the gap between the information received during studying in University and required competencies in corporation. Approbation of the organizational mechanism of interaction between the parties were shown on the basis of organization of interaction between Moscow Aviation Institute and The Public Join-Stock Company «Russian Aircraft Corporation «MiG» (PJSC «RAC «MiG»).

Keywords: aviation industry, aircraft corporations, dual format of education, dual educational technologies, education, integrated in practice, organizational management, the systems and procedures experts, lean management, communication processes

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