The traditional approach in the study of engine control is based, as is known, on the linearization of the engine models and the control system (control) and, basically, this leads to the desired results. This approach allows to establish the main physical phenomena, omitting minor details. Thus, the linear model allows to estimate the basic properties of ATS, such as accuracy, stability, controllability and robustness. Three main methods of ATS synthesis have been developed and successfully applied: the desired amplitude-phase frequency characteristics, the root locus and the state space method. However, due to the interest in the features of the workflow and, especially, for the study of engine acceleration regulators, simulation modeling using the fundamental conservation equations becomes more and more relevant. The transition to models of this kind is caused by the impossibility of describing devices with variable structure or the operation of systems with large control signals using linear stationary equations. The article deals with the issues related to the problems of numerical simulation of dynamic processes occurring in the hydromechanical control systems of the aircraft engine, in a nonlinear formulation. Mathematical models of an astatic controller in a nonlinear formulation and a complex model of a gas turbine engine and its automatic control system are given. It is noted that for a complete understanding of the processes occurring in complex hydraulics automatic devices, as well as for a legitimate rational selection of preliminary design parameters, a thorough refinement of the existing models of hydromechanical devices presented in a linear formulation is necessary.

Keywords: aircraft engine, diagnostic modeling, nonlinear phenomena, hydraulic automation devices, mathematical models, numerical research, numerical experiment.

Pavel V. Petrov (Ufa, Russian Federation) – CSc in Technical Sciences, Associate Professor of Applied Hydromechanics Department, Ufa State Aviation Technical University (12, K. Marksa st., Ufa, 450008, Russian Federation, e-mail: pgl.petrov@mail.ru).

Vladimir A. Tselischev (Ufa, Russian Federation) – Doctor of Technical Sciences, Professor, Head of Applied Hydromechanics Department, Ufa State Aviation Technical University (12, K. Marksa st., Ufa, 450008, Russian Federation, e-mail: pgl.ugatu@mail.ru).

1. P.V. Petrov, V.A. Tselischev, Bases of nonlinear hydrome-chanical devices algorithmic modeling, (in Russian). Ufa: Ufa state aviation technical university, 2012.

2. I.A. Krivosheev, G.I. Pogorelov, V.S. Phatikov, A.G. Godovanyuk, «Methodology of presentation and use of multi-dimensional characteristics propfan with aided design GTE and ACS», (in Russian), in Vestnik UGATU, vol. 13, no. 1(34), рр. 3-8, 2009.

3. A.A. Koeva, P.V. Petrov, V.A. Tselischev, “Concept of compound energy systems hydroautomatic de-vices researches,” (in Russian), in Vestnik UGATU, vol. 16, no. 5 (50), pp. 103-108, 2012.

4. O.S. Gurevich, Automatic control systems for aircraft GTE: Encyclopedic Reference, (in Russian). Moscow: TORUS PRESS, 2011. pp. 153-160.

5. D.A. Akhmedzyanov, I.A. Krivosheev, R.A. Sunarchin, «The joint work aviation gas turbine engines and fuel system at the acceleration and deceleration modes», (in Russian), in Vestnik SGAU, no. 1, рр. 24-25, 2006.

6. D.A. Akhmedzyanov, E.S. Vlasova, A.E. Kishalov, «Methodology of modeling unsteady works modes of aircraft gas turbine engines», (in Russian), in Vestnik SGAU, no. 2(10), рр. 41-44, 2006.

7. D.A. Akhmedzyanov, «Unsteady works modes aircraft GTE», (in Russian), in Vestnik UGATU, vol. 7, no. 1(14), рр. 36-46, 2006.

8. P.V. Petrov, V.A. Tselischev, A.A. Koeva. “Methodical bases of aviation engine automatic control systems research,” (in Russian), in Vestnik UGATU, vol. 16, no. 8(53), pp. 7-14, 2012.

9. Musina L.S., Petrov P.V. Numerical study of nonlinear hydraulic systems // in the collection: XIII Royal readings. International youth scientific conference, proceedings. Samara state aerospace University named after academician S.P. Korolev (national research University). 2015. P. 269-270.

10. Kishalov A.E., Vlasova E.S. Parametricheskaja identifikacija matematicheskoj modeli GTD v sisteme DVIGwp [Parametric identification of the mathematical model of gas turbine engine system in DVIGwp] //
All-Russian NTK «Mavlyutovskie readings». – Ufa: USATU, 2007. Т. 1. pp. 56-57

11. Kishalov A.E., Klyuchev N.A. Modelirovanie i analiz harakteristik TRDDFsm dlja samoljotov V pokolenija v sisteme DVIGw [Simulation and analysis performance for afterburning turbofan engine airplanes V generation system DVIGw] // Mavlyutovskie readings: Materials of All-Russian Youth Scientific Conference «Mavlyutovskie readings». Ufa: USATU, 2016. pp. 199-203.

12. A.B. Mikhailova, Methods and computer-aided technology for gas turbine engines compressor two-level gas dynamic simulation: candidate of science thesis. Ufa: Ufa State Aviation Technical University, 2011.

13. Krivosheev I.A., Akhmedzyanov D.A., Kishalov A.E. Imitacionnoe modelirovanie raboty aviacionnyh GTD s jelementami sistem upravlenija [Imitation modeling of gas turbine engines with controls systems] // Vestnik UGATU. – Ufa: USATU, 2008. No. 2(29). pp. 3-11.

14. Akhmedzyanov D.A., Kishalov A.E. Modelirovanie perehodnyh processov, protekajushhih pri otladke avtomatiki pri ispytanijah TRDDF [Modelling of transients occurring when you debug automation at afterburning turbofan engine test] / The Bulletin of VSTU. Voronezh, 2011. vol. 7(8). pp. 152-158

15. Akhmedzyanov D.A., Kishalov A.E., Shabelnik J.A., Markina K.V., Polezhaev N.I. Obzor i analiz parametrov potoka v osnovnyh uzlah aviacionnyh dvigatelej [Review and analysis of flow parameters in the main nodes aviation engines] // Youth herald USATU – Ufa: USATU, 2012. No. 4(5). pp. 25-36.

In the design of turbopump units of liquid rocket engines (LRE) is currently used mainly known empirical relationships and approach associated with the numerical simulation of the elements of the flow parts. The design results require experimental refinement and testing. The use of reliable design techniques reduces the time of product implementation and the associated material costs.

When designing, it is necessary to take into account the energy losses in the elements of the flow path, both turbines and centrifugal pumps, since these losses must be compensated by additional costs of the unit power.

Most of the criterion-empirical methods of design of rocket engine turbopump did not fully correspond to the present realities, in connection with the existing tendency of increasing the number of revolutions of the rotor. Known techniques have passed the verification and testing for speeds of the order of 40,000 rpm, the design of a modern rocket engine turbopump a tendency to increase frequency of rotation, which can reach about 100 000 and 120 000 rpm (especially when transitioning to environmentally friendly cryogenic fuel components). Increasing the speed leads to higher mass-energy characteristics. Changing the boundary conditions requires clarification of the used calculation dependencies and methods. The results of an analytical study to determine the calculated dependences of the coefficients of disc friction losses are presented. Analytical expressions allow us to determine the drag torque and power loss disc friction of centrifugal pumps turbopump rocket engine. In comparison

with the empirical dependences obtained by other authors, the use of the degree of turbulent dynamic spatial boundary layer (depending on the rotor speed) significantly expands the range of the region and reliable determination of disk friction.

Keywords: disk friction, energy loss, efficiency, power balance, design procedure, turbopump, liquid rocket engine, power.

Alexander A. Zuev (Krasnoyarsk, Russian Federation) – CSc in technical sciences, associate professor of Aircraft Engines Department, Siberian State University of Science and Technologies named after M.F. Reshetnev (31, Krasnoyarsky Rabochy аv., Krasnoyarsk, 660037, Russian Federation, e-mail: dla2011@inbox.ru).

Vladimir P. Nazarov (Krasnoyarsk, Russian Federation) – CSc in technical sciences, Professor of Aircraft Engines Department, Siberian State University of Science and Technologies named after M.F. Reshetnev (31, Krasnoyarsky Rabochy аv., Krasnoyarsk, 660037, Russian Federation, e-mail: nazarov@mail.sibsau.ru).

Anna A. Arngold (Krasnoyarsk, Russian Federation) – Head of Special Connectors and Instruments
Department, JSC “Krasnoyarsk Machine-Building Plant” (29, Krasnoyarsky Rabochy аv., Krasnoyarsk, 660123, Russian Federation, e-mail: arngoldanna@mail.ru).

Ivan M. Petrov (Krasnoyarsk, Russian Federation) – Deputy chief designer for engines, propulsion systems and power plants, JSC “Krasnoyarsk Machine-Building Plant” (29, Krasnoyarsky Rabochy аv., Krasnoyarsk, 660123, Russian Federation, e-mail: petroof777@mail.ru).

1. Abo Elyamin, G.R.H., Bassily, M.A., Khalil, K.Y., & Gomaa, M.S. (2019). Effect of impeller blades number on the performance of a centrifugal pump. Alexandria Engineering Journal. doi: 10.1016/j.aej.2019.02.004
2. Ding, H., Li, Z., Gong, X., & Li, M. (2018). The influence of blade outlet angle on the performance of centrifugal pump with high specific speed. Vacuum, 2019, No. 58, P. 39-48. DOI: 10.1016/j.vacuum.2018.10.049
3. Wang, C., Shi, W., Wang, X., Jiang, X., Yang, Y., Li, W., & Zhou, L. (2017). Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics. Applied Energy, 2017, No. 187, pp. 10-26. DOI: 10.1016/j.apenergy.2016.11.046
4. Skrzypacz, J., & Bieganowski, M. (2018). The influence of micro grooves on the parameters of the centrifugal pump impeller. International Journal of Mechanical Sciences, 2018, no. 144, pp. 827-835. doi: 10.1016/j.ijmecsci.2017.01.039
5. Salehi, S., Raisee, M., J. Cervantes, M., & Nourbakhsh, A. (2018). On the flow field and performance of a centrifugal pump under operational and geometrical uncertainties. Applied Mathematical Modelling, 2018, no. 61, pp. 540-560. doi:10.1016/j.apm.2018.05.008
6. Adu D., Zhang J., Jieyun M., Asomani S.N., Osman Koranteng M. (2018). Numerical investigation of Transient vortices and turbulent flow behaviour in centrifugal pump operating in reverse mode as Turbine. Materials Science for Energy Technologies, 2019, No. 2, pp. 356-364. doi: 10.1016/j.mset.2018.12.002
7. Mansour M., Wunderlich B., Thévenin D. (2018). Effect of tip clearance gap and inducer on the transport of two-phase air-water flows by centrifugal pumps // Experimental Thermal and Fluid Science, 2018, No. 99, pp. 487-509. DOI: 10.1016/j.expthermflusci.2018.08.018
8. Leto A., Votta R., Bonfiglioli A. (2016). Preliminary Design Method of a Turbopump Feed System for Liquid Rocket Engine Expander Cycle. Energy Procedia, 2016, no.101, pp. 614-621. DOI:10.1016/j.egypro.2016.11.078
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The purpose of work was the optimization of a welded compartment of the supersonic aircraft taking into account structural and technological schemes allowing designing rationally a welded structure of a compartment taking into account factors: thermomechanical forces, models of materials, structural and technological schemes.

Current works of national and foreign authors have been analyzed [1-16]. Article has been written [17] by results in which approach to the solution of a problem of rational design, regarding parametrical optimization of the top panel of a compartment by criterion of mass of all compartment has been offered.

During the further research of the proposed model, dependences between the strain-stress state of a compartment and its frame are revealed. It is established that on the strain-stress state of the loaded welded compartment considerable influence is rendered by the chosen structural and technological scheme both on deflections, and on their distribution. Influence of the sequence of welding on critical state of a welded compartment is revealed.

As a result, the offered approach has allowed performing structural and parametrical optimization of the chosen welded design for a compartment of the supersonic aircraft that has allowed reducing the mass. Rational options of structural and technological scheme for the welded compartment set like loading taking into account the sequence of welding have been defined.

Keywords: supersonic aircraft, airframe, welded compartments, welding, residual stresses, the finite element method (FEM), finite-element model, heat-affected zone (HAZ).

Ilia E. Merkulov (Moscow, Russian Federation) – PhD Student of Aircraft Design Department 101, Moscow Aviation Institute (National Research University) (4, Volokolamskoe av., Moscow, 125993, Russian Federation), engineer, Russian Aircraft Corporation “MiG” (7, 1-st Botkinsky drive, Moscow, 125284, Russian Federation, e-mail: ilia.merkulov@gmail.com).

Askold I. Endogur (Moscow, Russian Federation) – Doctor of Technical Sciences, Professor of Aircraft Design Department 101, Moscow Aviation Institute (National Research University) (4, Volokolamskoe av., Moscow, 125993, Russian Federation, e-mail: endogur@yandex.ru).

1. Okerblom N.O. Konstruktivno-tekhnologicheskoye proyektirovaniye svarnykh konstruktsiy [Structural and technological design of welded structures]. Moscow: Mashinostroyeniye, 1964.
2. Vinokurov V.A. Svarochnyye deformatsii i napryazheniya. Metody ikh ustraneniya [Welding deformations and stresses. Methods to eliminate them]. Moscow: Mashinostroyeniye, 1968.
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5. Kurkina S.A., Vinokurov V.A., Vershinskiy S.V. et al. Proyektirovaniye svarnykh konstruktsiy v mashinostroyenii [Design of welded structures in mechanical engineering]. Moscow: Mashinostroyeniye, 1975.
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12. Islam M., Buijk A., Rais-Rohani M., Motoyama K. Simulation-based numerical optimization of arc welding process for reduced distortion in welded structures. Finite Elements in Analysis and Design, 2014, No. 84, pp. 54-64.
13. Endogur A.I. Konstruktsiya samoletov. Konstruirovaniye detaley i uzlov [The design of the aircraft. Construction of parts and components]. Moscow: Publishing House of MAI, 2013.
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15. H. Murakawa, D. Deng, N. Ma, J. Wang. Applications of inherent strain and interface element to simulation of welding deformation in thin plate structures. Computational Materials Science, 2011, No. 51, pp. 43-52.
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17. Riks E. An incremental approach to the solution to the solution of buckling anssnapping problems. Int. J. Solids Struct., 1979, No. 15, pp. 524-551.
18. Merkulov I.E., Endogur A.I. Sozdaniye modeli svarnogo otseka sverkhzvukovogo samoleta s uchetom konstruktivno-tekhnologicheskoy skhemy [Creating a model of a welded compartment of a supersonic aircraft, taking into account the design and technological scheme]. Trudy MAI, 2017, no. 94, 18 p. URL: http://www.trudymai.ru/upload/iblock/973/merkulov_enogur_rus.pdf (date of the application: 28.05.2019).

The temperature state is one of the main factors determining the performance of high-energy structures. As a rule, between the calculated and experimental data of temperature field parameters there are significant differences, the causes of which still do not have an exhaustive explanation. However, under given conditions of thermal loading, thermal conductivity λ, isobaric specific heat capacity cp and density ρ of materials are largely responsible for the temperature conductivity of temperature fields and temperature levels achieved in structural elements. From the literature review it follows, that the course of the temperature curves of the thermophysical characteristics λ(T), ср(Т) and ρ(T) of refractory metals is considered separately, without any relationship between themselves. The expediency of studying the interrelationships between the thermophysical characteristics of metals is noted. The author draws attention to the Berman solution: improving of the accuracy of measuring thermal conductivity based on Fourier's law in its tractability for a solid as a continuous medium is achievable when taking into account the nonlinearity of λ = bT, where in the simplest experiment b = const in the extended temperature range ΔT . Thereby it was suggested and proved that in the volume of the metal during the creation of the temperature gradient, the heat transport realized by conductivity electrons is accompanied by heat transfer by photon emission. The scientific substantiation of the expression for the complex of thermophysical properties K = λ1/3cpr of metals, as well as the results of its experimental verification are given.
A generalized formula for the temperature dependence of the thermal conductivity λ(T) of refractory metals is proposed for the purpose of numerical solution of thermal problems based on the differential equation of transient thermal conductivity. The utmost attention is paid to the necessity of taking into consideration of all determining factors when calculating temperature fields.

Keywords: metallic elements, temperature state, thermal conductivity, Fourier law, Debye formula, Stefan-Boltzmann law, internal photon emission, generalized formula for thermal conductivity.

Valentin S. Koshman (Perm, Russian Federation) – CSc in technical sciences, associate professor of  Farm machines and equipment  department, Perm State Agro-Technological University named after academician D.N. Pryanishnikov (23, Petropavlovskaya st., Perm, 614990, Russian Federation, e-mail: koshman31337@yandex.ru).

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2.  Zarubin V.S., Stankevich I.V. Raschet teplonapryazhennykh konstruktsiy [Calculation of heat-stressed structures]. Moscow: Mashinostroenie, 2005, 352 p.

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4.  Serovojskij V.M., Chuyan R.K. Issledovaniye teplovykh poley v elementakh konstruktsii dvigateley LA [The study of thermal fields in the structural elements of the engines LA]. In book: Gagarinskiye nauchnyye chteniya po kosmonavtike i aviatsii, 1986, Moscow: Nauka, 1987, P. 182.

5.  Libenson G.A. Proizvodstvo poroshkovykh izdeliy: uchebnik [Powder production: a textbook]. Moscow: Metallurgiya, 1990, 420 p.

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10.  Muchnik G.F., Rubashov I.B. Metody teorii teploobmena. Ch. 1. Teploprovodnost: uchebnoye posobiye [Methods of heat transfer theory. Part 1. Thermal conductivity: a manual]. Moscow: Vysshaya shkola, 1970, 288 p.

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15.  Koshman V.S. O zakonomernostyakh vzaimosvyazi elektroprovodnosti, teploprovodnosti i teplovogo sostoyaniya elementov agroinzhenernykh sistem [On the regularities of the relationship of electrical conductivity, thermal conductivity and thermal state of elements of agro-engineering systems]. Perm Agrarian Journal, 2015, no. 4, pp. 40-48.

16.  Koshman V.S. O zakonomernostyakh dlya integralnoy kharakteristiki teplofizicheskikh svoystv elementov periodicheskoy sistemy D. I. Mendeleyeva [On Regularities for the Integral Characteristic of Thermophysical Properties of the Elements of the Periodic System of D.I. Mendeleev]. Perm Agrarian Journal, 2014, no. 1, pp. 22-27.

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18.  Koshman V.S. O temperaturnoy zavisimosti kompleksa teplofizicheskikh svoystv elementov periodicheskoy sistemy D.I. Mendeleyeva [On the Temperature Dependence of the Complex of Thermophysical Properties of the Elements of the Periodic Table D.I. Mendeleev]. Perm Agrarian Journal, 2014, no. 4, pp. 22-26.

Analysis of the main problems of experimental investigations of gas turbine engines strength reliability is carried out. The main directions of the modernization of the experimental base organized in CIAM for strength investigations are considered. The most important directions of such investigations are mentioned. These directions include special qualification and formation of an electronic data base of structural strength of new materials (metallic alloys, different types of composite materials; materials with gradient of properties; materials produced using additive technologies); provision and confirmation of strength reliability during optimization of new structural and technological solutions; integrity investigations at extremely high temperatures; prevention of fractures due to high cycle fatigue; confirmation that engines meet new certification requirements including confirmation of safe service life of engine main parts taking info account possible defects.

Special attention is paid to modernization of spin pit rigs. Original methods, hardware and software were developed for receiving necessary thermal condition of being tested rotor, for execution of tests at required cycle of loading, for contactless measurement of rotating object deformations and displacements, for object illumination required for receiving qualitative high-speed video recording, for testing with foreign object injection, for receiving rotor part fracture at required rotation speed, for on-line determination of crack in revolving detail, etc. A lot of unique tests were conducted.

Keywords: gas turbine engine, strength reliability, spin pit rig, rotor, burst test, cyclic test, vibration test, containment of rotor fragments, resistance to bird impact, high speed videorecording.

Yuri A. Nozhnitsky (Moscow, Russian Federation) – Doctor of Technical Sciences, deputy general director – director of research center of Dynamic, Strength, Reliability, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: nozhnitsky@ciam.ru).

Boris A. Baluev (Moscow, Russian Federation) – CSc in Technical Sciences, head of department, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: baluev@rtc.ciam.ru).

Yulia A. Fedina (Moscow, Russian Federation) – CSc in Technical Sciences, head of sector, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: yafedina@ciam.ru).

Dmitry V. Shadrin (Moscow, Russian Federation) – head of sector, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: dvshadrin@ciam.ru).

1. Nozhnitsky Yu.A. The Problem of Ensuring Reliability of Gas Turbine Engines. ATCES 2017, IOP Conf. Series: Materials Science and Engineering, 2018, no. 302 (2018), 9 p. DOI: 10.10.1088/1757-899X/302/1/01/20182.
2. Yu.A. Nozhnitsky, B.A. Baluev. Otraslevaya eksperimentalnaya baza prochnostnyh issledovaniy aviatsionnyh dvigateley [Industry experimental base of strength research of aircraft engines]. Proceedings of All-Russia Technical Science Conference «Metrologicheskoe obespechenie ispytaniy i izmereniy v aviatsionno-kosmicheskoy promyshlennosti», Moscow, 2013, pp. 76-87.
3. Yu.A. Nozhnitsky, B.A. Baluev, Yu.A. Fedina. Eksperimentalnye issledovaniya prochnostnoy nadezhnosti perspektivnyh gazoturbinnyh dvigateley [Experimental studies of the strength reliability of promising gas turbine engines]. Vestnik UGATU, 2015, vol. 19, no. 3(69), pp. 4-14.
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The paper is dealing with the peculiarities in design of first rotor of multistage low pressure compressor (LPC) in case of absence of intel guide vane (IGV) on base of in-house software package “3D-INVERSE.EXBL” user to solve 3D invers problem. Presented in the paper inverse solution provides effectiveness and operability of LPS first rotor for a wide range of RPM.

Inverse problem is based on desired static pressure distribution on suction side of blade, given blade thickness and pressure difference (named loading) in corresponding points of suction and pressure sides of blade. Inlet and outlet gas-dynamic parameters (pressure, density and flow velocity vector) are taken from direct solution of flow within multistage compressor and remains unchanged during inverse problem solution.

Solution of inverse problem is determined using moving grid. Normal speed of face of grid cell adjacent to blade surface is determined using given static pressure (inverse mode) with the aid of relationships, which are the elements of Godunov scheme applied for integration of flow equations.

In the paper inverse solution provides effectiveness and operability of first rotor of multistage low-pressure compressor (LPC) for a wide range of rpm (70¸100 %) in case of absence of inlet guide vane (IGV).

Keywords: transonic fan rotor, design, low-pressure compressor, 3D-Inverse problem, wide range speed.

Viktor I. Mileshin (Moscow, Russian Federation) – CSc in Physical and Mathematical sciences, head of division, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: mileshin@ciam.ru).

Igor K. Orekhov (Moscow, Russian Federation) – Senior Researcher, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation; e-mail: orekhov@ciam.ru).

Sergey K. Shchipin (Moscow, Russian Federation) – CSc in Technical sciences, deputy chief designer, Russian Aircraft Corporation "MiG" (7, 1-st Botkinsky drive, Moscow, 125284, Russian Federation; e-mail: Sershchipin@mail.ru).

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High pressure ratios in advanced axial compressors lead to a decrease in height of the flow path and, consequently, a decreased blade height in HPC last stages. The blade tip clearance can’t be reduced relatively to the blade chord length or height by the same relative value as in first stages. Moreover, HPC operation in transient conditions can cause an increase in tip clearances, so that clearances in last stages can exceed normal values. This may affect the operating range and characteristics of the compressor as a whole. Circumferential groove casing treatments can be used to compensate for negative effects associated with an increase in tip clearances.

The test unit used in this work is a D-77M stage – the large-scale (1 m) model of the HPC last stage designed for studies of flow specifics in axial stages with a big hub-to-tip ratio equal to 0.925. It consists of 3 blade rows: inlet guide vanes (IGV) with 90 vanes (ZIGV), which provide the same flow swirling as in an actual compressor, a rotor with 82 blades (ZR) and a tandem stator with 134+134 vanes (ZSII). The D-77M stage has the following design parameters: mass air flow 15.4 kg/s; tip speed 264 m/s; total pressure ratio 1.24.

The purpose of the circumferential grooves is recovery the stall margin, pressure ratio and maximum level of efficiency, which have decreased due to an increase in the tip clearance. Two values of the tip clearance are studied: a) 0.4 mm – design value of the tip clearance, and b) 0.8 mm – increased value of the tip clearance.

Keywords: compressor last stage, circumferential grooves casing treatment, radial clearance, adiabatic efficiency, stall margin.

Viktor I. Mileshin (Moscow, Russian Federation) – CSc in Physical and Mathematical Sciences, Head of Divisiоn, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation, e-mail: mileshin@ciam.ru).

Aleksandr M. Petrovichev (Moscow, Russian Federation) – CSc in Technical Sciences, Head of Department, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation).

Svetlana I. Bayeva (Moscow, Russian Federation) – Leading Engineer, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation).

Vladislav V. Zhdanov (Moscow, Russian Federation) – Engineer, Central Institute of Aviation Motors named after P.I. Baranov (CIAM) (2, Aviamotornaya st., Moscow, 111116, Russian Federation, e-mail: vldzhdanov@yandex.ru).

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The article is devoted to the automation of testing control systems that are designed for converted gas turbine plants. Under the converted gas turbine installations here refers to aircraft engines, converted for ground use as a power actuator for electric generators. At present, gas turbine power plants of small and medium capacity, built on their base, are one of the main elements of a distributed electric power industry. The perfection of automatic control systems is one of the important conditions for achieving the required indicators of the quality of generated electricity. The article shows that, due to the complexity and responsibility of the assignment, energy facilities, as a rule, do not allow carrying out a full set of field experiments necessary for testing the control systems, and limited field experiments do not allow evaluating the operation of the automatic control system with the necessary reliability and, moreover, are very laborious. Therefore, in order to improve the quality indicators of control systems, it is necessary to take into account the behavior of the electrical system at the earliest possible stages of design, since it determines the operating mode of the gas turbine unit. To this end, it has been proposed to include in the testing process, already at the stages of research testing, a mathematical model of the electrical system into the composition of the testing facilities. Such a model should be multi-mode, it should simulate the electrical system of arbitrary structure and composition of elements. The description of the developed model and software systems created on its basis, considered as a means of testing the algorithms of gas turbine control systems for the power industry, is given. The advantage of this test method and its relevance for the industry is evaluated.

Keywords: test automation, gas turbine installation, electrical system, automatic control system, mathematical
modeling.

Boris V. Kavalerov (Perm, Russian Federation) – Doctor of Technical Sciences, Associate Professor, Head of Electrical Engineering and Electromechanics department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: kbv@pstu.ru).

Artem I. Suslov (Perm, Russian Federation) – Student, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: 1_suslov@mail.ru).

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6. Akhmedzianov D.A., Kishalov A.E., Sukhanov A.V. Obmen dannymi mezhdu SCADA-sistemoi i sistemoi imitatsionnogo modelirovaniia aviatsionnykh dvigatelei v protsesse ispytanii [Data exchange between the SCADA system and the aircraft engine simulation system during the testing process]. Molodoy uchenyy, 2011, no. 8, vol.1, pp. 50-53.

7. Shmidt I.A. Avtomatizatsiia ispytanii SAU GTD na osnove tsifrovykh bystro reshaemykh modelei [Test automation system for automatic control of gas turbine engines based on digital rapidly solvable models]. Ph. D. thesis. Ufa, 1991, 103 p.

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One of the perspective directions of development of aviation industry is development of unmanned aerial vehicles. Creation of reliable and economic unmanned aerial vehicles is a relevant problem of the modern aircraft industry which is intimately bound to optimization of dimensions and principal specifications of aircraft.

Within this subject the problem of ensuring reliability of fastening of the technical equipment on the unmanned aerial vehicle is investigated. The design of the fastener (bracket) at equipment installation has to guarantee trouble-free operation of the unmanned aerial vehicle at the given service conditions and also taking into account a condition of the invariance of weight of the device in general.

The task is set within carrying out tests for stability and durability of the system consisting of the electronic instrumentation fixed by brackets at the vibrostand to impact of accidental vibration. The solution of the problem, the bound to ensuring reliability of fastening of equipment on the unmanned aerial vehicle, numerically is realized in the Solid Edge Simulation Express software package. The three-dimensional limited-element model of the bracket, which applied to fastening of electronic equipment, is considered. The analysis of a stress-strained state of a bracket in the conditions of operational loadings which arise at flying of the unmanned aerial vehicle is given. Bracket sections dangerous in terms of destruction are investigated, influence of power factors on strength of structure is estimated. Verification of the results of numerical analysis based of the experimental tests on the strength of the fastening of the equipment made. Improved bracket construction for mounting electronic equipment on unmanned aerial vehicle was developed, that provides durability and reliability in operation. The analysis of an intense strained state of the loaded bracket was allowed to develop recommendations on the basis of which the additional stiffening rib is injected into a design.

The solution to the problem of ensuring the reliability and strength of bracket was not affected significantly the change in weight of the aircraft as a whole, thus, rigid structural requirements for the weight of the aircraft observed. The developed design of a bracket is recommended for use for fastening of an inventory on board the unmanned aerial vehicle “Orion”.

Keywords: bracket, strength, mathematical modeling, fracture, reliability, unmanned aerial vehicle, construction, stresses, strain, numerical analysis, improving the design, the fastening element.

Tatyana E. Melnikova (Perm, Russian Federation) – Csc in Technical Sciences, Associate Professor of Dynamics and Strength of Machines Department, Perm National Research Polytechnic University (29, Komso­molsky av., Perm, 614990, Russian Federation, e-mail: taevmel@gmail.com).

Yuliya A. Kazarinova (Perm, Russian Federation) – Master of Dynamics and Strength of Machines Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian federation, e-mail: monic17@mail.ru).

1. Biard w., maklain w. Malye bespilotnye letatelnye apparaty [small unmanned aerial vehicles]. Moscow: technosfera, 2018, 311 p.

2. Bespilotnye letatelnye apparaty. [unmanned aerial vehicles]. Voronezh: nauchnaya kniga, 2015, 616 p.

3. V.s. fetisov. Bespilotnaia aviatsiia [unmanned aviation]. Ufa: foton, 2014, 217 p.

4. Rendal w. Biard, timoty w. Maclain. Malye bespilotnye letatelnye apparaty: teoriia i practika [Small unmanned aerial vehicles: theory and practice]. Moscow: tekhnosfera, 2015, 312 p.

5. Shatalov n.v. osobennosty klassificatsii bpla samoletnogo tipa [features of classification of bla airplane type]. Perspektivy razvitiya informatsionnykh tekhnologiy, 2016, no. 29, pp. 34-39.

6. Chepurnych I.V. Prochnost konstrukcii letatelnych apparatov [Durability of construction of aircrafts]. Komsomolsk-na-amure: Komsomolsk-na-amure state university, 2013, 197 p.

7. Kobylin O.V. Bespilotnyi letatelnyi apparat “Orion” [Unmanned aerial vehicle "Orion"]. Aviatsiya Rossii: proshloye, nastoyashcheye, budushcheye: sb. trudov II nauchno-prakticheskoy konferentsii, posvyashchennoy 100-letiyu sozdaniya FGUP «TSAGI», Zhukovskiy, 21-23 november 2018 [Proc. of The II Sientifically-practical conf., sanctified to the 100-year of creation CAGI]. Moscow: MAI, 2018, pp. 107–112.

8. Segerlind l. Primenenie metoda konechnykh elementov [applied finite element analysis]. Moscow: mir, 1979, 392 p.

9. Rudakov к.n. ugs femap 9.3. Geometricheskoe i konechno-elementnoe modelirovanie konstruktsii [ugs femap 9.3. Geometrical and limited-elementecal design of constructions]. Кiev: igor sikorsky kyiv polytechnic institute, 2011, 317 p.

10. Rychkov s.p. modelirovanie konstruktsyi v srede femap with nx nastran [design of constructions in femap with nx nastran]. Мoscow: dmk press, 2012, 784 p.

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12. Marochnik staley i splavov [brands of steels and alloys]. Мoscow: mashinostroenie, 2014, 1216 p.

13. Zaitsev v.n., rudakov v.l. konstruktsiia i prochnoct samoletov [construction and durability of airplanes]. Kiev: vysshaia shkola, 1978, 488 p.

14. Richard baker. Vvedenie v vibratsiiu [introduction in vibration]. Мoscow: lds, 1994, 44 p.

15. Firsov v.g., zastrogin yu.f., kulebiakin a.z. avtomatizirovannye pribory diagnostiki i ispytanii [automated devices of diagnostics and tests]. Мoscow: mashinostroenie, 1995, 288 p.

16. Sukhanov v.l., shibaev v.i., gorodkhenko v.i., remizov d.i. ekspertiza letnoi godnosti bespilotnykh aviatsionnykh system na ispytatelnye i demonstratsionnye polety [examination of flightworthiness of the pilotless aviation systems on test and demonstration flights]. Problemy bezopasnosti poletov, 2016, no. 2, pp. 49-57.

The article presents the results of work to determine the degree of influence of the quality of blanks, milling scheme, as well as finishing technological operations of surface plastic deformation (FPD) on the fatigue resistance of the blades of an axial compressor stage of an aviation gas turbine engine (GTE).

The results of the analysis of the input control of mechanical properties for bars from titanium alloy VT9 of all batches for three years of supply are given.

The compliance of mechanical properties of bars OST 1 90006–86 was verified. The mechanical properties and the microstructure of the material were investigated on samples from forgings.

The evaluation of the method of forming the edges, as well as the degree of wear of the cutting tool during milling for fatigue resistance and the condition of the surface layer of the blade section has been carried out.

Studies were conducted for two groups of blades:

- 1st group - blades made according to the current technology (processing stockings "stocking");

- 2nd group - blades with a change in the scheme of milling edges (longitudinal-side milling of edges by the method of "cutting").

The influence of FPD on the blades with the technological processes of producing blanks and machining the feather profile for two groups of blades corrected at the previous stages was analyzed:

- 1st group without performing technological operations of hardening and vibration treatment;

- 2nd group with hardening operations performed with micro beads and vibro-processing according to the current technology.

The measures on the adjustment of the technological process aimed at improving and stability of the characteristics of fatigue resistance are considered. The analysis of the results of experimental studies with the determination of the optimal parameters of the technological process of manufacturing a working blade, followed by its approval as a policy.

Keywords: gas turbine engine, compressor, blade, fatigue resistance, regression analysis, hardening, milling, workpiece.

Kirill G. Nepein (Samara, Russian Federation) – Head of a division, of strength and thermal physics department, JSC “Kuznetsov”; PhD student of Construction and design of aircraft engines department, Samara national research university named after academician S.P. Korolev (29, Zavodskoe av., Samara, 443022, Russian Federation; e-mail: kirill.nepein@gmail.com).

Igor A. Selivanov (Samara, Russian Federation) – Head of division, of strength and thermal physics department, JSC “Kuznetsov”; PhD student of Construction and design of aircraft engines department, Samara national research university named after academician S.P. Korolev (29, Zavodskoe av., Samara, 443022, Russian Federation; e-mail: selivanov.i.a@yandex.ru).

1. Normy prochnosti aviatsionnykh gazoturbinnykh dvigateley grazhdanskoy aviatsii [Strength Standards for Civil Aviation Gas Turbine Engines]. Moscow: Central Institute of Aviation Motors, 2004, Is.6, 260 p.
2. Anurov Yu.M., Fedorchenko D.G. Osnovy obespecheniya prochnostnoy nadëzhnosti aviatsionnykh dvigateley i silovykh ustanovok [Fundamentals of ensuring the strength reliability of aircraft engines and power plants]. StPeterburg: Publishing house of Peter the Great St. Petersburg Polytechnic University, 2004, 390 p.
3. Gusev A.S. Teoreticheskiye osnovy raschetov na soprotivleniye ustalosti [Theoretical bases of calculations on fatigue resistance]. Moscow, 2014, 49 p.
4. Kravchuk V.S., Abu Ayash Yousef, Kravchuk A.V. Soprotivleniye deformirovaniyu i razrusheniyu poverkhnostno-uprochnennykh detaley mashin i elementov konstruktsiy [Resistance to deformation and destruction of surface-hardened machine parts and structural elements]. Odessa, 2000, 160 p.
5. Petrov Ju.V. Soprotivleniye materialov. Spetsialnyye voprosy soprotivleniya materialov [Strength of materials. Special issues of material resistance]. Moscow, 2017, 61 p.
6. Minaev A.M. Obrabotka metallov rezaniyem [Metal cutting]. Tambov: Tambov State Technical University, 2008, 72 p.
7. Ledenev V.V., Odnolko V.G., Nguen Z.H. Teoreticheskiye osnovy mekhaniki deformirovaniya i razrusheniya [Theoretical foundations of the mechanics of deformation and fracture]. Tambov: Tambov State Technical University, 2013, 312 p.
8. Malceva L.A., Gervasev G.A., Kutin A.B. Materialovedeniye [Materials Science]. Ekaterinburg, 2007, 340 p.
9. Barishev G.A. Materialovedeniye [Materials Science]. Tambov: Tambov State Technical University, 2007, 85 p.
10. Pereboeva A.A. Tekhnologiya termicheskoy obrabotki metallov [Technology of heat treatment of metals]. Krasnoyarsk, 2007, 143 p.
11. Shashkov V.B. Prikladnoy regressionnyy analiz [Applied Regression Analysis]. Orenburg, 2003, 362 p.
12. Stepanova T.Ju. Tekhnologii poverkhnostnogo uprochneniya detaley mashin [Surface hardening technology for machine parts]. Ivanovo, 2009, 64 p.
13. Ivanov D.V., Dol A.V. Vvedeniye v metod konechnykh elementov [Introduction in finite element analysis]. Saratov: Amirit, 2016, 84 p.
14. Arzamasov V.B., Volchkov A.N., Golovin V.A. et. al. Materialovedeniye i tekhnologiya konst­ruktsionnykh materialov [Materials science and technology of construction materials]. Moscow: Akademiya, 2007, 538 p.
15. Panov A.A. Obrabotka metallov rezaniyem. Spravochnik tekhnologa [Metal Cutting. Handbook of Technologist]. Moscow: Mashinostroyeniye, 1988, 736 p.

The combustion of low-grade non-standard fuel gases has recently acquired particular importance. To accomplish this task, it is advisable to develop domestic utilization microturbine installations instead of imported Capstone-type installations. However, the existing plants of this class are designed primarily for burning standard fuel gases such as methane, propane, natural gas, etc. When developing new domestic utilization plants, it is necessary, first of all, to take into account the heterogeneous composition and heat output of fuel gases, which places increased demands on the preparation of fuel-air mixtures.

When burning non-standard fuel gases in utilization gas turbine power plants, there are increased requirements for the emission of harmful substances. To date, various designs of low-emission combustion chambers as part of gas turbine units have been proposed and are being developed. This paper discusses the homogenization of the fuel-air mixture in the mixing chamber before it is fed into the combustion chamber. Available studies show that with a homogeneous combustion of a previously prepared mixture, the emission of harmful substances is significantly reduced compared with diffusion burning with a separate supply of components. The paper discusses the cyclone method of preparing a fuel-air mixture with a tangential supply of air and fuel gas. The mathematical model is based on the laws of conservation of the total mass, momentum and enthalpy of the mixture, the mass concentration of the oxidizer and fuel. Turbulent transport characteristics are obtained using the k-e-turbulence model. Variant calculations of mixing with different residence times and relative flow rates are carried out. The analysis of speeds, air excess factors and uneven air excess factors by volume of the mixing chamber is given. Recommendations on the use of generalized characteristics (time of stay and relative flow intensity) in determining the geometric dimensions of the mixing chamber are proposed.

Keywords: mixing chamber, fuel-air mixture, homogeneous combustion, unevenness of the coefficient of excess air, residence time, relative flow rate, geometric dimensions of the mixing chamber.

Alyona A. Shilova (Perm, Russian Federation) – engineer of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: alyona1203@gmail.com).

Ivan S. Kuznetsov (Perm, Russian Federation) – student, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: radiofm_2010@mail.ru).

Nikolay L. Bachev (Perm, Russian Federation) – CSc in Technical Sciences, Professor of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: bnl54@yandex.ru).

Roman V. Bulbovich (Perm, Russian Federation) – Doctor of Technical Sciences, Professor of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: Bulbovich@pstu.ru).

1. Inozemtsev A. A., etc. Osnovy konstruirovaniya aviatsionnykh dvigateley i energeticheskikh ustanovok [Bases of designing of aviation enginesandpowerstations]. Moscow: Mashinostroyeniye, 2008, vol. 2, 368 p.
2. Vedeshkin G.K., Sverdlov E.D. Organizatsiya nizkoemissionnogo szhiganiya gaza v gazoturbinnykh ustanovkakh [Organization of low-emission gas combustion in gas-turbine installations]. Teploenergetika, 2005, no. 11, pp. 10-13.
3. S.G. Matveyev, S.V. Lukachov, M.YU. Orlov, I.V. Chechet, Yu.V. Krasovskaya. Raschetobrazovaniya CO i NOx v kamerakh sgoraniya GTD: elektron. ucheb. posobiye [Calculation of the formation of CO and NOx in combustion chambers GTE: electron. training. allowance]. Samara, Samara university, 2012, 41 p.
4. Skibin V.A., Volkov S.A. Vybrosy vrednykh veshchestv ot aviatsionnykh dvigateley [Emissions of harmful substances from aircraft engines]. Aerokosmicheskiy kuryer, Central Institute of Aviation Motors, 2003, no. 2, рр. 18-19.
5. Postnikov A.M. Snizheniye oksidov azota i vykhlopnykh gazov GTU [Reduction of nitrogen oxides and exhaust gases of gas turbines]. Samara: Publishing house of the Samara Scientific Center of the Russian Academy of Sciences, 2002, 286 p.
6. Tumanovskiy A.G. idr. Perspektivy sozdaniya vysokotemperaturnykh malotoksichnykh kamer sgoraniya statsionarnykh GTU [Prospects for the creation of high-temperature low-toxic combustion chambers of stationary gas turbines]. Teploenergetika, 2002, no. 10, pp. 23-26.
7. Kashapov R.S., Maksimov D.A., Skiba D.V., Kulikov S.V., Bashtannikov M.N. Issledovaniye avtokolebaniy davleniya v kamere sgoraniya s predvaritelnym smesheniyem topliva [Investigation of auto-oscillations of pressure in the combustion chamber with preliminary mixing of fuel]. Gazoturbinnyye tekhnologii, 2001, no. 4(13), pp. 34-37.
8. Kashapov R.S., Maksimov D.A., Skiba D.V., Kulikov S.V., Bashtannikov M.N. Razrabotka dinamicheskoy modeli kamery sgoraniya s predvaritelnym smesheniyem topliva [Development of a dynamic model of a combustion chamber with preliminary mixing of fuel]. VESTNIK of Samara University. Aerospace and Mechanical Engineering, 2012, no. 2(2), pp. 52-59.
9. Kamera predvaritel'nogo smeshivaniya dlya gazovykh turbin [Chamber of preliminary mixing for gas turbines]. Patent 2262638 Russian Federation: MKP F23 R3/30. Mei Luchano, Mil’ani Alessio, Din Entoni. № 2000124312/06.
10. N.V. Kolpakova, A.S. Kolpakov. Gazosnabzheniye :uchebnoye posobiye [Gas supply: study guide]. Yekaterinburg: Publishing house of the Ural University, 2014, 200 p.
11. Udyma P.G. Apparaty s pogruzhnymi gorelkami [Devices with immersion burners]. Moscow: Mashinostroyeniye, 1973, 272 p.
12. Bachev N.L., Betinskaya O.A., Bulbovich R.V. Chislennoye modelirovaniye rabochego protsessa v kamere sgoraniya dlya utilizatsii poputnogo neftyanogo gaza [Numerical simulation of the working process in the combustion chamber for utilization of associated petroleum gas]. Journal of Engineering Physics and Thermophysics, 2016, vol. 89, no. 1, pp. 212-220.
13. Bachev N.L., Matyunin O.O., Kozlov A.A. Chislennoye modelirovaniye rabochego protsessa v kamere sgoraniya zhidkostnykh raketnykh dvigateley s dozhiganiyem generatornogo gaza pri sverkhkriticheskikh parametrakh [Numerical simulation of the working process in the combustion chamber of liquid rocket engines with afterburning of generator gas at supercritical parameters]. Aerospace MAI Journal, 2011, vol. 18, no. 2, pp. 108-116.
14. Varnatts Yu., Maas U., Dibbl R. Goreniye. Fizicheskiye i khimicheskiye aspekty, modelirovaniye, eksperimenty, obrazovaniye zagryaznyayushchikh veshchestv [Physical and chemical aspects, modeling, experiments, the formation of pollutants]. Moscow: Fizmatlit, 2003, 352 p.
15. FlowVision. Versiya 2.5. Rukovodstvo polzovatelya [FlowVision. Version 2.5. User's manual]. Moscow: TESIS, 2008, 285 p.

The ability of ball autobalancers to perform auto-balancing of rotors at their supercritical rotation frequencies and the absence of such ability at subcritical frequencies, necessitates the study of the dynamics of rotors with autobalancer at transient rotation modes. For the numerical study of the peculiarities of such modes in this article the mathematical model of dynamics of the single-disc symmetric inter-supported rotor with the ball auto-balancing device, taking into account the non-stationarity of the rotor speed, the impact of gravity and rolling friction of the balls in the cage, is derived. For the case of two-ball autobalancer, a computational model in the form of a system of differential equations in the form of Cauchy is proposed, and the results of numerical simulation of different rotation modes using this model are presented. Herewith, at the steady-state rotation mode it is modeled the dynamics with an abrupt change in the eccentricity of the center of mass of the disk. The results of isotropic rotor simulation are represented by graphs of changes in the deflection of the rotor and the coordinates of its instantaneous center of mass, the displacements of balls along the cage. For the anisotropic rotor, two maxima of the deflection amplitude and the orbit of the forward and backward precessions typical to its dynamics are shown. The given graphs of calculations taking into account and without taking into account the impact of gravity demonstrate that precessional motion of the rotor under consideration occurs relative to its axis shifted under the influence of weight force. The influence of the ball autobalancer on the rotor dynamics in transient and steady-state modes is illustrated by graphs of changes in the coordinates of its instantaneous center of mass, and the dynamics of balls in the cage corresponding to these modes is shown on the graphs of their movements.

Keywords: single-disk rotor, ball auto-balancing device, transient and steady-state modes, instantaneous center of mass, amplitude of deflection, orbit of precession.

Nikolay N. Zaytsev (Perm, Russian Federation) – Doctor of Technical Sciences, Professor of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: znn@perm.ru).

Denis N. Zaytsev (Perm, Russian Federation) – leading engineer of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: rkt@pstu.ru).

Dmitriy A. Mineev (Perm, Russian Federation) – PhD student of Rocket and Space Engineering and Power Generating Systems Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: mda886@mail.ru).

1. Gusarov A. A. Avtobalansiruyushchie ustroystva pryamogo deystviya [Autobalancing device of direct action]. Moscow: Nauka, 2002, 119 p.

2. Gorbenko A.N. Vliyanie sily tyazhesti na kolebaniya rotora s sharikovym avtobalansiruyushchim ustroystvom [Influence of gravity on vibrations of a rotor with ball autobalancing device]. Vestnik Tekhnologicheskogo universiteta Podolya, 2000, № 1, pp. 110–114.

3. Bolton J.N. Single- and dual-plane automatic balancing of an elastically mounted cylindrical rotor with considerations of coulomb friction and gravity. Dissertation for the degree of Doctor of Philosophy In
Engineering Mechanics, 2010. URL: https://vtechworks.lib.vt.edu/bitstream/handle/10919/29946/Bolton_JN_ D_2010.pdf?sequence=1 (Treatment date: 04/05/2019).

4. Goncharov V.V., Filimonikhin G. B. Vid i struktura differentsialnykh uravneniy dvizheniya i protsessa uravnoveshivaniya rotornoy mashiny s avtobalansirami [Form and structure of differential equations of motion and process of auto-balancing in the rotor machine with auto-balancers]. Bulletin of the Tomsk Polytechnic University, 2015, vol. 326, no. 12, pp. 20-30.

5. Oliynichenko L.S., Goncharov V.V., Sidey V.N., Gorpinchenko O.V. Eksperimentalnoe issledovanie protsessa staticheskoy i dinamicheskoy balansirovki sharovymi avtobalansirami krylchatki osevogo ventilyatora [Experimental study of the process of static and dynamic balancing of the axial fan impeller by ball autobalancers]. Eastern-European Journal Of Enterprise Technologies, 2017, vol. 2, no. 1, pp. 42-50.

6. Zaytsev N.N., Zaytsev D.N., Mineev D.A. Modelirovanie dinamiki gorizontalnogo rotora s dvumya dvukhsharovymi avtobalansirami [Simulation of horizontal rotor dynamics with two double-ball autobalances]. Aerokosmicheskaya tekhnika, vysokie tekhnologii i innovatsii – 2018: Materials of the XIX All-Russian Scientific and Technical Conference (Perm, 15–17 November, 2018), Perm: Perm National Research Polytechnic University, 2018, pp. 113-118.

7. Makram M. Experimental investigation of ABB effect on unbalanced rotor vibration / M. Makram1, S.S. Kossa1, M.K. Khalil, A.F. Nemnem, G. Samer // Journal of Coupled Systems and Multiscale Dynamics, 2017, Vol. 5, pp. -231. DOI: 10.1166/jcsmd.2017.1135

8. Chung J. Effect of gravity and angular velocity on an automatic ball balancer / Shuichi Yoshida, Teruyuki Naka. SICE Journal of Control, Measurement, and System Integration, May 2014, Vol. 7, No. 3, pp. 141-146.

9. Shuichi Yoshida, Teruyuki Naka. Reduction Method of Residual Balancing Error on Auto-Balancer Mechanism. SICE Journal of Control, Measurement, and System Integration. - May 2014, Vol. 7, No. 3, pp. 141-146.

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In the process of the modern aviation gas turbine engines development, a significant complication of the automatic control systems (ACS) is observed, which increases the risks of various disturbances in the measurement channel and makes the control tasks more complicated.

To ensure the failure tolerance of the automatic control system of an aircraft bypass turbofan engine, an algorithmic method of redundancy is proposed which involves using an optimal observer - the Kalman filter.

The optimal observer lays the groundwork for solving various control tasks, as well as provides for the information redundancy, which allows to increase the failure tolerance of the automatic control system, that is - its ability to perform its functions after the occurrence of a failure.

The article presents the results of the simulation of the optimal filter, consistent with the mathematical model of the ACS TRDD, according to flight tests of a modern PS-90A type engine as part of a Tu-214 aircraft in December 2018, both on stationary and on transient modes of engine operation, during normal operation of ACS and sensor failures.

The analysis of the quality of the obtained estimates of the output vector of the ACS turbofan engines has been carried out The results of the simulation of the optimal observer and the analysis of the quality of assessments, both on stationary and transient modes of engine operation, with normal operation of ACS and sensor failures are presented in the form of tables and graphs. The parameters of the turbofan engines are given as a percentage of the maximum values.

It is demonstrated that the proposed algorithm meets the requirements for the accuracy of the estimates of the output vector of the automatic control system of a gas turbine engine and can be recommended for use in the ACS of bypass turbofan engines.

Keywords: mathematical model, failure tolerance, optimal estimates, Kalman filter, optimal observer.

Aleksandr A. Inozemtsev (Perm, Russian Federation) – Doctor of Technical Sciences, Professor, Corresponding Member of the Russian Academy of Sciences; Head of Aviation Engines Department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation), Managing Director – General Designer, JSC “UEC-Aviadvigatel” (93, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: office@avid.ru).

Nadezhda G. Lamanova (Perm, Russian Federation) – Associate Professor of Applied Mathematics department, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: nglaman@mail.ru).

Alexey N. Sazhenkov (Perm, Russian Federation) – CSc in Technical Sciences, General Designer Assistant, Head of Administrative Department, JSC “UEC-Aviadvigatel” (93, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: sazhenkov@avid.ru).

Igor G. Lisovin (Perm, Russian Federation) – CSc in Technical Sciences, Head of Automated Control Systems Department, JSC “UEC-Aviadvigatel” (93, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: lisovin@avid.ru).

Igor N. Gribkov (Perm, Russian Federation) – Deputy Head of Engineering and Experimental Works and design of Automated Control Systems Department, JSC “UEC-Aviadvigatel” (93, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: gribkov@avid.ru).

Artur S. Pleshivykh (Perm, Russian Federation) – Student, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation; e-mail: arthur.p.s.1995@mail.ru).

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