# Vol 19, No 1 (2020)

**Year:**2020**Articles:**11**URL:**https://journals.ssau.ru/vestnik/issue/view/419

## Full Issue

## AIRCRAFT AND SPACE ROCKET ENGINEERING

### Using signals from the gas-turbine engine shaft speed sensor in the diagnosis of the technical condition of its reduction gearbox

#### Abstract

It is shown that analyzing the signals from “standard” sensors of gas-turbine engine shaft speed we can resolve some issues of diagnostics of the technical condition of the reduction gearbox without installing any additional vibration transducers. It was found, in particular, that the vibration spectrum component generated by the wear of the differential reduction device’s gear teeth causing resonant oscillations of the turbocharger blades produces torsional vibration at the appropriate frequency. The analysis of the parameters of the instantaneous rotational speed of the reduction gear output link (the shaft of the rear screw) made it possible to obtain some diagnostic indicators of the value of the reduction gear teeth wear on the basis of evaluation of the frequency deviations’ variance. It was established that the value of the diagnostic indicator is linearly dependent on the value of wear. The norm for this indicator was established for the engine under investigation. Significant influence of the load on its level was shown.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):7-17

### Algorithm for predicting the vibrational state of a turbine rotor using machine learning

#### Abstract

A machine learning algorithm has been developed to solve the problem of predicting a vibrational state in order to improve the turbine rotor assembly processes using its digital twin. The digital twin of the rotor includes a parametric 3D model specially created in the CAD module of the NX program and a design project in the ANSYS system in which the working conditions of the rotor are simulated. The parameters of vibration acceleration and the reaction force of the rotor supports at critical speeds depending on geometric errors were calculated. To reduce the complexity of the calculations, neural network architectures were chosen to predict the parameters of the vibrational state depending on the geometric errors of the rotors. The novelty of the work lies in the creation and use of the original numerical model of balancing, taking into account the rotor manufacturing tolerances.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):18-27

### Control over maintaining accuracy of integrity of reference surfaces of spacecraft components in their joint functioning at various stages of design

#### Abstract

The paper deals with ensuring the accuracy of integrity of spacecraft components’ reference surfaces at various stages of design. It is shown that the main problem consists in the fact that the accuracy of integrity of the reference surfaces of the components making up the complex is maintained in the framework of the internal structure of a part. We propose a method of control over ensuring the accuracy of integrity of spacecraft components’ reference surfaces at various stages of design in the framework of their external structures. The method is implemented by introducing the coordinate system of the complex into the scheme of the complex of components that perform interrelated service functions. Concepts and definitions are introduced in the framework of the method that make possible formal representation of accuracy of integrity of the components’ reference surfaces in the form of a set of pairs of points the appropriate annotated dimensions are fixed on. Graphical interpretation of the method at the stages of development of technical requirements for the components is presented. An example of potential implementation of the method at the stage of design documentation development is given.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):28-40

### Optimal command control of hypersonic aircraft flight path in conditions of atmospheric disturbances

#### Abstract

Disturbed flight of a hypersonic vehicle in accelerated climb is analyzed. Disturbances are deviations of atmospheric density from the values of a standard model. The following concepts and definitions are used in the paper. The nominal optimal angle-of-attack control program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of standard atmosphere (hereafter – nominal program). The “disturbed” nominal optimal program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of disturbed atmosphere on the condition that the disturbances are known (hereafter “disturbed” program. The command optimal program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of disturbed atmosphere on the condition that the disturbances are unknown (hereafter command program, command control). A multi-step control process is accepted. At each step of control the angle-of-attack control program is defined using the method of Pontryagin’s maximum principle. The nominal control program is used at the first step. The results of modeling disturbed motion with angle-of-attack command control are presented for maximum “rarefied” and maximum “dense” atmosphere. In the case of “rarefied” atmosphere the angle-of-attack restriction is violated at the end of the flight segment under consideration in solving the boundary value problem, while the prescribed terminal velocity, altitude and flight path inclination conditions are satisfied. In the case of dense atmosphere the terminal altitude and flight path inclination conditions are satisfied, but the terminal velocity condition is not. Since there is no violation of the above-mentioned control and phase coordinate restrictions in the case of the “disturbed” program, further line of research in the area of optimal command control is related to the improvement of the algorithm of solving the boundary value problem.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):41-50

### Method of calculating dynamic designs of space launch vehicles for designing systems of stabilization of their motion

#### Abstract

Dynamic designs of tandem space launch vehicles are calculated according to the standard

OST 92-4548-85. The eigenmodes and eigenfrequencies of the elastic structure are calculated using the MSC Nastran or a similar program. We propose an addition to the existing methods of calculating dynamic designs of liquid-propellant rockets with account for their elasticity applying a method oriented towards operational generation of input data for developing systems of stabilizing their motion. We developed a procedure containing calculation of eigenmodes and eigenfrequencies of missile body elastic modes and the coefficients of impact of the elastic modes and surplus degrees of freedom. To demonstrate the method’s efficiency, in taking down the results for tandem launch vehicles in the analytical form the OST formulas are re-derived. In validating the proposed method of calculating design schemes we obtained results practically coincident with the already applied formulas for the range of tasks under examination. The versatility of the proposed method is illustrated by calculation of coefficients absent from the OST because the factors influencing rocket dynamics are not taken into account in the standard. The proposed method is distinguished by its generality, which allows describing various types of launch vehicles while taking into account all significant factors that influence the dynamics of their motion.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):51-63

### Optimizing the process of changing spacecraft orbital parameters by using a spinning electrodynamic tether sytem

#### Abstract

The paper considers parametric optimization of the process of changing orbital parameters by using a spinning electrodynamic tether system. Changes in the semi-major axis and eccentricity are taken as the two major goals, and two control laws are proposed accordingly. Current is regulated according to the instantaneous position of the conductive tether, which allows ensuring the calculated direction of the Lorentz force produced by the interaction of the conductive tether with the Earth’s magnetic field. A combined control scheme for simultaneous changes in the semi-major axis and eccentricity is proposed. The parameters of control laws are optimized on the basis of the Nelder-Mead method by using different objective functions and constraints. It is also shown that, by using the criteria of quick response and minimum impulse, we obtain optimal solutions corresponding to the boundary values of the selected parameters. Therefore, a convolution of these criteria is proposed as a compromise, which ensures a specified change in the orbital parameters of the system mass center.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):64-77

### Method for optimizing mass and size characteristics of a high-pressure turbine disk

#### Abstract

The article presents the results of weight and size optimization of a high-pressure turbine working disk for an augmented turbofan. The issues of modeling the operation of the engine’s first stage with a cover plate providing the delivery of cooling air to the blades are considered. Strength calculation of the stresses arising from the action of centrifugal forces under high-temperature conditions was carried out. A three-dimensional model of the disc was obtained. The finite element method was used. The pattern of temperature distribution in the disk body was obtained on the basis of heat calculation. Based on the strength calculation, the stresses and strains of the turbine disk were determined. Maximum stresses in the disc are located at the junction of the disc frontal area and the cooling air feed holes. Plastic deformation is observed in the area of the cavities for cooling air feed. It is shown that the stepped part of the disc should be made of a material with lower heat resistance and a higher value of permissible limit stress. Based on the study, a bimetallic disk design made by powder metallurgy was proposed.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):78-86

### Mathematical model of the “tank – nozzle” cooling system

#### Abstract

The task of increasing heat transfer of hydrocarbon fuel in the channels of cooling systems of liquid rocket engines is a matter of current interest. The article discusses the results of developing a mathematical model of an engine cooling system operating on super-circulation of fuel between the tank and the nozzle. The model makes it possible to determine the conditions under which the ratio of kerosene circulation in the nozzle cooling circuit would ensure that the selected material is used as the nozzle wall material, to find the minimum amount of kerosene in the tank required for cooling the nozzle by the proposed method.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):87-95

### Bringing spacecraft into solar-oriented attitude by the measurements of a single-axis angular-rate sensor and an optical solar sensor

#### Abstract

The algorithm of the turn of the spacecraft from an initial arbitrary angular position at an arbitrary angular rate to a solar-oriented attitude is investigated. Minimum essential equipment of the motion control system required for the purpose of ensuring maintenance of solar orientation is defined: a solar sensor, a single-axis angular-rate sensor, low-thrust liquid rocket engines. A solution of the problem of defining the spacecraft angular rate vector by the measurements of the deviation of the optical axis of the solar sensor from the sun vector and the single-axis angular-rate sensor is presented. The conditions under which control action on the rocket engines for the purpose of changing the value of the angular-rate vector for the Sun to get into the field of viewing of the solar sensor or for the spacecraft stabilization are defined. Mathematical modeling of the spacecraft attitude control system with the unknown initial state vector of motion is carried out. The results of mathematical modeling confirmed the efficiency of the proposed algorithm in terms of reducing propellant fuel consumption and high-speed performance. In comparison with the known methods of solving the problem of reducing angular speed (a lengthy process with the use of a magnetic system or a fast process with the use of a three-axis angular-rate sensor and rocket engines) the duration of the process of reducing angular speeds is the same as in normal operation, however, at the same time the problem of bringing spacecraft into the solar –oriented attitude is solved.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):96-105

## MECHANICAL ENGINEERING

### Cyclic compression of a multi-layer multi-span corrugated package with plastic deformation of its tapes

#### Abstract

In this article we present our solution of the problem of cyclic compression of a single-layer and multi-layer corrugation, as well as of a single-layer multi-span corrugation by the FEM method using Ansys. This problem can be considered as the first part of the general complex nonlinear problem of cyclic compression of a multi-layer multi-span corrugated package with dry friction on the contact surfaces. We conducted an analysis of the known published solutions to this problem, and we discovered inaccuracy of some of them and the physical reason resulting in this unacceptable error. A very large number of published solutions to this problem are generally explained by the presence of successful examples of their practical application in the field of aircraft and rocket engine manufacturing, by the wide possibilities of their use as damping devices in both of these areas, and, for example, in the automotive industry, by their high elastic-friction, strength and performance characteristics. All the known published solutions to this problem were obtained for cyclic compression of a multilayer multi-span package in the region of its elastic deformations and for the same geometric shape of the corrugation. The task of improving the mass characteristics of an engineering unit is quite relevant for the development of shock-proof single-shot damping devices that increase the passive safety of the car – bumper protective devices. This can be solved by using single-layer or two-layer, multi-span packages with an optimally selected geometric shape of the corrugation, deformable in the elastic-plastic region. Therefore, the above-mentioned problems are solved taking into account the elastic-plastic deformation of the corrugations for any of their geometric shapes. The obtained solutions make it possible to construct any loading processes in the field of elastic-hysteresis package loops. We also investigated the influence of the parameters of the corrugated package on its elastic-friction characteristics (including the shape of the corrugation and the presence of gaps between the tapes of the package at the tops of their corrugations).

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):106-117

### New technologies implemented in the design of a low-emission combustion chamber of a gas-turbine unit

#### Abstract

Metallist-Samara JSC has developed a fundamentally new design of a unified double-circuit burner of a low-emission combustion chamber (LECC) of a ground-based gas turbine unit (GTU), adapted for manufacturing with the help of an innovative technology by selective laser melting (SLM) of metal powders using CAD models. Several batches of burners were made and control studies were carried out characterizing the quality of manufacturing according to the established procedure. Deficiencies inherent in the SLM process were discovered, the main of which are: raised roughness, in particular, of the fuel channels of the main and duty zones; microporosity, microalloying; microcracks; instability of flow characteristics; local non-sintering zones of the layers grown on the burner body. As a result of the analysis of the state of the manufactured burners, research and refinements, it was found that most of the identified shortcomings can be eliminated during further development of the modes and parameters of the technological process. Currently, difficult engineering problems associated with the implementation of additive manufacturing technologies have been overcome.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2020;19(1):118-126