# Vol 17, No 1 (2018)

**Year:**2018**Articles:**15**URL:**https://journals.ssau.ru/vestnik/issue/view/288

## Full Issue

## AIRCRAFT AND SPACE ROCKET ENGINEERING

### Optimizing a vehicle trans-atmospheric motion using Pontryagin’s maximum principle

#### Abstract

The task of optimizing trans-atmospheric motion of a flight vehicle in order to maximize its final velocity with prescribed finite values of the height and flight path angle is considered. The angle of attack acts as control in passive motion of a vehicle. Previously, the sequential linearization method was used to solve this optimization task. It is shown that at great altitudes the control programs are slightly different depending on the chosen initial approximation. Therefore, the aim of this work is to determine the optimum control program on the basis of a “strict” solution of the optimization task using the Pontryagin’s maximum principle. Solving the problem of optimizing trans-atmospheric motion of a flight vehicle is illustrated by passive climb of the sub-hypersonic vehicle MPV (the first stage of the aerospace system RASCAL designed in the USA). The coefficient of lift (angle of attack) increases in the greater part of the trajectory to provide the prescribed finite values of height and path inclination and then decreases to provide maximum final velocity. The correctness of the obtained solutions of the optimization task using the maximum principle is confirmed by the zero Hamiltonian value in the optimum trajectory. The results of vehicle motion simulation with optimal control and various initial conditions of motion and the vehicle mass are discussed. The results obtained show that the solutions of the optimization task under consideration using the maximum principle and the sequential linearization principle are in close agreement.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):7-19

### Determination of spacecraft antenna directivity pattern with the use of an Earth-based station

#### Abstract

The problem of defining characteristics of the spacecraft antenna directivity pattern is considered in the paper. The solution of the problem will make it possible to estimate changes of antenna parameters with time. A method of defining the spacecraft antenna directivity pattern with the use of the earth-based data receiving stations is proposed for solving the problem. The results of simulation modeling of distribution of electromagnetic radiation over the Earth's surface for different routes of flight are presented in the paper. These results show the possibility of using an earth-based data receiving station for the construction of the spacecraft antenna directivity pattern. An algorithm of calculating parts of the direction characteristic with their subsequent integration is given in the article. The conditions limiting the accuracy of the proposed method as well as the ways of speeding up the construction of the spacecraft antenna directivity pattern are determined. Approbation of the proposed method through the example of the antenna of the small spacecraft “AIST-2D” is discussed. The directivity pattern of the antenna of the radio data link for transmitting target information of the satellite was constructed for this purpose and characteristic parts of the antenna directivity pattern are defined. The results of the comparative experiment with changes in the antenna radiation direction and definition of changes in information reception characteristics are presented.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):20-27

### Inertial measuring units for future-generation aerospace products: fault-tolerance

#### Abstract

A Strapdown Inertial Measurement Unit (SIMU) with structural redundancy intended for improving fault-tolerance and accuracy of inertial navigation systems for space applications is considered. The SIMU includes six angular rate sensors and six accelerometers, which allows for identification and correction of one fault with high probability and two faults with lower probability for each type of sensor. Known theoretical and practical techniques developed and used in this area are briefly described. The problem of optimization of measurement axes orientation is considered. The accuracy of estimation of the measured vector projections in the orthogonal instrument coordinate system serves as the criterion of optimization. A solution of this problem for no faults, one fault, and two faults is proposed. Algorithms of failure detection, identification and correction (FDIC) are analyzed. The results of testing FDIC basic algorithms with the help of mathematical simulation are considered. Optimal measurement axes configurations are compared with each other from the FDIC efficiency point of view. It is shown that neither of the methods yields 100-percent correct diagnostics not only for two faults but for one fault as well. Possible sources of incorrect diagnostics are analyzed.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):28-44

### Estimation of systematic errors in the results of navigational measurements with the use of spacecraft robot onboard facilities

#### Abstract

The article presents the results of an analytical study of the accuracy of estimating systematic optical errors of onboard navigation measurements that, along with the vector characterizing the motion of the center of mass of the space robot, are included in the vector of the parameters to be specified. The range to the orbital reference point, the relative speed of its motion and the angles between the directions to the orbital landmark and to the navigational stars, one of which is in the plane of the space robot’s orbit, and the direction to the second one coincides with the normal to this plane are chosen as the primary navigation parameters to be measured by the space robot onboard facilities. The conditions that make it possible to specify the augmented vector of the parameters to be determined are defined. Estimating the systematic errors of measurements we make assumptions about the central gravitational field of the Earth, the normal law of measurement errors with known variances and the constancy of the unknown systematic errors. Analytical expressions of the covariance matrices that make it possible to estimate the maximum achievable accuracy of solving the task depending on the kind of navigational measurements, variances of measurement errors and the number of measurements during a selected measuring interval are obtained. The presented results can be applied to justify the ways of improving the accuracy of the autonomous navigation of a space robot in diagnosing the technical condition of an orbital object.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):45-54

### Photoelectric converters in the power supply system of an atmospheric pseudo satellite

#### Abstract

Unmanned aerial vehicles have enormous potential and prospects in expanding the field of application from photo and video to providing cellular communications and relaying signals. An atmospheric pseudo satellite that is expected to function exclusively at the expense of solar energy is being developed at S.P. Korolyov Samara National Research University. A study of the efficiency of using photoelectric converters in the onboard equipment of an atmospheric pseudo satellite based on the unmanned aerial vehicle Foton-601 was carried out. A comparative analysis of various types of photovoltaic converters made of amorphous silicon was performed. A mathematical model was developed and the area of solar cells coating required to generate sufficient power was calculated. The mass of the solar cells for the appropriate coating area was calculated. Also, in order to reduce the mass of an unmanned aerial vehicle and, as a result, its energy consumption, a method of mathematical calculation to determine minimum and sufficient required battery capacity was developed, on the basis of the maximum amount of solar energy that can be converted within 24 hours. The results of flight tests were analyzed and the prospects for the use of photoelectric converters as components of solar cells of atmospheric pseudo satellites were specified.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):55-60

### Methods of evaluating low-cycle fatigue of gas turbine engine parts exemplified by a high-pressure turbine cover plate

#### Abstract

This article presents an example of calculating the durability of a real part of a gas turbine engine. The part under examination had problems in its operation due to origination of cracks, exhaustion of load bearing capacity and non-localized fracture owing to crack development arising as a result of low-cyclic fatigue of material in the inter-labyrinth zone of the part. The part design analysis carried out with the use of engineering methods in conformity with the standard procedure accepted at the time of design did not presuppose any strength problems owing to low-cyclic fatigue. Mass manifestations of the defect “crack in the radius of the deflector flange center pilot transition” called for the necessity of evaluating the safety of subsequent use of products containing these parts before they reach the end of their assigned service life. Based on the results of metallurgical studies, a conclusion of the causes of defects was made and a complex of technological measures to prevent these defects in the future was proposed. Some methods of evaluating low-cyclic fatigue are presented in the article. They are widely used in engine design and development at the present time (in the absence of a data bank on the properties of materials under the “hard” loading cycle).

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):61-71

### Optimization of ducted counter–rotating fan blades on the basis of solving a 3d inverse problem with the aim of improving fan gasdynamic characteristics

#### Abstract

When developing counter-rotating fans for advanced aircraft engines with ducted blades (CRTF), it is very important to ensure high acoustic and aerodynamic characteristics. To provide investigations of aerodynamic and acoustic performance of the original version of an advanced counter-rotating CRTF1 fan model with in the C-3A anechoic chamber (CIAM), its experimental and mathematical models were developed and 3D steady viscous flow and integral characteristics were calculated. The paper presents a comparison of data computed by “mixing plane” approximation and the experimental CRTF1 data. This comparison shall demonstrate the validity of designing the CRTF2A second version without taking unsteady interaction into consideration. These comparisons of computed and measured data give evidence of good agreement at . The degree of coincidence between the computed and experimental data at is satisfactory – maximum error is <2%. This paper presents some results of gasdynamic and aeroacoustic optimization of the configuration of a ducted fan carbon composite blade on the basis of the solution of a 3D-inverse problem [3]. A distinctive feature of a carbon composite blade as compared with a solid titanium blade is thicker leading and trailing edges and increased maximum blade profile thickness.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):72-86

### Optimization of open counter – rotation fan blades on the basis of solving a 3D Navier-Stokes inverse problem with the aim of reducing tonal noise

#### Abstract

The paper presents some results of gas-dynamic and aero-acoustic optimization of the blade profile of an unducted counter-rotation fan (CRF) by using a 3D inverse problem. It was established on the basis of unsteady-state 3D Navier-Stokes equations that the interaction of tip vortices of the first and second rotors as well as potential interaction of the rotors is one of the key sources of tonal noise. Using the 3D solver of the inverse problem, aerodynamic loads are redistributed along the height of the blades of R1 and R2 rotors so as to reduce tip vortex intensity and potential rotor interaction in case of possible increase of the CRF thrust. To check the acoustic characteristics of the modified CRF, tonal noise modeling was carried out for the original and modified CRFs using CIAM’s aero-acoustic 3DAS solver for the solution of unsteady-state equations. The near acoustic field and directivity diagrams in the far field were found. The fan tonal noise in take-off and landing was decreased by 4 dB without any thrust or efficiency losses.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):87-99

## MECHANICAL ENGINEERING

### Сhoice of materials for producing dimensionally stable load-carrying structures

#### Abstract

The article deals with the problems of choosing materials for producing dimensionally stable load-carrying structures of space optical electronic complexes. Physical and mechanical properties of successfully applied and promising composite materials obtained by theoretical and experimental research are presented. A comparative analysis of properties of carbon-filled plastics is given according to the percentage of filler content in a composite matrix and the elastic modulus of carbon fiber. Experimental data related to the properties of carbon-filled plastics based on various fibers are presented. The dependence of the temperature coefficient of linear expansion (TCLE) of various carbon-filled plastics with unidirectional and quasi-isotropic structures is studied theoretically and experimentally. The stability of TCLE is shown to be approximately equal to 1·10^{-6} ˚C^{-1} in the area with 50-60% volume filler content. The TCLEs and elastic moduli of carbon-filled plastics and optical glasses of telescope elements are compared. The task of developing a composite material with a TCLE value characteristic of titanium alloys is discussed. Recommendations for applying the analyzed composite materials in the development of dimensionally stable space structures are given.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):100-117

### Residual stresses and fatigue resistance of toothed wheels

#### Abstract

Residual stresses in the dangerous section of toothed wheels made of materials and according to practices accepted in aviation engine construction have been determined using a mechanical method. The influence of the technology of manufacturing of toothed wheels, thermo-chemical treatment, hardening and coating on the residual stresses has been examined. Current technologies of manufacturing toothed wheels lead to significant dispersion of residual stresses, especially after thermo-chemical treatment. Therefore, the results have been statistically processed for each batch of parts and the average values are shown on the residual stress diagrams. We demonstrate the possibility of determining residual stress distribution in the dangerous section of a wheel tooth by the initial deformations of the reference specimen, which makes it possible to keep the part under examination unimpaired. A plate made of the same material as the toothed wheel and hardened simultaneously with the part under examination was used as a reference specimen. The influence of residual stresses on the fatigue resistance of toothed wheels by the average integral residual stresses criterion that takes into account both the value of residual stresses and the nature of their distribution in the dangerous section of toothed wheels was examined.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):118-127

### Relation between characyeristics of low-cycle and high-cycle fatigue of threaded parts and residual stresses

#### Abstract

The dependence of low-cycle and high-cycle fatigue characteristics of threaded parts on the criterion of average integral residual stresses is examined in the article. These characteristics play an essential role in ensuring reliability of aeronautical equipment. The study was carried out using titanium-alloy M6 bolts with various ways of producing residual stresses. In all the cases the dependences are quadratic. Further analysis showed linear dependence between the increment of cycle life and the limiting cycle amplitude under changes of residual stresses. This conclusion holds for all examined ways of producing residual stresses. The increments mentioned are linear functions of the criterion of average integral residual stresses. A procedure for determining the increment of the limiting cycle amplitude with the use of the criterion of average integral stresses is presented. Special attention is given to the method of finding the coefficient of residual stress influence on the limiting cycle amplitude for the constant mean stress. The approach to determining the increment of cycle life by a known value of the increment of the limiting cycle amplitude calculated with the use of the criterion of average integral residual stresses is validated.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):128-136

### Topology optimization of a load-bearing structure via the method of convex linearization

#### Abstract

A method of topology optimization based on the convex linearization approach is proposed. The problem formulation implies minimization of the strain energy of a structure subject to volume constraint. The solution is based on explicit, convex and separable Lagrangian approximation with the involvement of the duality theory. A non-linear model is used to relate design variables (density) and elastic properties of the material (modulus of elasticity). The sensitivity of the gain function and the constraint function is analyzed. The basic design formulae for the iteration algorithm of topology optimization are obtained. A number of test problems that correspond to the basic load states: tension, shear and torsion are considered. For all cases the load-carrying factor is calculated: both analytically and with the use of finite-element models. The resulting topologies are shown to be in full compliance with engineering concepts of theoretically optimal structures.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):137-149

### Rotor-pendulum self-synchronization of parametrical vibration generators on an isotropic elastic foundation

#### Abstract

Significant improvement of dynamic characteristics of vibration machines on the basis of the use of resonant oscillatory systems with two or more degrees of freedom is proposed. It is shown that reasonable complication of models due to the increase in the number of degrees of freedom, taking account of nonlinearity makes it possible to increase reciprocal enhancement of vibrations of partial subsystems and to open additional opportunities in the development of new equipment and technologies. The involvement of objects of an oscillatory system in collective interaction is achieved on the basis of using compound resonances which occur in coupled systems only. Combination parametric resonance caused by pair-wise interaction of free modes of oscillations represents this kind of resonance. The results of theoretical and experimental studies of self-synchronization of parametric rotor-pendulum vibration generators installed on a common elastic isotropic foundation are presented in the paper. The dynamic model of a vibration machine is represented by a set of peer interacting nonlinear oscillators (pendulums) under resonant excitement of which the Huygens's effect, that is, pendulum clock-type self-synchronization (pendulum self-synchronization) occurs. One or several oscillators perform the functions of the working body of the vibration machine. Other oscillators of this system act as the inertial element of a rotor-pendulum vibration generator. It is shown that in the case of combined action of at least two rotors-pendulum vibration generators unbalanced rotor-type self-synchronization (rotor self-synchronization) takes place. Thus, the device under examination at the same time combines rotor and pendulum self-synchronization. The results of numerical modeling in the form of amplitude-frequency characteristics and dependences of generation frequencies on the frequency of parametric excitation are presented. It is established that the amplitude of the working body oscillations, due to resonant interactions with the generator pendulums, underreacts to an increase in damping. The sum of natural frequencies of pendulums and the working body meets the condition of combination parametric resonance over the whole range of the instability region.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):150-159

### Analysis of the mechanism of fatigue crack arrest in a cylindrical notched specimen

#### Abstract

The phenomenon of fatigue crack arrest in surface-hardened cylindrical specimens with stress concentrators is examined from the perspective of linear fracture mechanics. The stress intensity coefficient (SIC) is considered as the criterion, its scope determines the speed of fatigue crack growth in the case of cyclic loading. The calculations of the study were carried out by the Finite Elements Modeling method using the calculation complex ANSYS. The calculation complex ANSYS that uses the Finite Elements Modeling method in the form of displacements was applied to determine the stress intensity coefficient under bending of cylindrical surface-hardened and non- hardened specimens with the diameter of 10 mm with a semicircular notch with the radius of 0,5 mm. It is established that the stress intensity coefficient has two extremes in the initial area of the fatigue crack development: the minimum and maximum values. The results of the calculation indicate that the minimum value of SIC is lower than its threshold value below which the crack does not develop in the case of a cylindrical surface-hardened notched specimen. This fact is in good agreement with the results of tests of these specimens as non-propagating fatigue cracks were revealed in these specimens only. It is also established that the depth of a crack is approximately 0,02 of the minimum size of the section of a cylindrical specimen for the maximum value of the stress intensity coefficient. The study carried out validates the use of the criterion of average integral residual stresses to calculate the increase of the endurance limit of surface-hardened specimens and parts with stress concentrators due to compressive residual stresses.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):160-169

## INFORMATION SCIENCE, COMPUTING TECHNOLOGY AND CONTROL

### Arrangement of data for the formation of a multidimensional array of essential insights in automated enterprise management system

#### Abstract

The article proposes a way of organizing and storing information to generate a multidimensional array of related current data that reflect a documented fact of performing economic operations in a common information space. The proposed method is based on structuring the data conforming to primary documents, detailed to logically complete economic operations and rigidly interconnected. The essence of the method is discussed in the paper. The experience of creating an automated control system on the basis of the developed method of organizing and storing data on economic activity is described. We propose to use the resulting array of structured data for integration with functional accounting systems to automate basic processes in enterprise management on the basis of the generated OLAP system. Examples of external influences on the automated control systems and ways of troubleshooting are described. Conclusions about the positive effect of introducing an automated system of enterprise management based on the developed method of organizing and storing actual data about purchases, sales and own expenses, as well as their relationship to functional automated systems are drawn.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2018;17(1):170-179