Section 3 - Track 3

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Valery Bogdanovich and Mikhail Giorbelidze
Mathematical modeling of features of heating of a cylindrical surface at plasma spraying
A mathematical model for determining the temperature in the coating-base system during plasma deposition of powder material on the inner cylindrical surface has been developed. The mathematical model takes into account the transformation of the Gauss heat source, the speed of relative motion of the plasma torch and the angle of the plasma jet with respect to the sputtered surface. The influence of technological parameters of sputtering on the heat stress of the process and the quality of plasma coatings is analyzed.

Andrey Agafonov, Ksenia Milanina, Anatolii Eremin and Vasiliy Gavrilov
Application of molecular dynamics for modeling processes in microfluidic devices
The article considers the possibility of using the molecular dynamics (MD) as part of multi-level models for describing processes in microfluidic devices. Much attention is paid to issues related to the use of MD to describe processes at a gas-solid interface.

Dmitriy Ivanov and Aleksandr Zhdanov
Numerically stable algorithm for identification of linear dynamical systems by extended instrumental variables
Instrumental variables are widely used to identify linear dynamical systems. The advantages of instrumental variables include low computational complexity, as well as the possibility of identification for different models of color noise. Often the method of instrumental variables leads to ill-conditioned problems, which significantly limits the application of this method. The paper proposes a solution to the problem of extended instrumental variables based on augmented normal equations. Test examples showed high accuracy of the proposed approach.

Andrey Dmitriev, Ilnur Madyshev, Aliya Khafizova and Andrey Nikolaev
Hydrodynamics in counterflow cooling tower with corrugated inclined contact elements
Packing for liquid cooling with counter flow of liquid and gas phases had developed by authors of paper. This packing is different from other devices in that it has quite simple design where self distribution of liquid in apparatus working area is organized. In paper an estimating calculations of packing operating mode with maximum efficiency of performed heat and mass transfer processes had conducted. The performed numerical study is showing that at mean gas velocity up to 4 m/s, contact device width equal to 0.1 m and liquid column height on contact stage – 0.02 m the share of liquid that forced through by gas flow is not more then 2 %. Decreasing of holes diameter on inclined contact elements results in increasing of bubbled liquid share.

Tatiana Mikhailova, Eldar Miftakhov, Vladimir Mikhailov and Sofia Mustafina
About an algorithm for modeling the isoprene polymerization process in the cascade of reactors using the Monte Carlo method
The article describes an algorithm for modeling the isoprene polymerization process based on the Monte Carlo method. The algorithm can be used to simulate polymerization processes carried out in batch or continuous mode. The possible polycentricity of the catalyst used is also taken into account. The model on the basis of this algorithm makes it possible to study the properties of the polymerization product and calculate the molecular weight distribution for different points in time.

Victor Ryazhskikh, Alexander Nikolenko and Dmitry Konovalov
On the structure of the orthotropic 3D permeability tensor of an anisotropic porous body in heat and mass transfer problems
The structure of a 3D permeability tensor with orthotropic properties is proposed to describe various heat and mass transfer processes in anisotropic porous media. This structure of the permeability tensor has advantages over the monoclinic and triclinic because of the minimum number of elements to be determined, which greatly simplifies the formulation, conduct and processing of the corresponding experiments. In addition, the confirmation of the operability of such a structure opens up new opportunities for the artificial creation of porous materials with specified properties and the required anisotropy architecture on 3D printers. Using the Jacobians of rotations in the Cartesian reference system, the matrix of rotations is found as a result of successive multiplication of Jacobians by different angles around the axes of the base coordinate system. The final form of the tensor is identified as the product of the orthotropic tensor on the left and right by the turn matrix and the transposed turn matrix, respectively. This representation allowed us to calculate the inverse permeability tensor and synthesize a mathematical 3D model of Darcy-Brinkman type of unidirectional flow in a porous channel of rectangular cross-section on the example of hydrodynamic filtration of a Newtonian fluid. It is shown that such linearization does not level the property of anisotropy in a porous medium, while maintaining three-dimensionality.

Vladimir Aslanov and Daria Andrievskaia
Delivery of a returned container from the surface of Phobos using electrostatic forces
The original scheme of delivery of a returned container with soil samples from the surface of Phobos to the orbital spacecraft is proposed. The scenario of this mission consists of two stages: the launch of the container from Phobos using a simple spring mechanism and capture of the container by the orbiting spacecraft using the Coulomb force. A mathematical model of the container's motion relative to the spacecraft has been developed. A motion analysis is carried out, based on which the following characteristics of the system are selected: initial velocity of the container, value of the Coulomb force, and height of the lift of the container.

Oleg Krol, Volodymyr Sokolov, Petko Tsankov and Olexandr Logunov
Modelling of machining center vibration stavility by the D-partitions method
The stability of operation, vibration-free processing of products various types at high-speed machining centers suggests the improvement of research in the field of the dynamics of machine tools and their main forming units. The three-dimensional models of the forming spindle node and the corner table of the machining center for the drilling-milling-boring type in the CAD environment KOMPAS-3D have been developed. An algorithm for analyzing the dynamic quality of the machine elastic parts based on the constructed static and frequency formular in the mathematical environment MAPLE is proposed. Programs have been developed and graphs of the main frequency characteristics and the hodograph of the transfer function for the spindle node in the specialized Signal Processing module have been obtained. The method of D-partitions using to estimate the vibration stability of the forming units on an example of 4 coordinate milling machining centers is introduced. Experiments on two variants of technological adjustments with different dimensions of the tool block (the cantilever part of the spindle assembly) were carried out. The analysis of stability in the plane of the cutting process optimized parameter (specific cutting force) was carried out. The region and the boundary of the stable functioning of the machine and, on this basis, the optimum modes of machining by the criterion of vibration stability are revealed.

Sergey Volgin, Maksim Ivanushkin and Ivan Tkachenko
Modelling of onboard systems operation of small satellites based on general logical-probabilistic method
An approach for simulating the operation of onboard systems of small satellites has been developed. The purpose of the technique is to simulate all possible combinations of malfunctions in the onboard systems of the small satellite, leading to the occurrence of abnormal situations during their operation. As a result of using the technique, a list of emergency situations is created, which is later used to create programs for complex testing of small satellite on-board equipment at the ground testing stage. The use of the technique leads to a reduction in time for the preparation of tests, provides support in making decisions on the management of the small satellites and reduces the response time to emergency situations that arise during operation.

Iliya Grachev, Michael Bolotov, Vadim Pechenin and Evgeny Kudashov
Comparative analysis of simulation options for the real geometry of the surfaces of gas turbine engine parts
Geometric deviations of parts surfaces inevitably occur during parts manufacture. It is known that the accumulated defects of parts surfaces and assembly units impact their functional characteristics throughout the entire product life cycle. Often, assembly simulation and dimensional ties analysis of products are performed by using the nominal geometry of parts without taking into account geometric deviations of the shape and location of parts surfaces. The accuracy of dimensional analysis without taking into account geometric deviations of the shape and location of parts surfaces is not sufficient to solve technological problems in digital production. The purpose of this article is the study of the influence of methods and models for constructing the real geometry on the accuracy of its reproduction. The subject of the research is the assembly unit of the rotor of a low-pressure turbine of an aircraft engine. The article considers three methods for constructing the real geometry, which are used to realize assembly virtual simulation. Comparative results of assembly simulation with the use of considered methods of real geometry constructing are presented, as well as their influence on the controlled assembly parameters is estimated.

Vadim Salmin, Vladimir Kurenkov, Sergey Safronov, Ivan Tkachenko, Artem Yakischik, Maksim Ivanushkin, Sergey Volgin and Anastasiia Krestina
Development of tools for computer-aided engineering and simulation of the remote sensing satellite systems, taking into account the requirements and limitations on customer resources
This article examines approaches to the selection of design parameters and modelling the functioning of the remote sensing satellite systems, taking into account the requirements and restrictions on customer resources. The objective of this research is to increase the efficiency of the use of space systems to solve urgent tasks of monitoring the earth's surface. Firstly, an analysis of the requirements for space imagery materials and consumer information support for solving regional problems was carried out, secondly, mathematical models of remote sensing equipment and onboard systems of small spacecraft, as well as the ground-based complex for receiving and processing information, were developed, and finally, a database with the technical characteristics of the onboard systems and remote sensing equipment of spacecraft, launch vehicles and ground-based reception and processing information facilities was created. As a result, software to determine main design parameters and modelling the functioning of cost-effective remote sensing satellite systems was developed.

Elena Demyanenko, Anastasia Kosolapova and Igor Popov
Modeling of the process of plastic deformation as applied to thin-walled shells of the type of bottoms
Disclosed is a method of producing bottom-type parts based on a flanging process. Results of physical modeling of equivalent-thickness parts of bottom type are presented. Parameters of rheological model of cold deformation are determined. The procedure of procurement calculation and simulation results are given.

Vadim Zinurov, Nailya Dubkova, Oksana Popkova and Oksana Dmitrieva
Influence of separation elements shape on device efficiency
A paper deals with the urgent problem of studying the separation process of gas flow from fine-dispersed particles. A device developed to intensify gas flow separation from fine-dispersed particles. The principle of operation of the device is given. The effect of the shape of separation elements, gas flow velocity, as well as size and density of particles on device efficiency has been investigated. As a result of the study, the maximum efficiency of gas flow separation (on average 85 %) is achieved at a gas velocity of 8 m/s. Moreover, the separation increases when the density and diameter of the particles begin to grow. The double-T shape of separation elements was demonstrated as the most effective types of geometry.

Andrey Parfiriev, Oksana Parfirieva and Igor Ishchuk
Quadcopter directorial control algorithm with the possibility of flying around obstacles
The article solves the problem of developing an autonomous flight control system that allows an unmanned aerial vehicle of a copter type, a quadrocopter, to fly along a given route with the possibility of flying around obstacles. The problem is solved by developing a detailed mathematical model of a quadrocopter with four propellers, taking into account the influence of the working environment and the algorithm for trajectory control of an unmanned aerial vehicle. The mathematical model is based on the basic law of dynamics for translational motion and the basic equation of dynamics for rotational motion. The trajectory control algorithm aimed at maintaining the required linear coordinates of the quadrocopter over the entire length of the route was developed using a proportional-integral-differentiating (PID) controller. A PID controller is also used to maintain angular coordinates. The coefficients of the PID controller are calculated by the tangential method or the Ziegler-Nichols method. The trajectory control algorithm is implemented in an object-oriented programming environment. The mathematical model is based on the basic law of dynamics for translational motion and the basic equation of dynamics for rotational motion.

Irina Papkova
On a static solution to the contact interaction of a flexible rectangular in plane of a microshell with a rectangular in plane of microplate
The mathematical model of the contact interaction of a flexible rectangular in plane of a spherical microshell and a flexible rectangular microplate is constructed. The material of the shell and plate is elastic isotropic and homogeneous. Kirchhoff hypotheses are taken into account. A system of nonlinear partial differential equations is derived from the Hamiltonian energy principle on the basis of a modified couple stress theory. The contact pressure function was determined according to the theory of B.Ya. Cantor. Contact interaction of sensitive elements of micromechanical sensors of inertial information in the form of a micro-shell and micro-plate is investigated. A micro-shell is affected by a static, uniformly distributed load. The static solution is determined by the establishment method. A new phenomenon related to the loss of stability is obtained.

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