Electromagnetic vibroexciters find wide adaptation in technological processes of condensation of environments, for movement in conveyors of materials, in test beds, etc. In each case loading is the weight which can be located on mobile parts (rotor) electromagnetic exciters directly, or through elastic elements (springs). For formation of movement of an rotor in the form of weights vibration it is neces-sary to know power parameters electromagnetic vibroexciter. The detailed analysis and a conclusion of power correlation taking into account of mechanical loadings and frequencies of mobile system elec-tromagnetic exciters vibrations are absent, though some brief data about power electromagnetic exciters in the literature are available. In this paper an attempt is made to further define the energy indicators of electromagnetic exciters with regard to the vibratory motion of the mass and losses arising in electrical and mechanical parts.

Keywords:
anchor, air gap, damping, rigidity, oscillatory system

Bozhko A.E., Ivanov E.M., Ivanova Z.A., Myagkohleb K.B. An investigation of the power of the electromagnetic modulator of vibrations . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 14-18.

On the basis of the classical theory of elasticity of an anisotropic body compared stress-strain state of multilayer thick-walled cylinder of finite length under the action of internal pressure and temperature. The protective layer of the cylinder is made of aluminium and carbon fiber. Kinematic and static contact conditions on the surfaces of adjacent layers are considered ideal. The solution of the problem was obtained in axisymmetric setting. The internal pressure and temperature load change sinusoidal the length of the cylinder. It is noted that the replacement of the dural protective layer composite pipes in carbon, significantly affects its stress state. Protective layer of carbon fiber was more effective version when comparing the stress-strain state of the considered design options cylinders.

Keywords:
hollow cylinder, temperature; fiberglass; carbon fiber

Vereshchaka S.M., Deineka A.V. Comparison of thermal stress for multilayer pipes with a protective layer of duralumin or carbon fiber . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 19-30.

In this paper was carried out a brief overview of the current state of the problem and analysis of publications on it. The aim of this article is to adapt the method to calculate the energy balance oscillators with variable mass under the action of dry friction force. First we considered the problem of the oscillator at a constant value of dry friction force. The problem is reduced to the integration of non-linear differential equations with variable coefficients. With the modified method of energy balance were obtained approximate formulas for the calculation of the amplitude and the mass of the oscillator at the end of the k-th magnitude. We also obtain estimates for the limited number of ranges oscillator with variable mass. Exact, but one-sided estimates of scale were constructed by comparing oscillator variable and constant mass. The second was considered problem of the oscillator with a variable frictional force. Here, based on the energy balance method, formulas for calculating the amplitude of the oscillations at the end of the k-th magnitude were obtained. The conditions are investigated under which the process of the oscillator are complete. The work carried out numerical calculations in which a comparison of oscillation amplitudes obtained by the method of energy balance and the WBK method. A good agree-ment between the values in the amplitude calculated in different ways. Review the adequacy of two-sided estimates for the number of oscillation amplitudes. Also was compared the values of the amplitudes obtained by approximate formulas with the results of numerical integration of initial differ-ential equations. Calculations were confirmed that received an upgraded energy method are quite suit-able formula for calculating the amplitude damped oscillator linearly variable mass under the action of dry friction force.

Keywords:
free vibrations, linear-variable mass, dry friction

Ol’shanskij V.P., Ol’shanskij S.V. Free fluctuations of linearly-variable weights oscillator with dry friction. NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 67-76.

The article in presence is devoted to analysis of the coupled electromagnetic and mechanical fields in composite structures. High-intensity electromagnetic fields are conditions for a variety of tech-nical and technological objects. The interaction of electromagnetic fields with conductive bodies can cause their movement and deformation. Energy levels that are developed by an electromagnetic field can be significant to such an extent that it can lead to the destruction of elements of structures and ma-chines. The creation of effective methods of analysis of the stress-strain state of the conductive bodies under the influence of electromagnetic fields is an important problem in scientific and practical terms. The paper presents a general approach to the analysis of deformation of the conductive bodies in the electromagnetic field. This approach relies on the analysis of the distribution of a vector of characteris-tics of the electromagnetic field and tensor characteristics of the deformation process. These characteris-tics are determined from the solutions of the two groups of differential equations. The first group de-scribes the propagation of the electromagnetic field in the material, while the most often used represen-tation of Maxwell, which formed the basis of the differential equations of the vector electric and mag-netic field vector electric and magnetic induction currents and charges. Unsteady deformation of a sys-tem of interacting bodies is described by the known relationships, which include differential equations of motion (equilibrium), the geometric dependence (in the form of Cauchy) and the equation of state. Coupling of “electromagnetic” and “mechanical” processes is taken into account through the introduc-tion of “electromagnetic” forces. To conduct the numerical analysis of the propagation vector compo-nent of the electromagnetic field in the article the concept of a vector magnetic potential is used.

Keywords:
electromagnetic fields, vector magnetic potential, finite element method, stress-strain state

Lavinsky D.V. Analysis of electromagnetic and mechanical fields in compound constructions . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 31-36.

The paper researches the dynamic process of establishment and development scientific – peda-gogical activity of professors of mechanics of National Technical University “Kharkiv Polytechnical Institute» in the 19 – 21 centuries. The origination of the Ukrainian technical science in the field of theory of control systems is connected with the NTU «KhPI». It discovered and explored the main scientific trends of evolution of establishing optimal control of moving objects and technological proc-esses. Main phases of formation and development of research and design school of NTU «KhPI», its earlier spacecraft related works, subsequent work in the present-day period and implications for the spacecraft industry in Ukraine are shown. Names of persons are referred to, which were associated with the NTU «KhPI» school or left it. The Kharkiv oldest, rocket and space enterprises «Kommunar» and «Khartron» are the largest, producer’s control systems for ballistic rockets and spaceships. Additionally to specific space products (launchers, satellites, space components, etc.) scientists оf NTU «KhPI» also created the number of «common» products for the needs of machinery, power production, etc.

Keywords:
mechanics, dynamics, scientific – pedagogical activity, higher technical education, guided missile, theory of control, launchers, satellites, spacecraft industry, engineers, designers

Аndreev А.G., Nazarenko S.A. Main results of scientific and pedagogical activity of professors of mechanics and control systems of NTU «KHPI» . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 3-14.

The paper deals with a multiscale finite element modelling of the pneumatic tire deformation in a contact with the road. The modeling gave a possibility to find cycles of the stresses in the most loaded layers of tire. Geometric and finite-element model of a pneumatic tire has been created. The model has multilayer structure with unique properties of each layer. Neo-Hookean law is used for rubber-like materials. The orthotropy of mechanical properties of rubber-cord layers (carcass and belt) has been also taken into account. The orthotropy was set using local finite-toroidal coordinate systems. These features causes a problem with numerical convergency for large FE models. So, the calcu-lation of accurate results of strains and stresses makes the demand of successive mesh refining by sub-modelling aproach. Three scale of models were developed.The analysis of contact interaction between pneumatic tire and pavement (road surface) has been carried out on the base of first scale of modelling. It included geometrical and physical nonlinearity. The general deformation was obtained. These results are used as boundary conditions for sub-models. Refined calculations were done for second and third scale of modelling.As a result of this calculation we have obtained the character of stress’s and strain’s distribution. According to results the most deformed zone of reinforced layers were identified and stress’s cycles of the working tire were built at control zones for cord and rubber component separately. A phenomena of double stress’s peaks in one cycle for shoulder zone of carcass and belt was identified.

Keywords:
pneumatic tire, rubber-cord composites, stress’s cycles, sub-modeling

Larin O.O., Petrova Ju.A. A sub-modeling procedure on stress cycles determination of pneumatic tire structural elements . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 37-49.

In this paper an analytical study on a stress-strain state of a steel pipeline section with a repair fi-berglass viscoelastic layer is described. The layer is considered long enough that allows to solve the problem in a flat axisymmetric statement. The analytical model including accounting of an isotropic viscoelasticity involves the need to construct and solve the boundary value problem for a system of integro-differential equations. In order to do it an approach based on a method of differentiation of integral equations is proposed. It is shown that for the initial time moment a solution of viscoelastic problem coincides with an elastic solution. Calculation results are presented as displacement and stress distributions versus radius and time curves. The viscoelastic model lets detect and discover such impor-tant properties of viscoelasticity as an increase of displacement over time and a stress relaxation in the composite layer. It is observed that at the same time the stress relaxation in the layer causes an increase of dangerous circumferential stresses in the steel pipeline. According to these results a conclusion about an impact of viscoelasticity on an overall assessment of strength of the construction is made. Also it is shown that for the specific set of physical and geometrical parameters of the construction stress relaxa-tion in layer occurs in the moment of time with a value 200 hours and the maximum circumferential stress value increases by seven percent. The time result coincide with relaxation time obtained using numerical model based on a finite-element method of a commercial computer-aided engineering com-plex. The stress increase result also responds to the numerical assessment and this value can be much higher in case of stress concentration due to presence of defects in pipeline walls. Proposed analytical model allows to save computational resources and to extend its application to more complex cases of the stress-strain state.

Keywords:
pipeline, layer, viscoelasticity, integral equation

Lvov G.I., Martynenko V.G. Analytical study of contact behavior of a section of a pipeline with a viscoelastic repair layer. NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 49-56.

Computational studies on the search of a calculation finite-element model of a rotor of a gas tur-bine unit installed on magnetic bearings based on incomplete data is described. This model is intended for in-depth analysis of its dynamic behavior. These studies were performed using a parametric model-ing and a series of variant static and dynamic calculations in order to determine parameters of the calcu-lation model by comparison with the known data. Variable parameters were diameters of the rotor sec-tions, as well as density and elastic modulus (Young’s modulus) of the material of its components. Known data based on which model identification was performed were scheme of the rotor, overall dimensions and dimensions between supports, masses, transverse and equatorial moments of inertia and centers of gravity of the turbocharger, the generator and the drive shafting, as well as natural frequen-cies and forms of the rotor of the gas turbine unit. While performing variant calculations beam finite element model of the rotor, consisting of three-dimensional beam finite elements with circular and annular sections with different sizes for different parts of the rotor, was used. Modeling of active mag-netic bearings was performed using special elastic-damper finite elements. Using this model, two types of analyzes were carried out. To search for a variant of the model with given masses, moments of inertia and mass centers series of static calculations with different densities and diameters of the sections was provided. After finding the values of these parameters a search of the model was made by selection of the elastic modules (Young) to match the natural frequencies with their reference values in a given range. Final checking of the model was performed by calculating of the natural frequencies depending on a rotational speed of the rotor, formation of Campbell diagram for finding the critical speeds and comparing it with the given diagram. Numerical results show an adequacy of the found calculation model and its suitability for further researches.

Keywords:
gas turbine power plant, rotor dynamics, magnetic bearings

Martynenko G.Yu., Oliinyk O.V. Identification of a calculation model of rotor of gas turbine unit installed on magnetic bearings according to geometric and dynamic parameters . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 56-67.

The problem of the calculation of creep strains of non linearly-viscoelastic materials under different regimes of nonstationary deformation, namely in terms of a stationary, single-stage and cyclic deformation is considered. The calculation is based on the nonlinear model of viscoelasticity with time-independent nonlinearity due to the use of diagrams instantaneous deformation as isochronous for zero time and smoothing cubic splines as approximations of nonlinear instantaneous deformation diagrams that define the non-linearity of the model. The nonstationary loading regimes are given by the Hevyside’s function. The calculation results of creep strains and stress relaxation of some nonlinear-viscoelastic materials under additional loading, partial unloading and cyclic loading have been approved experimentally.

Keywords:
nonlinear viscoelastic, nonlinear creep, nonlinear relaxation, exponentional-fractional hereditary kernel, nonlinear viscoelastic materials, nonstationary loading

Pavluyk Y.V. On the calculation of the stress relaxation of nonlinear viscoelastic materials under uniaxial loading regimes. NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 77-91.

The solution of the problem of finding the heat flux density in the plate of the heat sink is presented in the work. The task of the work is to use the asymptotic double hybrid approach to nonlinear differential equations that describe the processes of heat exchange in various designs. The method of expansion by the parameter with a nonlinear component is used for external decomposition. The idea of the inner expansion is to combine the methods of phase integrals and Bubnov-Galerkin method. To find the missing value of the derivative function a closed analytic solution is found. The use of dual asymptotic approach greatly increased the range of the parameter with a non-linear component. A comparative analysis of the results with those obtained by other methods is conducted.

Keywords:
asymptotic methods, dual hybrid WKB-Galerkin method, the heat flux density, a plate of a heat sink

Pogrebitskaya A.M. Finding heat flux density in the plate of a heat sink by means of asymptotic Galerkin WKB-hybrid approach . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 91-96.

Piecewise linear systems of differential equations model various technological processes. Such systems are commonly used to model dynamics of systems with clearances, flexible couplings, gear trains and splined connections. Piecewise linear systems show complex dynamical behavior. A problem of obtaining Shaw-Pierre nonlinear normal modes for piecewise linear systems is considered in the paper. A modification of the Shaw-Pierre normal modes technique is suggested to half the number of corresponding algebraic equations. Efficiency of the method is demonstrated using a mathematical model of torsional oscillations of a power transmission in a triplex transport engine. Bilinear and symmetric trilinear types of elastic force are considered. A conclusion about connection between Shaw-Pierre and Rosenberg nonlinear normal modes has been made. Results of form calculations are numerically verified by comparing with expected system dynamics.

Keywords:
nonlinear normal modes, Pierre-Shaw normal modes, piecewise linear system, torsional oscillations, free oscillations, power transmission.

Uspensky B.V., Avramov K.V. Using Pierre-Shaw nonlinear normal modes for analysis of free torsional oscillations in power transmissions . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 96-105.

Interference fit is one of the most common widely in construction and engineering strained com-pounds, some cases replacing bolted and riveted joints, partially drills and screw. In this paper proposes a program integrated with a PC ANSYS, which allows the analysis of compounds with interference shafts and bushings under the influence of different forms of axial loads. The program consists of a control unit, which consists of two main components. The first component allows you to perform data integration, given the program from your PC ANSYS, perform calculations and store the result in a file format vrml. Another component reads the data obtained from this file and means of the built-in OpenGL library has the ability to visualize them. This approach allows the development of a program to limit the use of third-party plug-ins in it to demonstrate the three-dimensional interactive vector graph-ics. Allows you to put more emphasis on the user interface directly with an interactive program. Reduc-ing thus the time to design and allowing more focus on the analysis.

Keywords:
shaped connection, interference, program

Shevchenko R.A., Аndreev А.G. Computer modelling of some types of shaped connections with interference at axial loadings . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 106-114.

A theoretical study of the wave propagation in the sapphire rods with different orientation of the crystallographic axes is performed. The problem of propagation of Rayleigh waves in a sapphire rod under longitudinal impact is formulated and solved. The theoretical dependence of the wave velocity from the rotation angle of the crystallographic axes in the rod is obtained. A comparison of calculation results with data obtained by the classical rod model is performed. It is found the velocities of the wave propagation received by the Rayleigh model and the classical rod model for the considered long sap-phire rod are practically identical. It is shown that the velocity of waves in a rod essentially depends on the orientation of the crystallographic axes of the sapphire in it. The theoretical results are compared with experimental data studies of wave propagation obtained with wide range strain measurement tech-nique. The good agreement of the theoretical results with the experimental data is established.

Keywords:
elasticity theory, wave propagation, Rayleigh wave, impact loading, anisotropy, sapphire

Shupikov A.N., Lytvynov L.A., Ugrimov S.V., Sotrikhin S.Yu., Yareschenko S.Yu. Theoretical and experimental investigation of wave propagation in the sapphire rod . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 115-125.

The problem of experimental study of the reaction of rigid plates on a bird strike by dynamic broadband strain measurement are considered in work. Data of experimental researches of influence of kinematical factors on response of a deformable plate-target at collision with a bird are presented. A series of experiments by definition of deformations of a flat plate are carried out at impact by the birds. Influence of different impact angles and velocities on maximum deformations of target is investigated. Extensive full-scale experiments in investigating the response of a plate have demonstrated that the maximum plate strain values decrease with decreasing impact angle. It is shown that, with increasing velocity of the fired object, the plate strain grows, the strain vs. velocity dependence being close to a quadratic one. Experimental date, obtained by using the dynamic wide-range strain measurement tech-nique, are in good agreement with theoretical results.

Keywords:
experimental research, strain gauges, deformation, dynamics, birdstrike resistance

Yareschenko V.G. Experimental research of the reaction of rigid plates on bird strike . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 126-133.

Considered working capacity steam turbine foundations with significant time of operation using. Particular attention is paid to the foundation with vibration levels higher than current standard rates. We consider first the most common of existing bases in Eastern Europe, which are made of reinforced concrete. The general and subsidiary мethodics of research and forecasting efficiency foundations for long life are proposed. These methods are based on laws documents, experimental and calculated data bases of operation of steam turbine power plants. The methodology is to assess the current state of the design for the control parameters. As parameters, according to existing regulations, proposed to use speed vibration, movement or vibration, acceleration vibration. These options are experimental meas-urements and the results of calculations. Developed methodics of available for use in power plants for existing and new steam turbine foundations.

Keywords:
performance, vibration, forced oscillations, foundation, steam turbine

Krasnikov S.V. Method for research and forecasting of working capacity for steam turbine foundations . NTU «KhPI» Bulletin: Series «Dynamics and Strength of Machines». 2014. No. 57. Pp. 133-137.