The paper presents a study of the effect of adding Mo and MoS₂ on the microstructure and properties of a powder coating based on austenitic steels. The coatings have been studied using X-ray diffraction (XRD), optical microscopy, scanning electron microscopy (SEM), a Vickers hardness tester, and abrasion wear resistance has been determined by the Pin on disk method. The results show that a coating that does not contain Mo and MoS₂ consists of the phases g(Fe), M₇(C, B)₃ and (Fe, Cr)₂B. The addition of Mo and MoS₂ leads to the formation of phases M₂₃(C, B)₆, Mo₂(B, C) and Fe₃Mo₃(C, B), where M = Fe, Cr, Mo. The main goal of these studies was to study characteristics of Mo and MoS₂ distribution and the effect of their addition on the microstructure, hardness, and abrasion wear resistance of an alloy coating based on austenitic steels. Composite materials based on austenitic steels obtained by diffusion alloying (Aus0Mo), which has a nearly spherical shape with a diameter of 50–100 μm, have been used for deposition. 3–7 wt. % of Mo powder and 1.0–1.5 wt. % of MoS₂ powder with a diameter  less than 50 μm have been added in the powder of the composite material based on austenitic steels (Aus3Mo, Aus5Mo, Aus7Mo). Surfacing methods, including gas arc welding with a tungsten electrode, arc welding in shielding gas, plasma surfacing (PTA) and laser surfacing are widely used in industry to increase wear resistance of surfaces. The most important differences between these methods are deposition rate, applicability of materials, substrate dilution, microstructure and hardness stability after exposure to high temperatures, as well as manufacturing cost. Among the methods described above, plasma spraying followed by fusion is a good alternative to other surfacing processes. The coating should not be overheated until it is completely  melted, since in this case the primary crystals of chromium carbides and borides pass into a liquid solution and upon subsequent crystallization, form a coarser structure, worsening the quality of the coating. This is precisely what does not occur during plasma spraying followed by reflow; in addition, the method is cheap, coatings are of high quality, competitive wear resistance and high stability of properties at high temperature.

One of the most effective methods of treating intravascular formations at present is the use of stepped ultrasonic waveguide systems of a tubular type (concentrators-waveguides) with a hollow spherical tip, the presence of which makesit possible to supply liquid media to the dislocation zone of an intravascular formation with the aim of additional cavitation effect and as efficiently as possible. destroy intravascular formations due to vibration impact. Based on the results of the analysis on the features of the existing shaping methods for obtaining a hollow spherical tip of the concentrator-waveguide, it is advisable to use methods of plastic deformation – expansion and crimping. The paper presents results of preliminary calculations, numerical modeling and experimental studies of tip shaping processes of the concentrator-waveguide by distribution and crimping. On the basis of the finite element method in the environment of the ABAQUS software package, modeling of the expansion and crimping of a pipe billet was carried out, which has made it possible to: evaluate the stress-strain state of the deformable conical section of the billet, the change in wall thickness during the forming process and calculate the length of the billet for the design of the conical section; to establish the patterns of the influence of geometric parameters on the power modes of the distribution process; to set the parameters of the modes of forming the tip of the concentrator-waveguide by the method of distribution and crimping, which ensure the formation of the required geometry. The obtained results of preliminary calculation, numerical modeling and experimental studies of tip shaping processes of the concentrator-waveguide by distribution and crimping have similar values, which confirms the correctness of using both the method of preliminary calculation and numerical modeling in the development of the technology for manufacturing the concentrator-waveguide.

. Nanostructured NiFe films were synthesized by pulsed electrolytic deposition on silicon with a gold sublayer, after which they have been subjected to to temperature treatment at 373-673 K in order to study the effect of heat treatment on the microstructure and mechanical properties of the objects under study. High-resolution atomic force microscopy has made it possible  to trace the stages of  microstructure evolution under the  influence of  heat treatment, including the process of  nonlinear increase in grain growth and two-stage agglomeration. It is shown that with an increase in heat treatment temperature to 673 K, the grain size increases from 68 to 580 nm in comparison with the initial sample, undergoing agglomeration processes at temperatures of  100 and 300 °C. The mechanical properties of nanostructured NiFe films have been studied by the nanoindentation method. The dependences of the hardness of Young’s modulus and the values of the resistance to elastoplastic deformation on depth have been obtained and analyzed in the paper. This approach has permitted to reveal differences in the behavior of the mechanical properties of the surface layer and the internal volume of the film under the action of different heat treatment temperatures, as well as to demonstrate the opposite reaction of different material layers to an increase in temperature. As a result of a thorough analysis of the deformation curves of nanoindentation, it has been found that the homogenization of the surface in combination with the activation of oxidation processes leads to the strengthening of near-surface layer of NiFe films. At the same time, the internal volume of the material is characterized by a nonlinear decrease in hardness and Young’s modulus with an increase in the heat treatment temperature. The explanation for this phenomenon has been found in the complex effect of a decrease in the number of grain boundaries (due to an increase in the average grain size with increasing temperature) and an increase in the concentration of gold atoms diffusing from the sublayer more actively with an increase in the processing temperature of NiFe films.

The paper provides a comparative analysis of the influence of ring concentrator shape in ultrasonic systems on their amplitude-frequency characteristics. Devices are known in which elastic elements are used either as resonators or as working tools of ultrasonic technological systems. However, the use of elastic elements as concentrators of ultrasonic vibrations is insufficiently studied and requires comprehensive research and development of recommendations for their practical application. For this purpose, a theoretical analysis has been carried out in the paper while using the ANSYS computer program, which made it possible to perform modal and harmonic analysis of ring models with various shapes. The round ring has a nominal outer diameter of  50 mm and a variable cross-section. Three ring  models  have  been  analyzed:  one  round  model and two models of oval shape. To conduct a comparative analysis and identify frequencies at which resonance occurs, the vibration characteristics of the rings have been considered in the frequency range from 1 to 26 kHz. Results of the analysis show that, depending on the frequency of  forced vibrations, bending vibrations are formed in the rings, which act in different coordinate planes. In this case, a change in the shape of the rings is accompanied by a change in the amplitude of the bending vibrations. The most intense ring vibrations along the vertical axis have been achieved in circular rings. It has been found that with an increase in the frequency of forced oscillations, an increase in the number of oscillation periods is observed. If in the region of low vibration frequencies only a one-period vibration mode is formed in the ring, then in the region of ultrasonic vibrations the number of vibration periods increases to two and three. All the considered ring models have several natural vibration frequencies with a certain periodicity in different coordinate planes depending on the shape of the rings. The intensity of the vibrations is different in different directions and depends on the shape and frequency of the forced vibrations. Examples of vibration mode variations for various ring shapes are demonstrated in the paper.

The paper presents the results of research on the dynamics of end milling of thin-walled work-pieces having complex geometric shapes. Since the milling process with shallow depths of cut is characterized by high intermittent cutting, the proportion of regenerative vibrations decreases, and the effect of forced vibrations on the dynamics of the process, on the contrary, increases. The influence of  axial depth of cut on the vibrations arising during processing, and roughness of the processed surface have been studied in paper.  The experiments have been carried out in a wide range of changes in the spindle speed at different axial cutting depths.  Vibrations of a thin-walled work-piece  have been recorded with an inductive sensor and recorded in digital form. Then an oscillogram has been used to estimate the amplitude and frequency of oscillations. The profilograms of the machined surface have been analysed. Roughness has been evaluated by the parameter Ra. The results have shown similar relationships for each of the investigated axial cutting depths. The worst cutting conditions  have been observed when the natural vibration frequency coincided with the tooth frequency or its harmonics. It is shown that the main cause of vibrations in high-speed milling  is forced rather than regenerative vibrations. Increasing the axial depth of cut at the same spindle speed increases the vibration amplitude. However, this does not significantly affect the roughness of the processed surface in cases when it comes to vibration-resistant processing.

The widespread use of green public transport is a priority strategy to reduce a congestion and pollution from road traffic in many cities. The trolleybus is a type of urban public electric transport, which is considered as a promising tool for  increasing the efficiency of public transport and achieving the goals of sustainable development and quality of life in the city. The operation control of service brake system and secondary brake system (braking torque of traction electric motor) is realized with the help of one pedal in the trolleybus. Thus, there are modes of joint operation for these systems during the braking process. The author has focused his main attention on the development of an algorithm for blending control of the traction electric motor and the anti-lock braking system to enhance the overall braking efficiency of a vehicle. For this purpose, a mathematical model of the trolleybus braking dynamics has been developed. Bench and road tests have been carried out on various road surfaces to determine parameters of vehicle braking efficiency and to validate the developed mathematical model. The corresponding experimental data were used to analyse the efficiency of the proposed strategy for combining the blending control of traction electric motor and anti-lock braking system of the trolleybus. As a result, the efficiency of the proposed control algorithm has been confirmed, which provides the required braking efficiency and high braking stability of the vehicle. 

Waste generation in the life of people and enterprises is an inevitable process today. The level of utilization of municipal waste has increased on average to 23 % in Belarus. The paper provides an assessment of the existing systems for the collection and disposal of waste solid household items based on  technological stages (preparation of waste for loading into a garbage collection vehicle; organization of temporary storage of waste in households, at enterprises; collection and removal of waste from the territories of households, organizations and enterprises; neutralization, processing and recycling of waste). The consequences of untimely collection of solid household and industrial waste are considered in the paper. The paper presents the factors that have a harmful effect on the human environment and the ecology of the territories of settlements and enterprises. An analysis of the effectiveness of the timely removal of such components in the systems of municipal services of cities and enterprises as an important component providing social, economic and environmental significance is given in the paper. At the present stage of the development of technology and available technologies, one of the most rational and economically justified ways of delivering waste to the areas for their sorting and processing is vacuum transportation using pipeline transport. Its application is justified for industrial zones and settlements with high and medium population density. Moreover, such a pipeline can be laid next to existing pipeline and other transport communications.

Abstract. To increase the efficiency of operation of heating networks located in non-passable channels, a schematic and structural solution of regenerative-utilization heat use was previously proposed and at the same time it is shown that it isdifficult to create an acceptable full-scale experimental installation or the difficulty of conducting a passive experiment on existing heating mains in non-passable channels. As an alternative solution for performing research, it is proposed to create and use a virtual experimental setup developed on the basis of the ANSYS software package, which has received wide recognition in the world. The initial results of  model verification showed that the study of heat transfer and aerodynamics in blown-through non-passable heating mains using such a solution is promising. A study has been carried out using a virtual experimental setup based on a six-factor second-order rotatble plan containing 46 points on a hypersphere with six star points. It is shown that there is no need to randomize the order of conducting and repeating the study at the points of computational experiment plan. Second-order regression equations have obtained for calculating a complex of objective functions: the required air pressure to achieve a given flow rate, the intensity of heat transfer directly from the pipes of the heating main, as well as from the walls of the channel to the blown air. The geometry of the channels of typical standard sizes of heating mains, the length of the sections, the temperature of the outside air and soil, and the air flow rate in the channel have been taken as the influencing factors in the calculations.  For the obtained regression equations, significant coefficients have been established and the transition from dimensionless to natural factors has been carried out. The adequacy of the obtained regression equations has been determined using standard statistical estimation methods based on the calculated values of the Fisher’s, Student’s and other criteria. 

In accordance with the energy conservation law, the total energy of a closed physical system must remain constant at any moment of time. The energy of a traveling elastic wave consists of the kinetic energy in the oscillating particles of the medium and the potential energy of  its elastic deformation. In the existing theory of elastic waves, it is believed that the kinetic and potential energy densities of a traveling wave without losses  are the same at any moment of time and vary according to the same law. Accordingly, the total energy density of such wave is different at various moment of time, and only its time-averaged value remains constant. Thus, in the existing theory of elastic waves, the energy conservation law is not fulfilled. The purpose of this work is to give a physically correct description of these waves. A new description of a sound wave in an ideal gas has been proposed and it is based on the use of a wave equation system for perturbing the oscillation velocity of gas particles, which determines their kinetic energy, and for elastic deformation, which determines their potential energy. It has been shown that harmonic solutions describing the oscillations of the gas particles velocity perturbation and their elastic deformation, which are phase shifted by p/2, are considered as physically correct solutions of such equations system for a traveling sound wave. It has been found that the positions of the kinetic and potential energy maxima in the elastic wave, described by such solutions, alternate in space every quarter of the wavelength. It has been established that every quarter of a period in a wave without losses, the kinetic energy is completely converted to potential and vice versa, while at each spatial point of the wave its total energy density is the same at any time, which is consistent with the energy conservation law. The energy flux density of such traveling elastic wave is described by the expression for the Umov vector. It has been concluded that such traveling sound wave without losses  in an ideal gas can be considered as a harmonic oscillator.

It is known that boundary value problems for the Laplace  and Poisson equations are equivalent to the problem of the calculus of variations  – the minimum of an integral for which the given partial differential equation is the Euler – Lagrange equation.  For example, the problem of the minimum of the Dirichlet integral in the unit disc centered at the origin on some admissible set of functions for given values of the normal derivative on the circle is equivalent to the Neimann boundary value problem for the Laplace equation in this domain. An effective approximate dilogarithm representation of the solution of the above equivalent variational boundary value problem is constructed on the basis of the known exact solution of the Neumann Boundary value problem for a circle using a special approximate formula for the Dini integral. The approximate formula is effective in the sense that it is quite simple in numerical implementation, stable, and the error estimation, which is  uniform over a circle, allows calculations with the given accuracy. A special quadrature formula for the Dini integral has a remarkable property – its coefficients are non-negative. Quadrature formulas with non-negative coefficients occupy a special place in the theory of approximate calculations of definite integrals and its applications. Naturally, this property becomes even more significant when the coefficient are not number, but some functions. The performed numerical analysis of the approximate solution confirms its effectiveness.

The purpose of this paper is a spectrum analysis of signals of various nature, construction of the signal scalogram using Morlet wavelet, modification of the scalogram to obtain a more informative graphic representation of the signal. Spectral analysis of the signal is constructed by means of the Fourier transform. A modification of the graphical representation of the result of the wavelet transform has been developed with the help of  the Mathematica system. For this, a wavelet scalogram has been used as a two-dimensional representation of the original signal. A scale has been introduced on it for the value of the signal amplitude depending on the time and period of its constituent components. This graphical representation allows us to obtain additional information about the dynamic properties of the original signal.  A modification of the representation of the original signal scalogram has been developed for a more complete spectrum analysis (determination of the period of the constituent components). The paper contains an example using a modified scalogram for the analysis of a signal containing two pulses, an audio signal and white noise. The basic wavelet in this case is the Morlet wavelet. A comparison of the scalogram, obtained using the built-in function, and the modified scalogram has been made in the paper. The disadvantage of the first scalogram is the impossibility of assessing the frequency of the signal; its advantage is the ability to assess the localization of the pulse. For a modified scalogram, the advantage is the estimation of the signal periodicity, and the disadvantage is the inaccuracy in determining the range of pulse localization. For spectrum analysis in Mathematica, it is recommended to use a combination of two approaches (using a standard built-in function to determine the localization of the pulse) and a modified scalogram (to determine the periods of the constituent components).

The bilinear programming problem is considered, where a column, which corresponds to one of the variables, is not fixed but can be chosen from a convex set. This problem is known as the Dantzig – Wolfe problem. Earlier, a modified support method was proposed to solve the problem, using the decomposition of the problem constraints of the Dantzig – Wolfe method. The author of the paper has developed a direct exact method for solving the formulated problem. The method is based on the idea of the solving a linear programming problem with generalized direct constraints and a general concept of an adaptive solution method. The notions of support, support plan, optimal and suboptimal (e-optimal) plan are introduced which is a given approximation of the objective function to the optimal plan of the problem. Criteria for optimality and suboptimality of the support plan have been formulated and have been proved in the paper. The search for the optimal solution is based on the idea of maximizing the increment of the objective function. This approach allows more fully to take into account the main target and structure of the problem. Improving a support plan consists of two parts: replacing the plan and replacing the support. To find a suitable direction, a special derived problem is solved while taking into account the main constraints of the problem. The replacement of the support is based on the search for the optimal plan of the dual problem. The method leads to an optimal solution to the problem in a finite number of iterations (in the case of a non-degenerate value).