An axisymmetric problem of the elasticity theory on torsion of an elastic half-space with inhomogeneous in depth coating of periodic structure by a non-deformable circular punch is considered. The coating is represented by a set of alternating soft and hard layers. The boundaries of the layers can be clear (piecewise-constant variation of the shear modulus) or smooth (continuously inhomogeneous or functionally-graded coatings). The approximate analytical solution to the problem of high accuracy is constructed which is effective for any coating thickness. The effect of the number of layers, and of the coating inhomogeneity type on the kernel transform of the integral equation and on the contact stresses distribution under the punch is investigated. It is shown that with certain values of the problem parameters, the substantial difference between the results for the continuous and piecewise constant type of the variation of the shear modulus in depth is obtained.

An effective analytical solution to an axisymmetric contact problem on the interaction between a circular plate and a double-layer elastic half-space is considered. For this, a bilateral asymptotic method is applied. The plate bends under the load and the foundation response. The solution is constructed for different layer thickness and plate flexibility parameters. Cases when half-space layer properties differ significantly are considered. For these cases, kernel transform approximates of the high-accuracy problem integral equation are constructed. The obtained results accuracy is checked through the comparison with the known solution to the problem on the circular plate bending on an elastic layer bearing on the non-deformable foundation. The effect of the distributed load on flexible and rigid plates depending on the interlayer thickness and its stiffness against the underlying half-place is investigated.

The solution to the equilibrium problem for half-plane and stripe weakened by straight transverse cracks and reinforced by thin flexible plates is considered. Boundary conditions of a special form are used as a mathematical model of a thin plate. To establish the limits of the model applicability, a numerical study of these conditions is carried out. On the basis of the equilibrium equations, the problem is converted to the solution of the singular integral equation of the first kind with the Cauchy kernel relating to the function derivative of the crack opening. At this, the generalized integral transform method is used. In various ranges of the geometrical and physical problem parameters, solutions to the described above integral equation are constructed by small parameter and collocation methods. The stress intensity factor values in the neighborhood of the crack periphery are obtained. The multivariate analysis of the plate impact on the critical condition of cracks in the substrate is carried out.

The asymptotic solution to a problem of the hydrodynamic calculation of the radial two-layer porous bearing of infinite length with account for the permeability anisotropy of porous layers is presented. The solution is based on full nonlinear Navier — Stokes equations and Darcy's equation. The case when the porous layer permeability changes continuously in the radial direction, and then — the case when axes change both in radial and in circumferential directions are considered. As a result, a velocity and pressure field in the lubricant and porous layers is found. Analytical expressions for the main performance data of the bearing are obtained. The effect of nonlinear factors and anisotropy on the bearing basic performance is assessed. The conditions under which a radial non-uniform two-layer bearing according to the carrying capacity offers the double action property are determined. The most rational values of the design, operating, and other functional data defining the bearing operability are established.

The mathematical model of training success based on the factor analysis method is presented. The psychological characteristics of the students obtained as a result of the conducted experiment are considered as factors of this method. The academic progress of students determined by the examination record is chosen as a resultant factor. The psychological experiment was conducted in DSTU groups of students of specialty 030300 by means of R. Cattell's 16 PF test. The test results allowed making up a sufficiently complete “psychological portrait” of the second-year students which has been served as a good database for the consequential development of the training success mathematical model. A two-way analysis of variance has been applied to calculate the model. Each binary pair of factors is classified under two ranking levels: low level — high level. An example of the model analysis is given, the impact of various factor pairs and their combinations on training success is analyzed. Having a sufficiently complete database, it is possible to use the presented model, and to facilitate the educational process for teachers and students after revealing the patterns.

A method of manufacturing involute sprocket by a standard cutter for the toothed chain is suggested. The application of involute sprockets compared with straight and standard tooth profiles has a number of advantages: noise abatement under operation, wear resistance and durability increase, etc. The selection order of a standard cutter (hob gear) for cutting involute sprockets is presented. A computer program simulating the sprocket cutting process with different values of the chain pitch and various numbers of teeth is developed. The resource allows determining the tool module, and inspecting tooth for sharpening and facing. The characteristic feature of cutting sprockets with the involute tooth profile is the application of two corrections (radial and tangential). Their computation procedure is presented. The calculations for the chain pitch t_ц = 12.7 mm are carried out. The results are summarized in the table. The range of cutting involute sprockets with a standard cutter by the chain pitch t_ц, the module (m), and the number of sprocket teeth (z) is determined including the need to eliminate tooth sharpening and facing.

Complete information on the component reliability of the complex man-machine systems is obtained in the case of availability of the component uptime distribution laws and of their parameters, as well as of the information on the components independence. Under the violation of one of these conditions it should be assumed that the information on the complex man-machine system (MMS) component reliability is incomplete which complicates in whole the calculation and analysis of the MMS hardware reliability. Based on the long-term author’s studies, a problem-solving technique for the hardware reliability analysis of various man-machine systems is developed on the basis of the interval average theory tenets. The technique takes account for the limitation of the source information, system component dependence, and the possibility of describing uncertainty. Examples of the reliability analysis in the event of information on the component reliability independence, in its absence, and under the man-machine restorable system reliability are presented.

The problem on building the output mechanism for the intellectual information system designed for decision-making on the technological control of combines in the field is considered. The domain of the agricultural machines operation is briefly analyzed. The domain objects are complex hierarchical multilevel systems affected by the ever changing external factors. It determines complexity and multiplicity of the mathematical approaches to the output mechanism formation, and lack of the uniform formal logic approach to the optimal decision-making strategy construction. It is shown that under the conditions of lots of possible factors causing deviation of complex machinery performance indices whose probabilities are unknown or are estimated by experts, and when a dynamic response is required, it is expedient to use a game-theory approach to the selection of the optimal behavior strategy based on the analysis of the information system knowledgebase. The concepts of the performance factor matrix, and the matrix of ineffective decision-making risks are introduced. The concepts allow using the criterion-based approach to the optimal decision-making. An example of selecting the strategy of appropriate response for eliminating the cause of trouble in the harvesting workflow is given. The selection of the optimal strategy for eliminating the process quality indices deviation based on Laplace and Savage criteria used for decision-making in the “games with nature” is considered. A model example is used to illustrate the one-step procedure for decision-making under uncertainty with the application of the specified criteria. The obtained results are analyzed. Both the scope of the proposed approach and the conditions under which it can be applied are discussed.

The physical and mathematical mass-transfer model of the ion-beam crystallization method is developed. The derivatization of photoactive structures Si(n⁺)/Si(p)/Si(p⁺) on 100 mm substrates through ion-beam crystallization is considered. The optimum conditions for the process: residual pressure in the growth chamber — 10⁻⁴ Pa; the substrate temperature — 550 °C; ion current density — 2 mA/cm²; acceleration voltage — 400 V; target — substrate distance — 150 mm are determined. The scanning electron microscopy data show that the grown photoactive structures have closely a faultless surface. The results demonstrate that the photoactive structures Si(n⁺)/Si(p)/Si(p⁺) offer the external quantum efficiency over 90 % in the wavelength range of 550—900 nm (spectrum AM 1.5) under the following conditions: front layer thickness Si(n⁺) — 100 nm; donor doping density n⁺ = 5∙10¹⁸ cm⁻³; layer thickness Si(p) — 130 μm; acceptor doping density p = 2∙10¹⁶ cm⁻³; layer thickness Si(p⁺) — 500 nm; acceptor doping density p⁺ = 1∙10¹⁸ cm⁻³.

Statistical spread of the electrical device parameters appears often to be a problem for their operation analysis and a precise determination of their optimum modes. Under such conditions, mathematical algorithms permitting to diagnose these devices with the accuracy sufficient for the engineer analysis are required. A new algorithm of calculating the moment-slip characteristic of the three-phase asynchronous motor is offered. It permits to determine its maximum torque and critical slip. To this end, the initial characteristic section obtained experimentally is processed statistically. This significantly universal technique of solving such electrotechnical problems is based on the common mathematical approaches. In this context, it can form the basis for the microprocessor-based electronic diagnostic device.

Repair and restoration features of the electric wheel-set tyre roll surface on a wheel-type milling machine are considered. The processing is performed by a form cutter at speeds up to 180 rpm. Low speed and a substantial weight of the machine (37.5 tons) suggest that noise characteristics in the work area are determined by the processed wheels and cutting tools sound radiation. The study results of the cutter acoustic characteristics are presented. Bending vibration equations are solved with account for the rate of oscillatory energy loss which determines the cutting unit dissipation function. Thus, tool vibration velocity values are obtained. The installation of the mandrel with vibration cushioning elements, and the right roller bearing support upgrading allow increasing the cutting unit dissipation function. However, it may not be as sufficient for the cutting tool noise level lowering up to the admissible limit values. In this case, an acoustic baffle placed near the noise source can be used. At this, the acoustic baffle design becomes more simple, and its dimensions (length and height) — less.

The problem on stabilizing the toolpath generation relative to the workpiece taking into account the parametric self-excitation is considered. Factors causing the cyclic parameter variations in the cutting dynamic system are analyzed. These factors are related to the spatial anisotropy of elastic properties in the workpiece subsystem, allowance on workpiece rotation perimeter variations, kinematic perturbations from the drive hardware of the machine executive elements, and to the periodic processes in the cutting zone. The generic dynamic model of the periodic system is given. The effect of the periodically varying parameters on the path stability is studied. Buckling collapse features specific for cutting dynamic systems are disclosed. It is also shown that through the parametric actions, with increase in cutting speed under the spindle row growth, there always exists critical frequency at which the system loses its stability.

Fatigue calculation is of primary importance when designing parts and assemblies made of composite materials to operate under the variable load. The finite element modeling of the representative bulk in the stress-strain state conforming to the operation conditions is considered. The calculation methods of polymer composites high-cycle fatigue is based on it. The calculations are carried out in the paper. The unidirectional reinforced composite obtained through thermal curing of the glass-reinforced epoxide is studied. Mechanical properties of such materials (including fatigue life) to quite a great extent depend on the manufacturing technology. The calculation permitting to estimate changing strength properties for fatigue life under the breach of the technology requirements to the composite components percent is resulted.

Side shoots and plant branches unlike trunks are often not rectilinear — they can be compared with various mathematical curves. Xylem of such branches copies their curvilinearity. It motivates the spatial curvature of the chains of its tracheids and vessels. A mathematical model of water lifting and distribution caused by the surface tension forces in the symmetrical curved capillary branches of various configurations is considered. The process analysis shows that with the expansion in number of branches, water advancing in the curvilinear capillary system increases. Water volume rising in the side curvilinear capillary branches, other factors being equal, is greater than in rectilinear ones. It is found that the total water rise height in the vertical (rectilinear) capillary — if there are side curvilinear capillaries — increases, and it does not depend on the type of the function that describes the curvature of the lateral curvilinear capillaries.

The experiments supporting theoretical conclusions on the process regularities of the vibration excitation and noise generation are considered. As part of the study, part blanks, such as thin plates and of a complex profile, were machined on the presses of T 1228 and T 1225 Models. Thus, sound levels (dBA), as well as noise pressure and vibration speed levels in octave and 1/3-octave frequency intervals were specified. Experimental data were recorded by the multifunctional acoustic meter “Ekofizika”. Noise measurements were performed by the preamplifier and microphone capsule, and vibration measurements — by the three-component accelerometer. The most intense components of the spectrum are recorded in the low and mid-range frequencies (31.5—500 Hz). At higher frequencies, the sound radiation intensity is falling off — 3—5 dBA per octave.

Some issues on forming movement modeling when drilling deep holes with the dynamic link generated under cutting are considered. The results of the spindle frequency drift trajectories simulation in Matlab according to the parameters of the servo motor and process characteristics are presented. For the first time, metal drilling cut processes with the ever increasing section modulus determined by chip making are simulated. The phase path describing the forming movement dynamics under drilling deep holes with the increasing section modulus associated with chip making is exemplified. The phase portrait transformation depending on the servo motor parameters and the production process is shown. Recommendations on the motor parameters selection are given. They depend on the processing dynamic characteristics, and on the modulus effect determined by chip making.

The numerical solution to the problem of the elastic contact between two teeth of the helical gear with circular tooth profile in the face section is described. The problem is solved with the software system of finite element analysis ANSYS. Principles of geometry and finite element model of two elliptical gear teeth engagement are formulated. Testing of the finite element model using the integrated criteria is held. The surface distribution of contact pressure on the tooth working face is shown. The maximum contact pressure in the elliptical and involute gears is compared. In the testing tasks solution, it was found that the distribution of contact pressure in an elliptical gear with a circular tooth is uneven. At the periphery of the contact patterns, stress concentrators are located — the surface pressure may be higher than the maximum pressure in the involute gear here.

According to the papers of the German and French specialists, the rail corrugation stimulates increasing the rail sound radiation intensity. Besides, the consideration of the rail corrugation actually explains the high-frequency noise spectrum. The rail corrugation is characterized by two key parameters — the corrugation amplitude and spacing. The corrugation occurrence leads to the high-frequency impact on the rail under the rolling stock operation, since the influence frequency represents motion speed/corrugation spacing ratio. Lagrange equations are used to define the force impact on the rail under the rolling stock operation. Rail vibration velocities are obtained from the differential equations of the bending oscillations for various methods of the rail laying: on the slab track, on timber and concrete sleepers. It is shown that the motion speed effects to a greater extent on the noise level increase involving the corrugation.

The experimental results of noise and vibration in the section of the centrifugal treatment of the helicopter longeron tubes are given. Noise sources determining very high level increase over limitary spectra are identified. As the noise reduction up to the sanitary norms in the source itself is impossible, observing the sanitary standards is possible only through calculating and designing a soundproof construction with the required acoustic protection value. Thus, the noise protection system diagram presenting a safeguard with a high degree of pressurization is given at the end of the paper. The sanitary standards control is achieved as a result of the introduction of the package of measures including the noise enclosure for the facilities of the centrifugal treatment and the sound-absorbing revetment application on the shopfloor walls and the ceiling.

The generalized trajectory of the power drill (PD) operational cycle is considered. In the case under study, the PD shows the increased speed and positioning accuracy of the fluid-feed. An automated hydraulic drive for providing the structural parametric control over the operational cycle and PD positioning is offered. A generalized mathematical model of the PD feed drive dynamic system is presented. The simulation experiment has permitted to determine kinematic and dynamic characteristics of the tool-feeding drive under the metering-out control. The cutting feed rate effect on the tool positioning accuracy under the deceleration and at the end of processing is determined. This allows forming time-optimal and ideal for positioning accuracy cycles under the field processing conditions.

The described algorithm of the business reputation valuation by the future discount cashflow (DCF) technique allows the justified investment decision-making. The technique is characterized by the computation complexity since a considerable volume of information is required for the model building. It should be noted that in the future discount cashflow model, the business reputation valuation for the investment purpose does not require the computation refinement as business reputation is an intangible asset, and its accurate evaluation is impossible. In this case, the computation simplification considering only essential model parameters is admissible. To conduct a correct comparative analysis of the investment objects, it is necessary to estimate materiality level for each of the compared organisations.

A general methodological approach to the management of the creation and development of economic associations is considered. It is based on their representation in the form of a focused and evolving process whose driving force is the dialectical unity and struggle between the need and the opportunity, between the conceptual and constructive layouts of the association. Structurally, the process is presented in the form of a directed graph integrating its steps and sub-steps. Consistent implementation of the tasks of these steps ensures the generation of justified decisions on the creation and development of economic associations. The complexity and diversity of these problems calls for their formalization. At that, a key formalization element is a formal representation of the comparative evaluation procedure for the options of the state associations. The comparative evaluation methodology for the variants of their unification is described through the formal apparatus of the theory of sets.

The research objective is efficiency increase of the development, estimation, and improvement of quality management systems (QMS) of the machine-building enterprises. The existing classifications and operation algorithms of the QMS basic types allow optimizing the processes of product improvement, and the quality of life of the system participants improvement. The presented model algorithm reflects all possible action variants directed on the improvement and the most effective use of non-conforming product. The algorithm respects the interests of both consumer and manufacturer, and it can be applied at different product life cycle stages. The data analysis of the non-conforming product control results allows improving the applied models and developing the optimization techniques. Thus, there appear options for using products inconsistent with requirements for the initial or near it appointment. Consequently, they would not be completely processed.

Various trends of the state environmental regulation in the industrial waste handling sphere in Rostov Region are considered. The assessment of the regulation operating mechanisms in the industrial waste generation permits to elicit its key failing. A package plan oriented to improving the regulatory tools of the state environmental regulation in the industrial waste handling sphere is offered. The regulatory background development will promote the solution to the problems connected with the industrial wastes generation, accumulation, unauthorized disposal in Rostov Region. The efficiency of the state environmental regulation in the industrial waste generation will go up. Besides, industrial enterprises will have an economic interest in the environmental hazard reduction.