Introduction. Prof A.V. Belokon’s (1941-2013; former Rector of Rostov State University and President of Southern Federal University) PhD thesis was devoted to asymptotical methods in contact problems of the elasticity theory for bodies of cylindrical shape (1969). In the present paper, a contact problem of the elasticity theory on torsion of an infinite hollow cylinder by a rigid insert is investigated. The outer cylinder surface is rigidly fixed. The insert of a finite length is inside the cylinder. In 1971, this problem was formulated and analyzed by A.V. Belokon. He reduced it to an integral equation with respect to the unknown contact stress by using the Fourier integral transformation. A.V. Belokon derived a complete solution to this problem for the case of thick-walled cylinders when the kernel symbol of the integral equation can be approximated by the function corresponding to the torsion of the space with a cylindrical cavity. In the present paper, the case of thin-walled cylinders being complementary to Belokon’s case is mainly considered. Materials and Methods . The cylinder material is supposed to be linearly elastic. The method of integral transformations is used to solve the problem. The singular asymptotic method is applied to solve the integral equation. Research Results . On the basis of studying the properties of the integral equation kernel symbol function, a new special easily factorable approximation applicable for any cylinder thickness is suggested. The Monte-Carlo method is used to determine optimal approximation parameters. Calculations are mainly made for thin-walled cylinders. As a result, an analytic asymptotical solution to the integral equation is obtained. Discussion and Conclusions . The new solution can be effective for relatively long rigid inserts whose length is bigger than the internal diameter of the cylinder. The method based on new approximation remains applicable also for the cases when a cylinder can be regarded as a cylindrical shell. The asymptotical solution can be recommended to engineers for the strength analysis of elastic machine parts of the cylindrical form twisted by a rigid insert.

Introduction. The work objective is to develop a new universal numerical method for solving boundary value problems for linear elliptic equations. Materials and Methods . The proposed method is based on the transformation of the original mathematical physics equation to a simpler inhomogeneous equation with the known fundamental solution. From this equation, the transition to an inhomogeneous integral equation with the kernel expressed by the known fundamental solution is carried out. The obtained integral equation with boundary conditions is solved numerically. An approximate solution, the field potential being in an analytical form, is resulted. That allows not only find an approximate value of the field potential at any point in the solutions domain, but also differentiate this potential, and all without perceptible loss of accuracy. This property of the developed numerical method sets it apart from the traditional numerical methods for solving boundary value problems, such as the finite element method. Research Results . To confirm the effectiveness of the proposed numerical method, the two-dimensional and three-dimensional boundary value problems with the known solutions are solved. The dependences of the numerical solution error on the number of linear equations in the resulting system are obtained. It is shown that even at a small number of equations in the system (some hundreds) the solution accuracy is achieved at the level of hundredths of a percent. Another major illustration of the proposed method effectiveness is the solution to quantum mechanical problems for the one-dimensional and two-dimensional quantum oscillators. It is shown that the given method allows finding the energy eigenvalues and eigenfunctions with an acceptable accuracy. The developed numerical technique allows greatly extend the application domain of the traditional point source method in solving applied problems for modeling fields of different physical nature, including the eigenvalue problems. Discussion and Conclusions. The results obtained confirm that a physical field described by any linear elliptic equation can be represented as a superposition of point source fields satisfying a simpler equation, the solution of which is obtained through the method of point source of the field. Therefore, the numerical method presented in this paper can be considered as a generalized point source method.

Introduction. The paper is devoted to the development of an ingenious mechanical-mathematical model of the unbalanced non-rigid gimbal gear with account for its axis flexibility. The work objective is to create a new highly adequate model of the imbalance of the basic non-rigid high-speed gimbal drive as an efficient means to solve the problems of balancing under car designing, manufacturing and servicing. Materials and Methods. The descriptive content of the model of the unbalanced transmission is presented as a set of allowances. Formalized schemes of the model of the non-rigid gimbal gear imbalance before and after driving it into rotation are built on their basis. These schemes represent a double-beat model and a model- fragment of the multiple-bearing gimbal gear. Using the relations available in the literature, the following is determined: additional elastic deflection of the axis of the rotating transmission from the initial technological deflection of its axis according to the first eigenform; the coefficient of the elastic deflection modification; and the imbalance of the elastic deflection of non-rigid cardan shaft axles. Research Results . New mathematical models of the cardan transmission imbalance are developed. They help to determine the initial and compensating imbalances in the transmission correction planes perfectly balanced at low speed and driven into rotation at an operating speed. The effect of the compensating imbalances established in the correction planes is considered when balancing the transmission at the operating rotation speed. In this connection, a method for determining the coefficient of change in the elastic deflection of the gear rotation axis is developed. The value of the deflection of the rotation axis of the non-rigid gimbal gear is determined. Discussion and Conclusions. With the help of the obtained results and relations, the following can be performed with high reliability: the substantiation of the standards of accuracy of the transmission balancing; the analysis of its operational imbalance; the classification of the basic car cardan gears by the “flexibility” criterion; the formalization of the solution to the design tasks of the gimbal gear balancing and to other problems of ensuring the balance of this transmission in operation.

Introduction. The paper is devoted to forecasting the operational properties of the existing and newly developed high speed steels depending on their chemical composition by the investigation of thermodynamic processes in the friction zone under cutting, and by receiving analytical dependences for evaluating friction and wear characteristics. The work objective is the prediction of wear resistance of high speed steels on the base of the structural sensitive parameters of the absolute or relative thermo-EMF and entropy of the material which can be calculated by the additivity rule at the known chemical composition. Materials and Methods . The theoretical relationship between the change in entropy of steels and their thermo-EMF is obtained. According to it, a smaller value of the absolute thermo-EMF corresponds to a larger value of the material entropy. This theoretical relationship is experimentally tested on various compositions of high speed steels. Research Results. To determine the relationship between entropy as a thermoelectric characteristic of high speed steels and their wear resistance, experimental tests on friction for the cylindrical samples of high speed steels of different types, and study on the wear properties of drills under steels machining are carried out. Measurements of relative thermo-EMF of these samples are performed; and their absolute values are calculated. The results of these tests show maximum wear resistance of high-speed steels having high values of entropy and low values of the absolute (relative) thermo-EMF. Discussion and Conclusions . The relationship between the wear resistance parameters of high speed steels and their structurally-sensitive characteristics at the micro-level - entropy and absolute thermo-EMF, is established. To reduce wear during friction and cutting, it is necessary to apply the types of high speed steels with maximal entropy and minimal thermo-EMF. Entropy, which with ease can be calculated on the known chemical composition of the material, can be used to assess the operating properties and to predict the wear resistance of both existing and newly developed compositions of high speed steels.

Introduction. The work objectives are pilot studies of vibrowave processes in the utilization technology of combine harvester parts through the example of guide pulleys, and the determination of the most effective abrasive environment. Materials and Methods . Combine harvester aggregates are considered - four idlers of the poly-V-belt with the diameter of 150 mm with various degrees of the oil consumption pollution, and old paint and soil remains. The following is accepted as an operating environment: broken abrasive disks; porcelain balls ( d =6-8mm); abrasive PT grains of 15×15; steel balls ( d =5-7mm). At the exterior check of the parts, it is noticed that all rollers have oil consumption pollution and old paint remains. The samples are contaminated approximately equally. The rollers are weighed. The treatment is performed in the vibration hydrocarbon gas unit 4×10. The processing mode is as follows: A = 2.5 mm; frequency of oscillations - 30 Hz; treatment time t = 30 min.). 2% solution of soda ash is used as a process liquid (PL). At the end of the 30-minute vibration washing and scrubbing operation, the samples were washed with water, dried and weighed. An external examination of the rollers after processing was performed. It was marked that the idler rollers were most effectively cleaned when processing in a medium consisting of the broken abrasive disks and 15×15 PT grains. However, the surface of the samples was not completely cleaned. The next stage of the experiment was performed - fault defection of the parts and determination of their conformity with the specifications. It is described how much the processed samples are suitable for the further use. Research Results . According to the measurement results, under the identical conditions for the vibratory treatment of guide pulleys, it is most effective to clean the surface using broken abrasive disks. Discussion and Conclusions . After specifying the most effective purification component, the defective parts are inspected and their TU compliance is determined. As the research results show, 3 out of 4 parts are suitable for recycling in the production.

Introduction. Reliability-Based Design Optimization (RBDO) model reduces the structural weight in uncritical regions; it provides not only an improved design but also a higher level of confidence in the design. Materials and Methods. The classical RBDO approach can be carried out in two separate spaces: the physical space and the normalized space. Since lots of repeated researches are needed in the above two spaces, the computational time for such an optimization is a big problem. Fortunately, an efficient method called the Hybrid Method (HM) has been elaborated by which the optimization process is carried out in a Hybrid Design Space (HDS). When designing free vibrated structures, the HM can be used with a big implementation complexity, and that leads to high computing time. An efficient method called Safest Point (SP) method is developed to overcome this drawback. Research Results. A numerical application on the composite aircraft wing under free vibrations shows the efficiency of the proposed method relative to the HM. The SP method can reduce efficiently the computing time relative to the HM. Discussion and Conclusions. The simplified implementation framework of the SP strategy consists of decoupling the RBDO problem into a number of simple problems. That provides designers with efficient solutions that should be economically justified for a required reliability level for dynamic cases (modal studies).

Introduction. The work is devoted to the problem of the hydrogen saturation of steel parts skin at their high-speed impacts with a water-drop flow. A hypothesis of the water molecules dissociation at high-speed drop impacts was suggested in a number of papers. This hypothesis was confirmed by some experimental data. The effect of this dissociation is hydrogen embrittlement of the metal surface layer. The work objective is the calculation and experimental verification of the given mechanism of the erosion destruction of the steel surface. Materials and Methods. Energy equations of various ways of the water molecules dissociation are considered for the calculation-analytical estimates. The Tate and van der Waals equations are used with allowance for the change in the phase states of water at impact. Experimental data are obtained on the basis of spectral analysis using visible monochromatic (qualitative analysis) and infrared (quantitative analysis) emissions. Research Results. An improved calculation apparatus is proposed to determine the energy level of the water molecules dissociation and free hydrogen release with account for the compressibility of water at achievable impact speeds. The results of spectral studies of bubble tracks formed on the experimental steel samples under the bench erosion tests are presented. The spectral analysis shows that the tracks are composed of air bubbles. Free hydrogen is not detected in them. Discussion and Conclusions. The calculated and experimental data obtained in this paper do not give grounds for confirming the hypothesis of hydrogen dissociation under the water-drop impacts with a steel surface in the impact velocity range of 200-600 m / s. Therefore, the mechanism of hydrogen embrittlement, apparently, should be excluded from the number of additive components of the droplet impingement erosive wear.

Introduction. The paper presents the key aspects of constructing a management system for the state of multi-operation computer-controlled machines based on the information-control module of e-Mind Machine and the apparatus of fuzzy sets and fuzzy logic. It is shown that the input effects of the control system are formed due to the sets of inheriting and operating components of the status parameters. The work objective is to develop a system for monitoring the condition, detecting dimensional wear, and determining the period of tool life on the basis of the fuzzy logic methods. Materials and Methods. A new algorithm for constructing an expert system based on the fuzzy logic methods is proposed. The applicability of fuzzy neuron methods for solving the problems on determining the service life of the instrument through comparing the calculated values to the data of the manufacturing firms is demonstrated. The study is based on the application of the concept of electronic services using expert systems. Research Results. The basic principles of the construction and application of the status monitoring system are substantiated. They provide the possibility, under managing, to adapt to the emerging situation and to predict state changes when processing the parts. The monitoring functions include not only the processing of data obtained from the test units of the mechatronic system and external equipment, but both the forecasting of the residual dimensional tool life and the durability for the period of normal wear and tear. The decision-making process on managing the tool status is presented in the form of an algorithm for the expert system activity based on the use of a fuzzy neuron controller. Discussion and Conclusions. The results obtained can be applied in the parts production where accuracy is one of the key parameters. Automated control systems for the machine condition allow reducing costs due to equipment downtime, and monitoring the tool status can reduce the rejection rate. The characteristic examples of decision-making in the fuzzy neuron system are given.

Introduction. The analysis of the research papers shows the relevance of this topic, since there are no publications devoted to the determination of the spectral components of the power sequence of the milling process which makes it difficult to analyze models of the noise and vibration excitation. The noise exposure limits excess due to the high tool speed presents a critical problem. The highest speed is observed when the copy milling machines are operated. In the cutting conditions standards, only the power action amplitude is specified for woodworking which makes it difficult to determine the noise spectra. This study is devoted to determining parameters of the power sequence arising under the circular moulding. Materials and Methods. Methods of the cutting theory, spectral analysis, and statistical processing are used in the course of this study. Techniques of the noise and vibration levels analysis are largely determined by specifying the power action as a time function. Research Results. As a result of the conducted research, the mechanism of the force generation under milling; rules of the forces distribution over the projections; and patterns of variation in the cut-off allowance under milling are determined and specified. Discussion and Conclusions. The constructed mathematical model of the milling process dynamics and the software developed on its basis make it possible to evaluate the sound pressure levels created by both the cutting tool and the spindle case. This sound pressure actually determines the excess of noise levels over the maximum permissible values.

Introduction. The development of the adaptive hydraulic drive with the volumetric tool-feeding speed control of the production machines using the example of the portable URB-2.5 drilling unit is considered. A hydraulic control circuit is developed for adapting the tool-feeding hydraulic drive to the discontinuous load on the main motion drive in the course of drilling. The circuit includes a multifunctional hydromechanical transmitter executing functions of the drilling process monitoring and the original hydraulic valve control that allows generating the control pressure of the tool-feed hydraulic drive. Materials and Methods . A generic mathematical model of an adaptive hydraulic drive with delivery control is developed. A computational experiment is carried out to identify processes in the original hydraulic motor control circuit and in the tool-feed drive as a whole. Research Results. New mathematical and computational models of the adaptive hydraulic drive with the volumetric method of the revolution control of the dual-mass dynamic system and the hydraulic control circuit with a hydromechanical multifunctional device are obtained. The processes running in the hydraulic control circuit are identified; the efficiency of the offered sheet-oriented solutions is proved. Quantitative and qualitative characteristics of the adaptive hydraulic drive, dependences of the tool feed and rotation velocities and their variation range are specified. Discussion and Conclusions. The obtained results can be used to create new drilling rigs with various characteristics. The application of the developed mathematical and computational models will allow reducing time and resource expenditures under designing an adaptive hydraulic drive of the drilling rig, and creating prototype models and commissioning activities.

Introduction. Currently, in the Russian metallurgy, waste-gas heat under steelmaking in the electric arc furnace (EAF) is used inefficiently. This determines the urgency of the task to develop methods for СО to СО₂ afterburning degree control under steelmaking in the EAF. Materials and Methods . A mathematical model of the decarburization and combustible gas afterburning modes under the reduced pellets electrosmelting at their continuous feed to the EAF bath is used to solve the problem. The proposed model allows estimating the mode parameters of the decarburization and combustible gas afterburning in the electric arc furnace. The role of the rate of carbon oxidation components in the common mode of decarburization and gas afterburning in the EAF is studied. Research Results . The possibility and efficiency of the CO afterburning by the oxygen beams in the counter gas flow system is experimentally confirmed. This allows accelerate the processes of metal heating and decarburization, as well as improve other technological parameters of the steel electrosmelting. Discussion and Conclusions . The mathematical modeling results show that a new method of supplying oxygen through the oxyfuel burners and the oxygen lance provides an increase in the energy efficiency of the steel electrosmelting in the electric arc furnace.

Introduction. Promising modern high-performance combine harvesters should be created on the basis of new principles and solutions for improving the quality of the threshing and grain separation processes in field operations. Grain infestation is a factor complicating threshing. To optimize threshing, it is advisable to adjust the threshing-separating device parameters, to determine the grain separation and its contamination regularities due to humidity, changes in the grain feeding, the threshing gap dimension and the drum rotation frequency. Materials and Methods. The experiments were carried out on the threshing of winter wheat of the Don semi-dwarf variety. A laboratory-field threshing apparatus was used. In the course of the experiments, the separating property of the threshing-separating device of a tangential-axial type in the form of a one-nappe revolution hyperboloid was studied. Research Results. Based on the results of the experiments, the charts of the threshed material separation and clogging depending on the grain feeding, the threshing clearance, the humidity of the threshed mass and the drum rotational speed are plotted. Discussion and Conclusions. As a result of the studies, a significant effect of the working parameters of the thresher on the quality factors and the level of grain losses in threshing is proved.

Introduction. The feeding effect on the cut face surface under waterjet cutting is considered. Cutting is done by water and abradant mixture emitted from the nozzle at high speed and high pressure. Under the cutting jet action, the erosion damage of the material occurs, the abrasive particles remove the microchipping layer, and water evacuates them from the cutting zone. Waterjet cutting can process almost any material.The cutting process is "cold", there is no thermal effect on the metal. It is possible to cut both 3D and 5D complex geometries, for example, to preprocess bladed integrated disks of the gas-turbine engines. Materials and Methods. The research was carried out on the basis of the JSC "Rostvertol" enterprise on the waterjet cutting plant of the Flow company. The materials most frequently used in the aircraft industry were chosen: steel 30 KhGSA, aluminum alloy D16Т, and composite material (fiberglass-titanium). The recommendations that allow reducing the number of defects under the waterjet cutting are given. Research Results. The effect of the waterjet-cutting nozzle feeding on the cut face roughness is theoretically investigated. The dependences of the surface roughness determination for the distinguished segment of the cut face are obtained. The experimental studies confirming the adequacy of the theoretical models obtained are performed. Discussions and Conclusions. As a result of the studies, it is found that the roughness of the treated surface deteriorates with increase in feeding. Furthermore, the deterioration is nonuniformly distributed along the cross- section of the cut. To reduce the width of the corrugated cut, the feedrate should be reduced.

Introduction. The effect of the low-frequency oscillations of the reaper on crop losses of the domestic combine harvesters is considered. In the study, various speeds of the machine, various mass-geometric and elastic-dissipative characteristics of the units are taken into account. The geometrics of the overhead system of the combine reaping section which ensures smooth running and reduces crop losses for the reaper is determined. Taking into account the mass-geometric and elastic-dissipative characteristics, the amplitude and frequency spectra of the oscillations of the domestic machines of the agroindustrial complex are determined. The mathematical dependence of the reaper oscillations on the combine operation conditions is proposed. Materials and Methods. The mathematical modeling of units vibrations is used with account for the longitudinal-vertical oscillations of the separator body and the heaving of the reaper. The equation in the frequency domain is solved. Research Results . A two-mass oscillatory model is constructed, and the corresponding differential equations of motion are obtained. The graphs of dependences of RMS loads on shoes with different parameters of the suspension are presented. The geometrics of the suspension system of the harvester reaping part ensuring smooth running and lower crop losses for the reaper, is established. The relationship between the change in the number of detachments of the shoes, the linear speed of the machine and the parameters of the reaper suspension is educed. Discussion and Conclusions . The conducted investigation allows drawing the following conclusions. Frequency characteristics of the shoes response are caused by parameters of the reaper and separator suspensions. The reaper suspension system in the domestic grain harvesters does not ensure the continuous operation of the reaper in the copy mode of the soil microrelief which leads to generating additional oscillations of the body and crop loss. The parasitic vibrations strength can be reduced by increasing the extension of the reaping part of the separator body and reducing the rigidity of the reaper suspension.

Introduction. An advanced technique of the livestock waste disinfection is considered. The essence of the method is in the integral physicochemical action of the alternating magnetic field combined with a chemical agent. The inductor can implement this method. A residual number of the colony-forming units of total coliforms is selected as the most critical parameter characterizing the quality of the disinfection process of livestock effluents. It is proposed to use the mathematical experimental design theory to improve the efficiency of investigating the disinfection process of livestock waste. Its application implies a normal law of distribution of the value frequency of colony-forming units of total coliforms. Materials and Methods . In the course of this study, the following methods were used: direct and indirect instrumental measurement; micrographics; least quadrants, theoretical definition of the random distribution, and statistical data processing. Research Results . The hypothesis on a normal distribution law was tested by setting up an experiment at the stand with certain conditions. As a result of the conducted experiments, a sample of values consisting of 100 observations is obtained. Based on the aprior information analysis, a hypothesis on the normal distribution law of the value frequency of colony-forming units of total coliforms was adopted. Discussion and Conclusions. In the course of studying the distribution law of the value frequency of colony-forming units of total coliforms characterizing the quality of the disinfection process, the accepted critical value of the Pearson test was compared to the calculated one. Since the design value is less than the adopted critical one, the hypothesis on a normal distribution law is accepted.

Introduction. The work objection is the investigation of the industrial safety of the foundry. The task to estimate a disperse composition of dust which determines the microclimate of the foundry working area is being solved. The dependence between the particle size and their motion speed under the gravitational or centrifugal forces is revealed. Materials and Methods. The granulometric composition analysis of a powder dust sample is carried out by the laser diffraction method implemented on the laser particle analyzer Fritsch NanoTec “ANALISETTE 22”. Research Results . The data analysis shows that all phases of the process determine the microclimate of the internal environment and, under the emission dispersion, the medium in the intercase zone. The impact degree depends on the dispersion and chemical composition of dust particles. The other harmful airborne substances deposited on dust particles make it more dangerous. For example, an increase in SiO2 content toughens the requirements for clean air in the working area. Therefore, it is necessary to take into account more rigorous values of maximum permissible concentrations (MPC). Discussion and Conclusions. The most dangerous areas of the foundry production in the eco-risk terms are identified; and proposals on the development of the dust-collecting system with water wash are made. The research results can be used in foundries of the machinery production.