MATHEMATICAL AND NATURAL SCIENCES
The aim o f t his p a p e r is t h e e fficie n c y im p r o v e m e n t o f o n e o f t h e m o s t a d v a n c e d t e c h niq u e s o f s olvin g t h e ellip tic b o u n d a r y v alu e p r o ble m s — t h e field p oin t- s o u r c e m e t h o d d e sig n a t e d a s t h e f u n d a m e n t al s olu tio n t e c h niq u e in t h e f o r eig n lit e r a t u r e. N o w it is u s e d p rim a rily f o r s olvin g L a pla c e e q u a tio n . S e v e r al alt e r n a t e n u m e ric al s olu tio n s t o t h e b o u n d a r y v alu e p r o ble m s f o r P ois s o n e q u a tio n u sin g t h e field p oin t - s o u r c e m e t h o d a r e p r o p o s e d . T his m e t h o d a p plic a tio n t o t h e n o n h o m o g e n e o u s e q u a tio n s olu tio n, s u c h a s P ois s o n e q u a tio n, in m o s t c a s e s le a d s t o t h e d r a m a tic in c r e a s e o f t h e n u m e ric al e r r o r d u e t o mis t a k e s in P ois s o n e q u a tio n s p e cific s olu tio n. T h e rig h t m e m b e r o f P ois s o n e q u a tio n is a p p r o xim a t e d b y a t w o - dim e n sio n al trig o n o m e tric p oly n o mial (in t h e s olu tio n o f t w o - dim e n sio n al b o u n d a r y v alu e p r o ble m s ), t h e n it b e c o m e s p o s sible t o o b t ain t h e s p e cific s olu tio n n e c e s s a r y fo r s olvin g a n initial b o u n d a r y v alu e p r o ble m b y t h e field p oin t- s o u r c e m e t h o d. T h e t e s tin g r e s ult s o f t h e p r o p o s e d t e c h niq u e im ply it s e fficie n c y , a s t h e y allo w o b t ainin g t h e s olu tio n wit h a r ela tiv e e r r o r o f 1 0 − 6 a t minim u m m a c hin e tim e s p e n din g . T h e d e v elo p e d t e c h niq u e o f t h e n u m e ric al s olu tio n t o t h e b o u n d a r y v alu e p r o ble m s fo r P ois s o n e q u a tio n c a n b e u s e d f o r m o d elin g p h y sic al field s in t h e e n gin e e rin g d e vic e s o f v a rio u s a p plic a tio n s . K e y w o r d s : P ois s o n e q u a tio n , ellip tic b o u n d a r y v alu e p r o ble m s , field p oin t- s o u r c e m e t h o d, m e t h o d o f f u n d a m e n t al s olu tio n s.
Some new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond—Leontiev generalized differentiation operator be continuous in the space of the analytic functions in simply connected region G of a complex plane. It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. The set M(G) with the property M(G)·G⊆G is called multiplier G. Let the region multiplier be connected, and it does not align with identity. It is proved in the paper that the functions under consideration will be univalent under these conditions. If multiplier G is unconnected, then there is always a generalized differentiation Gelfond—Leontiev operator with a many-valued generating function.
The predator-prey interactions on the spatial heterogeneous two-dimensional area are described. The model is written as a system of nonlinear parabolic equations for two closely related predator populations and two prey populations competing for the general resource. It is shown that under certain relationships between the parameters and the variable natural habitat resource functions, the model belongs to the class of the cosymmetric dynamical systems. In this case, there is a continuous family of stationary distributions of the coexistent populations. The simulation experiment is based on the method of straight lines, and on the scheme of staggered grids. The balance method is used for the approximation in spatial variables of the task on a rectangular area. The results showing the model capabilities for describing the formation of the population stationary distributions are presented. The formation of the biological structures is studied under the growth parameter heterogeneity; the conditions for the coexistence of closely related types are analyzed.
Amplitude-frequency characteristics of the piezoceramic elements in the forms of a thin plate and a rod are studied through ANSYS program. Resonance and antiresonance frequencies of the first two disk radial modes, the thickness mode of the thin plate, and the axial mode of the rectangular cross-section long rod are measured. The numerical results are compared to the known determination techniques of the elastic Sij, piezoelectric dij, and dielectric εij constants of the piezoelectric materials. The improved procedure for determining elasticity constant SE13 on one specimen of only radial disk oscillations is suggested and substantiated. The method is based upon the relationships between the elastic constants of piezoceramics and the dispersion of longitudinal waves. The new method usage domain is studied. As compared to the known techniques, the proposed method facilitates the measure procedure and allows determining the elastic constant with the extended precision. A fundamentally new technique of measuring resonant and antiresonant frequencies of piezoelements with losses is developed for defining a full range of material constants of ideal elements without losses according to the Russian branch standards and the Institute of Radio Engineers (USA) standards for piezoelectric crystals.
ENGINEERING, TECHNOLOGY AND TECHNICAL SCIENCES
The dominant occupational hazards at the welding sites are identified. They are elevated air pollution and dustiness. Depending on the welding forms, the concentrations of harmful substances (carbon oxide, iron and magnesium oxides) exceed the sanitary-hygienic standards by 7‒10 times. The heat and mass transfer of harmful substances and heat in the industrial environment with dynamic ventilation and pollutant sources is considered. Its nonstationary 3D mathematical model is presented. The model permits the turbulence of air flows which differs it from the existing models of the occupational hazard spread. The developed software enables to solve various tasks of the ventilation system installation and operation. Specifically, it is referred to the rational distribution of various engineering devices of the given system, its control issues, and of the optimal worksite location. To ensure safe working conditions for the welding operators, the recommendations on the rational organization of the local ventilation system operation are developed. The corresponding constructive solutions are proposed.
The property change of the unified dynamic system is considered by the example of the deephole machining process. It is shown that due to the nonlinear relationship formed by the cutting process, in the system, as a rule, the only balance point with the bounded domain of attraction is constructed. The given materials on investigating the domain of attraction show that it depends on the control and cutting forces presented in the state coordinates of the interacting subsystems. While shaving is being accumulated in the chip clearance grooves, this domain degenerates, and the system becomes totally unstable. At this, the tool is blocked, and as a rule, broken. It is shown that the domain of attraction and evolutionary changes of the system properties depending on the shaving accumulation in the drill flutes are basically related to the interacting servomotors parameters. It is proposed to adjust the servomotor parameters on the basis of the introduction of special links.
Steelmaking in arc 150-ton electric furnace using iron-rich pellets is considered. It is shown that the melting results are determined by the conditions of the simultaneous processes of the pellet melting and the melt oxidation refining. At that, it is important to monitor both the level of the bath thermal supply baths, and the decarburation and steel reheating processes. The technique of the synchronous control over the heating modes, and the bath decarburation with varying in the course of melting metal weight, is developed on the basis of the data acquired under the operating conditions. It is found that the basic energotechnological process indicators (including those taking place in the complex steel processing facilities) improve if the melting of the metallized raw materials is conducted in the field of the optimal steel superheated area above the liquidus line with full immersion of the electric arcs in foamed slag. The proposed flowchart and algorithm of parameter determination for the heat-and-power mode under the ladle treatment in the ladle-furnace ensure the saving energy costs by 39.5‒40.5 kWh per 1 ton of the steel made in the EAF.
The basic principles of the construction and operation of the machine monitoring system in the computer-integrated manufacturing are described. The tool condition and the tooling backup control are the focus of attention. The proposed approach is aimed at creating conditions for the effective functioning, and the tool state management using a knowledge system of TOOL unit of the machine Smart-passport. The unit architecture is presented by a set of modules including a data acquisition module, a module for observing changes in the tool state and control, a monitoring module, and others. The significant innovation of the research is the introduction of the concepts of fuzzy boundary and border lines of sizing wear, and of overall tool life based on the theory of fuzzy knowledge concepts. The introduction of these concepts is related to the necessity to adapt modes of cutting and decision making depending on the tool state and its effect on the part accuracy.
The application of the complex artificial neural networks (CANN) to the inverse identification problem of the elastic and dissipative properties of deformable solids is considered. The additional information to the inverse problem is components of the displacement vector measured in a set of points at the solid boundary (positional measurement). This solid performs harmonic oscillations in the first resonant frequency. The process of displacement measurement is simulated using the calculation of finite elements software ANSYS, the building of the amplitude-frequency characteristics (AFC) of the displacement, and of the selection of their values for a set of frequencies (frequency measurement). In the given numerical example, problems on the accurate identification of the elastic modulus, and material quality depending on the number of measure points and their location, as well as on the neural network architecture and the length of the training process performed by the complex-value error back propagation (CBP) algorithm are investigated.
The functional diagram of a grain-cleaner with two ducts and certain air speed characteristics is described. Each pneumatic duct is segmented into blocks with various probabilistic characteristics of the airflow velocity distribution, various density composition and terminal velocities of each component. The mathematical expressions averaging the air separation indices full-width of two sequentially operating pneumatic ducts are defined. A stochastic quasi-static mathematical model of the operation process of a grain-cleaner with two pneumatic ducts is developed. The air-separation process at the specified manufacturing characteristics of the heap components, their fractional value in the heap, and of the structure of the airflow entering the pneumatic ducts, is simulated. The results of the parametric air-flow classification synthesis, the technological characteristics of its operation are described; the heap fractional makeup and measurable characteristics in each separated fraction are given; the possibility of the air-flow classification of the crushed haulm heap on the controlled factions with the output of 0,689 kg/(m∙s) is defined.
The main ways of increasing the bulk separation efficiency in the seed refiner which is a system of the particular technological operations allowing selecting grain material with the tailored properties are determined. The impact of the particular technological operations proceeding in the seed purifier on the entire system of the postharvest handling of the grain material is analysed. Operation schemes of various seed-cleaning units containing a specified set of machines for processing the grain material of the program quality are presented. A structural design model of the seed refiner performance is developed. Using the results of the field and bench testing, as well as the mathematical models whose adequacy has been earlier proved, the functioning of the various schemes of grain cleaning machines is simulated. An economic analysis of the seed refiner performance data based on the simulation results is made at various prices on the original and refined grain.
The decomposition of knowledge into an array of “micro-knowledge” permitting a single-valued binary test score is studied. In this case, the test task is formulated as a set of micro-knowledge responses jointly revealing the knowledge level of the specific subsection. It allows presenting the development of a set of responses to a test question as the objective of investigating the multifactor dependence. Thus, the development process of a set of responses can be considered from the perspective of planning a multifactor two-level experiment. This approach allows a good formalization of the test construction, and its result estimation which becomes available to the teachers who do not specialize in the test task development. The method is illustrated by an example of the test construction, and application to assess the knowledge level on the automatic control theory. The data statistics has shown the respondents’ knowledge level, as well as the degree of a tester’s belief to the response awareness.
The kinematic synthesis of the rectilinearly enveloping mechanism parameters that allows determining the circuit constants and the accuracy characteristics of the prescribed motion of the function element to reference sizes of the working space is presented. A crimping press for recycling carbodies with the compound enveloping motion of the working member is considered. The presented database allows determining its kinematic parameters. At this, the press is much smaller in dimensions than other presses performing the given operation. This predetermines its perspectiveness with account for the significance of the body utilization and recycling. The presented synthesis is based on the function approximation method describing the motion trajectory of the mechanism guide point to the guided path. As it follows from the given example, the crimping and sliding accuracy parameters are not critical for the carbody strain process under the disposal, therefore, they can vary quite substantially.
Measuring methods of the gas concentration in the working area air of the mechanical-engineering repair facilities are considered. The gas-sensitive sensor types are compared. A classification of the occupational hazards is presented; their health effect is described. The object of this study is a standard repair facility of the mechanical-engineering industry. The workplace assessment charts of one of the electric locomotive repair works are analyzed. Some issues on the acceptable working conditions ensuring, and on decreasing their harmful level are considered. To solve the task of monitoring the occupational hazards, the application of the wireless sensor networks (WSNs) is proposed. The sensor types best suited for the application in the WSN are described. The results of the research conducted allowed making the conclusions on the feasibility of the wireless sensor networks in the safety management systems in the mechanical-engineering repair facilities.
A plant xylem is a complex system of pipes in which the movement of water occurs both vertically and horizontally. Rectilinear capillaries are arranged vertically in the trunks of lots of plants. However, a stem crown growing upwards can execute an independent circular motion called circular nutation. Some plants always wind around the bearer resulting in the spiral growth. The xylem of such plants should conform to their curved parts. A spiral water rise occurs in the rectilinear stems of some plants as well. Currently, the calculation of the water rise in the spiral capillaries is not described in the scientific literature. The problem on the mathematical modeling of the water rise in capillaries having the form of a cylindrical spiral is solved in the paper. It is shown that more water moves through the spiral capillary than through the rectilinear and curvilinear capillaries of the same length.
In the process of gearing breaking-in, teeth are worn down. The estimation algorithm of such wear rate in the circular helical point gearing is described. The algorithm performance is illustrated by the example of calculating the circular helical gearing with the circular tooth profile in the frontal cross section. The problem is solved using ANSYS software system of the finite-element analysis. The application of the developed algorithm for a finite-element model of meshing a pair of gearing teeth is described. The variation of the contact pressure surface distribution is analyzed in relation to the wear rate under the teeth breaking-in. The following is established. The gear with a circular tooth contour in the front cross section shows new properties compared to the gears with a linear or point contact. Breaking-in of the teeth in the gearing with circular contours is considered. In this case, under increasing the wear rate, peak contact pressures decrease and move from the mean line of the tooth to the tooth bearing centre.
The biogeosystem engineering is considered, and the verification of the biological, recreational, productive-economic resources of the soil-reclamation agrotechnics based on the rotary milling subsoiling is performed. The test data of the first-generation rotary milling subsoiling facility is provided. A fundamentally new engineering solution is developed. The structural synthesis of the new rotary milling subsoiling facility options in the second- and third-order approximations is performed. The draught minimization of the new facility under its operation is provided. The optimization criterion for the engineering solution synthesis results is developed; the facility parametric synthesis is performed; comparative energy characteristics of the new facility and prototype are given. The rotary milling chisel plough—gearbox transmits torque without passive draught to the tillage tool, and to the subsoiling one that operates full dip being horizontally located and moving progressively at the given depth of 20‒48 cm. The possibility of the reliable operation in the soil of the new engineering solution interconnect system is proved. The assignment and reliability indices of the subsoiling rotary milling facilities are given. Performance physics and physics of failures are considered; the new engineering solution reliability is proved. The fundamentally new principles of the innovation project development and the implementation of the land development plans in Russia are proposed.
Algorithms of solving the “minimax” weighted graph coloring problem are considered and compared. The mathematical formulation of the problem is presented; the solution optimality criteria are stated. The exact algorithm that always finds the minimum count of colors through Maghout method and then finds the “minimax” option using 3 versions of the critical path method is described. Three fast heuristic algorithms are described: the algorithm that works with the list of vertexes arranged by the local degrees; the algorithm based on the removal of the points and adjacent edges; the algorithm using the vertex saturation rate. All algorithms are considered with examples. To evaluate the algorithm efficiency, a computational experiment on several hundred of randomly generated graphs is set up. The algorithms were compared by the operating speed and the proximity of the result to the "minimax" version of coloring.
CONCISE INFORMATION
A fundamentally new design of the contactless inductive sensor for the conduction control of the liquids applied in the chemical, oil-extracting, food, and other industries is offered. The sensor magnetic field is studied using modeling software system Elcut 5.6 Professional. In the course of the investigations, the impact of the excitation current magnitude, its frequency, as well as the diameter of the pipe with conducting liquid, on the magnetic-field pattern is estimated. Thus, the fluid speed was assumed rather low, unaffecting the pickup signal. The studies of the electromagnetic field excited by the alternating current in a cylindrical tube filled with the conductive fluid under its constant parameters are resulted. On the basis of the electromagnetic process simulation results, the recommendations on the optimum parameter ratio dependent on the test medium characteristics are obtained.
The comparative analysis of various processing techniques used for the problem solution — improving the reliability and service life of the heavy duty cutting blades through the example of combine harvesters — is described. The possibility of increasing the wear resistance of the cutting knives for the agricultural machinery by the vibrowave strengthening treatment techniques is established and proved. The application domains of the vibrowave treatment in the mechanical and instrument production engineering are considered. The dynamic nature of the hardening process is described. The technological capabilities of the vibrowave treatment method and the mechanism of the product surface layer quality indices generation are presented. The exploratory field research of the vibrowave treatment impact on the hardened surface layer value and the wear of the cutting blades made of hard steels R6M5, X12M, R18 is resulted. The studies on the impact of the vibrowave treatment modes: vibration amplitudes and frequencies, steel balls diameter, variation of the hardened layer depth of knives made of steel X12M, are resulted as well.
