Mathematical Model For Calculation Research Articles

Results of studies on extending the time operation of gin and linter grates

Results of studies on extending the time operation of gin and linter grates by hardening of the working area by high-frequency current are given in article. Mathematical models for calculation of key parameters of the mode of hardening of the working area of gin and linter grates are made. As a result of the executed researches the following conclusions are drawn: change of a gap between grates in a grate lattice leads to change of parameters of process of ginning and finally to deterioration of products. Mathematical models for calculations of parameters of process of hardening of the working area of grates are received. On the received mathematical models key parameters of hardening process current of high frequency which have the following values are calculated: depth of the tempered layer – 2.0 mm, the optimum frequency of current – 60000, specific power – 500 W/cm2, hardening time – 10, studying hardness tempered and not tempered sites of grates by method of Rockwell showed increase in hardness of the tempered site to HRC 55 against HRC 45 at not tempered by the working area.

A mathematical model for calculation of the influence of ferromagnetic components in Vertical Displacement Events and stability simulations of tokamak plasmas

Iron core transformer tokamaks have a distinct element, namely the iron core which can affect the plasma stability of the plasma. As a consequence of the high non-linear dependence of the magneto-hydrodynamic solutions on the iron permeability μ Fe in JET tokamak for example, Vertical Displacement Events (VDEs), equilibrium and stability calculations are more complicated and more time consuming than in air core transformer tokamaks. By considering the ferromagnetic components as a linear, isotropic and homogeneous media on subdomains, it is known that these media can be replaced by a homogeneous one (vacuum) and a surface-current density distribution i Fe(l) on the separation surfaces between subdomains, with l the curve taken along the curve separating two different magnetic media. For the case of geometry with rotational symmetry, this surface-current density distribution along a curve, in a meridian plane, is given by a Fredholm integral equation of second kind. Practically, the advantage of this method is more obvious for the inverse formulation of the VDEs and stability problems by moving the non-linear term (due to the iron permeability μ Fe ) from the differential operator to the r.h.s. of the equations. In this paper, we are presenting how the influence of ferromagnetic components in the equations of the surface currents developed in the vessel structures during Wall Touching Kink Modes (WTKMs) can be taken into account and are reviewing the equations to be solved in order to simulate the influence of the ferromagnetic components in VDEs and equilibrium stability calculations. The numerical results of these simulations for a real JET tokamak structure and plasma parameters will be reported in a future paper.

ГИДРОДИНАМИЧЕСКИЙ РАСЧЕТ КЛИНОВИДНОЙ СИСТЕМЫ «ПОЛЗУН - НАПРАВЛЯЮЩАЯ», РАБОТАЮЩЕЙ НА СЖИМАЕМОМ СМАЗОЧНОМ МАТЕРИАЛЕ В УСЛОВИЯХ НАЛИЧИЯ РАСПЛАВА НА ПОВЕРХНОСТИ НАПРАВЛЯЮЩЕЙ

Recently, various methods have been used to ensure the hydrodynamic mode of lubrication, one of the methods is devoted to this scientific article. In the article, on the basis of the equation of motion of a compressible, truly viscous liquid for a "thin layer", the equations of state, the continuity equation, as well as the equations describing the profile of the molten contour of the surface of the support ring, an asymptotic and self-similar solution is found for the zero (without taking into account the melt) and the first (taking into account the melt) approximation, for determining the velocity field and pressure in the lubricating layer. For the profile of the molten contour and the pressure, the solution is found by the method of sequential approximation, for the extreme and non-extreme case. As a result, a refined mathematical calculation model of a wedge-shaped sliding support with a low-melting metal coating on the movable contact surface is developed, which compensates for the emergency lack of lubricant and provides a stable hydrodynamic lubrication mode, which allows determining the bearing capacity and friction force. As a result of numerical analysis, the obtained refined mathematical calculation model of a wedge-shaped sliding support with a low-melting metal coating on the surface of the support ring, taking into account the compressibility of the liquid lubricant and the coating melt, and experimental research, the effectiveness of the obtained complex of refined models that allow performing both pre-design evaluation and design engineering calculations, in a wide range of operational load-speed modes, as well as the mechanism and stages of transition to lubrication with metal sprays is established, providing an increase in the level of the main tribotechnical parameters and the resource of tribosystems.

TECHNIQUE FOR ESTIMATING THE EFFICIENCY OF NOISE PROTECTIVE ACOUSTIC SCREENS IN THE PRESENCE OF FLAT ANTI-DIFFRACTORS

To increase the efficiency of acoustic screens when protecting against acoustic noise, anti-diffractors are used to reduce the diffraction level on the upper edge of the screen. The aim of the work is to refine the mathematical model used to assess noise protection efficiency with the help of an acoustic screen with an installed one-sided flat-type anti-diffractor. The well-known techniques based on the principle of the amplitude dependence of the sound wave intensity from two sources are analyzed: a point-type noise source and a secondary cylindrical wave source - the screen edge, on which the sound wave is diffracted. Taking into account that the change in the distance between the anti-diffractor and the working point in the acoustic shadow zone is associated with a change in the diffraction angle, it is proposed to evaluate the acoustic screen effectiveness by comparing the initial sound wave propagation paths. An approach to a mathematical calculation model formation is proposed, in which the diffraction point located at the intersection of two components of the wave path to the operating point is considered to be the location of the sound wave secondary source in the area of the screen upper edge: from the noise source to the flat-type anti-diffractor installed on the upper edge of the screen, and from the anti-diffractor rear edge to the operating point. Relationships that make it possible to solve the problem of analytical assessment of noise-protective acoustic screens' effectiveness when installing anti-diffractors on their upper face in the form of flat hinged panels oriented towards the acoustic shadow are obtained.

Гидродинамический расчет клиновидной системы «ползун-направляющая», работающей на сжимаемом смазочном материале в условиях наличия расплава на поверхности направляющей

In the article on the basis of the equation of motion of the compressible lubricant for the «thin layer», continuity, state, and the equation describing the profile of the molten contour taking into account the formula of mechanical energy dissipation the asymptotic and self-similar solution is found for the extreme (when the speed tends to infinity) and non-extreme case. As a result of solving the problem, a refined mathematical calculation model of a wedgeshaped sliding support with a low-melting metal coating on a movable contact surface is obtained, which compensates for an emergency lack of lubricant and provides a stable hydrodynamic lubrication mode

Mathematical calculation model of a ferromagnetic lubricant with incomplete filling of the working clearance

Mathematical calculation model of a ferromagnetic lubricant with incomplete filling of the working clearance

Determination of the angle of the device inclination relative to the horizon using a measuring system based on the MPU6050 microelectromechanical sensor

At present time microelectromechanical systems have become widely used. Accelerometers and gyroscopes are prominent examples of a microelectromechanical system. In this article we consider the possibility of using a measuring system based on the microelectromechanical sensor module MPU6050 for determination the angle of device inclination relative to the horizon. This module can be used for the digital protractors, in various devices to stabilize the position, to determine the speed of inclination, etc. The main advantage of the microelectromechanical sensor MPU6050 over all others sensors are its low cost and wide possibilities of parameters measurement, as well as the possibility to obtain digital data output. The MPU6050 allows to measure acceleration and rotation speed, however the ability of direct measurement of the inclination angle is not provided. To measure the inclination angle a "side effect" is used, which changes the value of the acceleration of free fall when changing the inclination angle relative to the horizon. The main problem related to application of this module is a strong noise in output values. This limits the ability of using of this sensor for accurate measurements and measurements at high movement speeds. But using of mathematical processing of measurement results makes it possible to obtain static values with an accuracy of 0.05 degrees, which allows using the MPU6050 sensor analogously to other sensors designed for measurement of the inclination angle. The processing technique given by the authors allows to significantly reduce the digital noise that occurs when the sensor is in a static position. The reduction of digital noise is achieved due to the fact that the microelectromechanical sensor MPU6050 allows to measure the angular velocity, consequently the inclination angle relative to the horizon cannot be changed at static position of the sensor, i.e. when the angular velocity around the axis is equal to zero. Conversely, when the angular velocity is not equal to zero, the inclination angle of the sensor changes. Moreover, the greater the value of the angular velocity leads to the faster change the of inclination angle values, this phenomenon is taken into account in the mathematical model of inclination angle calculation.

Unification of Calculating the Performance of Vehicles and Transport-Technological Facilities

Introduction. In agricultural production during transportation of goods it is accepted to allocate transport and transport-technological processes with the corresponding methods of rationing works. The peculiarity of the processes is the sequential execution of cyclic operations, providing transportation of technological material to the destination directly or with preliminary collection (subsequent distribution) on the field. At the same time, if the goods are moved directly between points, excluding technological (field) operations, this process can be considered a purely transport one, a special case of the transport and technological process. In this regard, it is proposed to consider this process as a component of the transport and technological process, which in turn requires correcting the applied methods for setting performance standards. The aim of the study is to develop a mathematical model and algorithm for standardizing the calculation of the performance of different vehicles and transport and technological facilities through formulating the dependence of the performance components on the power of the said facilities as their main classifier. Materials and Methods. The performance standards were identified by the extrapolation, interpolation or approximation methods based on their estimated performance. The classical method of differentiating functions was used to find the extrema. Результаты исследования.At length of fertilizer transportation by direct-flow technology LГ = 9 km and application dose U = 0.06 kg/m2, the following values of transport and technological facilities performance have been obtained: a) for vehicles to deliver fertilizers to fertilizer storehouses by Ural-432065 truck (body) W = 9.1 t/h, W = 6.3 t/h for tractor with MTZ-82 trailer. 1+2PTS-6; b) for transport and technological facilities to transport and distribute fertilizers by Ural-432065 (Amazone spreader) W = 5.5 t/h, W = 3.9 t/h for tractor with MTZ-82.1+RUM-6 trailer. Discussion and Conclusion. Based on the analysis of methods, the authors have made the case for the unification of calculating the standardized volumes of works, choice of composition, and comparison of the effectiveness of using vehicles, if they are used as transport and transport-technological facilities. A mathematical model and algorithm for a uniform calculation of the performance of different transport and technological facilities are presented. The way to determine the approximate rate of generation of funds that do not have standard indicators of work. The explanation of the innovations is accompanied by a formula device, which is based on the conclusion of the dependencies of out- and in-cycle components of the shift time balance on the engine power of the mobile device. The block diagram of the algorithm to calculate performance standards for vehicles is illustrated. The implementation of the algorithm is given by the example of using a specialized vehicle for transport and transport-technological operations.

Deployment of Conservation Voltage Reduction in Sample Feeders: A Systemwide Energy-Savings Analysis

The estimation of energy-savings analysis based on conservation voltage reduction (CVR) deployment is fundamental to establish its effectiveness. Historically, utilities conduct pilot CVR projects on a limited number of feeders where the time series (TS) voltage and power data are measured, preprocessed, and utilized in a mathematical model for energy-savings calculation for each individual CVR-deployed feeder. The challenge is establishing energy savings in large-scale projects where CVR is running on thousands of feeders, and feeder-by-feeder data processing and savings analysis could be cumbersome.

Study of feedwater regenerative heating operating modes at reduced loads of a turbogenerator by 300 MW power unit capacity

The article presents the results of numerical studies and analysis of the feedwater regenerative heating operating modes depending on power unit capacity. The main parameters of this system are the enthalpy of the turbine steam extraction for heaters, as well as the steam consumption in these extractions. The dependences of the turbine unit steam flow rate and the change in expansion process of the steam turbine during the load regulation were investigated. The mathematical model of calculation the thermal power plant for a 300 MW power unit capacity was developed. Following on the results of the calculation conclusions of feed water regenerative heating operating modes at reduced loads of a turbine-generator for a 300 MW unit.

DRG-Oriented Mathematical Calculation Model and Method of Integrated Medical Service Cost.

In the context of the new round of medical and health reform, in order to alleviate the problem of “difficult to see a doctor and expensive to see a doctor,” the state focuses on reducing the cost of medical services, so it puts forward the calculation and method research of medical costs. The purpose of this study is to calculate and predict the cost of medical services in a DRG-oriented integrated environment. In this study, activity-based costing and weighted moving average methods are used. First, basic data of medical services are collected, then all medical activities are confirmed and all service costs are collected, then a cost database is established, and a calculation model of medical costs is designed. Finally, calculation suggestions and optimization methods are put forward by analyzing the calculated data. The experimental results show that the actual demand of drugs predicted by the general moving average method is relatively insufficient, with the maximum error of 41%, the minimum of 5%, and the average error of 19.8%; the maximum error of drug demand predicted by the weighted moving average method is 24%, the minimum is 2%, and the average is 15.4%. It can be concluded that the prediction effect of the weighted moving average method is better than that of the ordinary moving average method, which plays a good and effective role in the prediction of medical cost. The activity-based costing method is more detailed and organized for the cost calculation and classification of medical services. It provides a certain value for the effective management and control of medical service cost.

Research on the Minimum Span of Constructions Crossing Natural Curve River

Ai, W.; Liu, H., and Zhu, P., 2020. Research on the minimum span of constructions crossing natural curve river. In: Wan, Z. (ed.), Coordinated Sustainable Development in Coastal Areas: Environment and Economy. Journal of Coastal Research, Special Issue No. 109, pp. 8–12. Coconut Creek (Florida), ISSN 0749-0208.The problem of determination method on the span of constructions crossing curved river is necessary to be researched not only because its close relation to navigation safety, but also because no clear method has been put forward so far, the minimum span of structures across natural curve river, which is considered as channel width (not considering the influence of tidal currents) is studied in this paper. From the perspective of navigation safety, the method of determining the minimum span of constructions crossing natural curve river can be obtained by establishing mathematical calculation models of flow-induced drift of natural curve and the range of turbulent flow around construction piers. The results show that the span of constructions crossing natural curved river is closely related to the navigation width of the ship, ship's drift distance induced by flow and wind, turbulent range of construction pier etc. The more the above factors are, the larger the minimum span of constructions crossing curved river is.

Investigation of Influence of Plasma Spraying Process Parameters on the Level of Residual Stresses

The method to determine thermal fields considering dependence of thermophysical and mechanical properties of coating materials and a base from the temperature, the running of plastic deformations and stresses relaxation at plasma spraying is suggested. The mathematical model of calculation of thermal field with moving boundary considering nonlinear feature of coating growth at layer-by-layer deposition and dependences from thermophysical properties of materials of the system «coating-base» is developed. The model application helps to estimate the effect of the parameters of plasma spraying process on the level of the residual stresses in the increased coatings.

Bread Dough Rheological Behavior Under the Influence of the Geometry of the Kneading Arms

The main objective of this study is validation of a proposed mathematical model for the estimation of the influence of kneading arms geometries on rheological properties of dough. Two types of kneading arms are studied, both mounted on the same industrial kneader type. A tridimensional numerical simulation for dough kneading is used for obtaining the Eddy viscosity values, which were introduced in a mathematical model for calculation of the dough�s resistant torque at the kneading arms, at 15 seconds time intervals. Real time torque diagrams developed by the kneading arms, were traced using a system for data acquisition and dough kneading control (SOPF), developed by BioTechnologiCreativ Company. These diagrams were used for mathematical model validation using the comparison between the torque values measured in real time and the ones obtained using the mathematical model, in which was introduced the Eddy viscosity value obtained with the 3D simulation. The obtained results have very similar values. With this study it is possible to predict the rheological behavior of dough during kneading process. Anticipation of the kneading diagram form can be helpful in the optimization of the entire technological process and the obtaining of dough with uniform consistency and optimal development during the stages of the manufacturing process.

Mathematical model of the hybrid wind-photovoltaic plant cost calculations

The article is described a new approach that allows to find the optimal solution to the problem of hybrid plant cost calculations of low and medium power facilities based on renewable energy sources. The calculation is performed using a multivariate analysis of the obtained results. The need to search for the system optimal configuration with maximum capacity at minimum cost is determined by the major setback to use of renewable energy sources, such as the high cost of equipment. Initial data for math model as an example of the Hybrid Plant cost calculation was from nature conditions in Volgograd and cost equipment in the demonstration Zone of Volgograd State Agricultural University. The demo zone was created in the educational research and production center of University for conducting experiments on the self-generated power supply of the facility management.

THE DESTRUCTIVE EFFORT OF THE CUTTING IN THE INTERACTION BETWEEN THE BLADES OF DISC KNIFE AND HERBAL MASS

The process of cutting is widely used during the stockpiling and preparation of fodder - the processing of stems by the direct application of the force that arises at the cutting edge of the knife. Almost 85% of stem fodder are ground fodder for the stockpiling of which the forage harvesters are used. Grinding of leaf mass is one of the most energy-consuming operations in the general process of stockpiling and the final quality of the fodder depends on it. The energy intensity of the grinding process is influenced by both the constructive and operating parameters of the machine, the cutting pair, and the physical and mechanical properties of the leaf-stem mass. Therefore, the development of grinding machines, the biter-knife in particular, should be carried out on the basis of detailed studies of the process of cutting grass mass, taking into account the current power and energy parameters. The object of the study in this article was the process of cutting a herbal mass with a biter-knife grinding machine containing an active disk knives. The purpose of the work was to establish the analytical dependence of the destructive cutting force in the interaction of the blade of the disk knive of biter-knife grinding machine with herbal mass. The task of the work was: to analyze the researches and publications on establishing the effort of cutting a layer of leaf stem and influence of various factors on its magnitude; to establish a mathematical model of calculation the critical effort of cutting a layer of grass mass with a cutting pair: double finger of the feed rotor - a disk knife during the cutting with sliding. The research methodology was based on the analysis of the interaction of the working parts of the grinding machine with herbal mass using the methods of theoretical mechanics. In the scientific work the interaction of single-blade blade of a disk knife of a biter-knife grinding machine with a leaf-stem mass is considered under the condition of double-backed cutting with sliding. The force interaction of the knife`s blade with the grass mass was analyzed and the dependence (3) of the calculation of the critical destructive cutting force Rkr was determined. From the obtained expression it is established that its magnitude is influenced by both the constructive parameters of the cutting steam and the technological parameters of the grinding machine. Also the magnitude of the destructive force is affected by the transformed angle of sharpening of the blade of the disk knife and the sliding angle.

Iron loss and temperature analysis of switched reluctance motor for electric vehicles

Based on a four-phase 8/6 structure switched reluctance machine for electric vehicles, the influence of different magnetic pole distributions on iron loss and temperature field is studied here. Firstly, by fitting the core silicon sheet iron loss data of the prototype, a mathematical calculation model of switched reluctance iron loss is constructed. Then, in order to analyse the flux density waveform of the iron core, a 2D finite element model is proposed. Under different magnetic pole distributions, the magnetic flux densities of the iron core are compared and the iron loss is calculated as well. Finally, the simulation results are obtained by establishing the 2D finite element thermal model of the prototype and analysed. Then, the experimental test platform is built and experimental data are recorded and analysed. By comparing the experimental results, it is found that the temperature rise is well consistent with the temperature rise of the 2D finite element thermal model.

A virtual monitoring method of operation conditions for mining and transporting equipment based on real-time data

ABSTRACT This paper presents a virtual monitoring method of operation conditions. The mathematical calculation model of a shearer and a scraper conveyor was established. Based on the model and the real-time motion trajectory of the shearer, measuring the pitch angles of 4–6 middle troughs as a priori information, the pitch angle of the next section could be calculated by rolling, thus the shape of a scraper conveyor was obtained. The method was programmed into the bottom layer of the Unity3D software. A real-time display and updating of virtual images were realised with data visualisation driving technology. The method was verified experimentally, with the results producing an error between the calculated and actual layout forms of the scraper conveyor of less than 15 mm. The actual operation state of the equipment remains synchronised in real time with the equipment in the virtual monitoring screen. Importantly, the detection accuracy satisfies the practical requirements.

Thermal Efficiency Simulation of Working Fluids Performance on Small Scale Organic Rankine Cycle (ORC) with Biomass Energy

This paper presents the comparative analysis of working fluids R-134a, R-414B, R-404A, and R-407C on small scale Organic Rankine Cycle (ORC) with biomass of coconut shell as heat energy. Simulation of the close system using Cycle Tempo software and compared with mathematical calculation models using Engineering Equation Solver (EES) software. The property of working fluids is obtained by using Reference Fluid Properties (REFPROP). The best result performance of ORC was shown by working fluid R-404A with thermal efficiency ranges between 7.48-7.53% and electric power output range between 0.074-0.091 kW. This condition operated on the turbine inlet temperature at 60 °C, difference turbine working temperature of 15 °C, condensing temperature of 25 °C, and water boiler mass flow rate of 3 lpm. A comparison of thermal efficiency simulated by Cycles Tempo and EES has an average coefficient of determination (R2) is 99.20%.

Development of the mathematical model for calculation of energy efficiency of mobile diesel compressor stations

The experience of development of domestic and foreign specialists in the sphere of energy loss reduction during gas cooling of mobile diesel compressor stations of the oil and gas industry is analyzed. The reason why the productivity of the compressors decreases after short period of operation, while the specific energy consump-tion increases. The disadvantages of existing cooling systems of compressed gas of mobile diesel compressor sta-tions are presented. Requirements for refrigerant coolants for compressor gas cooling systems are formulated. A reasonable choice of Freon R134a as a coolant for cooling of the compressed gas of the compressor stations is made. The structure and principle of operation of the system of high-efficiency reduction of temperature of the perspective system of cooling of compressed gas are presented. The tasks and basic assumptions of mathematical modeling of energy efficient scheme of gas cooling system are formulated. The purpose of this article is to investigate theoreti-cally the choice of coolant for a promising highly efficient system for cooling the compressed gas of mobile diesel compressor stations in the oil and gas industry. Inputs, outputs and general structure of mathematical model of multistage gas cooling of mobile diesel compressor stations are offered. The structure of the system of high-efficiency reduction of temperature of the perspective system of cooling of compressed gas and the principle of action are presented. The description and calculation formulas of the mathematical model of compressed gas cool-ing of mobile diesel compressor stations are given. When choosing a refrigerant with the condition of further use of the obtained energy, the main requirement was taken into account. The total specific energy costs for the opera-tion of the compressor installation according to the existing and perspective schemes and its energy efficiency indicators are determined.