Mathematical Model Of Process Research Articles

Electric discharge process modelling when piston pins recovery in internal combustion engines

Introduction. The relevance of the topic of the presented article is determined by the improvement of the technology for repairing and restoring machine parts. Currently, the technology of restoring piston pins of internal combustion engines (ICE) by a high-energy method of plastic deformation of metal using the energy of a high-voltage pulse discharge in a liquid is widely used – the electrohydraulic effect, and on its basis electrohydraulic processing. The purpose of the article is to increase the efficiency of the method of restoring piston pins of internal combustion engines due to the use of the electrohydraulic distribution method.Materials and methods. The research methods such as the analysis of the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston fingers depending on the relevant material were used. The article discusses a mathematical model of the electric discharge process when restoring piston pins. The calculation method determines the modes and parameters of the process of electrohydraulic distribution of piston pins while maintaining their fatigue life, static strength and wear resistance.Results. In this work, the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston pins, depending on the product material used, is established. A mathematical model of the electric discharge process during the restoration of piston pins has been developed, and based on them, the modes and parameters of the process of electrohydraulic distribution of piston pins have been determined while maintaining their fatigue life, static strength and wear resistance.Discussion and conclusions. The studies have shown that exploding wires made of iron, copper, and tungsten are not effective in restoring piston pins with an internal radius of up to 10 mm. The pressure in the case of their use does not exceed 100 MPa. Exploding Al wires with a diameter of less than one millimeter have the greatest effect. In this case, the inductance of the circuit should be minimal, because this provides the largest share of the energy released in the discharge channel from all stored in the capacitor. This ensures the highest pressure in the channel. Based on the same considerations, the capacity should be limited to a range of 3-12 UF. This method can be applied to the restoration of other car parts.

A mathematical model of the copper plating process in restoration of road transport equipment parts

Introduction. The use of restored parts of motor vehicles makes it possible to reduce the financial costs of repairing equipment. The cost of the restored parts should not exceed 50% of the cost of the new part. Increasing the productivity (deposition rate) of an electrolytic copper coating during the restoration of parts of motor vehicles requires taking into account the technological and economic aspects of the restoration process. The study of the factors (deposition conditions) that most affect the deposition process of the copper coating, the analysis of the experimental results and its statistical processing made it possible to optimize the technology of restoration of copper parts to create the most appropriate deposition modes with maximum productivity, thus reducing the cost of restoration of parts of motor vehicles. The purpose of the research is to develop a mathematical model of the effect of deposition conditions (electrolyte temperature, cathode current density) and electrolyte composition (concentration of copper sulfate and sulfuric acid) on the performance of the deposition process of copper coating, for further development of the most productive technology for restoring collectors of electric motors of motor vehicles.Materials and methods. The studies on equipment that allows obtaining the necessary data with the required accuracy were carried out. Mathematical processing using modern statistical data processing tools that excluded possible errors, providing to obtain the dependence of factors with the necessary accuracy was carried out.Results. In the course of studies of copper sulfate electrolytes to obtain an electrolytic copper coating, with the further development of technology for the restoration of automotive parts, it became necessary to determine the effect of deposition conditions – “factors” (cathode current density, electrolyte temperature, copper sulfate concentration, sulfuric acid concentration) on the deposition rate – “response”. It was found that the factor “cathode current density” and the combination of factors “cathode current density” and “sulfuric acid concentration” are the most significant. The deposition conditions in order to obtain the most productive technology for restoring collectors of electric motors of motor vehicles by depositing a copper coating have been optimized. According to the obtained model, the optimal values of the deposition conditions for obtaining the maximum deposition rate are the electrolyte temperature of 35...40 ° C, the cathode current density of more than 5 A/Dm2, the concentration of copper sulfate 200...250 g/l, the concentration of sulfuric acid 40...70 g/l.

Swelling kinetics of mixtures of soybean phosphatidylcholine and glycerol dioleate

Lipid-based drug delivery systems offer the potential to enhance bioavailability, reduce dosing frequency, and improve patient adherence. In aqueous environment, initially dry lipid depots take up water and form liquid crystalline phases. Variation of lipid composition, depot size and hydration-induced phase transitions will plausibly affect the diffusion in and out of the depot. Lipid depots of soybean phosphatidylcholine (SPC) and glycerol dioleate (GDO) mixtures were hydrated for varying time durations in a phosphate-buffered saline (PBS) buffer and then analyzed with Karl Fischer titration, magnetic resonance imaging (MRI) and gravimetrically. Mathematical modeling of the swelling process using diffusion equations, was used to estimate the parameters of diffusion. Both composition of lipid mixture and depot size affect swelling kinetics… The diffusion parameters obtained in Karl Fischer titration and MRI (with temporal and spatial resolution respectively) are in good agreement. Remarkably, the MRI results show a gradient of water content within the depot even after the end of diffusion process. Apparently contradicting the first Fick’s law in its classical form, these results find an explanation using the generalized Fick’s law that considers the gradient of chemical potential rather than concentration as the driving force of diffusion.

Method for expert evaluation of the technical con-dition of the cylinder-piston group of automotive engines after hydrolock

Problem: The study examines the thermogasdynamic process within an internal combustion engine cylinder during cold cranking mode while measuring compression. Analysis of various models and comparison of known data revealed unresolved challenges in constructing mathematical models of the engine operating cycle. The vast majority of practical data and recommendations for compression measurement in a cylinder are based on empirical knowledge, numerous experiments, and tests. Consequently, there arises a need for computational models of the compression measurement process and their theoretical justification, particularly in cases where engine damage occurs during hydrolock in a cylinder. Methodology. To address the identified issues, a mathematical model of the thermogasdynamic process within the cylinder during cold cranking while measuring compression was developed. Originality. Unlike existing models, this model describes the processes in the cylinder step by step, considering the real nature of intake-exhaust processes, air leakage through part interfaces, and heat exchange with the walls. Through modeling, the main patterns of compression changes depending on the modes and the nature of damage to associated parts of the valve mechanism and the cylinder-piston group were identified, including deformation of the connecting rod during hydraulic lock due to liquid entering the cylinder. Practical value. Based on the study results, it was concluded that the model's properties make it effectively applicable in diagnosing and monitoring the technical condition of automotive engines during operation.

Improving the efficiency of gear grinding technology for mine conveyor drives

The aim of this work is to develop a mathematical model of the gear grinding process using the method of high-performance profile copying and determine the optimal parameters of grinding modes according to the temperature criterion. It is shown that in order to ensure defect-free machining of gears under deep grinding conditions, it is necessary to significantly reduce the rate of the feed speed of the grinding wheel along the tooth of the gear wheel. For a grinding depth of 0.4 mm, it should be equal to 2.27 m/min. In this case, the machining productivity can be increased up to 5 times with the simultaneous elimination of the formation of sticking, microcracks and other temperature defects on the machined gear surfaces. This processing effect is achieved by using a modern HOFLER RAPID 1250 gear grinding machine and highly porous abrasive wheels, which are characterized by high cutting capacity. Thanks to the improved quality of gear processing, the quality and performance of manufactured mine conveyor drives (planetary gearboxes with a power of more than 200 kW) have been improved, and the number of repairs required in harsh mine conditions has been significantly reduced.

Study on aero engine thermal performance analysis using a new mathematical model of isentropic expansion (compression) process

At present, for the research of aero engine performance, it is necessary to calculate the overall thermal performance of the aero engine at the beginning of the research. For the mathematical model of the isentropic expansion (compression) process, most researchers use the ideal state value to calculate in the mathematical model, so that the calculated results have a certain error compared with the actual value. Therefore, the new isentropic expansion (compression) process mathematical model based on the Φ function is applied in this paper to the technical aero engine overall thermal performance calculation. After calculation and analysis, it is concluded that the calculation accuracy of the mathematical model provided in this paper is higher than that of the literature program for the overall thermodynamic performance parameters of the aero engine, whether it is the thrust of the aero engine, the unit fuel efficiency, or the thermal efficiency of the aero engine. It shows that it is feasible to revise and improve the mathematical model of isentropic compression and isentropic expansion process in this paper, more accurate calculation results can be obtained by using the new model in the performance analysis program, and more accurate numerical analysis can be carried out.

Mathematical modelling and techno-economic analysis of electric arc furnace steelmaking process with hot metal charging in China

Mathematical modelling and techno-economic analysis of electric arc furnace steelmaking process with hot metal charging in China

THE PROBLEM OF PROFESSIONAL TRAINING OF FUTURE IT SPECIALISTS IN THE RECEPTION ROOMS OF DOMESTIC SCIENTISTS OF THE LAST DECADE

In the article was analyzed the problem of professional training of future IT specialists in the receptions of domestic scientists of the last decade. It is found that the modern system of training specialists in higher education in Ukraine is focused on global trends in the development of higher education, such as globalization, integration, democratization, continuity, humanization, openness of education, academic freedom, autonomy, digitalization, etc., which leads to the transformation of training of highly qualified specialists, including IT specialists. It is proved that reception as a new methodological technology involves interpretation – one's own interpretation, addition to the previously created. Based on the analysis, it is determined that the professional training of future IT specialists involves the formation of their readiness to work and acquire relevant competencies in information technology, mathematical and computer modeling of processes and systems of various nature, forecasting, optimization, system analysis and decision-making, etc. The article characterizes the research of Ukrainian scientists related to the professional training of IT specialists in its multi-vector dimension over the past decade, such as I. Gerasymenko, A. Stryuk, A, M. Rassovutska, S. Semerikov, I. Tarasov, Y. Sikora, O. Glazunova, A. Kocharyan, S. Nikolayenko, V. Shynkaruk, V. Kovalchuk Y. Vasylenko, L. Dmytritsa, T. Bodnenko, V. Vlasenko, V. Bykov, A. Gurzhiy, M. Shyshkina, T. Voloshyna, T. Vakaliuk, T. Potapchuk, O. Malykhin, T. Yarmolchuk, S. Berezenska, N. Oliynyk, I. Varava, A. Kapiton, A. Schlichta, and others. It has been established that in the last decade, Ukrainian researchers have considered the professional training of future IT specialists in the context of their professional activities in a rather different way and have drawn certain analogies with the concept of competence as a person's ability to perform a certain type of activity

Working process model development of the gas turbine engine combustor fueling on methanol

The use of methanol as a fuel for aircraft and stationary gas turbine engines (GTE) is a priority direction in engine building. It is well known that when modeling the GTE performances using first-level mathematical models, there is an error in calculating specific fuel consumption, which is caused by the simplified description of the GTE combustor working process. The object of the study is the working process in the GTE combustor fueling on methanol. The peculiarity of the developed mathematical model of the working process of the GTE combustor is the use of enthalpy dependencies on temperature, pressure, and mixture composition. Enthalpy dependencies in this form implicitly account for the effect of thermal dissociation and allow for the correct formulation of the equivalent combustion reaction path. For two components (H2O and CO2), accounting for pressure leads to the fact that at standard temperature and partial pressures exceeding the saturation pressure, these components exist in a liquid state. This situation, with a constant enthalpy increment in the equivalent process of heating the combustion products from the standard temperature to the temperature at the end of adiabatic heat supply, decreases this temperature. Clarification of the temperature at the combustor outlet leads to changes in all calculated combustor performances, including the combustor fuel air ratio. The calculation results of the fuel air ratio are compared with known experimental data of the General Electric CF6-80A engine combustor (USA). The average calculation error of the fuel air ratio does not exceed 4 %. The developed model can be implemented in existing and developing mathematical models of gas turbine engines for temperatures at the end of the combustion process below 2,600 K

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Dynamic Modelling and Simulation of A Three-Phase Gravity Separator

Many studies have investigated the crude oil separation process’s separation mechanisms, size, and design, employing horizontal 3-Phase Gravity Separators in depth. There are, however, very few articles on their dynamics, modelling, and simulation. Understanding its dynamic behaviour will aid in designing and tuning the device that can manage water level, oil level, and gas pressure in response to feeding variations. This Scientific Paper gives a complete mathematical analysis, modelling, and simulation of a crude oil separation process using a horizontal 3-Phase Gravity Separator using Mathworks Matlab R2016b-x64 and Aspen Hysys V10. Bishoy’s Equations, which were constructed, will assist in operating this gadget, locating various variables, and observing the effect of modifying variables on the system’s variables. The rationale for this study was developed in response to the small number of articles discovered, which may be a covert issue held up by large oil companies, as well as the complicated equations related to this process that remain unsolved, and to monitor what is happening in this complex dynamic process. As a result, this Research Paper is unique and novel, and it can be compared to the work done by some authors who did not solve the obtained differential equations and did not go further in Aspen Hysys Modeling and Simulation, whereas this paper provides everything related to a three-phase gravity separator, including changing of variables and observing the effect on the system when those variables were modified. Furthermore, separators are designed with internal baffles to promote laminar flow and increase separator efficiency. However, it has been assumed that there are no baffles here, which is a significant problem, but with the help of these equations, the horizontal three-phase gravity separator can be operated at its maximum efficiency. The equations determined the following variables: The height of gas, water, oil, the height of oil when it jumped the weir, the pressure of the gas (in and out), water pressure (in and out), oil pressure (in and out), and the effect of increasing (control valve’s stem position) and decreasing Qin (inlet volumetric flowrate) on these variables have all been studied. This article discovered that increasing the control valve stem position and decreasing the inflow volumetric flowrate of both oil and water was highly unsafe and caused significant variations in the system’s heights and pressures using Matlab. The Aspen Hysys analysis optimally separates the oil, gas, and water to determine material, energy streams properties, and compositions. As a result, this complex dynamic behaviour was observed, and no additional articles were discovered that addressed this subject. This process monitoring will determine the best conditions for flawless separation, with the selectivity of the desired product or products as the primary goal. This research can revolutionize the way people think about oil and gas extraction and processing and benefit colossal oil and gas firms in Europe, Asia, and Africa.

A Mathematical Model of an Electoral Process and Predicting of Outcome

We developed and analysed a mathematical model to study the dynamics of an electoral process and predict the outcome in Nigeria with three political parties as major actors. We model the ruling party (P1); major opposition party (P2) and minority opposition parties (P3). The model includes party campaigners of the three political parties and a class of eligible voters. The model also incorporates the Independent National Electoral Commission (INEC), electoral observers, judiciary, security personnel and thugs. The influx of voters into the system is determined by the registration rate of voter cards. The model’s interest lies in the measure of positive influence that the party campaigners who eligible voters to join their party. With this, the model mirrors election’s outcome and the movement of voters between the three groups of political parties involved. The model has proven that the pattern of election’s outcome for each political party is affected by the defection of party members and lack of policy consistency. We determine the equilibria analytically and discuss the stability of the system. Numerical simulations are graphed in combination with curve fitting to compare each party’s performances over the years. The result shows that no political party remains in power steadily from 2007 to 2019. Thus, the prediction of elections outcome to the political space of any region in Nigeria depends on political party structures and voters’ decisions.

Basics of calculation of a two-circuit air purification system for polydisperse dust

Purpose. To increase the level of environmental safety of enterprises by improving the quality of air purification from polydisperse dust in two-circuit closed systems, in particular, to obtain the basic design relations for the engineering calculation of such systems. Methodology. The aim of the study was realised by mathematical and numerical modelling of hydrodynamic processes in the elements of a closed double-circuit purification system. Findings. A methodology for hydraulic calculation of a closed two-circuit cleaning system was proposed by drawing up a pressure balance of individual circuits, and a dependence for the complex coefficient of hydraulic losses of the collection-return apparatus was determined. Originality. The hydraulic calculation of two-circuit closed cleaning systems is proposed to be carried out by compiling the pressure balance of individual circuits. To calculate a specific element of the system – the collection-return apparatus – the concept of a complex hydraulic loss coefficient is introduced, which takes into account both local pressure losses and losses along the length, and also indirectly reflects the effect of flow swirl on the hydraulic resistance of this element. For the complex coefficient of hydraulic losses, the quantitative results necessary for engineering calculations were obtained by numerical modelling of hydrodynamic processes of the swirling flow in an annular pressure channel. Practical value. The obtained results make it possible to design two-circuit closed cleaning systems for different production conditions, which, in turn, makes it possible to replace typical and inefficient direct-flow systems with a system in which the efficiency of polydisperse dust capture is significantly increased due to separate cleaning.

EXPLORING THE IMPACT OF PTH THERAPY ON BONE REMODELING: A MATHEMATICAL INVESTIGATION

The regulatory influence of the parathyroid hormone (PTH) is exerted on bone, which serves as a vital reservoir of calcium within the body. While various aspects of bone growth, turnover, and mechanisms operate independently of gonadal hormones, a crucial role is assumed by sex steroids, particularly estrogen, in maintaining bone equilibrium in adults. In order to unravel the underlying mechanisms of bone remodeling mediated by PTH, a distinguished mathematical model of this intricate process is presented. Subsequently, the temporal effects of Plasma PTH and PTH external dosages are investigated using the proposed mathematical model. Among the limited repertoire of approved and accessible anabolic treatments for severe osteoporosis, daily injections of PTH stand out. This pharmaceutical marvel possesses a unique dual action, capable of acting either anabolically or catabolically, contingent upon the mode of administration. The study aims to accurately predict osteogenic responses to introduced and endogenous PTH, incorporating factors such as [Formula: see text]-[Formula: see text], [Formula: see text], and bisphosphonates in osteoblast–osteoclast signaling, as well as considering PTH’s influence on the gland and the regulatory roles of [Formula: see text], [Formula: see text], and [Formula: see text] in osteoblast apoptosis and bone volume effects. Through diverse methods including illustrative depictions, numerical simulations, sensitivity analysis, and stability analysis, this work seeks to comprehend how PTH therapy impacts bone volume, enhancing its therapeutic relevance.

Determination of optimal technological parameters of a horizontal mixer of loose compound feeds

The quality of the compound feeds for animals and poultry directly depends not only on the components included in it but also on the type of mixer used. Horizontal mixers as compared to the vertical ones allow for a shorter period of time to obtain high-quality mixtures due to the intensification of the process of material movement by belt working bodies. The aim of the research is to determine optimal technological parameters of a horizontal mixer with a 0.3 m3 mixing chamber with a belt working body. The mixer is designed to produce mixed compound feeds of high uniformity in production lines, workshops or can be used as an independent machine for mixing loose components. The research was carried through multifactorial experiment. As the result, mathematical models of the mixer working process were obtained, two-dimensional cross sections of the response surfaces were built. The obtained mathematical models make it possible at the design stage to identify the dependence of qualitative and energy indicators on factors at the considered levels of variation. According to the results of the multifactorial experiment, it has been established that the best mixing quality of 94.8 % is achieved when the mixing chamber is loaded by 58 % at a speed of rotation of the mixer shaft of 30 min-1, mixing time of 6 minutes with simultaneous supply of the control and the main components. At the same time, the throughput is 0.78 t/h, and the specific energy consumption is 2.04 kWh/t.

Investigation of electromagnetic processes in the case of static eccentricity of a two-pole induction motor with a short-circuited rotor

Purpose. Correction of the mathematical model of electromagnetic processes in a two-pole induction motor with a short-circuited rotor, taking into account static rotor eccentricity to identify diagnostic correlations. Methodology. Analytical modeling using the method of specific magnetic conductivity, mathematical modeling of electromagnetic fields in a three-phase induction motor with a short-circuited rotor using methods of electromagnetic field theory and finite element methods. Obtained results. The necessity of improving mathematical models for induction motors with short-circuited rotors to establish new or refine connections between diagnostic features and diagnosed defects has been demonstrated. Refined mathematical expressions for calculating the specific conductivity of non-uniform air gaps in induction motors with static eccentricity are provided. Modeling was performed using the FEMM environment for a statically eccentric two-pole induction motor with a short-circuited rotor. It has been proven that the harmonic order values obtained using the numerical-field method are consistent with those obtained analytically. Findings. Based on the field approach and using the finite elements method, an analysis of the distribution of magnetic field in a two-pole induction motor with a short-circuited rotor was conducted. Harmonic analysis of the magnetic field in the air gap was performed to identify the fundamental harmonic and higher and lower-order harmonics when eccentricity occurs. The influence of static rotor eccentricity on the electromagnetic processes of the induction motor was analyzed. Practical value. The results of the study can be utilized for functional diagnosis of the rotor winding of induction motors based on the radial component of the magnetic field. This will contribute to enhancing the reliability of induction motors and enable the prevention of failure in induction motors with short-circuited rotors.

STUDY OF EFFECT TO COLD PILGER ROLLING PARAMETERS ON THE TEMPERATURE REGIME OF PROCESS

The research is aimed at determining the optimal parameters that affect the efficiency of rolling and the quality of the product. The relationship between various parameters such as heat transfer, ultimate strength, friction index and temperature regime is analyzed to improve the technological parameters of cold mill rolling and increase the quality of products. Mathematical modeling of cold mill rolling processes allows not only a deeper understanding of the physical processes occurring during rolling, but also provides an opportunity to analyze the influence of various parameters on the temperature regime and, in general, on the quality of the final product.

Characterization of rotary valve control vibration system for vibration stress relief applications

To enhance the vibration system characteristic distortion and pressure loss, we propose a novel rotary valve control vibration system. The paper presents the designed structural composition and generation mechanism of the rotary valve control vibration system. It also derives the mathematical model for the rotary valve distribution process and the overall system. The flow field inside the rotary valve is dynamically simulated using the multiple reference frame model, allowing for the determination of the change rule of the rotary valve’s output characteristics. An AMESim model was developed to analyze the vibration characteristics of the rotary valve control system. The effects of parameters such as inlet pressure, motor speed, and oil supply pump displacement were investigated. A rotary valve control vibration system experimental bench was constructed to experimentally verify the output characteristics of the rotary valve and the vibration characteristics of the system. The results indicate that the characteristic curve of the designed vibration system closely resembles a sinusoidal wave. Additionally, the rotary valve exhibits low pressure loss, making it more suitable for vibration stress relief applications. By appropriately increasing the inlet pressure and decreasing the motor speed, the vibration characteristics of the system can be improved.

A Novel Model to Predict Shape Variation of Steel Strip During Feeding in Slab Continuous Casting

To comprehensively comprehend variation of strip shape (strip feeding depth and maximum steel sheath cross‐sectional area) under different process parameters (strip feeding speed, strip oscillation frequency, strip amplitude, molten steel superheat, strip width, and strip thickness), a mathematical model of feeding strip process has been developed herein. Flow near steel strip is analyzed. Meanwhile, the qualitative relationship between strip shape and process parameters is derived based on energy conservation within the system of molten steel and steel strip. The results show that strip feeding depth is positively correlated with strip feeding speed, strip width, and strip thickness, while it's negatively correlated with strip oscillation frequency, strip amplitude, and molten steel superheat; maximum steel sheath cross‐sectional area is positively correlated with strip width and strip thickness, while it's negatively correlated with strip feeding speed, strip oscillation frequency, strip amplitude, and molten steel superheat. Based on the calculated results, the quantitative relationships are proposed to predict the strip feeding depth and maximum steel sheath cross‐sectional area with aforementioned process parameters, which are suitable for the situations that the strip tip is located between the outlet of submerged entry nozzle and the end of the liquid core.

Modeling single cell trajectory using forward-backward stochastic differential equations.

Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.