Mathematical Modeling Of Dynamic Processes Research Articles

Features of mathematical modeling of dynamic processes of car passing railroad turnouts

Dimensions and tolerances in the “wheelset — railway track” system are interconnected, since the normative values of geometric parameters and shape of the elements of the wheelsets and the track's upper structure are directly de pendent. In 2018– 2019 in order to establish the minimum permissible thickness of wheel flanges for freight cars in operation and to determine the influence of the thickness and shape of wheel flanges on the safe passage of turnout elements, JSC “VNIIZhT” conducted comprehensive stu dies, including the development of a methodo logy and mathematical modeling of the interaction of wheelsets and turnout elements. Features of modeling the dynamic proces ses of the entry of the first bogie of a freight car into the railway turnout when running to the side track are presented. The process of moving a freight car along the turnout is described de pending on the geometric parameters of the wheelset and track elements of the turnout, the position in the gauge of its first bogie before running into the switch point. Results of calculations of the lateral forces of the interaction of the wheelset and the turnout show that when running on, the maximum forces occurred during wheel impacts in the turnout elements, which depend on the conditions of the bogie entering the turnout. The initial position of the bogie and the peculiarities of its motion in the gauge determine the position of the meeting point and the value of the angle of incidence, their combination determines the maximum value of the force when moving to the lateral track, which, depending on the entry conditions, can differ by more than twice. Calculations showed that a change in the angle of inclination of the flange from 60 to 70° leads to a decrease in the safety factor of rolling stock on the turnout by 1.5 times. Required minimum value of the inclination of the wheel flange, ensuring safety (qR parameter), is determined by the creation of conditions that do not allow the wheel to run onto the tip of the switch point. Under existing norms of wear of turnout elements and the relative position of their rail elements, as well as taking into account the results of the calculations, the permissible value of qR should be in the range of 6.0...6.5 mm.

Дослідження віброударного способу заглиблення паль

Палі для будівництва фундаментів використовувалися ще в далекій давнині. Спочатку палі використовувались при ущільненні ґрунтів з метою значного підвищення несучої здатності основ фундаментів, а потім – в якості несучих елементів, які можуть передавати навантаження від плити фундаментів на ґрунт. Палі спочатку виготовляли із лісоматеріалів і забивали ручними молотами. Голови паль зрізали нижче рівня води, захищаючи, тим самим, їх від дотикання із повітрям. В даний час в фундаментобудуванні використовується більш ніж 100 типів паль, які класифікуються по трьома найбільш суттєвими признаками: це по особливістю передачі навантаження на ґрунт (палі-стійки, висячі, ущільнення, тертя); – по способу заглиблення або вбудуванні палі в ґрунт (що виготовляються раніше і заглиблюються в готовому вигляді; виготовлені в проектному положенні; комбіновані); – по матеріалу: дерев’яні, бетонні, залізобетонні, комбіновані.По особливостям передачі навантаження на ґрунт найбільше розповсюджені палі -стійки і висячі палі. Палі-стійки передають навантаження на ґрунти в основному нижнім кінцем на малостиснутих ґрунтах (скалисті, пісчані, тверді глини). Висячі палі передають навантаження на любі ґрунти нижнім кінцем , а також за рахунок сил тертя по боковій поверхні.З кожним роком все більше набуває використання віброударного обладнання, так названих вібромолотів. Ця техніка успішно використовується при спорудженні надійних фундаментів під різні споруди.Здійснення сказаного вимагає вивчення і дослідження процесу віброударного заглиблення паль. а також створення найбільш продуктивних способів його виконання.Одним із перспективних напрямків є впровадження фундаментів із паль при будівництві споруд при щільній забудові в містах і селищах.Також необхідно відмітити, що спорудження фундаментів із паль дає можливість впроваджувати комплексну механізацію і автоматизацію технологічних процесів, що значно підвищує продуктивність робіт.Віброударне заглиблення паль є одним із найбільш продуктивних способів побудови надійного фундаменту під різні споруди . Віброударне заглиблення, котре широко впроваджується на будівництві , належить до ударної технології заглиблення паль. Метод віброударного заглиблення паль полягає в тому, що при вібрації суттєво зменшуються сили виникаючого тертя і сили зчеплення між палею і ґрунтом, а в результаті значно зменшуються сили опору заглибленню палі.В даний час, при проектуванні вібромолотів динамічні фактори при їх експлуатації не враховуються. Тому надійність можна підвищити, якщо на стадії їх проектування враховувати хвильовий характер навантажень віброударної техніки.Віброударне заглиблення паль нами розглядалося у взаємодії механічних і електромагнітних процесів і в результаті була отримана математична модель динамічних процесів при роботі вібромолота, котра включала нелінійні диференціальні рівняння руху мас вібромолота і лінійне диференціальне рівняння електромагнітних явищ в двигуні приводу.Аналізуючи отриману інформацію можна акцентувати, що віброударному методу заглиблення паль мало приділено уваги і широка інформація практично відсутня. Тому являється актуальним створення продуктивних зразків вібромолотів, методик їх розрахунків і проведення наукових досліджень динаміки робочих процесів цих машин на що і направлена дана магістерська робота.В даній роботі нами теоретично досліджено, з використанням математичного застосунку MathCAD, динаміку вібромолота і отримано результати котрі можуть бути використані при проектуванні та визначенні динамічних навантажень подібних віброударних машин.При розрахунку вібромолотів на статичну й утомленуміцність коливальні процеси конструкцій та їх динамічні навантаження, в цей час, не враховуються. Однак їх несучу здатність можна значно підвищити, якщо у розрахунках при їх проектуванні враховувати їхні амплітудно-частотні характеристики. Відсутність ж уточненої методики розрахунку сучасних вібраційних машин, в тому числі і вібромолотів, для здійснення ефективного занурення різноманітних паль ускладнює їхнє проектування і експлуатацію.Метою статті є висвітлення результатів математичного моделювання коливальних процесів при заглибленні паль вібромолотом та визначення динамічних навантажень на його елементи.В роботі теоретично досліджено, з використанням математичного програмного середовища MathCAD, динаміку механізму привода вібромолота і отримано результати які можуть бути використані при проектуванні, розрахунку та визначенні динамічних навантажень подібних вібраційних машин.

Математическое моделирование динамических процессов в системе питания маршевого двигателя космических ступеней ракет-носителей на активных и пассивных участках траектории полета

Математическое моделирование динамических процессов в системе питания маршевого двигателя космических ступеней ракет-носителей на активных и пассивных участках траектории полета

Mathematical model of dynamic processes during frictional hardening of the cylindrical surfaces of parts

The mathematical model of the elastic machine system has been developed, and describes the dynamic processes that occur during the frictional hardening of cylindrical surfaces of parts using a tool with transverse grooves on its working part, which forms a surface hardened metal layer with nanocrystalline structure. Transverse grooves on the working part of the tool increase the intensity of deformation of the surface layer in the contact area of the tool-part and the oscillating processes of the system. Differential equations that describe this process are based on Lagrange equations of the second kind. Based on the solution of the model’s the systems of equations, it is possible to determine the velocity and magnitude of displacement of a special device with autonomous drive of the tool, tool and treatment part during machining, reaction of device supports and spindle unit.

Design of parallel link mobile robot manipulator mechanisms based on function-oriented element base

To create effective mobile robot manipulators, a function-oriented element base is proposed. Element base selection is based on the analysis of schematics of mobile robot manipulators. It is substantiated that the effective schematics of manipulators are parallel link mechanisms. A rational structural scheme was adopted as a mechanism having six rods of variable length (hexapod). The schemes of mobile robot manipulators with different numbers and types of combined rod supports are considered. It is proved that the same type of element base in the form of spherical hinges can be used to implement a variety of schemes. Different embodiments of schematics of manipulators designed on the proposed function-oriented element base are considered. The basic requirements for the element base of mobile robot manipulators are defined. It is shown that the requirements are provided by the function-oriented element base on the basis of different hydrostatic or aerostatic hinges.A series of variants of schematics and design solutions of regulated spherical hydrostatic and aerostatic hinges are proposed. The hydrostatic spherical hinge, which includes an accurate ceramic (boron carbide) ball has high precision characteristics. Technological approbation of this schematic is conducted by manufacturing a production prototype.The regulated hydrostatic hinge is equipped with a mechatronic system for determining the spatial position of the sphere. This design solution allows you to adjust the position of the hinge sphere within the diametric clearance.The combined aerostatic-hydrostatic support unit aggregated with manipulator drives is proposed. The unit has a jet system for adjusting the support reactions of the aerostatic-hydrostatic supports of the spherical hinge. Technological testing of the developed device is carried out.In order to increase the efficiency of the proposed element base, special algorithms for controlling the position of the spherical manipulator hinges are developed. The algorithms are based on the mathematical modeling of dynamic processes in hinge devices. The algorithms include the implementation of spatial polyharmonic displacements of the sphere with the purposeful selection of the direction of the resulting displacements, which provides the necessary accuracy and speed of the process of adjusting the position of the manipulator.

Mathematical modeling of dynamic processes of lubricating layers thrust bearing turbochargers

Thrust bearings turbochargers, which include centrifugal and axial compressors partially operate in dynamic mode. These modes can be caused by installation errors, e.g., when installing the hard disk on the rotor with a skew or by external influences, such as rotating stall or surge of the turbocharger. If significant variations occur surge with a frequency of 1÷10 Hz total gas volume filling flow of the compressor and the network. Fluctuations in the gas result in changes of axial load, until the change of sign of the axial force, and hence a displacement of the rotor in the axial and radial directions. Variable turbochargers regimes can sometimes lead to shock loads on the thrust bearing and, consequently, to its destruction.

Stability with Respect to a Part of Variables under Constant Perturbations of the Partial Equilibrium Position of Differential Equation Nonlinear Systems

Introduction. It is impossible to take into account all the forces acting in the process of mathematical modeling of dynamic processes. In order that mathematical models the most accurately describe the dynamic processes, they must include the terms that correspond the constant perturbations. These problems arise in applied tasks. In this paper we consider the case when the system allows for the partial equilibrium position. The aim of this work is to prove the stability theorem for the partial equilibrium position at constant perturbations, which are small at every instant. Materials and Methods. The research objects are nonlinear systems of differential equations that allow for a partial equilibrium position. Using the second Lyapunov method, there are proved the stability theorems for the constant perturbations of the partial equilibrium position, which are small at every instant. Results. Together with the introduction of stability for a part of the variables, it has become necessary to introduce stability for the part of phase variables under constant perturbations. The first stability theorem of the part of phase variables under constant perturbations was obtained by A. S. Oziraner. In this work, we prove a theorem of the stability of the constant perturbations of the partial equilibrium position, small at every instant. It should be noted that there is no stability theorems of constant perturbations for the partial equilibrium position. Thus, the theorem proved in this work is of a pioneer nature. Conclusions. The theorem 3 proved in the work is the development of the mathematical theory of stability. The results of this work are applicable in the mechanics of controlled motion, nonlinear system.

Study of the dynamics of the working cell of the automatic mill of the pipe-rolling unit

Purpose. Determining the real spectrum and the level of dynamic loads would make it possible to develop recommendations for improving the TPA-350 automatic mill, with the aim of expanding its technological capabilities, improving the reliability of operation and durability. Metodology. This work was carried out on the basis of the development of a mathematical model of dynamic processes in the mechanical system of an automatic TPA mill, where an attempt was made to identify the features of the functioning of a working stand with a rolled sleeve in the formulation of dynamic problems. Obviously, the proposed approach is more correct and convenient when studying complex dynamic phenomena in the elements of an automatic TPA mill. Findings. The results of the study of the dynamics of the working stand of the automatic mill of the pipe-rolling unit (TPA) are given The basic parameters of the functioning of the working stand, such as the automatic mill TPA 350, are established, and a mathematical model of the basic problem of the dynamics of a mechanical system is developed. The differential equations of motion for the selected model of the working stand and the elastic elements of the bed retention mechanism on the support nodes of the automatic TPA mill have been compiled. The corresponding patterns of oscillations of the working stand were obtained. Some features of the functioning of the working stand are identified by the example of an automatic mill TPA 350. The dynamic parameters of the working stand of the mill, affecting the difference in the thickness of the rolled sleeves, are established. Originality. The interrelation of the working stand dynamics with the operating conditions of an automatic TPA mill on the basis of a simplified mathematical model of dynamic processes is established. A mathematical model of the mechanical system of a working working stand of an automatic TPA mill has been compiled. In the most general form, the mechanical system of a working stand of a mill is described using differential equations describing the behavior of the selected design scheme of a system with two degrees of freedom. Practical value. A scheme has been proposed for modernizing the working stand and the mechanism for holding the working stand of the TPA-350 automatic mill. IL. 4. Biblography: 8 titles.

Searching historical data segments for process identification in feedback control loops

Mathematical models of dynamic processes are often required for assessment, diagnosis and improvement of control loop performances in process industries. Data samples collected in daily operations of feedback control loops may enclose data segments suitable for process identification to obtain the mathematical models. This paper proposes a new method to search such data segments. The searching criterion is that the reference and process output in a feedback control loop should experience significant magnitude changes. Hypothesis tests are exploited to find changing positions of data segments with different probability distributions and to verify whether the reference and process output make significant magnitude changes inside one data segment or between two adjacent segments. Simulation and industrial examples are provided to illustrate the effectiveness of the proposed method.

Identifiability of mathematical models in medical biology

The analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling, and systems biology. The methods covered in this article can reduce the cost of experiments aimed at obtaining biological data. The problem of the identifiability of mathematical models in physiology, pharmacokinetics, and epidemiology is considered. The processes considered are modeled using nonlinear systems of ordinary differential equations. The mathematical modeling of dynamic processes is based on the use of the mass conservation law. The problem of estimating the parameters characterizing the process under study raises the question of nonuniqueness. When the input and output data are known, it is useful to perform an a priori analysis of the relevance of these data. The definition of the identifiability of mathematical models is considered. Methods for the analysis of the identifiability of dynamic models are reviewed. In this review article, the following approaches are considered: the transfer function method applied to linear models (useful for the analysis of pharmacokinetic data, since a large class of drugs is characterized by linear kinetics); the Taylor series expansion method applied to nonlinear models; the differential algebra methods (the structure of this algorithm allows it to be run on a computer); and a method based on graph theory (this method allows for the analysis of the identifiability of the model and finding a proper reparametrization reducing the initial model to an identifiable one). The need to perform a priori identifiability analysis before estimating the parameters characterizing any process is demonstrated with several examples. The examples of identifiability analysis of mathematical models in medical biology are presented.

Spectral properties of dynamic processes in a nuclear reactor

As a rule, mathematical modeling of dynamic processes in nuclear reactors is conducted using an approach that treats a neutron flux in the multigroup diffusion approximation. In this approach, the basic model involves a multidimensional system of coupled parabolic-type equations. Similarly to common thermal phenomena, it is possible here to separate a regular mode of nuclear reactor operation that is associated with a selfsimilar development of a neutron field at large times. In this case, the main feature of dynamic processes is a minimal eigenvalue of the corresponding spectral problem. In the present paper, calculations of various eigenvalues are performed via the two-group model and discussed for the VVER-1000 reactor without a reflector and HWR reactor.

INCREASING CONTROL’S EFFICIENCY FOR THE SHIP'S TWO-MASS ELECTRIC DRIVE

Purpose. For shipboard lifting and transporting machinery (LTM) with AC thyristor electric drives (ED) the problem of minimizing sway through the formation of the special law to change the principle of ED control over the lifting process is solved. Methodology. This goal was achieved through the following objectives: analysis of current studies on the reduction of the negative effects of load fluctuations, fixed on the suspension with variable parameters; determining the criteria to optimize the movement of the lifting mechanism and transfer control laws under which the load fluctuations are reduced; develop the methodology and experimental study of the main characteristics of the mobile model ED lifting mechanism with its load suspended from the perspective of both the parameterization of the control system (CS) as well as elements of ED. For realization of tasks in research methods of mathematical modeling of dynamic processes on the computer, structural methods of control theory, experimental studies in the laboratory setting have been used. Results. Based on analysis of current research can be concluded that the stability of the ED of LTM to the disturbing points provided coincidence zero electric coordinates and speed deviation diametric plane of the vessel from the vertical position. Criteria for optimizing CS used by the ED LTM mathematical description of its dynamics differential equations to the estimated coefficients derived from the functions of state variables. The experimental dependence of dynamic equations of motion of an object under the influence of disturbing forces in the coordinate plane allowed to parameterize characteristic equation to the form, providing the solution to sustainability since the motor shaft of LTM. The functional circuit of CS eliminates the aperiodic components in the control in compliance with the criteria of sustainability and quality of transients by applying all-range regulator coordinate characteristics of forcing overcoming the dead zone and increase electric resistance as the dynamic object. Practical value. Completion of the complex research may find practical application in the ED of ship’s LTM, which will improve their performance, decrease between the operating and maintenance simple.

ВЫБОР ЧИСЛЕННЫХ МЕТОДОВ ПРИ МОДЕЛИРОВАНИИ ДИНАМИКИ СИСТЕМ

The article deals with the creation of methodical support for mathematical modeling of dynamic processes in elements of the systems and complexes. As mathematical models ordinary differential equations have been used. The coefficients of the equations of the models can be nonlinear functions of the process. The projection-grid method is used as the main tool. It has been described iterative method algorithms taking into account the approximate solution prior to the first iteration and proposed adaptive control computing process. The original method of estimation error in the calculation solutions as well as for a given level of error of the technique solutions purpose adaptive method for solving configuration parameters is offered. A method for setting an adaptive method for solving the settings for a given level of error is given. The proposed method can be used for distributed computing.

Parallel Algorithm for Modeling of Dynamic Processes in Porous Media

Parallel algorithm for modeling the unsteady 2D gas flows through a porous media with energy sources is presented. A mathematical model of dynamic processes in porous heat-evolutional object is mentioned briefly. The structure of sequential algorithm and its parallel version is described in details. The performance and efficiency of parallel algorithm and its realization using OpenMP technology is evaluated.

Modeling of Atmospheric Processes Based on the Averaged Navier-Stokes Equations

This work is devoted to the mathematical and numerical modeling of atmospheric processes based on the ensemble-averaged Navier-Stokes equations with the implementation of large eddy simulation. Within the real scientific research work are shown features of modeling atmospheric processes, the mathematical model of dynamic processes was developed in the average atmosphere, the numerical scheme and algorithm of the problem solution were developed, and realization of the problem characterized by instability of Rayleigh-Taylor about convective mass substances transfer with various densities was made.

AUTOMATED CONTROL SYSTEM OF AIRCRAFT BAROMETRIC ALTIMETERS

To solve this problem the authors have developed a digital automated air pressure control system (ACS) based on automatic frequency pressure selector, which is different from air-operated ones due to the fact that it is a nonlinear system of automatic stabilization with the relay servo mechanism and adaptive control with high levels of accuracy, reliability and high-speed performance.An optimization of digital ACS of barometric pressure measuring equipment has been conducted, including aircraft barometric altimeters (BA), with its optimal accuracy and speed, with the desired transition process of providing one-way transition process without sacrificing the accuracy. The results can be used for the synthesis of high-speed automated control system, calibration and verification.Optimization of relay digital automated control system of measuring air pressure, optimal according to the criteria of accuracy and speed, with the desired one-way transition process has been carried out in order to remove BA variations indications. Optimization of the accuracy, speed and one-way transition process of the system (multi-criteria optimization problem) allowed choosing the relay servo mechanism as a result.Scientific novelty is that developed algorithm of ACS is of optimal performance, and operates in medium and low vacuum, which establishes a one-way approach to a given level of pressure without sacrificing accuracy.For a complete analysis of dynamic processes in the frequency ACS, including analog (pneumatic, mechanical, electrical) and digital conversions, a comprehensive mathematical model of dynamic processes in ACS has been developed.

Mathematical modeling of dynamic processes in a hydraulic drive with a discrete regulator of liquid flow

The paper presents a mathematical model of a hydraulic drive with a discrete liquid flow regulator in the form of a switched inertial device that has a damper of working medium oscillations at the output. A hydraulic actuator loaded with mass was used as a final control element. Transition processes occurring when the regulator is activated are calculated by modeling the dynamic processes with the help of the Simulink software package. The research shows the impact of the valve operating frequency and pulse ratio on the dynamics and efficiency of the hydraulic drive. It could be concluded that the use of a hydraulic attenuator results in decreasing the level of pressure ripples at the inertial tube input.

THE FEATURES OF TRAVELER WITH VACUUM AND SUCTION EQUIPMENT

The analysis of real mechanical system of the bridge crane with vacuum-sucker equipment is made and the design scheme for the mathematical model of dynamic processes created on the basis of the analysis is offered.

Mathematical Modeling of Dynamic Processes of Irreversible Deforming, Micro- and Macrofracture of Solids and Structures

Mathematical Modeling of Dynamic Processes of Irreversible Deforming, Micro- and Macrofracture of Solids and Structures

Strength and viscosity of metals in a wide range of strain rate variation

For a large class of problems of high-rate straining of metallic shells driven in one way or another toward the center or axis of symmetry, mathematical modeling of dynamic processes is carried out according to the scheme of nonstationary straining of a compressible viscoplastic medium in a region with free boundaries. The difficulties emerging in this case are due to the absence of reliable experimental data on the behavior of the dynamical yield limit {sigma}{sub s} and the dynamical viscosity coefficient {mu} for many metals in a wide range of the strain rates {epsilon} > 10{sup 3} - 10{sup 6} sec{sup -1}. In this paper we suggest a new technique for determining these characteristics of metals with the use of experiments on compressed cylindrical shells.