scholarly journals PIPELINE ROBOTS WITH ELASTIC ELEMENTS

Transport ◽  
2002 ◽  
Vol 17 (5) ◽  
pp. 177-181 ◽  
Author(s):  
Arvydas Matuliauskas ◽  
Bronislovas Spruogis
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Degrees Of Freedom ◽  
Vibration Exciter ◽  
Motion Equations ◽  
Two Degrees Of Freedom ◽  
One Dimensional ◽  
The Mathematical Model ◽  
Original Construction ◽  
Elastic Elements

In the article constructions of the pipeline robots with elastic elements are reviewed and the scheme of new original construction is presented. The mathematical models of a robot with one-dimensional vibration exciter with two degrees of freedom were developed and the equations of movement were formed and written. The mathematical model of the pipeline robot with circular elements is formed and its motion equations are presented.

Mathematical Model of the Servo Drive with Friction Wheals. Simulations and Real Object Examination Results

2013 ◽  
Vol 198 ◽  
pp. 15-20 ◽  
Author(s):  
Lukasz Fracczak
Keyword(s):  
Mathematical Model ◽  
Cardiac Surgery ◽  
Control System ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Real Object ◽  
Servo Drive ◽  
Two Degrees Of Freedom ◽  
The Mathematical Model

In this paper the servo drive with friction wheels is presented. The servo drive is designed to move the automatic laparoscope tool or laparoscope camera (thereinafter laparoscope sleeve or sleeve) in two Degrees of Freedom (DOF). The description of the drive mechanism, operating principle and mathematical model of this drive is presented. Based on this model, the Control System (CS) has been created, and used to the construction of a simulation model. The simulation illustrates the proper functionality of the mathematical model of the servo drive with the described CS. This paper also presents the servo drive test stand and the most important examination results from the point of view of using them in the cardiac surgery Robin Heart robot.

Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters

2013 ◽  
Vol 61 (2) ◽  
pp. 475-484 ◽  
Author(s):  
L. Baranowski
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integration Step ◽  
Six Degrees Of Freedom ◽  
Applied Model ◽  
Flight Parameters ◽  
The Mathematical Model ◽  
Artillery Projectile

Abstract In the paper the three different mathematical models of motion of a spin-stabilized, conventional artillery projectile, possessing at least trigonal symmetry, have been introduced. The vector six-degrees-of-freedom (6-DOF) differential equations of motion are an updated edition of those published by Lieske and McCoy and are consistent with STANAG 4355 (Ed. 3). The mathematical models have been used to developing software for simulating the flight of the Denel 155mm Assegai M2000 series artillery projectile and to conduct comprehensive research of the influence of the applied model and integration step on the accuracy and time of computation of projectile trajectory.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

2018 ◽  
Vol 73 (7) ◽  
pp. 595-607 ◽  
Author(s):  
Sezgin Kacar ◽  
Zhouchao Wei ◽  
Akif Akgul ◽  
Burak Aricioglu
Keyword(s):  
Mechanical System ◽  
Chaotic System ◽  
Degrees Of Freedom ◽  
Electronic Circuit ◽  
Chaotic Behaviour ◽  
Two Degrees Of Freedom ◽  
Nonlinear Mechanical System ◽  
Linear Mechanical System ◽  
Low Amplitude ◽  
The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

scholarly journals Diagnostics of supercapacitors

2018 ◽  
Vol 182 ◽  
pp. 01009 ◽  
Author(s):  
Valeriy Martynyuk ◽  
Oleksander Eromenko ◽  
Juliy Boiko ◽  
Tomasz Kałaczyński
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Methodological Approach ◽  
Frequency Dispersion ◽  
Technical Condition ◽  
Transient Processes ◽  
Nonlinear Frequency ◽  
Diagnostic Reliability ◽  
General Reliability ◽  
The Mathematical Model

The paper represents the mathematical model for diagnostics of supercapacitors. The research objectives are the problem of determining a supercapacitor technical condition during its operation. The general reliability of diagnostics is described as the methodological and instrumental reliabilities of diagnostics. The instrumental diagnostic reliability of supercapacitor includes the probabilities of errors of the first and second kind, α and β respectively. The methodological approach to increasing the reliability of supercapacitor diagnostic has been proposed, in terms of multi-parameter supercapacitor diagnostic by applying nonlinear, frequency dependent mathematical models of supercapacitors that take into account nonlinearity, frequency dispersion of parameters and the effect of transient processes in supercapacitors. The more frequencies, operating voltages and currents are applied in the supercapacitor diagnostics, the more methodological reliability of diagnostics will increase in relation to the methodological reliability of supercapacitor diagnostics when only one frequency, voltage and current are applied.

scholarly journals Mathematical model of pantograph cooperation with two degrees of freedom with a catenary system

2019 ◽  
Vol 294 ◽  
pp. 05005
Author(s):  
Marek Kaniewski ◽  
Michał Cichoński
Keyword(s):  
Mathematical Model ◽  
Discrete Model ◽  
Degrees Of Freedom ◽  
Variable Stiffness ◽  
System Model ◽  
Dynamic State ◽  
Rolling Stock ◽  
Two Degrees Of Freedom ◽  
Technical Specifications ◽  
Catenary System

The authors present a method of modeling pantograph cooperation with a catenary system by means of a computer program based on a pantograph discrete model with two degrees of freedom and a catenary system model as a focused mass that in the dynamic state has variable stiffness along the span. After performing the appropriate tests, the validation was carried out according to the proposed method in the PN EN 50318:2019-02 standard required in the Technical Specifications for the interoperability of the subsystem “Energy” and “Rolling stock -locomotives and passenger rolling stock” of the trans-European rail system in Europe.

Nonlinear waves in compacting media

1986 ◽  
Vol 164 ◽  
pp. 429-448 ◽  
Author(s):  
Victor Barcilon ◽  
Frank M. Richter
Keyword(s):  
Mathematical Model ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Nonlinear Interaction ◽  
Phase Speed ◽  
Governing Equations ◽  
One Dimensional ◽  
The Earth ◽  
Permanent Shape ◽  
The Mathematical Model

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

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