scholarly journals Development of the mathematical model of dynamic interaction in the vibrating technological equipment

2019 ◽  
Vol 632 ◽  
pp. 012098
Author(s):  
N K Kuznetzov ◽  
A V Eliseev ◽  
S. V. Eliseev
Keyword(s):  
Mathematical Model ◽  
Dynamic Interaction ◽  
Technological Equipment ◽  
The Mathematical Model

scholarly journals SUPPORT FOR VIBRATION ISOLATION OF THE TECHNOLOGICAL EQUIPMENT

2019 ◽  
Vol 15 (6) ◽  
pp. 866-876
Author(s):  
V. N. Sorokin ◽  
I. Yu. Efimov
Keyword(s):  
Mathematical Model ◽  
Elastic Element ◽  
Vibration Isolation ◽  
Negative Impact ◽  
Road Construction ◽  
Dynamic Loads ◽  
Toroidal Shell ◽  
Technological Equipment ◽  
Support Design ◽  
The Mathematical Model

Introduction. The most urgent tasks of road construction is to improve the sustainability of the roadway, on which the durability of the road surface largely depends and vibration processes are widely used. Moreover, the mechanization of production processes in  construction, the growth of power and speed of technological equipment lead to increasing in dynamic loads on its parts and assemblies. To reduce the dynamic loads in the parts and assemblies of construction machines and equipment, as well as to reduce the negative impact of vibration on the staff, it is necessary to isolate the vibration-generating units and assemblies from the base part of the machine.Materials and methods. The vibro-supports of various designs are used to isolate the vibro-active elements of machines. The authors propose the vibration support design with a quasi-zero stiffness effect, in which the rubber-cord shell of the I-09 type is used as a supporting elastic element, and also the toroid-shaped rubber shell that relies on four identical support segments. In addition, each segment represents the fourth part of the annular tube and cut into two parts by a vertical  cylindrical plane. The outer parts of each segment are connected with hinges to the posts and fixed on the support base, and the inner parts of each segment are also connected to a supporting elastic element and a  vibration-proof mass is connected by means of hinges. The authors describe the working procedure of the proposed construction and compile the mathematical model of vibration support with a quasi-zero stiffness  effect.Results. As a result, the equations of the mathematical model are performed in Matlab with the Simulink extension. The values of the equations are used to plot the strain variation of the toroidal shell of the corrector, which depends on the mass displacement, as well as on the motion patterns of a vibrationproof object of 100 kg for variants of the carrier spring without additional volume and with additional volume of the 1 - 10 Hz pneumatic spring carrier.Discussion and conclusions. The authors determine the pressure in the corrector shell, depending on the isolated object mass. Therefore, the deformation of the corrector shell could be provided with a support structure due to the elasticity of the shell material. The usage of additional volume together with the stiffness corrector allows to obtain a wider area of the load characteristics with quasi-zero stiffness and to improve the vibration-protective properties of the support.

Study on the Dynamic Interaction between Agricultural Tractor and Trailer during Braking Using Lagrange Equation

2014 ◽  
Vol 659 ◽  
pp. 515-520
Author(s):  
Mircea Nastasoiu ◽  
Nicolae Ispas
Keyword(s):  
Mathematical Model ◽  
Lagrange Equation ◽  
Dynamic Interaction ◽  
Braking System ◽  
System 1 ◽  
The Mathematical Model ◽  
Braking Dynamics ◽  
Agricultural Tractor

The paper elaborates a mathematical model in order to study the dynamics of tractor-trailer systems during braking. The braking dynamics is analyzed by considering two versions for the tractor’s braking system: 1) braking applied on the rear wheels and 2) braking applied on all four wheels. In both versions the trailer is braked on all wheels. This model enables us to determine the evolution of the following parameters: braking deceleration, braking forces, and force at the tractor-trailer hitch point. The authors present applications of the mathematical model elaborated on a tractor-trailer system used for transportation works.

Construction of a mathematical model of the signal propagation of the data exchange system between the control unit and the actuators located in the reactors of specialized chemical-technological equipment

2021 ◽  
Author(s):  
A.A. Kharchenko ◽  
S.I. Vidyakin ◽  
L.A. Tishchenko
Keyword(s):  
Mathematical Model ◽  
Magnetic Induction ◽  
Data Exchange ◽  
Control Unit ◽  
Signal Propagation ◽  
Metallographic Analysis ◽  
Telemetry System ◽  
Technological Equipment ◽  
Exchange System ◽  
The Mathematical Model

This paper presents a method for compiling a mathematical model of the signal propagation of the data exchange system between the control unit and the actuators located in the reactors of specialized chemical-technological equipment. The case of the implementation of a modern telemetry system and the main problems in the development of these systems are considered. To develop a mathematical model, a method was written for calculating the EMF of the secondary winding for the system under consideration, namely, the transformer with an open core. The search for a rational frequency for the simulated system is performed. The values of the magnetic induction for different distances between the windings are obtained. The scheme for studying the dependence of the magnetic induction on the magnetic field strength is assembled. To determine the grain size, a metallographic analysis of the pipeline microstructure was performed. The necessity of comparing the experimental data and the data obtained by theoretical calculation is revealed; corrections of the mathematical model are made. The signal propagation range was predicted at a distance of about a meter. Based on the comparison of the mathematical model and the experiment, it is necessary to adjust the first one and develop a methodology for choosing rational parameters of the telemetry system for designing a data exchange system. The developed mathematical model for estimating the parameters of the propagation of the e / m wave allows us to predict the propagation of the signal at a given distance.

Mathematical Model of Non-Stationary Hydraulic Processes Occurring in Gas Centrifuges for Uranium Enrichment

2015 ◽  
Vol 1084 ◽  
pp. 673-677 ◽  
Author(s):  
Aleksey A. Orlov ◽  
Sergey N. Timchenko ◽  
Vladimir S. Sidorenko
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Technological Equipment ◽  
Uranium Enrichment ◽  
Emergency Situations ◽  
Gas Centrifuge ◽  
The Mathematical Model ◽  
Hydraulic Processes ◽  
Centrifuge Cascades

In this article the mathematical model of non-stationary hydraulic processes occurring in gas centrifuge cascades for uranium enrichment is described. This model simulates the technological equipment behavior in standard and emergency situations for possible operational and disturbing influences. Also, the algorithm of differential equations system solving for this model is represented.

scholarly journals Mathematical model of the pneumatic actuator follower system

2021 ◽  
Vol 279 ◽  
pp. 01009
Author(s):  
Denis Medvedev ◽  
Vyacheslav Grishhenko ◽  
Viktor Martynov ◽  
Evgeniy Ivliev ◽  
Yurii Korol’kov
Keyword(s):  
Mathematical Model ◽  
Pid Controller ◽  
Tracking System ◽  
Technological Equipment ◽  
Pneumatic Actuators ◽  
Power And Control ◽  
Actuator System ◽  
And Control ◽  
The Mathematical Model ◽  
Qualitative Characteristics

The article considers a method of controlling the motion of the output links of the tracking system of pneumatic actuators of technological equipment actuators. Dynamic and qualitative characteristics are improved by means of proportional-integral-differential (PID) controller. The mathematical model of actuator system, which includes power and control parts, has been developed. By calculation experiment the dynamic characteristics of the actuator have been obtained, from which it has been found possible to reduce the energy consumed by the actuator system to about 30%.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

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