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

2020 ◽  
Vol 100 (4) ◽  
pp. 29-39
Author(s):  
Volodymyr Gurey ◽  
Ihor Kuzio
Keyword(s):  
Mathematical Model ◽  
Metal Layer ◽  
Nanocrystalline Structure ◽  
Dynamic Processes ◽  
Special Device ◽  
Lagrange Equations ◽  
Spindle Unit ◽  
Transverse Grooves ◽  
The Mathematical Model ◽  
Frictional Hardening

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.

scholarly journals Mathematical Model of Forest Fire Soil-thrower Movement

2020 ◽  
Author(s):  
Olga Dornyak ◽  
Ivan Bartenev ◽  
Mikhail Drapalyuk ◽  
Dmitry Stupnikov ◽  
Sergey Malyukov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Forest Fire ◽  
Forest Fires ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Steady Motion ◽  
Technological Parameters ◽  
Lagrange Equations ◽  
Milling Tool ◽  
The Mathematical Model

The design of a forest fire soil-thrower made to prevent and eliminate ground forest fires is presented. A mathematical model of machine movement has been developed, which enables to study the laws of the interaction process of the design with the soil. It is accepted that the machine has two degrees of freedom. The mathematical model has been obtained using the Lagrange equations of the second kind. The design and technological parameters of the forest fire soil-throwing machine, affecting the efficiency of its work, including mass and width of the grip of the ripper casing, mass, radius and frequency of rotation of the milling tool, the number and geometric parameters of the blades are taken into account. Mathematical model enables to determine the effect of these parameters on the characteristics of the movement of ripper casing and milling working body. A mathematical model is needed to synchronize the translational motion of the unit and the rotational motion of the rotor. Formulas have been obtained for the steady motion of the forest fire soil-thrower, that determine the hauling power of tractor and torque that ensures the operation of milling tools.

The Mathematical Model for the Generation of the Cylindrical Gear With Curved Cycloidal Teeth

2007 ◽  
Author(s):  
Iulian Stanasel ◽  
Adrian Ghionea ◽  
Ionut Ghionea ◽  
Petru Ungur ◽  
Oana Stanasel
Keyword(s):  
Mathematical Model ◽  
Production Costs ◽  
Reference Plane ◽  
Practical Implementation ◽  
Work Piece ◽  
Special Device ◽  
Technological Parameters ◽  
Cylindrical Gear ◽  
Processing Machine ◽  
The Mathematical Model

The performed studies regarding the cylindrical gears with curved teeth or in V showed that a uniform distribution of the load on the flanks is hard to realise, generally being necessary later finishing processing or modifying the gear by camber or flanking, which suppose supplementary expenses. On the basis of these mentions and taking into account the advantages of curved bevel gear, the purpose of this paper is to present an original study regarding the mathematical model for generation of a curved cylindrical gear with high performances. The cycloidal gear was chosen after a technical and an economical study regarding on the possibility of practical implementation with the lowest production costs using a special device, adapted on a Phauter processing machine of cylindrical gear. This was the main reason for choosing a cycloidal profile from several types of curved teeth (cycloidal arc, circle arc, Archimede’s spiral, involute arc). So, the main aim of the paper is to determine the equations of the flanks of cylindrical wheel with curved teeth in oblong cycloidal arc, in order to establish if the technical generation is possible. The curved cylindrical teeth with cycloidal flanks is generated by rolling with straight mobile line and continuous division by using a milling cutter with 1, 2, 3, 6 groups of knifes equidistantly placed, fixed on an adaptable device on a Phauter processing machine. The two curves which define the flank are simultaneously generated by correlated motions, and the flanks of the wheel part result as a roll of successive positions of generating hook materialized by the cutting edge of the tool. The shape of the contact curve between the conjugated surfaces of generating element and the wheel part can be obtained if you are taking into account the kinematic condition. Using this condition you can determine the relationship between the kinematic, geometric and technological parameters. The line of the flanks is studied in the reference plane and in parallel planes with this, and the profile of the flanks is determined in perpendicular planes on the work piece axis. Based on the parametric equations it was made the simulation program in MATLAB that indicates that this gears can be obtained, and constitutes the first step in practical manufacturing of this kind of gears. By analyzing the obtained shape they result useful conclusions for the manufacturing of the involute-tooth gear with curved oblong cycloidal arc. On the other hand, using Solid Edge it was made the spatial modeling of the cylindrical gear with curved cycloidal teeth that allows next FEA studies regarding on the contact and bending stress.

FEATURES OF THE WIRELESS ENERGY TRANSFER’S CHANNEL IN A DYNAMIC MODE

2018 ◽  
pp. 79-88 ◽  
Author(s):  
L. B. Kochin ◽  
S. Yu. Strakhov ◽  
S. A. Matveev
Keyword(s):  
Mathematical Model ◽  
Energy Transfer ◽  
Pulse Mode ◽  
Dynamic Processes ◽  
Dynamic Mode ◽  
Experimental Setup ◽  
Wireless Energy Transfer ◽  
Practical Applications ◽  
The Mathematical Model ◽  
Energy Channels

Work is devoted to wireless energy transfer to the removed devices by means of laser radiation. This problem is actual in some practical applications. The dynamic mode of the laser wireless energy transfer's channel is considered. The mathematical model is offered. Influence of terminal loading on dynamic processes in the channel is investigated. The factors increased of energy transfer channel's efficiency are analyzed. Parameters of lenses and beam expanders, accuracy of optical component's installation, uniformity of a photocell's light spot are investigated. It is shown, that in a pulse mode efficiency of energy channels depends also on an impedance of loading. Additional impedance increased of fluctuation's amplitude and reduced channel's efficiency. The description of experimental setup, data of measurements and their analysis are resulted.

scholarly journals Development and research of the rotating lever object as a dynamic model of a cycle mechanism

2018 ◽  
Vol 224 ◽  
pp. 02078 ◽  
Author(s):  
Viktor Telegin ◽  
Alexander Kozlov ◽  
Tatyana Shumilova
Keyword(s):  
Mathematical Model ◽  
Sharp Increase ◽  
High Speed ◽  
Quantitative Estimation ◽  
Automatic Machine ◽  
Dynamic Processes ◽  
Common Elements ◽  
Positioning Accuracy ◽  
Concentrated Masses ◽  
The Mathematical Model

The operation of high-speed automatic machine mechanisms causes oscillating (dynamic) processes because of the elastic deformation of their elements. This results in a sharp increase in loads in the mechanism links and a decrease in their positioning accuracy. The quantitative estimation of dynamic processes is performed on the basis of modeling the mechanisms by systems of concentrated masses connected by elastic-dissipative and kinematic bonds. One way to develop such systems and describe them mathematically is the method of representing the mechanism as a set of a limited number of objects, each of which represents either a typical mechanism or its separate part. This article considers the development and research of the mathematical model of the rotating lever as one of the most common elements of cycle mechanisms which also include cam-leverage, crank-and-rod and other mechanisms.

Mathematical Model of a Dummy Cranio-Cervical Complex in Frontal Impact Testing Device

2016 ◽  
Vol 822 ◽  
pp. 472-479
Author(s):  
Stefanita Ciunel ◽  
Bebe Tică ◽  
Dragos Laurentiu Popa
Keyword(s):  
Mathematical Model ◽  
Cervical Vertebrae ◽  
Impact Testing ◽  
Testing Device ◽  
Frontal Impact ◽  
Lagrange Equations ◽  
Functional Relations ◽  
The Mathematical Model ◽  
Head Neck

Biomechanics is the science that uses mechanical equations in studying biological structures such as bones, muscles, ligaments, joints and other body structures. It is important in understanding the mechanism of injury to the cervical spine (C1-C7) and head bones. We developed a mathematical approach to mechanical behavior of cervical vertebrae and inter-vertebral discs, in terms of laboratory testing. The paper presents the mathematical model based on Lagrange equations for a frontal impact testing head-neck system. The steps for the solving these equations are exposed in the paper. These studies were combined with FEA and dynamic analysis for determination of constants,parameters, forces and functional relations. Results and conclusions were analyzed in the final of the paper.

scholarly journals Numerical investigation of gas dynamics in the pyro actuator found in the mechanism for unfolding aerodynamic surfaces

2017 ◽  
pp. 37-42
Author(s):  
M. N. Pravidlo ◽  
N. A. Lyubimova ◽  
L. V. Bykov
Keyword(s):  
Mathematical Model ◽  
Numerical Investigation ◽  
Gas Dynamics ◽  
Software Package ◽  
Dynamic Processes ◽  
Ansys Software ◽  
Collector System ◽  
Gas Dynamic ◽  
The Mathematical Model ◽  
Aerodynamic Surfaces

The article presents a mathematical model of a pyro actuator found in the mechanism for unfolding aerodynamic surfaces of aircraft, which includes a collector system. The mathematical model proposed takes into account linked gas dynamic processes in the internal pyro actuator chambers and the dynamics of its mechanical traveller. We supply results of numerically investigating the main parameters of working body flow, obtained by using the ANSYS software package.

scholarly journals Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit

2016 ◽  
Vol 65 (1) ◽  
pp. 87-103 ◽  
Author(s):  
Antoni Sawicki ◽  
Maciej Haltof
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Power Supply ◽  
Electric Arc ◽  
Dynamic Processes ◽  
Model Parameters ◽  
Static Characteristics ◽  
Integral Methods ◽  
The Mathematical Model ◽  
Linear Shape

Abstract The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters.

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

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