INVESTIGATION OF THE INFLUENCE OF PRESSING BELTS TENSION OF THE BACK CIRCUIT OF PRESS - SELECTIVE PR-1.5

A brief analysis of suspension mechanisms and ways to improve the quality of press harvesting for flax harvesting is considered. By researching the mathematical model, the authors prove the possibility of increasing the stability of the elastic characteristics of the suspension mechanisms by changing the angle between the levers or changing the geometry of the structure, for example, the attachment point of a two-arm lever. Particular attention is drawn to the new term “reduced rigidity” of the suspension mechanism. Using this notion and the method of its determination, the authors recommend determining the optimal value of the reduced stiffness of the suspension in the way of mathematical modeling and using this indicator as the main optimization parameter. The results of theoretical and experimental studies were presented by the authors in the form of elastic characteristics of the suspension mechanisms. When conducting a study of the mathematical model, it is suggested to take into account the condition of equality of the maximum values of the moments of forces from the action of the tension forces of the belts or the mass of the working element and the moment of forces acting on the side of the tension springs. During the research of the suspension mechanism, the actual dimensions of the PR-1.5 baler design were adopted. At the same time, we briefly describe the design of the improved tensioning mechanism of a baler for flax harvesting. A rather detailed analysis is given by the authors of the obtained elastic characteristics of the suspension mechanism. Some new features of the elastic characteristics of the suspension mechanism that have not been previously detected are described. To confirm the correctness of the reasoning, the authors implemented their research in a real press-picker and conducted field research that confirmed the possibility of improving the quality of the upgraded version of the machine. To confirm the results of the research, the authors presented a fragment of the field test protocol. The task is solved, uniformity of the roll density is ensured and its density is increased.

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Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes

Open Physics ◽

10.1515/phys-2018-0011 ◽

2018 ◽

Vol 16 (1) ◽

pp. 57-62 ◽

Cited By ~ 1

Author(s):

Sebastian Różowicz

Keyword(s):

Mathematical Model ◽

Experimental Studies ◽

Fuel Mixture ◽

Spark Discharge ◽

Fuel Additives ◽

Ignition System ◽

Spark Plug ◽

The Mathematical Model

Abstract The paper presents the results of analytical and experimental studies concerning the influence of different kinds of fuel additives on the quality of the spark discharge for different configurations of the ignition system. The wear of the spark plug electrode and the value of spark discharge were determined for various impurities and configurations of the air-fuel mixture.

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DEVELOPMENT AND RESEARCH OF PROMISING SCHEMES FOR DIVIDING PIPES INTO DIMENSIONAL BILLETS

ENGINEERING, ENERGY, TRANSPORT AIC ◽

10.37128/2520-6168-2021-1-4 ◽

2021 ◽

pp. 30-37

Author(s):

Sergii Karnaukh

Keyword(s):

Mathematical Model ◽

Experimental Studies ◽

Connecting Rod ◽

High Quality ◽

Cutting Knife ◽

3D Software ◽

The Mathematical Model ◽

Cut Surface ◽

Deform 3D

The purpose of this work is to study the known method of division of pipes by introducing a figure knife and the development of promising designs of equipment for division of pipes into measured workpieces. Based on the analysis of the actuating crank-slider mechanisms used in the equipment for division of pipes into measured workpieces, promising schemes of short-connecting rod mechanisms have been discovered that provide a local pipe section along the perimeter. The developed design of the device for dividing pipes into dimensional workpieces by the eccentric twisting method, which contains a wedge-joint mechanism in combination with a compact circular actuator, also allows to reduce energy and power costs for separation, reduce the consequences of instantaneous unloading of equipment and ensure high quality workpieces. A mathematical model of the proposed equipment was developed and the modeling of the cutting process was carried out using the DEFORM-3D software package. The analysis of the results obtained showed that in the extreme positions of the knives, jamming of the knives is possible. To eliminate jamming, it is necessary that the knives do not reach the extreme position. The adequacy of the mathematical model is confirmed by experimental studies. The error of the calculated and measured values of the torque on the cutting knife does not exceed 10%. This is due to the need for a more correct accounting of friction on the contact surfaces of the equipment. Cut tubular blanks have high geometric accuracy and high quality of the cut surface.

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VIBRATION MODULATION CAUSES AT ROTATION FREQUENCY IN ROTARY MACHINES

Akustika ◽

10.36336/akustika201932151 ◽

2019 ◽

Vol 32 ◽

pp. 151-157

Author(s):

Sergey Alekseevich Rykov ◽

Irina Kudryavtseva ◽

Sergey Vladimirovich Rykov

Keyword(s):

Mathematical Model ◽

Experimental Studies ◽

Rotation Frequency ◽

Diagnostic Methods ◽

Bearing Unit ◽

Rotary Machines ◽

The Mathematical Model

The results of theoretical and experimental studies of the modulation of vibrations of rotary machines have been presented at rotation frequency. It has been shown that at the rotation frequency, the possible causes of the origin of the “side” spectral discrete components are the presence of a clearance and friction in bearing units. On the basis of the data obtained in the mathematical model, the diagnostic methods of the quality of functioning the bearing unit of rotary mechanisms are proposed.

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Mathematical model for estimation the stability of the vehicle's motion on overturning

Vehicle and Electronics Innovative Technologies ◽

10.30977/veit.2021.19.0.47 ◽

2021 ◽

pp. 47-52

Author(s):

Serhii Povaliaiev ◽

Olexii Saraiev

Keyword(s):

Mathematical Model ◽

Traffic Accidents ◽

Order Differential Equation ◽

Road Traffic ◽

Center Of Mass ◽

Conservation Of Energy ◽

The Stability ◽

The Moment ◽

The Mathematical Model ◽

Vehicle Movement

Problem. During the reconstruction of the circumstances of road traffic accidents with vehicles overturning, difficulties arise with determining the parameters of vehicles in the process of their overturning. This is due to the fact that the recommended calculation methods are often simplified. The main focus of such techniques is to determine the minimum speed of vehicles, which leads to their overturning. In fact, the speed of vehicles before overturning can be significantly higher. Goal. This paper is dedicated to developing mathematical model of overturning vehicles that makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement in the process of overturning. Methodology. The overturning of the vehicle occurs as a result of the action of inertial forces after collision with an immovable side obstacle. In this case, the moment from the force of gravity of the vehicle keeps it from overturning. In the process of overturning the vehicle, the moment from the force of gravity decreases due to the decrease in the arm of the force of gravity. To compile a mathematical model, the basic equation of dynamics during rotational motion was used. The mathematical model of a vehicle overturning is written in the form of a nonlinear homogeneous second order differential equation. An analytical solution of this equation is obtained. Results. Developed mathematical model makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement from the moment the center of mass begins to rise to the moment of its maximum rise in the process of overturning. For a particular case, when the critical speed of a vehicle during its overturning is determined, the developed mathematical model fully corresponds to the mathematical model based on the law of conservation of energy. For a specific vehicle, numerical results were obtained that fully correspond to the physics of the overturning process.

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MATHEMATICAL MODEL FOR DETERMINING THE STEP TIME AND DISTANCE COVERED BY THE DROPLETS OF LUQUID FIRE-FIGHTING AGENT DURING THE PROCESS OF FIRE EXTINGUISHING IN THE CLOSED ROOM

Fire Safety ◽

10.32447/20786662.32.2018.09 ◽

2018 ◽

pp. 63-68

Author(s):

O. Ukhanska ◽

N. Shtangret

Keyword(s):

Mathematical Model ◽

Effective Mass ◽

Horizontal Plane ◽

Experimental Studies ◽

Fire Fighting ◽

Effective Diameter ◽

Fire Extinguishing ◽

The Moment ◽

The Mathematical Model

The article deals with the mathematical model for determining the step time and distance covered by the droplet of liquid till the moment of contact with the horizontal plane. Numerical values of the step time and distance covered till the moment of contact with the horizontal plane are obtained. Experimental studies aimed on determining the effective diameter of the droplet are performed. According to effective diameter value an effective mass of the droplet is determined. After obtaining the effective mass value the step time and distance covered by the droplet of liquid till the moment of contact with the horizontal plane are calculated using a mathematical model.

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EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

Avtoshliakhovyk Ukrayiny ◽

10.33868/0365-8392-2019-4-260-10-16 ◽

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.

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

Criminalistics and Forensics ◽

10.33994/kndise.2020.65.43 ◽

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.

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Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.572.636 ◽

2013 ◽

Vol 572 ◽

pp. 636-639

Author(s):

Xi Chen ◽

Gang Wang

Keyword(s):

Mathematical Model ◽

Stability Analysis ◽

Stability Criterion ◽

Stability Margin ◽

Static Stability ◽

Matlab Simulation ◽

And Performance ◽

The Stability ◽

The Mathematical Model ◽

The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

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Thermal hardening and calculation of the mathematical model of face milling of parts made of steel 95X18-Sh to improve the quality of the surface layer

10.36652/1813-1336-2021-17-5-200-206 ◽

2021 ◽

pp. 200-206

Author(s):

I.N. Sedinin ◽

V.F. Makarov

Keyword(s):

Mathematical Model ◽

Cutting Speed ◽

Physical And Mechanical Properties ◽

Face Milling ◽

Experiment Planning ◽

Depth Of Cut ◽

Machined Surface ◽

The Mathematical Model ◽

Full Factorial

It is considered the complex of operations of the technological process for the heat treatment of steel 95X18-Sh, as a result of which the material of the samples increases the hardness to 59...61 HRC, and also improves the physical and mechanical properties. A full-scale full factorial experiment of face milling of samples was carried out using the method of mathematical planning. In the experiments, a high-precision machine and a carbide cutting tool were used. To calculate the values of the roughness function, the following are taken as independent variables: cutting speed, feed per tooth and depth of cut. In order to determine the coefficients of the linear equation, a central compositional orthogonal plan of the second order for three factors was used. A matrix of levels of variation of independent variable factors and a matrix of experiment planning were compiled. A regression analysis of the obtained experimental statistical data was carried out using the Microsoft Excel, Statistica and Wolfram Alpha programs. As a result of the calculations, a mathematical model of the roughness of the machined surface and optimal cutting conditions were determined.

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The envelope method in the problem of choosing a rational composition of measuring instruments

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2021-2-68-72 ◽

2021 ◽

pp. 68-72

Author(s):

Il'ya A. Meshchikhin ◽

Sergej S. Gavryushin

Keyword(s):

Mathematical Model ◽

Monitoring Systems ◽

Measuring Instruments ◽

Key Points ◽

Envelope Method ◽

Loaded State ◽

The Mathematical Model ◽

Selection Of ◽

Rational Composition

As part of the development of monitoring systems for the operation of technical objects, the problem of improving the quality of monitoring systems for the loaded state is considered. Based on the analysis of the mathematical model of the structure and its loading, a methodology for the selection of measuring instruments was developed. The urgency of the problem of calculating substantiation of the choice of key points of the structure is shown, at which it is possible to measure deformations for the subsequent restoration of the existing loads with maximum accuracy. An approach based on the envelope method for determining the rational composition of measuring instruments for restoring the loads acting on the structure is stated.

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