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

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.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

scholarly journals MODELING OF THE MECHANISM OF VEHICLE OVERTURNING IN THE PROCESS OF DEVELOPMENT OF ROAD TRAFFIC ACCIDENT

2019 ◽  
Vol 20 (2) ◽  
pp. 320-328
Author(s):  
S. Povalyaev ◽  
O. Saraiev
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Critical Speed ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Road Traffic Accidents ◽  
Basic Parameters ◽  
The Moment ◽  
Comparison Of The Results

The development of mathematical models of vehicle overturning has been given significant attention by many researchers because of the need to obtain reliable information on the circumstances of road traffic accidents. Research of road traffic accidents with the overturning of vehicles is related with the difficulty to determinate the mechanism of overturning, because expert calculation methods do not always use the adapted mathematical models. Most of the methods focus on determining the minimum (critical) speed of vehicles, which leads to its overturning. However, the real speed of vehicles before overturning can be much higher. In this paper, a mathematical model of the process of vehicle overturning after a collision with an immovable lateral obstacle is given. Thus the overturning moment caused by the inertia forces acts on the vehicle, and the moment from the gravity that holds the vehicle from overturning. It is necessary to mark that the shoulder of moment from gravity changes from a maximal value to 0 in the process of vehicle overturning. The mathematical model is based on the basic equation of dynamics for rotational motion. The developed mathematical model is a nonlinear homogeneous differential equation of second order. A solution of this equation is obtained that allows us to determine the conditions for the vehicles overturning and to investigate the basic parameters of the movement of vehicles in the process of overturning from the moment when the center of mass of the vehicle begins to rise until the moment of its maximum lifting. A comparison of the results of calculating the critical speed of vehicles with results obtained on the basis of the law of energy conservation was carried out. The results are fully agreed. The numerical results obtained using a mathematical model for a particular vehicle have been analyzed.

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

2018 ◽  
Vol 13 (2) ◽  
pp. 76-76
Author(s):  
Валерий Белов ◽  
Valeriy Belov ◽  
Леонид Рыбаков ◽  
Leonid Rybakov ◽  
Светлана Овчукова ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Experimental Studies ◽  
Field Research ◽  
Test Protocol ◽  
Optimal Value ◽  
The Stability ◽  
The Moment ◽  
The Mathematical Model ◽  
Elastic Characteristics

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.

scholarly journals Step-by-step analytical synthesis of the mathematical model of automotive unmanned aircraft

2021 ◽  
pp. 21-28
Author(s):  
A. A. Lobaty ◽  
A. Y. Bumai ◽  
S. S. Prohorovith
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Aerodynamic Characteristics ◽  
Unmanned Aircraft ◽  
Control Synthesis ◽  
Aerial Vehicle ◽  
Stage Synthesis ◽  
The Stability ◽  
The Mathematical Model ◽  
Analytical Synthesis

The problem of the stage-by-stage synthesis of the mathematical model of the autopilot of an unmanned aerial vehicle (UAV) is considered. At the first stage, an analytical synthesis of the control acceleration applied to the center of mass of the UAV is performed to form a specified trajectory of its flight. On the basis of the results received at the first stage, at the subsequent stages, the problem of synthesizing a mathematical model of the UAV autopilot is solved with the specified requirements for ensuring the stability and dynamic accuracy of UAV control. Under actual assumptions about the corresponding nature of changes in the trajectory parameters and variables that characterize the motion of the UAV in space, the use of a linear mathematical model of the evolution of the state vector of the UAV and its control system is substantiated. When synthesizing a mathematical model of the UAV autopilot, the method of modal control of the system was used for a specified mathematical model of the object. For a specified model of motion and aerodynamic characteristics of the UAV, the law of deviation of the control steering surface is analytically received, which depends on the parameters of the translational and rotational movement of the UAV. Computer simulation of the analytically received results of control synthesis for the specified characteristics of UAVs and specific using conditions was carried out, which clearly showed the efficiency and prospects of using this approach for the synthesis of control systems for UAVs of various purposes and design.

scholarly journals MATHEMATICAL SIMULATION OF THE CORRELATION BETWEEN THE FREQUENCY OF ROAD TRAFFIC ACCIDENTS AND DRIVING EXPERIENCE

Transport ◽  
2010 ◽  
Vol 25 (3) ◽  
pp. 237-243 ◽  
Author(s):  
Paulius Miškinis ◽  
Vaida Valuntaitė
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Road Traffic Accidents ◽  
Road Accidents ◽  
Driving Experience ◽  
The Mathematical Model ◽  
The Eu

Based on statistical analysis indicating the dependence of the number of road traffic accidents on driving experience, a mathematical model of such correlation is offered. The mathematical model has been tested generating a new approximation using the eigenfunctions of the introduced model applied to draw long‐term forecasts for the dependence of the number of potential road accidents on driving experience. Since we have more road traffic accidents per one hundred thousand inhabitants than other EU countries, comprehensive data analysis might also be useful for the EU community.

scholarly journals The Impact of the Efficiency of the System for Vibrations Damping on the Efficiency of Vehicle Braking

2018 ◽  
Vol 3 (1-2) ◽  
Author(s):  
N Manojlović ◽  
Drago Talijan ◽  
B Bajić
Keyword(s):  
Mathematical Model ◽  
Traffic Accidents ◽  
Braking System ◽  
Shock Absorbers ◽  
Two Systems ◽  
The Moment ◽  
The Impact ◽  
Vehicle Movement

This paper presents the plan and results of the research of the efficiency of the braking system depending on the condition of the shock absorbers and the velocity of the vehicle movement at the moment of braking. As expected, it has been proven that the braking efficiency decreases with decreasing efficiency of the system for damping vibrations. The interdependence of these two systems is also represented by a mathematical model that can serve for practical purposes in the analysis of traffic accidents.

Assessment of roadability and stability of a vehicle movement on the bend

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Road Surface ◽  
Inertia Force ◽  
Speed Limit ◽  
The Road ◽  
Inertial Moment ◽  
The Mathematical Model ◽  
Computer Imitation ◽  
Vehicle Movement

The paper presents the mathematical model and the technique of computer imitation of a vehicle movement on bend. Research of roadability and stability of the truck and the schedules illustrating change of characteristics of the steered movement have been obtained. The critical modes of the movement causing separation of wheels from road surface and side slippage have been defined. Speed limit of the steered movement on trajectory of the set curvature have been determined. Keywords vehicle, wheel, cross and longitudinal reactions of the road, inertia force, inertial moment, trajectory of a vehicle movement, angles of withdrawal of wheels, spring weight angle of heel, side slippage, vehicle drift

scholarly journals SYNTHESIS OF PROGRAM AND FINITE LAWS OF MOTION IN ANALYTICAL MODELS OF CONTROL OF THE FINAL STATE OF BIOMECHANICAL SYSTEMS

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99
Author(s):  
V Zagrevskiy ◽  
O Zagrevskiy
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Center Of Mass ◽  
Material Point ◽  
Object Motion ◽  
Reference Points ◽  
Analytical Models ◽  
Final State ◽  
Finite Control ◽  
The Mathematical Model

Aim. The article deals with developing a computer program to simulate the movement of the object with a given initial and final speed and fixed travel time. Materials and methods. The analysis, as a method of biomechanics, allows us to assess the biomechanical state of the athlete in real sports exercises. The function of motion synthesis is the ability to predict the trajectory and behavior of the biomechanical system at specified reference points of the phase structure of the simulated motion. The article deals with one of the methods of biomechanical synthesis of movements: synthesis of control of the final state of biomechanical systems, based on the reduction of finite control to a given program control after attenuation of the transient component of acceleration. The mathematical description of the object motion is based on the known law of finite control with feedback. Integration of the mathematical model constructed in the form of the differential equation of the second order was carried out by one of the numerical methods of integration: Runge–Kutta method of the fourth order of accuracy. Consideration of the method is based on a mathematical apparatus describing the motion of a material point, which can be represented by a common center of mass of a biomechanical system, a joint, a center of mass of a segment, etc. Results. The mathematical model of the motion of a material point with the given kinematic parameters of motion at the initial and final moments is implemented in a computer program in the Visual Basic 2010 language environment based on the integrated development environment Visual Studio Express 2013. The output provides numerical and visual support for simulation results. Conclusion. It is shown that the developed computer model of the method always implements the goal of motion: to transfer an object from a given initial state by speed to a given final state for a fixed time of movement.

scholarly journals MODELING OF THE SPINE COMPENSATORY RESPONSE TO DEFORMITY

2018 ◽  
Vol 15 (3) ◽  
pp. 85-91
Author(s):  
A. V. Krutko ◽  
A. V. Gladkov ◽  
V. V. Komissarov ◽  
N. V. Komissarova
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Sagittal Imbalance ◽  
Spine Deformity ◽  
Compensatory Mechanism ◽  
Spinal Deformities ◽  
Compensatory Response ◽  
The Mathematical Model ◽  
Pathological Situation

Objective. To analyze mathematical model of the efficiency of the compensatory mechanism of the deformed spine. Material and Methods. The developed basic kinematic model of the spine was used. The restoration of the position of the projection of the general center of mass (GCM) was mathematically modeled, and mechanogenesis of the spinal deformity and possibility of its compensation were evaluated. To assess the reliability of the mathematical model, spinal skiagrams taken from patients with clinically confirmed pathology and sagittal imbalance were used. Results. On the basis of quantitative characteristics of the primary spine deformity of a certain clinical case and using the developed algorithm, it is possible to create a model of both a primary deformity and a compensatory response from intact segments of the spine taking into account the influencing factors. This makes it possible to use the proposed kinematic model in scientific research on predicting the course of various types of spinal deformities. Conclusion. The proposed algorithms simulating the development of spinal deformities based on the restoration of the position of the GCM projection reflect their mechanogenesis and can be used to model various pathological conditions of the spine. A complete correction of the deformity does not mean a complete cure, since the required spinal fusion creates a new, prognostically less significant, but pathological situation.

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.

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