scholarly journals Mathematical model for assessing lateral stability of articulated tracked vehicles

2021 ◽  
Vol 2094 (4) ◽  
pp. 042005
Author(s):  
A P Chajkin ◽  
R Yu Dobretsov ◽  
V A Sokolova ◽  
I A Teterina ◽  
A V Kamenchukov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Critical Speed ◽  
Center Of Mass ◽  
Lateral Force ◽  
Operational Reliability ◽  
Lateral Stability ◽  
Steering Control ◽  
Tracked Vehicles ◽  
Propulsion Unit ◽  
Empirical Coefficients

Abstract The article considers the problem of increasing transport productivity, operational reliability and safety during cargo transportation by using articulated tracked vehicles and road trains with active trailers. The influence of the introduction of an electromechanical drive, the modernization of the propulsion unit and the steering control system on the lateral stability of an articulated tracked vehicle is analyzed. A mathematical model is described for calculating the lateral stability of the chassis of articulated tracked vehicles used in the regions of the Far North, Arctic and Antarctic. The model is based on developments carried out for the chassis of an articulated wheeled vehicle. The model allows calculating to determine the key geometric and kinematic parameters of the rotation, taking into account the action of external forces. The use of holonomic constraints in determining the critical speed of movement is determined by the physical picture of the beginning of overturning, which corresponds to the achievement of the critical folding angle of the sections. This approach makes it possible not to use empirical coefficients when assessing the instantaneous position of the center of gravity of the system, the center of rotation, the radius of rotation of the center of mass, and the critical speed of the chassis. The moment of the beginning of the rollover is determined by the disappearance of the normal reaction under the link caterpillar. The onset of lateral sliding is determined by the lateral force exceeding the lateral adhesion limit.

scholarly journals Investigation of the components of the cornering resistance of a tracked vehicle on a solid support base

2021 ◽  
Vol 1 (2) ◽  
pp. 51-62
Author(s):  
B.V. Padalkin ◽  
Keyword(s):  
Mathematical Model ◽  
Reaction Force ◽  
Vertical Axis ◽  
Support Surface ◽  
Tracked Vehicle ◽  
Tracked Vehicles ◽  
Contact Patch ◽  
Minimum Number ◽  
The Moment ◽  
Propulsion Unit

The purpose of the study is to increase the completeness and reliability of approaches to deter-mining the components of the cornering resistance a tracked vehicle, as well as to create a method for their assessment, which will be suitable for practical calculations. The article analyzes two components of the moment of cornering resistance of the tracked vehi-cle, which can be distinguished if we consider the interaction of the caterpillar with the support base through separate contact spots (active sections of the tracks located under the road wheels). The first component arises from the linear movement of the active sections of the tracks. The second is caused by the rotational movement of the contact patch about the vertical axis. The paper presents a mathematical model of the interaction of the propeller and a dense support base, which makes it possible to study the dependence of the components of the moment of corner-ing resistance on the geometric parameters of the undercarriage of a tracked vehicle. The horizontal reaction force in this case is presented as a function of the slip coefficient. The possibility of realiz-ing various adhesion qualities of the propulsion unit in the longitudinal and transverse directions of sliding is provided. The model assumes a preliminary division of the contact patch into a finite number of elementary areas. Since the number of elementary sites affects the result, the article con-ducted a study to determine the minimum number of sites to ensure acceptable accuracy. An analysis of the expressions available in the literature was carried out to determine the speci-fied component of the cornering resistance. The new empirical relationships that better agree with the mathematical model were proposed. The study of several existing tracked vehicles, differing in the mass and size of the track support surface, made it possible to conclude that it is advisable to take into account the moment of cornering resistance of the contact patch for various types of tracked vehicles.

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.

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 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 Reliability of the RBMK-1000 coolant flow measurement system

2019 ◽  
Vol 5 (1) ◽  
pp. 81-87
Author(s):  
Arkady I. Pereguda
Keyword(s):  
Mathematical Model ◽  
Measurement System ◽  
Flow Measurement ◽  
Rotation Period ◽  
Operation Time ◽  
Operational Reliability ◽  
Coolant Flow ◽  
Reliability Indicators ◽  
Parametric Reliability ◽  
Two Parameters

An analysis of statistical data of diagnostic measurements of two parameters determining the performance of the RBMK-1000 SHADR-8A flowmeters – the minimum value of the negative amplitude half-wave at the transistor flow measuring unit (TIBR) input and the mean-square deviation over the flowmeter ball rotation period – made it possible to develop a mathematical model of the flowmeter parametric reliability. This mathematical model is a random process, which is a superposition of two delayed renewal processes. Studying the flowmeter operational reliability model provides an exponential estimate of the probability that the parameters determining the flowmeter performance will not exceed the specified levels. Using the Bernoulli scheme and the probability-estimating relationship for the flowmeter performance parameters, it is possible to calculate the probability of failure-free operation of both a single reactor quadrant and the coolant flow measurement system. In addition, it becomes possible to estimate the quadrant failure rate. Important for practice is the possibility of predicting the number of failed flowmeters depending on the system operation time. An indicator of the system reliability can be the average number of failed flowmeters, the relation for which is given in the paper. All the research results were obtained without any additional assumptions about the random values distribution laws. The obtained results can be easily generalized for the cases when the vector dimension of the determining parameters is greater than two. The use of the results of this study is illustrated by calculated quantitative values of the flowmeter parametric reliability indicators and the coolant flow measurement system.

scholarly journals Effect of Mathematical Modeling and Fitting Procedures on the Assessment of Critical Speed and Its Relationship With Aerobic Fitness Parameters

2021 ◽  
Vol 12 ◽  
Author(s):  
Aurélien Patoz ◽  
Nicola Pedrani ◽  
Romain Spicher ◽  
André Berchtold ◽  
Fabio Borrani ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Aerobic Fitness ◽  
Critical Speed ◽  
Ventilatory Threshold ◽  
Information Criterion ◽  
Accurate Estimation ◽  
Running Speed ◽  
Fitting Procedure ◽  
Fitting Procedures ◽  
Fitness Parameters

An accurate estimation of critical speed (CS) is important to accurately define the boundary between heavy and severe intensity domains when prescribing exercise. Hence, our aim was to compare CS estimates obtained by statistically appropriate fitting procedures, i.e., regression analyses that correctly consider the dependent variables of the underlying models. A second aim was to determine the correlations between estimated CS and aerobic fitness parameters, i.e., ventilatory threshold, respiratory compensation point, and maximal rate of oxygen uptake. Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of the peak speed of the incremental test on a treadmill. Then, two mathematically equivalent formulations (time as function of running speed and distance as function of running speed) of three different mathematical models (two-parameter, three-parameter, and three-parameter exponential) were employed to estimate CS, the distance that can be run above CS (d′), and if applicable, the maximal instantaneous running speed (smax). A significant effect of the mathematical model was observed when estimating CS, d′, and smax (P < 0.001), but there was no effect of the fitting procedure (P > 0.77). The three-parameter model had the best fit quality (smallest Akaike information criterion) of the CS estimates but the highest 90% confidence intervals and combined standard error of estimates (%SEE). The 90% CI and %SEE were similar when comparing the two fitting procedures for a given model. High and very high correlations were obtained between CS and aerobic fitness parameters for the three different models (r ≥ 0.77) as well as reasonably small SEE (SEE ≤ 6.8%). However, our results showed no further support for selecting the best mathematical model to estimate critical speed. Nonetheless, we suggest coaches choosing a mathematical model beforehand to define intensity domains and maintaining it over the running seasons.

scholarly journals Analysis of Platform Leveling Systems for Tracked Feller-Buncher Machines

Inventions ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 96
Author(s):  
Andronov Alexandr ◽  
Bacherikov Ivan ◽  
Zverev Igor
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Slope Angle ◽  
Hydraulic Cylinder ◽  
Second Stage ◽  
Modeling Methods ◽  
The Third ◽  
Support Reaction ◽  
Third Stage ◽  
The Stability

The study was devoted to the analysis of feller buncher platform leveling systems. The widespread use of these systems in the design of modern feller-buncher machines makes the study relevant to assess operational efficiency. The analysis was conducted in five stages using analytical and stochastic mathematical modeling methods. In the first stage, the existing layouts of alignment systems were analyzed from the position of force on the hydraulic cylinder rods of the platform tilt drive. The three-cylinder layout scheme, where the force on the hydraulic cylinder rod was 50…60% less than that on the two-cylinder layout, appeared to be the most expedient. In the second stage, a mathematical model for determining changes in the position of the center of mass of the feller-buncher depending on the inclination angle of the platform was derived. In the third stage, a mathematical model was derived for determining the limiting angle of slope of the terrain when the feller buncher moved up the slope. For this purpose, two calculation schemes were considered when the machine moved up the slope without and with a tilted platform. Zero support reaction on the front roller was taken as the stability criterion. In the fourth stage, a mathematical model for determining the limiting angle of slope of the terrain during the roll of the feller-buncher machine was obtained. In the fifth stage, the efficiency of the application of leveling systems was evaluated. A graph of the dependence of changes in the terrain slope angle on the platform slope angle was plotted, and a regression dependence for an approximate estimate was obtained. A regression analysis was also carried out, and dependencies were obtained to determine the weight of a feller-buncher with a leveling system and the added pressure on the ground caused by the increase in the weight of the base machine. The analysis of platform leveling systems showed the effectiveness of their application in the designs of feller-buncher machines, as it allows the machines to work on slopes with an inclination of 50…60% more than without them.

The Influence of Frame Flexibility on the Lateral Stability of Motorcycles

1974 ◽  
Vol 16 (2) ◽  
pp. 117-120 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Rear Wheel ◽  
Lateral Stability

A mathematical model of a rigid-framed motorcycle running freely is extended to include the effects of torsional flexibility between the rear wheel and the frame.

Extended validation of a ground-based three-axis spacecraft simulator model

2020 ◽  
pp. 095441002093896
Author(s):  
H Sh Ousaloo ◽  
Gh Sharifi ◽  
B Akbarinia
Keyword(s):  
Mathematical Model ◽  
Attitude Control ◽  
Aerodynamic Drag ◽  
Center Of Mass ◽  
Model Development ◽  
Optimization Method ◽  
Experimental Results ◽  
Spacecraft Dynamics ◽  
Detailed Model ◽  
Mass Properties

The ground-based spacecraft dynamics simulator plays an important role in the implementation and validation of attitude control scenarios before a mission. The development of a comprehensive mathematical model of the platform is one of the indispensable and challenging steps during the control design process. A precise mathematical model should include mass properties, disturbances forces, mathematical models of actuators and uncertainties. This paper presents an approach for synthesizing a set of trajectories scenarios to estimate the platform inertia tensor, center of mass and aerodynamic drag coefficients. Reaction wheel drag torque is also estimated for having better performance. In order to verify the estimation techniques, a dynamics model of the satellite simulator using MATLAB software was developed, and the problem reduces to a parameter estimation problem to match the experimental results obtained from the simulator using a classical Lenevnberg-Marquardt optimization method. The process of parameter identification and mathematical model development has implemented on a three-axis spherical satellite simulator using air bearing, and several experiments are performed to validate the results. For validation of the simulator model, the model and experimental results must be carefully matched. The experimental results demonstrate that step-by-step implementation of this scenario leads to a detailed model of the platform which can be employed to design and develop control algorithms.

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