scholarly journals Vehicle Response to Kinematic Excitation, Numerical Simulation Versus Experiment

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 678
Author(s):  
Jozef Melcer ◽  
Eva Merčiaková ◽  
Mária Kúdelčíková ◽  
Veronika Valašková
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Statistical Characteristics ◽  
Kinematic Excitation ◽  
The Road ◽  
Characteristic Points ◽  
Dynamic Components ◽  
Digital Levels

The article is devoted to the numerical simulation and experimental verification of a vehicle’s response to kinematic excitation caused by driving along an asphalt road. The source of kinematic excitation was road unevenness, which was mapped by geodetic methods. Vertical unevenness was measured in 0.25 m increments in two longitudinal profiles of the road spaced two meters apart with precise leveling realized by geodetic digital levels. A space multi-body computational model of a Tatra 815 heavy truck was adopted. The model had 15 degrees of freedom. Nine degrees of freedom were tangible and six degrees of freedom were intangible. The equations of motion were derived in the form of second-order ordinary differential equations and were solved numerically by the Runge–Kutta method. A custom computer program in MATLAB was created for numerical simulation of vehicle movement (eps = 2−52). The program allowed simulation of quantities such as deflections, speeds, accelerations at characteristic points of the vehicle, and static or dynamic components of contact forces arising between the wheel and the road. The response of the vehicle (acceleration at characteristic points) at different speeds was experimentally tested. The experiment was numerically simulated and the results were mutually compared. The basic statistical characteristics of experimentally obtained and numerically simulated signals and their power spectral densities were compared.

Optimization of the characteristic angles of both front and rear McPherson suspensions on a circular track using multi-body numerical simulation

2009 ◽  
Vol 223 (9) ◽  
pp. 1119-1132 ◽  
Author(s):  
G Virzì Mariotti ◽  
G Ficarra
Keyword(s):  
Numerical Simulation ◽  
Contact Forces ◽  
Roll Motion ◽  
The Road ◽  
Virtual Vehicle ◽  
Circular Track ◽  
Characteristic Values ◽  
Optimal Values ◽  
Multi Body

The research reported in this paper aims to simulate the road-holding of a virtual vehicle using multi-body simulation to estimate both the contact forces between the tyre and ground and the roll motion when cornering. Furthermore, the effect of the characteristic angles on the variation in the forces of the tyre in contact with the ground is studied to determine optimal values for these angles. Emphasis is placed on an average-class vehicle, of which both the external dimensions and mass are chosen appropriately, with a McPherson suspension mounted on both the front and the rear. The characteristic values of the camber and toe-in angles, in both the front and the rear, are optimized for motion in the curve under constant traction. The results of numerical simulation are compared with results from the theory of stability in the curve (given the vertical configuration of the vehicle).

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

Computer Simulation of the Response of a Railway Vehicle Carbody

2002 ◽  
Author(s):  
M. Senthil Kumar ◽  
P. M. Jawahar
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Lateral Stiffness ◽  
Lateral Vibration ◽  
Kutta Method ◽  
Nonlinear Mathematical Model ◽  
Rail Vehicle ◽  
Runge Kutta Method

In this paper, a nonlinear mathematical model has been constructed by deriving the equations of motion of a Rail Vehicle carbody using Newton’s law. The nonlinear formula is used to evaluate the wheel rail contact forces. The nonlinear profile of wheel and rail are taken into account. Also the lateral stiffness of the track is taken into consideration. The equations of motion are derived for (a) Carbody with conventional wheelset (b) Carbody with unconventional wheelset (independently rotating wheels). For lateral vibration, 17 degrees of freedom are considered. The degrees of freedom represent lateral and yaw movements of 4 wheelsets and lateral, yaw and roll movements of the bogie and carbody. These equations of motion are transformed into a form suitable for numerical differential equation by Runge Kutta method. In the interest of computing economy, certain approximations have been introduced for calculating the creep forces. Sample results are given for a model of a typical railway vehicle used by the Indian Railways. The lateral dynamic response of the railway vehicle carbody for both conventional and unconventional wheelset has been analysed.

scholarly journals Sources of kinematic excitation of vehicle

2020 ◽  
Vol 310 ◽  
pp. 00005
Author(s):  
Eva Merčiaková
Keyword(s):  
Numerical Simulation ◽  
Moving Load ◽  
Load Effect ◽  
Kinematic Excitation ◽  
The Road

The road unevenness represents the main source of kinematic excitation of vehicle. During the process of solving the problem of vehicle road interaction the road unevenness represents the input value. The unevenness must be mapped, mathematically described and then used as an input value for numerical simulation of moving load effect on pavements. The submitted paper is dedicated to the description of such procedures.

scholarly journals Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

2014 ◽  
Vol 1 (2) ◽  
pp. 77 ◽  
Author(s):  
Mohamed A Omar
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Dynamic Equations ◽  
Solution Stability ◽  
Simulation Code ◽  
Tracked Vehicles ◽  
Main System ◽  
6 Degrees Of Freedom

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system.  The proposed self-contained modular approach could be interfaced to any exiting multibody simulation code without need to alter the existing solver architecture.  Each track is modeled as a super-component that can be treated separate from the main system.  The super-component can be efficiently used in parallel processing environment to reduce the simulation time.  In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF).  To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection.  The spatial algebra operator is used to express the motion quantities and develop the link’s nonlinear kinematic and dynamic equations of motion.  The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules.  Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties.  The interaction forces are expressed in the Cartesian system, applied to the link’s equation of motion and the corresponding bodies in the main system.  For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach.

Assessing the influence of the road-tire friction coefficient on the yaw and roll stability of articulated vehicles

2018 ◽  
Vol 233 (12) ◽  
pp. 2987-2999 ◽  
Author(s):  
André de Souza Mendes ◽  
Agenor de Toledo Fleury ◽  
Marko Ackermann ◽  
Fabrizio Leonardi ◽  
Roberto Bortolussi
Keyword(s):  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Convergence Region ◽  
The Road ◽  
Articulated Vehicles ◽  
Tire Friction

This article addresses the yaw stability of articulated vehicles by assessing the influence of the road-tire friction coefficient on the convergence region of a particular equilibrium condition. In addition, the boundaries of this region are compared to the boundaries of the non-jackknife and non-rollover regions to distinguish the instability phenomenon, jackknife or roll-over, responsible for this delimitation. The vehicle configuration considered in this analysis is composed by one tractor unit and one towed unit connected through an articulation point, for instance, a tractor-semitrailer combination. A nonlinear articulated bicycle model with four degrees of freedom is used together with a nonlinear lateral force tire model. To estimate the convergence region, the phase trajectory method is used. The equations of motion of the mathematical model are numerically integrated for different initial conditions in the phase plane, and the state orbits are monitored in order to verify the convergence point and the occurrence of instability events. In all cases, the longitudinal force on each tire, such as traction and braking, is not considered. The results show the existence of convergence regions delimited only by jackknife events, for low values of the friction coefficient, and only by rollover events, for high values of the friction coefficient. Moreover, the transition between these two conditions as the friction coefficient is changed is graphically presented. The main contributions of this article are the identification of the abrupt reduction of the convergence region as the value of the friction coefficient increases and the distinction of the instability events, jackknife or rollover, that define the boundaries of the convergence region.

Development of a Non-Linear Model of a Double Wishbone Suspension for the Characterization of Force Transmission to the Steering Column and Chassis

2004 ◽  
Author(s):  
Vinod Cherian ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Numerical Simulation ◽  
Linear Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Force Transmission ◽  
Non Linear ◽  
Tire Forces ◽  
Vehicle Chassis

A non-linear model of a double wishbone suspension is developed to investigate the effects of variation of suspension parameters on the transmission and distribution of tire forces acting on the wheel spindle to the steering system and the vehicle chassis. The suspension is idealized as a four degree-of-freedom model, with suspension members considered as rigid links and the bushings idealized as linear spring-damper elements. Degrees-of-freedom representing the longitudinal compliance of the suspension mounting bushings, steering and the rotation of the control arms are considered. The equations of motion are derived using the Lagrange multiplier method, and solved numerically using MATLAB. A system of relative co-ordinates is used to reduce the number of equations due to the large number of geometric and kinematic constraints for an efficient numerical simulation. The equations retain all the non-linearity’s associated with large changes in the geometric configuration of the suspension system. The analytical model can be used to develop a quantitative measure of the importance of the parameters such as mass, inertia of the control arms, suspension bushing stiffness and damping and spatial geometry of installation to the force distribution and force transmissibility to the vehicle chassis and the steering system. The results of numerical simulation are compared with simulation data obtained from ADAMS.

scholarly journals Development of the Lower Extremity Exoskeleton Dynamics Model Using in the Task of the Patient Verticalization

2021 ◽  
Vol 2096 (1) ◽  
pp. 012042
Author(s):  
M R Saypulaev ◽  
Yu Yu Zuev ◽  
G R Saypulaev
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lower Extremity ◽  
Degrees Of Freedom ◽  
Sagittal Plane ◽  
Equations Of Motion ◽  
Viscous Friction ◽  
Dynamics Model ◽  
Supporting Surface ◽  
The Right

Abstract The object of the study is an exoskeleton of the lower extremities with a rigid structure of the power frame, which has 7 degrees of freedom. The movement of the exoskeleton in the sagittal plane is considered with the assumption of symmetrical movement of the right and left legs. The aim of the study is to develop a mathematical model of the dynamics of the exoskeleton, taking into account the forces of viscous friction in the joints. The equations of motion are obtained under the condition that there is no slippage of the points of contact with the supporting surface. Based on the results of numerical simulation, the control moments were obtained, which must be created by the drives to provide program movement.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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