Countersteering to Recover Straight Ahead Running After a Disturbance

2016 ◽  
Author(s):  
Fabio della Rossa ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Degrees Of Freedom ◽  
Rear Axle ◽  
External Disturbance ◽  
Equations Of Motion ◽  
Driver Model ◽  
Steering Wheel ◽  
Non Linear ◽  
Oscillating Motion ◽  
Straight Ahead ◽  
Lateral Excitation

The paper deals with the analysis of a manoeuvre occurring frequently before crashes. Due to an external disturbance the straight ahead running of a vehicle is degradated into an oscillating motion. The driver is required to countersteer to recover the straight ahead motion. The bifurcation analysis of a simple model describing a vehicle+driver running straight ahead is performed. The mechanical model of the car has two degrees of freedom and the related equations of motion contain the non linear tyre characteristics. The driver is described by a non linear model defined by three parameters, namely the gain (steering wheel angle per lateral deviation from desired path), the prevision distance, the reaction time delay. Unreferenced bifurcations are discovered for the understeering vehicle. A supercritical Hopf bifurcation may occur as forward speed is increased. Also tangent (fold) bifurcations occur as the speed (or disturbance) are further increased. The vehicle+driver model is validated by means of a number of tests performed in a track. The validation relies on the identification of driver’s parameters. The track is equipped with a plank sliding laterally when the vehicle rear axle passes on it. Such a lateral excitation applies a disturbance to the vehicle which initiates a spin to be counteracted by the driver. An analysis is performed on driver’s parameters identification. Such parameter identification seems a possible way to assess single driver’s ability to perform recovery manoeuvres.

Straight ahead running of a non linear car and driver model

2016 ◽  
pp. 243-248 ◽  
Author(s):  
F. Delia Rossa ◽  
O. Sukharev ◽  
G. Mastinu
Keyword(s):  
Driver Model ◽  
Non Linear ◽  
Straight Ahead

Comparative Analysis of MacAdam Model and PI Control in a Predictive Driver Model

2021 ◽  
Vol 13 (4) ◽  
Author(s):  
C. Dias ◽  
J. Landre ◽  
P. Americo ◽  
M. Campolina ◽  
L. Marino Marino ◽  
...  
Keyword(s):  
Autonomous Vehicles ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Longitudinal Velocity ◽  
Pi Controller ◽  
Driver Model ◽  
Lateral Acceleration ◽  
Steering Wheel ◽  
Reference Path ◽  
Double Lane Change

Autonomous vehicles are the future of automotive engineering and understanding how this systems work is critical. In these vehicles, controller models are usually needed to generate signals that would normally be imposed by the driver e.g., steering angles, acceleration inputs and braking commands. Intuitively, each control method utilized has its peculiarities and presents different behaviours. In such situation, this paper aims to develop an error comparison between a car displacement and its reference path due the use of two different predictive driver controllers: The proportional-integrative and the MacAdam model. For this purpose, a 14 degrees of freedom vehicle model is used with the aid of MATLAB Simulink, whereas simulations were made using the double-lane change manoeuvre, a commonly used manoeuvre to analyse the vehicle dynamics performance. At the end of this paper, lateral acceleration, displacement and steering wheel angle analysis led the conclusion that the vehicle behaviour is smoother with the use of the proportional-integrative control regardless of longitudinal velocity. Nevertheless, the trajectory error is smaller for MacAdam model than PI controller is and therefore it is easier to follow the reference path with this one, although in aggressive maneuverers it can cause more discomfort and increase the risk of rolling when compared to the PI controller in a vehicle with the same body stiffness.

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

Nonlinear Modeling and Experimental Validation of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

2006 ◽  
Author(s):  
Virgile Ayglon ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Pinion Gear ◽  
Stiffness And Damping ◽  
Vehicle Chassis

This paper describes the model integration and validation that followed the development of nonlinear models of a tire with non-uniformities, a double wishbone suspension and rack-and-pinion power steering. These submodels are integrated to investigate the effects of variation of tire, suspension and steering parameters on the transmission of tire forces acting on the wheel spindle to the steering system and vehicle chassis. The tire model is based on a rigid ring model which includes mass imbalance and balancing mass. The suspension is idealized as rigid links with seven degrees-of-freedom and the bushings are represented by spring-damper elements. The equations of motion are derived using the Lagrange multiplier method in Maple, and solved numerically using Matlab DAE solver. The steering system is idealized as a four degree-of-freedom system and considers motion of the rack, rack housing, pinion gear and steering wheel. Nonlinear compliant friction is considered between the pinion gear / rack, and the steering column / chassis interfaces. The analytical model is used to develop a quantitative measure of the relative importance of the parameters such as mass/inertia, suspension bushing stiffness and damping, torsion bar stiffness and damping, rack friction and damping, to the force transmissibility to the vehicle chassis and the steering system. Experimental results include a modal analysis, a shop-testing and road testing, which are used to cross verify the numerical simulations. The testing shows the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear variation of the nibble phenomenon with vehicle speed and tire imbalance. Results obtained from simulation matches well with the experimental measurements.

Influence of Geometry on the Non-Linear Vibrations of Cylindrical Shells With Internal Flowing Fluid

2010 ◽  
Author(s):  
Zenon J. del Prado ◽  
Paulo B. Gonc¸alves ◽  
Michael P. Pai¨doussis
Keyword(s):  
Cylindrical Shell ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Dynamic Environment ◽  
Geometric Parameters ◽  
Flowing Fluid ◽  
Non Linear ◽  
Linear Vibrations

In this work, the influence of the characteristic geometric parameters of a cylindrical shell, such as radius-to-thickness and radius-to-length ratios, on both the linear and non-linear vibrations of a fluid-filled cylindrical shell with internal flowing fluid is studied. The Donnell non-linear shallow shell equations are used to study a simply supported cylindrical shell subjected to both lateral and axial time-dependent loads with internal flowing fluid. The fluid is assumed to be inviscid and incompressible and the flow isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic and five axisymmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the nonlinear equations of motion which are, in turn, solved by the Runge-Kutta method. First, the parametric linear equations are used to study the influence of geometry and physical properties on the natural frequencies, critical flow and critical circumferential wavenumber. Secondly, numerical methods are used to describe the influence of geometric characteristics on the non-linear frequency-amplitude relations of the shell. The results obtained show the influence of the geometric parameters on the vibration characteristics of the shell and can be used as a basic tool for design of cylindrical shells in a dynamic environment.

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 Geometrical Non-Linear Periodic Vibration of Plates

2000 ◽  
Author(s):  
M. Petyt ◽  
P. Ribeiro
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Internal Resonances ◽  
Resonance Frequencies ◽  
Modal Coupling ◽  
Non Linear ◽  
The Stability

Abstract Periodic, geometrically non-linear free and steady-state forced vibrations of fully clamped plates are investigated. The hierarchical finite element method (HFEM) and the harmonic balance method are used to derive the equations of motion in the frequency domain, which are solved by a continuation method. It is demonstrated that the HFEM requires far fewer degrees of freedom than the h-version of the FEM. Internal resonances due to modal coupling between modes with resonance frequencies related by a rational number, are discovered. In free vibration, internal resonances cause a very significant variation of the mode shape during the period of vibration. A similar behaviour is observed in steady-state forced vibration. The stability of the steady-state solutions is studied by Floquet’s theory and it is shown that stable multi-modal solutions occur.

scholarly journals Research on Curvilinear Motion of Automobile with the Application of On-Board Can Bus Data

2021 ◽  
Vol 23 (3) ◽  
pp. B211-B218
Author(s):  
Hubert Sar ◽  
Mateusz Brukalski ◽  
Krzysztof Rokicki
Keyword(s):  
Degrees Of Freedom ◽  
Rear Axle ◽  
Simulation Models ◽  
Steering Wheel ◽  
Area Network ◽  
Automotive Safety ◽  
The Road ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Computer Simulation Models

Modelling of vehicle’s motion is one of the solutions applied in the research of automotive safety. There is always a discussion which model should be used for computer simulation. Models with higher number of degrees of freedom require identification of many parameters, which are usually difficult to obtain. So, very often relatively simple flat model of vehicle’s motion is applied. It needs only such parameters as mass of a vehicle, location of centre of gravity from front and rear axle, yaw mass moment of inertia and side slip characteristics of the front and rear axle. In this paper the upper mentioned model was applied, considering different side slip characteristics of the front and rear axle. The scenario of vehicle’s motion was based on random changes of steering wheel angle during the road test, recording signals from on-board CAN (Controller Area Network) bus of automobile simultaneously, which were further applied in simulation.

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.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

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