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.

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.

The dynamics and design of a non-linear vibration absorber

1993 ◽  
Vol 207 (6) ◽  
pp. 363-374 ◽  
Author(s):  
D H Gonsalves ◽  
R D Neilson ◽  
A D S Barr
Keyword(s):  
Numerical Simulation ◽  
Equations Of Motion ◽  
Resonance Peak ◽  
Vibration Absorber ◽  
Linear Vibration ◽  
Frequency Range ◽  
Non Linear ◽  
Experimental Rig ◽  
Auxiliary Mass

This paper presents the design of an efficient non-linear vibration absorber. The system comprises a linear absorber with the addition of a spring between the two masses, which contacts the absorber mass when its displacement exceeds a certain value. The addition of this snubber stiffness facilitates a reduction in the amplitude of the second resonance peak of the linear absorber, which therefore enables the system to be operated over a wider frequency range without reaching larger amplitudes. The modification also has the effect of attenuating the response of the auxiliary mass. The equations of motion for the system are presented and optimization is carried out. A description of an experimental rig that was built follows. The results from the rig are compared with those from numerical simulation and show good correlation.

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.

scholarly journals Extension of modal reduction methods to non-linear coupled structure-acoustic problems

2011 ◽  
pp. 227-245
Author(s):  
Youssef Gerges ◽  
Emeline Sadoulet-Reboul ◽  
Morvan Ouisse ◽  
Noureddine Bouhaddi
Keyword(s):  
Numerical Simulations ◽  
Linear Model ◽  
Elastic Plate ◽  
Degrees Of Freedom ◽  
Reduction Method ◽  
Static Response ◽  
Acoustic Cavity ◽  
Modal Reduction ◽  
Non Linear ◽  
Reduction Methods

This paper proposes a robust reduction method dedicated to non-linear vibroacoustic problems in the context of localized geometrical non-linearities. The method consists in enriching the truncated uncoupled modal basis of the linear model by a static response due to unit forces on the non-linear degrees of freedom and by the static response of the fluid due to the interaction with the structure. To show the effectiveness of the proposed method, numerical simulations of responses of an elastic plate closing an acoustic cavity and a hang-on exhaust are performed.

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.

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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document