Static Turning Analysis of Vehicles Subject to Externally Applied Forces - A Moment Arm Ratio Formulation

A formulation for representing the static turning response of a two-axle vehicle due to applied external or control forces is expressed in terms of a simple ratio of two distances along the vehicle longitudinal axis. The two distancescoincide with points on the vehicle at which externally applied/ control forces and their reactive inertial forces act with respect to the vehicle neutral steer point. The resulting formulation is equivalent to the rotational equilibrium equation written with respect to the neutral steer point. The method allows a simple “visual analysis” of the steady turning process by showing how key forces and associated moment arms can change with respect to one another due to vehicle modifications or different operatingconditions, thereby affecting the static turning response of the vehicle.     

On Inverse Equations for Vehicle Dynamics

Abstract

Instead of writing equations which when solved yield the response of a vehicle to an input such as the front wheel steer angle, one can often invert the equations so that a response quantity is specified as an input and a new set of equations is solved yielding the steer angle required as an output. Using these equations one can discover the input steer angle a driver would need to impose in order to accomplish a specific maneuver for various vehicles.

It is shown that there are many possible inverse equation sets and that the eigenvalues of the inverse equations are hard to interpret since they may have little to do with the vehicle parameters. The linear single-input single-output case is studied first to fix ideas using a simple example. For the bicycle model vehicle, it is shown that any vehicle may have unstable inverse equations depending upon the response quantity used. Extensions to nonlinear and multiple-input multiple output systems are discussed.     

Roll Plane Analysis of Articulated Tank Vehicles During Steady Turning

SUMMARY

The rollover immunity levels of articulated tank vehicles with partial loads are investigated. A static roll plane model of the articulated vehicle employing partially filled cylindrical tank is developed. The vertical and lateral translation of the liquid cargo due to vehicle roll angle and lateral acceleration, encountered during steady turning, are evaluated. The roll moments arising from vertical and lateral translation of the liquid cargo are determined and incorporated in the roll plane model of the vehicle. The adverse influence of the unique interactions of the liquid within the tank vehicle, on the rollover limit of the articulated vehicle is demonstrated. The influence of compartmenting of the tank on the steady turning roll response of the vehicle is analyzed, and an optimal order of unloading the compartmented tank is discussed.     

Impact of Dynamic Fluid Slosh Loads on the Directional Response of Tank Vehicles

SUMMARY

A comprehensive directional dynamics model of a tractor-tank trailer is developed by integrating a non-linear dynamic fluid slosh model to the three-dimensional vehicle dynamics model. The nonlinear fluid slosh equations are solved in an Eulerian mesh to determine dynamic fluid slosh loads caused by the dynamic motion of the vehicle. The dynamic fluid slosh forces and moments are coupled with the vehicle dynamics model to study the directional response characteristics of tank vehicles. The directional response characteristics of partially filled tank vehicles employing dynamic slosh model are compared to those employing quasi-dynamic vehicle model, for steady as well as transient directional maneuvers. Simulation results reveal that during a steady steer maneuver, the dynamic fluid slosh loads introduce oscillatory directional response about a steady-state value calculated from the quasi-dynamic vehicle model. The directional response characteristics obtained using the quasi-dynamic and dynamic fluid slosh models during transient steer inputs show good correlation. Based on this study, it can be concluded that the quasi-dynamic model can predict the directional response characteristics of tank vehicles quite close to that evaluated using the comprehensive fluid slosh model.     

Stationar- und Ubergangsverhalten von Sattel- und Lasttugen bei der Kreisfahrt: Lineare Berechnungen

ABSTRACT

Steady and Transient Turning of Tractor-Semitrailer and Truck-Trailer Combinations: A Linear Analysis

A simplified analysis is made of the yaw stability and control of the two types of the commercial vehicle combinations (tractor-semitrailer, truck-trailer) at a constant forward velocity during steady and transient turning. The combined vehicle is treated as a linear dynamic system (Fig. 2). The steer angle at the front wheels of the tractor (or truck) and the steady-state responses if the road verhicle train (yaw rate, articulation angles and sideslip angle) are calculated (Equations 18 to 25). Exploratory calculations are performed to determine the influence of the cornering stiffness of the tires for the two types of the vehicle combinations upon the steady-state responses (Figs. 7 to 10). For a linear simplified model of articulated vehicle the steady-state turning behaviour is stable also under conditions of rather high driving speed (70 km/h). A simplified analysis of the transient turning behaviour of the two types of road trains has shown the tractor-semitrailer to preserve stability even under driving speeds exceeding 70 km/h (Fig. 13), whereas the truck-trailer combinations appear to become oscillatory unstable if the driving speed rises above the 60 km/h margin (Fig. 14).     

Influence of Liquid Load Shift on the Dynamic Response of Articulated Tank Vehicles

SUMMARY

The influence of the lateral load shift on the dynamic response characteristics of an articulated tank vehicle is investigated assuming inviscid fluid flow conditions. A quasi-dynamic roll plane model of a partially filled cleanbore tank of circular cross-section is developed and integrated to a three-dimensional model of the articulated vehicle, assuming constant forward speed. The destabilizing effects of liquid load shift are studied by comparing the directional dynamics of the partially filled tank vehicle to that of an equivalent rigid cargo vehicle subject to steady steer input. Dynamic response characteristics demonstrate that the stability of a partially filled tank vehicle is adversely affected by the Liquid load shift The distribution of cornering forces caused by the liquid load shift yield considerable deviation of the path followed by the liquid tank vehicle. The influence of the vehicle speed on the dynamics of the liquid tank vehicle is also investigated for variations in the fill levels and fluid density.     

Force control for path following of a 4WS4WD vehicle by the integration of PSO and SMC

The aim of this paper is to present a novel control method for a four-wheel steer and four-wheel drive (4WS4WD) vehicle. The novelty is in the integration of sliding mode control (SMC) and particle swarm optimization (PSO) that is proposed to solve the control problem caused by the nonlinear, highly coupled and over-actuated characteristics of the four-wheel steer and four-wheel drive (4WS4WD) vehicle. The validity of the control method is evaluated by two criterions, namely path following performance assessed by the vehicle's position errors with respect to the reference path, and motion quality reflected by the smoothness of vehicle's velocities and accelerations. In vehicle modelling, a kinematic model and a dynamic model considering all slip forces are proposed for the controller design. Simulation results are provided to demonstrate the applicability of the proposed methodology and its robustness.     

A Full-Car Roll Model of a Vehicle with Controlled Suspension

SUMMARY

The full-car roll model of a vehicle suspension with static and dynamic control (using wheel, body and seat) is described by means of vertical and lateral input for both static and dynamic states. It is shown that the control deteriorates the static performance of the vertical response and improves the performance of the lateral response.     

Vibrations Generated by Rail Vehicles: A Mathematical Model in the Frequency Domain

Movement of railway vehicles generates mechanical vibrations of a wide range of frequency. Depending on track materials, dissipation in form of viscous and hysteretic damping is present, and stiffness depends on strain-rate. In a previous paper (Castellani et al., 1998), a mathematical model to describe track materials has been developed in the frequency domain. The present paper applies this model, and attempts an analytical formulation of vehicle-track and soil interaction in the frequency domain. Rail vibrations during the passage of a vehicle are generated by three families of forces: a) the weight of the moving vehicle, b) the inertial reaction of the vehicle under the effect of corrugations over an undeformable rail, and, c) the vehicle inertial forces due to displacements of the rail. The first two groups of forces do not depend on the rail displacement, and the related mathematical formulation is a simple problem of forces at a mobile point of application. Formulation of the vehicle inertial forces, related to the rail vibration, requires reference to the acceleration of the rail, as seen by an observer in motion with the vehicle itself. Moreover, it is necessary to express the equilibrium equation of two dynamic systems, the vehicle and the track, at a the movable point of contact. There is no straight numerical procedure to solve this equation in the frequency domain. In the paper two theoretical propositions (Fryba, 1988; Grassie et al., 1982) are revisited with reference to the effect of the transit of a single wheel. Fryba infers that, in the absence of corrugations, the forces c) are null. Grassie et al. (1982) present a mathematical formulation of the interaction between wheel and rail, at mobile point of contact. At each position, the interaction force is of impulsive type. They presume that for a corrugation of harmonic type, of wavelength ?, the wheel is subject to a harmonic motion, of the frequency f = V/?, where V is the wheel velocity. All other frequency components, due to the impulse, are disregarded. Both these assumptions are shown to be inconsistent from a theoretical point of view, however they suggest suitable approaches to the solution.     

Design of Optimal Four-Wheel Steering System

SUMMARY

Optimal design of the four wheel steering (4WS) system of the ground vehicle is studied. 4WS vehicles with the optimal control scheme are considered first. General formulation of the optimal control law is developed based on the linear quadratic regulator theory. The vehicle speed function (VSF) based 4WS vehicle with a simple feedback controller is considered as a special case of the optimal system. Two new designs of the VSF 4WS system are proposed and their performances are compared with the optimal 4WS systems and the existing VSF 4WS system. The first system is designed for the maximum stability while the second system is designed to emulate the response of the optimal 4WS vehicle. Advantages of the new VSF designs are discussed.     

Simplified Analysis of Steady-state Turning Behaviour of Motor Vehicles. Part 1. Handling Diagrams of Simple Systems.

An approximate method is presented which produces a handling diagram useful for the study of steady-state turning behaviour at different values of steer angle, path radius and speed In three successive parts the steady state response of simple and more elaborate vehicle models and the stability of the resulting motion are discussed.     

Effect of Traction Force Distribution Control on Vehicle Dynamics

SUMMARY

The purpose of this study is to clarify vehicle dynamics effected by traction force distribution, not only between the front and rear wheels but also between the left and right wheels. Contribution of traction force distribution to vehicle turning performance was investigated using a mathematical simulation and an experimental vehicle. The results indicates that the control of traction control distribution between the left and right wheels greatly influences vehicle turning characteristics and improve the performance even in a marginal turning condition.     

Rail Vehicles' Riding Quality and Comfort Related to Theoretical and Experimental Optimization Application to High Speed Trains

SUMMARY

The literature concerned with road damage caused by heavy commercial vehicles is reviewed. The main types of vehicle-generated road damage are described and the methods that can be used to analyse them are presented. Attention is given to the principal features of the response of road surfaces to vehicle loads and mathematical models that have been developed to predict road response. Also discussed are those vehicle features which, to a first approximation, can be studied without consideration of the dynamics of the vehicle, including axle and tyre configurations, tyre contact conditions and static load sharing in axle group suspensions. The main emphasis of the paper is on the dynamic tyre forces generated by heavy vehicles: their principal characteristics, their simulation and measurement, the effects of suspension design on the forces and the methods that can be used to estimate their influence on road damage. Some critical research needs are identified.     

Semi-Active Attitude and Vibration Control

SUMMARY

The paper discusses the attitude and vibration control of a passenger car on the basis of a full vehicle model. The analysis presented consists of two parts: (I) The introduction of a newly developed semi-active anti-roll/pitch system, (ii) An example of an actively suspended full vehicle model using a simple control strategy to improve ride comfort. The attitude control using semi-actively generated compensation forces prevents the car from rolling in curves and pitching during braking or accelerating. The strength of the system is the small energy consumption. The performance of the combination of both attitude and vibration control can compete with a fully active suspension system.     

Vehicle Dynamic Control for In-Wheel Electric Vehicles Via Temperature Consideration of Braking Systems

?Vehicle dynamic control (VDC) systems play an important role with regard to vehicle stability and safety when turning. VDC systems prevent vehicles from spinning or slipping when cornering sharply by controlling vehicle yaw moment, which is generated by braking forces. Thus, it is important to control braking forces depending on the driving conditions of the vehicle. The required yaw moment to stabilize a vehicle is calculated through optimal control and a combination of braking forces used to generate the calculated yaw moment. However, braking forces can change due to frictional coefficients being affected by variations in temperature. This can cause vehicles to experience stability problems due an improper yaw moment being applied to the vehicle. In this paper, a brake temperature estimator based on the finite different method (FDM) was proposed with a friction coefficient estimator in order to solve this problem. The developed braking characteristic estimation model was used to develop a VDC cooperative control algorithm using hydraulic braking and the regenerative braking of an in-wheel motor. Performance simulations of the developed cooperative control algorithm were performed through cosimulation with MATLAB/Simulink and CarSim. From the simulation results, it was verified that vehicle stability was ensured despite any changes in the braking characteristics due to brake temperatures.     

I. Minutes of the IAVSD Board Meetings

SUMMARY

A theoretical analysis is presented to model a hydromechanical, semi-active suspension system, first as a single wheel station and then as fitted to each wheel of an off-road vehicle. Predicted results show that two benefits are obtained by comparison with the equivalent passive system. First, vehicle attitude is controlled for changes in body forces arising from static loads or braking/cornering inputs. Second, a significant improvement in ride comfort is obtained because low suspension stiffnesses can be used.     

Direct yaw moment control and power consumption of in-wheel motor vehicle in steady-state turning

Driving force distribution control is one of the characteristic performance aspects of in-wheel motor vehicles and various methods have been developed to control direct yaw moment while turning. However, while these controls significantly enhance vehicle dynamic performance, the additional power required to control vehicle motion still remains to be clarified. This paper constructed new formulae of the mechanism by which direct yaw moment alters the cornering resistance and mechanical power of all wheels based on a simple bicycle model, including the electric loss of the motors and the inverters. These formulation results were validated by an actual test vehicle equipped with in-wheel motors in steady-state turning. The validated theory was also applied to a comparison of several different driving force distribution mechanisms from the standpoint of innate mechanical power.     

Validation of an Articulated Vehicle Simulation

SUMMARY

Tests were performed on a typical UK articulated vehicle to measure dynamic tyre forces and sprung mass accelerations. The measured road profile data and vehicle response data are used to determine some of the important characteristics of articulated vehicle vibration behaviour. In particular, roll motions and their effect on dynamic tyre forces are examined. The measured data are used to validate two and three-dimensional computer models of the vehicle. Attention is given to modelling the tandem leaf-spring trailer suspension. The conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.     

DISCUSSION NOTE on Karnopp's article “Active Damping in Road Vehicle Suspension Systems”

SUMMARY

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.