Shear Force Development by Pneumatic Tyres in Steady State Conditions: A Review of Modelling Aspects

SUMMARY

Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems.

The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the behaviour of a particular tyre.

Conclusions relate to the structural and frictional mechanisms present in the shear force generation process, the contributions of carcass and tread elastic properties and of geometrical and frictional factors to the determination of the distributions of force through the contact region, the relationship between accuracy and computational load and the selection of methods for modelling tyre forces in a road vehicle dynamics context. Reference to the most pertinent literature in the field is made and possibilities for the further development of the state of the art are mentioned.     

Identification Methods for Vehicle System Dynamics

SUMMARY

The paper presents a survey on parameter identification techniques for complex vehicle models. In order to cope with the complexity of the model, the information on the system available from the equations of motion has to be included in the identification process. Basic methods for the solution of this problem are shown. The application of the approach is demonstrated by identification of the vertical automobile dynamics. It is concluded that the presented techniques will become more important with increasing applications of theoretical modeling in vehicle system dynamics.     

The Lateral Dynamics of Motorcycles and Bicycles

SUMMARY

The paper is a review of the state of knowledge and understanding of the steering behaviour of single-track vehicles, with the main accent on vehicle design, and vehicle design analysis and behaviour prediction.

The body of the paper consists of a chronological account of the steps which have been taken in establishing the current position. Scientific study of the motions of two-wheelers has been in progress for more than 100 years, but progress was slow and many conflicting conclusions were drawn until increasing understanding of tyre mechanics, systematic application of the laws of motion for systems of rigid bodies, digital computation and modern numerical methods, and improved mobile measurement, recording, and data processing capabilities allowed the pace to accelerate.

The current position, which is that a good understanding of the relationship between design and performance has been achieved, but that by no means have all the problems of significance been solved, is described at the end of the paper.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Abstract

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

Abstract

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

Solution of the Multiple Wheel and Rail Contact Dynamic Problem

SUMMARY

An unconventional method for calculating the forces developing in the wheel and rail contact patches of a railway vehicle has been implemented at the New Technology Laboratory of INRETS. It takes into account the elastic deformations of the materials in the Hertzian elliptical contact areas; the possibility of having simultaneously several contact patches on each wheel, is introduced in the simulation of the dynamic phenomena.

The theory is applied for a high speed bogie running on a perfectly straight track.     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Vehicle Motion Analysis in Relation to Vehicle Safety

SUMMARY

The influence of vehicle handling on the possible avoidance of accident situations is discussed. lit is shown that accident reconstruction at present does not provide the necessary information to relate the cause of accidents to the lack of road worthiness of vehicles. It follows that the vehicle behavior in proximity of its performance limit must be determined in order to infer its accident avoidance potential.

The paper presents a review of the state-of-the-art of vehicle modeling, simulation of vehicle maneuvers and full scale testing. The application of the direct method of the stability theory is suggested as a possible means of obtaining performance limit envelopes which are necessary for establishing standards of the performance of vehicles.     

Hybrid Laboratory Test Method for Anti-Lock Systems

SUMMARY

Railway vehicles with steered axles possess some unique dynamic characteristics. This paper reviews the reasons for the differences between these and more conventional vehicles and examines the results of analysis demonstrating the sensitivity of the phenomena to various mass, stiffness and geometric parameters. The implications which these results carry are discussed in terms of their design importance and their effect upon the performance boundaries of steel-wheeled rail vehicles. This review shows that a profound understanding of steered axle railway vehicles is developing and that this leads to the conclusion that a wide range of applications can benefit from their use.     

A Comparison of Various Computer Simulation Models for Predicting the Directional Responses of Articulated Vehicles

SUMMARY

This paper presents the results of a comparative study of the predictions, made using computer simulation models of different levels of complexity, of the directional responses of commercial articulated vehicles in steady-state and lane-change maneuvers. The differences in the predictions obtained using various models are examined and are compared with available experimental data. The objective of this study is to compare the capabilities and limitations of various simulation models for predicting the directional behavior of articulated vehicles.     

Prescribed Trajectory Vehicle Model

SUMMARY

The paper provides a comprehensive survey of active railway suspensions, covering both basic concepts and significant practical implications around the world. A critical review of technological opportunities, both current and future, is included, and the final section takes a speculative look at long term trends.     

Nonlinear Lateral and Yaw Dynamics and Stability of Snow mobiles

SUMMARY

This paper takes a close look at the mechanism of locomation in snowmobiles. A mathematical model is developed taking into account the inherent nonlinearities of the system. A piece-wise linear approach is presented. A nonlinear methodology is used to construct stability maps for the yaw dynamics. The strategy can be extended to assess the stability in lateral slip of the snowmobile when negotiating a turn. The developed models and strategies are useful design tools for a wide class of snowmobiles.     

Optimal Preview Control of Rear Suspension Using Nonlinear Neural Networks

SUMMARY

The performance of neural networks to be used for identification and optimal control of nonlinear vehicle suspensions is analyzed. It is shown that neuro-vehicle models can be efficiently trained to identify the dynamical characteristics of actual vehicle suspensions. After trained, this neuro-vehicle is used to train both front and rear suspension neuro-controllers under a nonlinear rear preview control scheme. To do that, a neuro-observer is trained to identify the inverse dynamics of the front suspension so that front road disturbances can be identified and used to improve the response of the rear suspension. The performance of the vehicle with neuro-control and with LQ control are compared.     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

SUMMARY

A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis.

Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are calculated, and the implications are discussed.

It is concluded that typical levels of structural compliance in models (a) and (c) contribute significantly to the steering behaviour properties of large motorcycles, and their observed behaviour can be understood better in terms of the new results than of those existing previously. Some conclusions relating to optimal structural stiffness properties are also drawn.     

Development and Evaluation of Vehicle Simulation Models for a 4WS Application

SUMMARY

In the scope of the European Prometheus project a passenger car with active rear wheel steering was developed by TNO in cooperation with PSA. During development and engineering of the rear wheel steering system simulation tools have been used to reduce development costs. This paper describes the evaluation of different simulation models, from simple to complex, with results of full vehicle driving tests. The optimal balance for model complexity and accuracy was achieved with a 2-dimensional model with an added roll degree of freedom. The results show that validation using time responses can give ambiguous and inaccurate results, and that frequency response functions are much more usable in validation.     

Ride Vibration Measurements of Agricultural Tractor and Trailer Combinations

SUMMARY

Tractor ride vibration levels have been measured when operating with and without a two wheel (2W) unbalanced and a four wheel (4W) balanced trailer. Measurements were made in the vertical, pitch, longitudinal and roll directions with the trailers unladen and laden over four typical farm surfaces

The results showed that tractor ride vibration levels were usually increased in all directions-particularly the longitudinal direction- when operating with the laden trailers. But for the unladen trailers, they were increased only in the longitudinal direction. Predominant tractor frequencies tended to be lower with the trailers attached, and coupling between the tractor longitudinal, vertical, roll and pitch co-ordinates was generally increased

Comparisons of the results with the trends predicted by a simplified theoretical model of a tractor and 2W trailer, suggested that the model should be extended to include, (a) the roll direction, (b) more realistic ground inputs, and (c) a 4W trailer     

Human Control of Road Vehicles

SUMMARY

This paper reviews the present state of knowledge of human control of road vehicles. Lateral and longitudinal control of motorcycles and automobiles are discussed, whenever information is available. Although knowledge has increased greatly in the last decade, the major part of this concerns lateral control and most is of an ad hoc nature. Adequate mathematical models for longitudinal motion of the vehicle are yet to be developed. Their development is a necessary step in the attainment of a complete understanding of longitudinal control.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Controller Development and Evaluation

SUMMARY

Due to increased traffic congestion and travel times, research in Advanced Vehicle Control Systems (AVCS) has focused on automated lateral and headway control. Automated vehicles are seen as a way to increase freeway capacity and vehicle speeds while reducing accidents due to human error. Recent research in automated lateral control has focused on vehicle control during low-g maneuvers. To increase safety, automated lateral controllers will need to recognize and react to emergency situations.

This paper investigates the effects of vehicle and tire model order on the response of automated vehicles to an emergency step lane change using a controller based on linear vehicle and tire models. From these studies it is concluded that control strategies based solely on linear vehicle and tire models are inadequate for emergency vehicle maneuvers.

A strategy is then proposed to automatically control vehicles through emergency maneuvers. Here the response of a nonlinear vehicle model is used with a linear state model to optimize controller gains for nonlinear maneuvers. An emergency step lane change is used as a preliminary test of the method.