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.     

In-Plane and Out-of-Plane Dynamics of Pneumatic Tyres

During the last decade research has been conducted on the dvnamics of the tvre considered as a vehiclecomponent. Asurvey is given of these developments where tyre mass plays an important role. The underlying theoretical considerations concerning the massless tyre have been discussed as well. Two groups of tyre response have been distinguished: the lateral (out-of-plane) response and the vertical/longitudinal (in-plane) response to motions of the wheel. In both categories tyre compliance, slip and inertia have influence. The dynamic properties of the rolling tyre have been presented in the form of transfer functions and/or differential equations. The frequency of the imposed oscillations is assumed to be below ca. 40 Hz. Non-linear effects and modelling have been briefly touched on.     

A theoretical model of speed-dependent steering torque for rolling tyres

ABSTRACT

It is well known that the tyre steering torque is highly dependent on the tyre rolling speed. In limited cases, i.e. parking manoeuvre, the steering torque approaches the maximum. With the increasing tyre speed, the steering torque decreased rapidly. Accurate modelling of the speed-dependent behaviour for the tyre steering torque is a key factor to calibrate the electric power steering (EPS) system and tune the handling performance of vehicles. However, no satisfactory theoretical model can be found in the existing literature to explain this phenomenon. This paper proposes a new theoretical framework to model this important tyre behaviour, which includes three key factors: (1) tyre three-dimensional transient rolling kinematics with turn-slip; (2) dynamical force and moment generation; and (3) the mixed Lagrange–Euler method for contact deformation solving. A nonlinear finite-element code has been developed to implement the proposed approach. It can be found that the main mechanism for the speed-dependent steering torque is due to turn-slip-related kinematics. This paper provides a theory to explain the complex mechanism of the tyre steering torque generation, which helps to understand the speed-dependent tyre steering torque, tyre road feeling and EPS calibration.     

The Tyre as a Sensor to Estimate Friction

SUMMARY

Continuously updated knowledge of the friction potential and the friction demand can help to improve manoeuvrability and thereby safety of vehicles under slippery road conditions. An on line friction estimation method is presented using a simple brush type tyre model. First the method is verified by outdoor experiments using a tyre test trailer. Then the setup of a low-cost measurement system in a vehicle is discussed and results from both simulations and outdoor experiments are presented. Neural networks have been used both for modelling and identification of friction potential and friction demand.     

A real-time approach to robust identification of tyre–road friction characteristics on mixed-μ roads

ABSTRACT

The interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.     

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.     

Study of the Pneumatic Tyre Behaviour on Dry and Rigid Road by Finite Element Method

SUMMARY

The paper presents a physical tyre model capable of describing the complete pneumatic tyre behaviour during steady and transient states. Given the radial deflection, the longitudinal and lateral slip, the camber angle, the inner pressure and the mechanical parameters describing the tyre structure, the model returns the vertical load, the longitudinal and lateral forces, the self aligning torque. Particular attention has been devoted to the computation (by f.e.m.) of tyre carcass and tread deformations; it is explained how side force increases by moderate braking at constant slip angle. An experimental verification validates the model, although more studies could be needed to improve model effectiveness.     

Investigation of Features of Tyre Rolling at Non-Small Velocities on the Basis of a Simple Tyre Model with Distributed Mass Periphery

SUMMARY

On the basis of the brush-type tyre model the paper considers the interaction between steady-state rolling deformable wheel and flat road surface as well as corresponding force and moment characteristics of the wheel.

At least two zones of sliding, anisotropic dry friction, sliding friction coefficient speed-dependent and instantaneous leap of the friction coefficient when transition from sliding to adhesion zone occurs, have been taken into account, as well as distributed peripheral mass of tyre, elasticity, pseudo-dry friction and damping properties in radial, tangential and lateral directions of the elements at the wheel periphery, including a visco-elastic belt. Vertical force distribution in the contact area is not supposed to be known in advance and follows from the calculation. As a result, sliding zone lengths, distributed forces in contact area, six components of generalized road reaction reduced to the wheel center, and rolling resistance moment are found as functions of vertical load, movement velocity, longitudinal and side slip, friction in contact area with road, stiffnesses, dry friction and damping in the tyre model elements and of distributed peripheral mass.

A computer program developed in Fortran and results of calculations are of particular interest for qualitative analysis including steady rolling of studded tyre and also racing car and aircraft tyres which peripheral mass shows itself in a special way because of great movement velocities.     

Noise,vibration, harshness model of a rotating tyre

ABSTRACT

The tyre plays a fundamental role in the generation of acoustically perceptible driving noise and vibrations inside the vehicle. An essential part of these vibrations is induced by the road excitation and transferred via the tyre into the vehicle. There are two basic ways to study noise, vibration, harshness (NVH) behaviour: Simulations in time and frequency domains. Modelling the tyre transfer behaviour in frequency domain requires special attention to the rotation of the tyre. This paper shows the approach taken by the authors to include the transfer behaviour in the frequency range up to 250?Hz from geometric road excitations to resulting spindle forces in frequency domain. This paper validates the derived NVH tyre model by comparison with appropriate transient simulations of the base transient model.     

Straight-ahead running of road vehicles – analytical formulae including full tyre characteristics

ABSTRACT

During straight-ahead running, the longitudinal axis of road vehicles, notably cars, is not parallel to road axis. This occurrence is general and is due both to road cross slope (road banking) and to tyre characteristics, particularly ply-steer and conicity. In order to describe such a phenomenon, the paper develops a new and relatively simple analytical model. Despite the model is linear, the solution which is provided is exact, since straight-ahead motion occurs with small angles and both the elastokinematics of suspension system and tyre characteristics can be modelled by linearised equations. The Handling Diagram theory is updated and completed by introducing the actual shifts of tyre characteristics. The validation of the analytical expressions is performed by using a MSC Adams^TM full model of a car. A subjective-objective experimental test campaign provides preliminary substantiation of the ability of the derived formulae to describe tyre performance. By means of the unreferenced analytical formulae developed in the paper, we allow, given the vehicle, the proper tyre design specification and vice-versa. In particular, a formula is given to make null the steering torque during straight-ahead driving. The derived analytical formulae may provide a sound understanding of the straight-ahead running of road vehicles.     

Emergency steering control of autonomous vehicle for collision avoidance and stabilisation

ABSTRACT

Collision avoidance and stabilisation are two of the most crucial concerns when an autonomous vehicle finds itself in emergency situations, which usually occur in a short time horizon and require large actuator inputs, together with highly nonlinear tyre cornering response. In order to avoid collision while stabilising autonomous vehicle under dynamic driving situations at handling limits, this paper proposes a novel emergency steering control strategy based on hierarchical control architecture consisting of decision-making layer and motion control layer. In decision-making layer, a dynamic threat assessment model continuously evaluates the risk associated with collision and destabilisation, and a path planner based on kinematics and dynamics of vehicle system determines a collision-free path when it suddenly encounters emergency scenarios. In motion control layer, a lateral motion controller considering nonlinearity of tyre cornering response and unknown external disturbance is designed using tyre lateral force estimation-based backstepping sliding-mode control to track a collision-free path, and to ensure the robustness and stability of the closed-loop system. Both simulation and experiment results show that the proposed control scheme can effectively perform an emergency collision avoidance manoeuvre while maintaining the stability of autonomous vehicle in different running conditions.     

An easy procedure to determine Magic Formula parameters: a comparative study between the starting value optimization technique and the IMMa optimization algorithm

In 2004, a new searching algorithm for Magic Formula tyre model parameters was presented. Now, a summary of the results, for pure and combined slip, that this algorithm is able to achieve is presented. The Magic Formula tyre model needs a set of parameters to describe the tyre properties. The determination of these parameters is dealt with in this article. A new method, called IMMa Optimization Algorithm (IOA), based on genetic techniques, is used to determine these parameters. Here, we show the computational cost that has been used to obtain the optimum parameters of every characteristic of the Magic Formula tyre model, called Delft Tyre 96. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. Hence, to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters (null sensitivity to starting values). The search can be started with a randomly generated set of parameters between [0, 1]. Nowadays, MF-Tool, an application developed by TNO, uses an optimization technique to fit Magic Formula parameters from Matlab toolbox [van Oosten, J.J.M. and Bakker, E., 1993, {Determination of magic tyre model parameters}. Vehicle System Dynamics, 21, 19–29; van Oosten, J.J.M., Savi, C., Augustin, M., Bouhet, O., Sommer, J. and Colinot, J.P., 1999, {Time, tire, measurements, forces and moments, a new standard for steady state cornering tyre testing}. EAEC Conference, Barcelona, 30 June–2 July.]. We refer to that algorithm as the starting value optimization technique. The comparison between the optimization technique employed by TNO and the proposed IOA method is discussed in this article. In order to give a relative idea of adjustment accuracy, the sum-squared error and the mean-squared error, from the curves of the tyre model with the parameters optimized by both applications compared with test data are evaluated.     

Analysis of wheel speed vibrations for road friction classification

ABSTRACT

With higher level of vehicle automation, it becomes increasingly important to know the maximum possible tyre forces during normal driving. An interesting method in this respect is estimating the tyre–road friction from the resonance peak in the wheel speed signal, excited by road roughness. A simulation environment using the MF-Swift tyre model is proposed, which gives insight in the correctness and functioning of this method. From implementing the estimation algorithm and considering the tyre torsional vibration system, it is concluded that frequencies and damping ratios can be estimated with reasonable accuracy and that the trends observed with changing road friction are consistent. Furthermore, the proposed simulation environment gives opportunity to investigate other issues like robustness of the estimation method to road roughness. Additionally, the tyre modelling aspect of the estimation method is analysed and improvements are proposed.     

An Evaluation of Passive Automotive Suspension Systems with Variable Stiffness and Damping Parameters

SUMMARY

Passenger discomfort, suspension working space and dynamic tyre loading parameters are calculated for different combinations of spring stiffness and damping coefficient representing the suspension system in a quarter car model subject to realistic random disturbance inputs from roads of widely differing quality. Sprung and unsprung masses and the tyre vertical stiffness and damping coefficient employed derive from a current production car. Designs which are best for the specific conditions represented are identified and their performance properties in other (off-design) conditions are considered, and conventional design is explained as the inevitable consequence of the need to compromise if fixed suspension parameters are used. Performance improvements possible if variable parameters can be employed are evaluated as a function of the ranges of variability provided, and a stratagem for controlling parameters is proposed.     

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.     

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.