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

SUMMARY

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.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

轮胎垂直振动动力学模型

本文提出一种自适应轮膜模型参数的简易测定方法，给出轮胎垂直振动动力学方程及相应的求解方法，并进行计算分析与试验测定。将分析结果与通常的点接触式模型相比较，对点接触式模型及本文所建立的自适应模型做了综合评价，结果表明，本模型的计算结果是令人满意的。     

Vehicle-Generated Road Damage: A Review

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.     

A study on the effect of different tyre imperfections on steering wheel vibration

Multibody dynamics and tyre models have made possible detailed analysis not only for ride and handling, but also for determining their effects on tyre nonuniformities. The aim of this paper is to analyse the steering wheel vibration, both shimmy and shake, excited by different tyre imperfections by using the commercial simulation package ADAMS/car 2005R2 and FTire. Different settings with respect to imperfection locations, amount, and the combined effects of defects have been studied. An interesting beat phenomenon is observed when all the wheels have imperfections. A procedure to determine the type of imperfections in the tyre from the results of the test rig has also been proposed.     

3D brush model to predict longitudinal tyre characteristics

A 3D tyre brush model, which aims to predict the longitudinal tyre characteristic under steady-state conditions by modelling the occurring physical effects in the tyre–road contact patch, is presented. The model includes an analytical method to describe the tyre footprint geometry, the pressure distribution, the slip due to the lateral tyre contour, the slip due to braking or traction and the longitudinal as well as the lateral shear stresses on a flattened tyre. The presented development tool offers a method to investigate different rubber friction data (caused by different tread compounds and/or surface textures) and to analyse its influence on longitudinal tyre characteristics. The tyre design is fixed (same casing, dimension and pattern). The results include the shear stresses as well as the different sliding velocities in the contact patch for different slip conditions. The model was developed for a standard summer pattern design and a standard tyre dimension (205/55R16). It can also be adapted to other tread designs and tyre dimensions. To offer a good comparability between model results and test bench measurements, the surface curvature of an internal test rig is considered.     

A finite-element-based approach to characterising FTire model for extended range of operation conditions

In order to accurately predict vehicle dynamic responses when traversing high obstacles or large bumps, appropriate tyre models need to be developed and characterised. Tyre models used in vehicle ride and durability are usually characterised by experimental tests on the tyre. However, limitations in rig design and operating conditions restrict the range of test conditions under which the tyre can be tested, hence characterisation of the tyre behaviour during extreme manoeuvres may not be possible using physical tests. In this study, a combination of experimental tests and finite-element (FE) modelling is used in deriving Flexible Ring Tire (FTire) Models appropriate for different levels of tyre/road interaction severity. It is shown that FE modelling can be used to accurately characterise the behaviour of a tyre where limitations in experimental facilities prevent tyre characterisation using the required level of input severity in physical tests. Multi-body simulation is used to demonstrate that the FTire model derived using extended range of obstacles produces more accurate transient dynamic response when traversing low and high road obstacles.     

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.     

Measurement and analysis of tyre and tread block dynamics due to contact phenomena

This paper deals with the dynamic behaviour of tyres and it is aimed at describing their dynamic features in the frequency band above 1 kHz, a range difficult to manage due to measurement noise and to the unreliability of numerical models, where the main influence is that of tread and blocks. Measurements have been made possible by fixing three three-axial micro-electro-mechanical system accelerometers on the liner and exciting the tyre under test by means of a dedicated test bench, suitably designed and constructed. Different kinds of tests have been considered in this research and described in the present paper. All of them show that a strong link exists between contact phenomena and tyre response in the frequency band over 1 kHz. This field is dominated by the tread and block dynamic responses. Furthermore, it is shown that vibrations of a sliding tyre give contributions in that frequency range for the above-mentioned reasons. It is thought that the study of the tyre behaviour over 1 kHz, though affected by significant uncertainties, can provide a proper knowledge to improve breaking effectiveness.     

Influence of tyre–road contact model on vehicle vibration response

The influence of the tyre–road contact model on the simulated vertical vibration response was analysed. Three contact models were compared: tyre–road point contact model, moving averaged profile and tyre-enveloping model. In total, 1600 real asphalt concrete and Portland cement concrete longitudinal road profiles were processed. The linear planar model of automobile with 12 degrees of freedom (DOF) was used. Five vibration responses as the measures of ride comfort, ride safety and dynamic load of cargo were investigated. The results were calculated as a function of vibration response, vehicle velocity, road quality and road surface type. The marked differences in the dynamic tyre forces and the negligible differences in the ride comfort quantities were observed among the tyre–road contact models. The seat acceleration response for three contact models and 331 DOF multibody model of the truck semi-trailer was compared with the measured response for a known profile of test section.     

Lateral Tyre Force by a Milliken Test on a Flat Track Roadway Simulator

The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].     

Lateral Tyre Force by a Milliken Test on a Flat Track Roadway Simulator

The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].     

Tyre–road grip coefficient assessment. Part 1: off-line methodology using multibody dynamic simulation and genetic algorithms

A key factor to understand the vehicle dynamic behaviour is to know as accurately as possible the interaction that occurs between the tyre and the road, since it depends on many factors that influence the dynamic response of the vehicle. This paper aims to develop a methodology in order to characterise the tyre–road behaviour, applying it to obtain the tyre–road grip coefficient. This methodology is based on the use of dynamic simulation of a virtual model, integrated into a genetic algorithm that identifies the tyre–road friction coefficient in order to adjust the response obtained by simulation to real data. The numerical model was developed in collaboration with SEAT Technical Centre and it was implemented in multibody dynamic simulation software Adams®, from MSC®.     

Development of a slip control anti-lock braking system model

This paper describes the initial phase of work carried out as part of an on going study investigating the interaction between the tyre, suspension system and an antilock braking system (ABS). The modelling, analysis simulations and integration of results have been performed using an industry standard Multibody Systems Analysis (MBS) program. A quarter vehicle model has been used together with an individual front suspension system represented by interconnected rigid bodies. The tyre model used can be integrated into vehicle handling simulations but only the theory associated with the generation of longitudinal braking forces is described here. An ABS model based on slip control has been used to formulate the braking forces described in this paper. The simulations, which have been performed braking on wet and dry road surfaces, compare the performance of two different tyres.     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Neural-empirical tyre model based on recursive lazy learning under combined longitudinal and lateral slip conditions

The behaviour of the tyre plays an important role in the vehicle handling. An accurate tyre model that estimates these forces and moments it is highly essential for the studies of vehicle behaviour. For the last ten years neural networks have attracted a great deal of attention in vehicle dynamics and control. Neural networks have been effectively applied to model complex systems due to their good learning capability. In this paper a recursive lazy learning method based on neural networks is considered to model the tyre characteristics under combined braking and cornering. The proposed method is validated by comparison with experimental obtained responses. Results show the estimated model correlates very well with the data obtained experimentally. Moreover, the neural model proposed allows to include the asymetric tyre behaviour in the tyre model without difficulty.