Shear forces in the contact patch of a braked-racing tyre

This article identifies tyre modelling features that are fundamental to the accurate simulation of the shear forces in the contact patch of a steady-rolling, slipping and cambered racing tyre. The features investigated include contact patch shape, contact pressure distribution, carcass flexibility, rolling radius (RR) variations and friction coefficient. Using a previously described physical tyre model of modular nature, validated for static conditions, the influence of each feature on the shear forces generated is examined under different running conditions, including normal loads of 1500, 3000 and 4500 N, camber angles of 0° and?3°, and longitudinal slip ratios from 0 to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest in terms of its connection with the limit-handling feel. The results of the simulations reveal that true representations of the contact patch shape, carcass flexibility and lateral RR variation are essential for an accurate prediction of the distribution and the magnitude of the shear forces generated at the tread–road interface of the cambered tyre. Independent of the camber angle, the contact pressure distribution primarily influences the shear force distribution and the slip characteristics around the peak longitudinal force. At low brake-slip ratios, the friction coefficient affects the shear forces in terms of their distribution, while, at medium to high-slip ratios, the force magnitude is significantly affected. On the one hand, these findings help in the creation of efficient yet accurate tyre models. On the other hand, the research results allow improved understanding of how individual tyre components affect the generation of shear forces in the contact patch of a rolling and slipping tyre.     

Tyre rolling kinematics and prediction of tyre forces and moments: part I – theory and method

A new method to describe tyre rolling kinematics and how to calculate tyre forces and moments is presented. The Lagrange–Euler method is used to calculate the velocity and contact deformation of a tyre structure under large deformation. The calculation of structure deformation is based on the Lagrange method, while the Euler method is used to analyse the deformation and forces in the contact area. The method to predict tyre forces and moments is built using kinematic theory and nonlinear finite element analysis. A detailed analysis of the tyre tangential contact velocity and the relationships between contact forces, contact areas, lateral forces, and yaw and camber angles has been performed for specific tyres. Research on the parametric sensitivity of tyre lateral forces and self-aligning torque on tread stiffness and friction coefficients is carried out in the second part of this paper.     

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.     

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.     

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.     

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.     

接地面部分溶化条件下冰面轮胎摩擦力的研究

综合运用流体动力润滑理论的能量守恒定律，提出了接地面部分溶化条件下冰面上汽车轮胎的摩擦力或牵引力的理论计算模型。证明了正常工作条件下，接地面上冰产生溶化的可能。对不同制动和驱动条件下轮胎摩擦力进行了计算，取得了同试验数据吻合很好的预测结果。并同已有预测模型进行了比较，比较结果表明：本文依据严格的润滑理论所推导出的冰面轮胎牵引力模型比其它已有理论模型更接近试验结果。     

New tyre-road contact model for applications at low speed

Most of the tyre models have been developed for high speed, combined forces, etc., however, in certain tests it is necessary to know tyre behaviour at very low speed in order to evaluate different systems. So, during vehicle inspection and maintenance of the steering and brake system, by means of sideslip tester and roller brake tester respectively, the forces transmitted by the tyres are measured; all of these inspections are carried out at low speeds. Furthermore, usually, automobile vehicles run at low speeds during an important part of their operating life (less than 60 km/h), mainly during urban traffic, and in steady state conditions. Therefore, it is particularly interesting to develop an accurate model of the contact patch tyrepavement for low speeds without the complexity of models that cover a wide speed range but provide less precision at very low speeds. The dynamometer plate has proved to be an appropriate test equipment to characterise the tyre-pavement contact at low speed and the steering geometry and wheel alignment. It has the feature of being able to carry out tests with the tyre installed in the vehicle as in completely real conditions. The main aim of this research is to set up a contact model between tyre and pavement at very low speed based on the measurement of longitudinal and lateral forces. A test methodology that allows carrying out the experimental tests in a systematic and controlled way with the dynamometer plate has also been developed. From this model it will be possible to estimate the forces that tyres are capable of transmitting in different situations to act in the parameters which affect these forces and maximize them.     

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.     

Micro-shimmy of towed structures in experimentally uncharted unstable parameter domain

In this paper, the lateral instability of towed structures (trailers, caravans and articulated buses) is investigated with special attention to the small amplitude lateral vibration that leads to a higher energy consumption in certain parameter domains. A low degree-of-freedom mechanical model of a shimmying towed tyre is used that describes the dynamics of the tyre–ground contact patch by the time delayed differential equation. Stability charts are calculated and the theoretically predicted linear unstable islands of small amplitude shimmy motions are validated by laboratory experiments. A tyre is towed by a relatively long caster, and its temperature and the input current of the conveyor belt are measured in order to show the increased value of the rolling resistance.     

Tyre rolling kinematics and prediction of tyre forces and moments: part II – simulation and experiment

There are two aims for the second part of this paper: verifying the theory presented in the first part through parameter variation and comparison between simulation and experiment, and to study the effect of the belt structure on the cornering properties of radial tyres. Research has been carried out with a passenger car radial tyre and two different kinds of truck or bus radial tyres using both simulation and experiment. This second part of the paper shows that belt structure plays an important role in the generation of tyre forces and moments in addition to the effects of the tread stiffness and friction coefficients. The theory and method presented in this paper opens a new robust way to predict the tyre forces and moments from the tyre design and provides a reliable model for a generation mechanism.     

Optimal tyre usage for a Formula One car

Variations in track temperature, surface conditions and layout have led tyre manufacturers to produce a range of rubber compounds for race events. Each compound has unique friction and durability characteristics. Efficient tyre management over a full race distance is a crucial component of a competitive race strategy. A minimum lap time optimal control calculation and a thermodynamic tyre wear model are used to establish optimal tyre warming and tyre usage strategies. Lap time sensitivities demonstrate that relatively small changes in control strategy can lead to significant reductions in the associated wear metrics. The illustrated methodology shows how vehicle setup parameters can be optimised for minimum tyre usage.     

Tyre–road grip coefficient assessment – Part II: online estimation using instrumented vehicle,extended Kalman filter,and neural network

The main objective of this work is to determine the limit of safe driving conditions by identifying the maximal friction coefficient in a real vehicle. The study will focus on finding a method to determine this limit before reaching the skid, which is valuable information in the context of traffic safety. Since it is not possible to measure the friction coefficient directly, it will be estimated using the appropriate tools in order to get the most accurate information. A real vehicle is instrumented to collect information of general kinematics and steering tie-rod forces. A real-time algorithm is developed to estimate forces and aligning torque in the tyres using an extended Kalman filter and neural networks techniques. The methodology is based on determining the aligning torque; this variable allows evaluation of the behaviour of the tyre. It transmits interesting information from the tyre–road contact and can be used to predict the maximal tyre grip and safety margin. The maximal grip coefficient is estimated according to a knowledge base, extracted from computer simulation of a high detailed three-dimensional model, using Adams^® software. The proposed methodology is validated and applied to real driving conditions, in which maximal grip and safety margin are properly estimated.     

Environmental effects on Pacejka’s scaling factors

A set of scaling factors has been introduced by Pacejka [Pacejka, H.B., 2002, Tyre and Vehicle Dynamics (Oxford: Butterworth Heinemann Editions)] into his Magic Formula tyre model to take into account the influence of a number of external overall parameters such as road roughness, weather conditions, suspension characteristics and so on. These scaling factors are important for a correct prediction of tyre–road contact forces, but are not a function of the tyre itself. Changing the point of view, one could say that scaling factors should remain constant for different tyres on the same circuit, with the same weather conditions and with the same car. After characterizing different tyres through indoor tests (that do not consider external overall parameters) and after having identified Pacejka’s coefficients with scaling factors equal to one, several outdoor experimental tests have been carried out to assess the influence of vehicle and road surface conditions on scaling factors. These experimental data allowed us to identify, through a minimization approach, the ‘best’ set of Pacejka’s scaling factors for that vehicle and for that tyre on that track. Scaling factors for equal track and vehicle but different tyres were compared to check whether their values remained constant. To access the validity of scaling factors, a comparison between experimental data, collected on an instrumented passenger car, and MB simulations considering unity and identified scaling factors’ values, were carried out. All experimental data shown in this article come from tests carried out within the VERTEC project, a European founded research project (Task 2.a and 2.b) that puts together knowledge coming from vehicle manufacturers (Volvo, Porsche and Centro Ricerche Fiat CRF), tyre manufacturers (Pirelli and Nokian Tyres), control logic manufacturers (Lucas Varity GmbH), road maintenance experts (Centres d’Études Techniques de l’Équipement CETE), transport research organizations (Transport Research Laboratory TRL, Swedish National Road and Transport Research Institute VTI) and universities (Helsinki University of Technology HUT, Politecnico di Milano and University of Florence UNIFI).     

Bifurcation analysis of an automobile model negotiating a curve

The paper deals with the bifurcation analysis of a rather simple model describing an automobile negotiating a curve. The mechanical model has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. Bifurcation analysis is adopted as the proper procedure for analysing steady-state cornering. Two independent parameters referring to running conditions, namely steering angle and speed, are varied. Ten different combinations of front and rear tyre characteristics (featuring understeer or oversteer automobiles) are considered for the bifurcation analysis. Many different dynamical behaviours of the model are obtained by slightly varying the parameters describing the tyre characteristics. Both simple and extremely complex bifurcations may occur. Homoclinic bifurcations, stable and unstable limit cycles (of considerable amplitude) are found, giving a sound and ultimate interpretation to some actual (rare but very dangerous) dynamic behaviours of automobiles, as reported by professional drivers. The presented results are cross-validated by exploiting handling diagram theory. The knowledge of the derived set of bifurcations is dramatically important to fully understand the actual vehicle yaw motions occurring while running on an even surface. Such a knowledge is a pre-requisite for robustly designing the chassis and for enhancing the active safety of vehicles.