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®.     

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.     

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.     

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.     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.     

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.     

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.     

Energy analysis of the Von Schlippe tyre model with application to shimmy

Shimmy is an engineering example of self-excited vibrations. Much research on shimmy has considered the tyre as a positive feedback or negative damping to introduce instability of the entire system. In this context, we focus on the behaviour of the tyre under periodic excitations. The Von Schlippe tyre model is selected and the energy flow method is applied to illustrate the energy transfer by the tyre during shimmy. The energy flow method evaluates the tyre performance with a prescribed sinusoidal motion and provides a novel evaluation method for tyre models. With the help of straight contact line assumption in the Von Schlippe tyre model, the relative motion between the contact line and the wheel centre is studied to understand the path dependency of the energy transfer. It turns out that the tyre is extracting energy from the forward motion to induce unstable lateral and yaw vibrations when the motion or orientation of the contact line has a phase lead with respect to the wheel centre.     

Design of tyre force excitation for tyre–road friction estimation

Knowledge of the current tyre–road friction coefficient is essential for future autonomous vehicles. The environmental conditions, and the tyre–road friction in particular, determine both the braking distance and the maximum cornering velocity and thus set the boundaries for the vehicle. Tyre–road friction is difficult to estimate during normal driving due to low levels of tyre force excitation. This problem can be solved by using active tyre force excitation. A torque is added to one or several wheels in the purpose of estimating the tyre–road friction coefficient. Active tyre force excitation provides the opportunity to design the tyre force excitation freely. This study investigates how the tyre force should be applied to minimise the error of the tyre–road friction estimate. The performance of different excitation strategies was found to be dependent on both tyre model choice and noise level. Furthermore, the advantage with using tyre models with more parameters decreased when noise was added to the force and slip ratio.     

基于虚拟路面的整车路噪轮胎参数相关性研究

为了在设计阶段保证整车的NVH性能,通过搭建虚拟路面仿真平台探究轮胎关键物理参数对于整车路面振动噪声的影响规律。结合实车采集的试验场NVH路面PSD、高精度物理轮胎CDTire模型以及整车声固耦合模型,建立完整的整车路噪仿真环境。通过某款SUV的仿真结果表明,不同款轮胎及同款轮胎不同批次对整车路面振动噪声有直接的影响。虚拟路面方法可以在整车开发早期甄别出在车辆噪声中起主导作用的频率段,从而排查明显的NVH设计缺陷,同时,可以为车型NVH正向开发提供轮胎选型依据。     

某型纯电动汽车路噪仿真与优化

在纯电动汽车开发过程中,如何有效基于有限元手段实现低频结构路噪的预测与优化,对纯电动汽车NVH性能具有重要意义。文章基于Spindle Loads方法对某型纯电动SUV汽车在大粗糙路60km/h工况下的低频结构路噪进行仿真预测,通过与实车测试结果对比,显示低频结构路噪有限元模拟结果与试验结果曲线整体趋势一致性较好;对53Hz与127Hz风险频率点原因进行剖析并提出相关优化方案,实车验证有效。     

Optimization of Vehicles Elasto-Damping Elements Characteristics from the Aspect of Ride Comfort

SUMMARY

Spatial random vibrations of a vehicle that arise during driving represent an important factor in functioning of a dynamic system: Driver - Vehicle - Environment. They carry certain information for driver and also cause fatigue of driver and passenger.

This is the reason why the tendency is towards the minimization of vibratory loads, what in practice can be achieved by optimization of characteristics of elasto - damping elements of a vehicle.

In this paper for optimization of elasto - damping elements of a vehicle we used a complex nonlinear model of a driver and a vehicle during the straight - line motion of the vehicle on a rough road. Optimization was performed by application of the Hooke - Jeeves method and by use of outside penalty functions as well as the objective function that enabled simultaneous optimization of vertical vibrations of the driver's seat, vibrations of the steering wheel, and normal reactions in the contact surface of the tyre and road. The optimization was performed with application of the computer HP 9000/800 SE on the example of a medium passenger car.     

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.     

Tyre friction behaviour under abrupt wheel torque transients on slippery road surfaces: experimental analysis and modelling

The paper shows that, during abrupt wheel torque transients for ice surface and low vehicle speeds, the tyre can develop significantly larger longitudinal force than the peak value of the tyre static curve. This so-called dynamic tyre friction potential (DTFP) effect has many influencing factors such as the rate of change of the wheel torque, the vehicle speed, and the tyre dwell time. The paper presents a detailed analysis of the DTFP behaviour based on the experimental data collected by using an in-wheel motor-based tyre test vehicle. The analysis results and an insight into the brush structure of a tyre model lead to the hypothesis that the different influencing factors may be predominantly explained by the bristle dwell time (BDT) effect. Following this hypothesis, the LuGre model of the tyre friction dynamics is extended with a physical BDT sub-model. The experimental validation results show that the proposed model can accurately capture the low-speed tyre–ice friction behaviour during abrupt wheel torque transients.