Railway Wheel and Automotive Tyre

SUMMARY

In the present paper the theories of the railway wheel and the automotive tyre are discussed. After an introduction the paper opens with a discussion of the common ground, viz. the rolling motion of deformable bodies. Then the railway wheel is discussed, and it is shown that all aspects may be calculated numerically from the material constants Poisson's ratio, Young's modulus, and the coefficient of friction, and from the geometry of wheel and rail. Next the automotive wheel is considered. Such a wheel is very anisotropic, to the extent that the theory of the lateral motion (out-of-plane dynamics) is radically different from the longitudinal, or in-plane motion. Moreover, the analysis of the automotive wheel heavily relies on experiments. In the conclusion, the theories are compared.     

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.     

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.     

Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons

Friction dampers of mechanical systems are frequently exposed to medium-frequency (M-F) dither generated in the surrounding environment. A dithered system of technical importance is the railway freight wagon with friction dampers in the primary suspension developing two-dimensional friction, where dither is generated by the rolling contact of wheel and rail. This paper presents some results of the investigation of the influence of dither on dry friction damping. This influence has been studied experimentally and theoretically, and the parameters of dither influencing dry friction damping have been indicated. An experimental set-up has been designed that allows investigating friction damping in the presence of dither. The experiments have shown that friction damping in the presence of the M-F dither behaves like viscous damping. This means that dither smoothes dry friction as far as damping is concerned. To investigate this phenomenon theoretically, a rheological model of dry friction has been proposed that is applicable to one- and two-dimensional friction. In the latter case, the model takes into account friction anisotropy. According to performed numerical simulations of freight wagon motion, with dither supplied to the model through measured vertical accelerations of axle boxes, smoothing dry friction by dither strongly influences ride dynamics of the wagon with friction dampers in the primary suspension. Smoothing dry friction by dither should be accounted for in numerical simulations of motion of vehicles with friction dampers in the primary suspension by employing a proper model of the two-dimensional friction and application of realistic dither generated by rolling contact.     

论轮胎与路面间的摩擦

对轮胎与路面间摩擦产生的机理和影响因素进行了分析。其中产生的机理可归纳为轮胎与路面间分子引力的作用、轮胎与路面间的粘着作用、胎面橡胶的弹性变形及路面上小尺寸微凸体的微切削作用四种；影响轮胎与路面间摩擦的主要因素有滑移率，轮胎类型，胎面花纹的类型、密度系数、深度，路面粗糙度，路面污染情况，路面水膜，气候及充气压力等。     

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.     

Railway Wheel and Automotive Tyre

In the present paper the theories of the railway wheel and the automotive tyre are discussed. After an introduction the paper opens with a discussion of the common ground, viz. the rolling motion of deformable bodies. Then the railway wheel is discussed, and it is shown that all aspects may be calculated numerically from the material constants Poisson's ratio, Young's modulus, and the coefficient of friction, and from the geometry of wheel and rail. Next the automotive wheel is considered. Such a wheel is very anisotropic, to the extent that the theory of the lateral motion (out-of-plane dynamics) is radically different from the longitudinal, or in-plane motion. Moreover, the analysis of the automotive wheel heavily relies on experiments. In the conclusion, the theories are compared.     

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.     

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre–road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force.

The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficient.     

轮胎侧偏动力模型的非线性分析

轮胎径向变形与轮胎接地印迹长度呈非线性关系，从而导致轮胎侧偏力和回正力矩与车轮动载荷也是非线性关系。本文用一轮胎模型对这一现象进行了理论分析，并得到了与实验数据基本一致的结果。     

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 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.     

Longitudinal wheel slip during ABS braking

Anti-lock braking system (ABS) braking tests with two subcompact passenger cars were performed on dry and wet asphalt, as well as on snow and ice surfaces. The operating conditions of the tyres in terms of wheel slip were evaluated using histograms of the wheel slip data. The results showed different average slip levels for different road surfaces. It was also found that changes in the tyre tread stiffness affected the slip operating range through a modification of the slip value at which the maximum longitudinal force is achieved. Variation of the tyre footprint length through modifications in the inflation pressure affected the slip operating range as well. Differences in the slip distribution between vehicles with different brake controllers were also observed. The changes in slip operating range in turn modified the relative local sliding speeds between the tyre and the road. The results highlight the importance of the ABS controller's ability to adapt to changing slip–force characteristics of tyres and provide estimates of the magnitude of the effects of different tyre and road operating conditions.     

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.     

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

In this first part of a two-part article, a previously described and validated finite-element model of a racing-car tyre is developed further to yield detailed information on carcass deflections and contact pressure and shear stress distributions for a steady rolling, slipping, and cambered tyre. Variations in running conditions simulated include loads of 1500, 3000 and 4500 N, camber angles of 0° and ?3°, and longitudinal slips from 0% to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest. Results generated are in broad agreement with limited experimental results from the literature and they provide considerable insight into how the tyre deforms and how the contact stresses are distributed as functions of the running conditions. Generally, each rib of the tyre behaves differently from the others, especially when the wheel is cambered. The results form a basis for the development of a simpler physical tyre model, the purpose of which is to retain accuracy over the full operating range while demanding much less computational resource. The physical tyre model is the topic of the second part of the article.     

A thermo-frictional tyre model including the effect of flash temperature

A new tyre model is developed that can predict the influence of both macroscopic and local flash temperature on tyre force generation. The model comprises two heat-transfer solvers. A macroscopic solver calculates the 3D temperature distribution across the tread and sidewall at a resolution of a few millimetres. A separate flash-temperature solver calculates the local hot-spot temperature distribution at the macro-asperity tyre-road contact interface at a resolution of micrometres. The two heat-transfer solvers are coupled with a structural model for the calculation of tyre forces and the sliding speed distribution along the contact patch. The sliding speed distribution feeds into the flash-temperature model and the local coefficient of friction is found as a function of sliding speed, flash temperature, normal pressure, road roughness and the complex modulus of rubber. The proposed tyre model is the first to include the effect of a changing macroscopic temperature distribution on the build-up of the local flash temperature, and to account for road-tread conduction at the macro-asperity contact interface. The model is applicable for identifying the friction envelope and optimum temperature range for tyres on roads with known roughness. This is important in motorsport where knowledge of grip offers a competitive advantage.     

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.     

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.