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.     

Measurement of stress distributions in truck tyre contact patch in real rolling conditions

Stress distributions on three orthogonal directions have been measured across the contact patch of truck tyres using the complex measuring system that contains a transducer assembly with 30 sensing elements placed in the road surface. The measurements have been performed in straight line, in real rolling conditions. Software applications for calibration, data acquisition, and data processing were developed. The influence of changes in inflation pressure and rolling speed on the shapes and sizes of truck tyre contact patch has been shown. The shapes and magnitudes of normal, longitudinal, and lateral stress distributions, measured at low speed, have been presented and commented. The effect of wheel toe-in and camber on the stress distribution results was observed. The paper highlights the impact of the longitudinal tread ribs on the shear stress distributions. The ratios of stress distributions in the truck tyre contact patch have been computed and discussed.     

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。     

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

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.     

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.     

胎面单元对轮胎薄膜湿牵引性能的影响

在潮湿的天气或雨后，轮胎胎面或路面上存在一层很薄的水膜，该水膜使车辆行驶的牵引力降低。建立了轮胎胎面单元挤压膜问题的数学模型，并进行了数值求解，分析了胎面单元的几何参数，液膜厚度和柔性对轮胎薄膜湿牵引性能的影响，为轮胎胎面花纹的合理设计提供了理论依据。     

Time-optimal control of the race car: influence of a thermodynamic tyre model

The robustness of an existing numerical method for the time-optimal control of the race car is demonstrated through its application to a model of a Formula 1 car equipped with a simplified thermodynamic tyre model. The tyre model includes a temperature- and frequency-dependent model of road/tyre friction. A lumped parameter approach is used to model the thermodynamics of the various parts of the tyre such as the tread, carcass and inflation gas. The influence of tyre, track surface and ambient temperatures on time-optimal manoeuvring is presented.     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

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.     

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.     

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.     

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.     

Research into the problem of wheel tread spalling caused by wheelset longitudinal vibration

This study mainly focuses on the mechanism of wheel tread spalling through wheelset longitudinal vibration that has been often neglected. Analysis of two actual cases of the wheel tread spalling problem leads to the conclusion that the wheel tread spalling is closely related to the wheelset longitudinal vibration in some locomotives, and many of these problems can be reasonably explained if the wheelset longitudinal vibration is considered. For better understanding of some abnormal wheel spalling problems, the formations of the wheelset longitudinal vibration and the wheel/rail contact parameters were analysed in the initial wheel tread spalling. With the preliminary analytical results, the wheelset longitudinal dynamic behaviour, the characteristics of wheel/rail contact and the mechanics in the condition of the wheelset longitudinal vibration were further studied quantitatively. The results showed that the wheelset longitudinal vibration changed not only the limit of these parameters and the position of principal stress, but also the direction of the principal stress on the surface of wheel/rail contact patch. It is likely that the significant stress changes provoke too much stress on the surface of wheel/rail contact patch, cause fatigue in wheel/rail contact patch and eventually lead to wheel tread spalling. The results of these studies suggest that the suppression of the wheelset longitudinal vibration extends wheel/rail life and the addition of a vertical damper with an ahead angle provides a possible solution to the wheel spalling problem.     

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。     

中型载货汽车轮胎异常磨损的原因分析及解决措施

中型载货汽车轮胎常发生异常磨损现象，磨损形式是横向花纹轮胎呈锯齿状磨损，从胎冠上方向下看，胎肩处花纹块呈前高后低状，也有少部分呈前低后高状，形状似锯齿；纵向花纹轮胎一侧胎肩磨损明显大于另一侧。分析了此现象产生的原因，并提出了相应的解决措施。     

Analysis of lateral tyre friction dynamics1

The tyre friction model is a key part of the overall multi-body tyre dynamics model. The LuGre dynamic tyre friction model is analytically linearised for pure cornering conditions. The linearised model parameters are conveniently expressed as functions of static curve slope parameters. The linearised lateral force and self-aligning torque submodels are described by equivalent mechanical systems. The linearised model and equivalent system parameters are analysed for different slip angle and wheel centre speed operating points. An example of the application of linearised tyre friction model to tyre vibration analysis is presented as well.     

A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis

Pacejka's Magic Formula Tyre Model is widely used to represent force and moment characteristics in vehicle simulation studies meant to improve handling behaviour during steady-state cornering. The experimental technique required to determine this tyre model parameters is fairly involved and highly sophisticated. Also, total test facilities are not available in most countries. As force and moment characteristics are affected by tyre design attributes and tread patterns, manufacturing of separate tyres for each design alternative affects tyre development cycle time and economics significantly. The objective of this work is to identify the interactions among various tyre design attributes-cum-operating conditions and the Magic Formula coefficients. This objective is achieved by eliminating actual prototyping of tyres for various design alternatives as well as total experimentation on each tyre through simulation using finite element analysis. Mixed Lagrangian–Eulerian finite element technique, a specialized technique in ABAQUS, is used to simulate the steady-state cornering behaviour; it is also efficient and cost-effective. Predicted force and moment characteristics are represented as Magic Formula Tyre Model parameters through non-linear least-squares fit using MATLAB. Issues involved in the Magic Formula Tyre Model representation are also discussed. A detailed analysis is made to understand the influence of various design attributes and operating conditions on the Magic Formula parameters. Tread pattern, tread material properties, belt angle, inflation pressure, frictional behaviour at the tyre–road contact interface and their interactions are found to significantly influence vehicle-handling characteristics.     

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.