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.     

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.     

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.     

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.     

Tuning and objective performance evaluation of a driving simulator to investigate tyre behaviour in on-centre handling manoeuvres

Driving simulation aims at reproducing, within a safe and controlled environment, sensorial stimuli as close to those perceived during the actual drive as possible, in order to induce driving behaviour similar to the real one. This paper illustrates an activity carried out on the driving simulator Virtual Environment for Road Safety, bound for system performance optimisation while dealing with subjective and objective tyres evaluation in the field of on-centre manoeuvres. Such activity can be divided into two main steps. The first one, described herewith, has been focusing on platform motion algorithms tuning and has led to driving simulator objective validation within the on-centre range. Device capability of reproducing dynamics, worked out by the vehicle model, has been thoroughly examined. Simulator sensitivity to a few tyre parameters influencing vehicle lateral dynamics has been analysed too. The second step – calling for the support of experienced drivers – will pursue subjective validation.     

A tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel independent brake from moderate driving to limit handling

This paper presents a tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel braking for enhanced performance from moderate driving to limit handling. The proposed algorithm adopted hierarchical structure: supervisor – desired motion tracking controller – optimisation-based control allocation. In the supervisor, by considering transient cornering characteristics, desired vehicle motion is calculated. In the desired motion tracking controller, in order to track desired vehicle motion, virtual control input is determined in the manner of sliding mode control. In the control allocation, virtual control input is allocated to minimise cost function. The cost function consists of two major parts. First part is a slip-based tyre friction utilisation quantification, which does not need a tyre force estimation. Second part is an allocation guideline, which guides optimally allocated inputs to predefined solution. The proposed algorithm has been investigated via simulation from moderate driving to limit handling scenario. Compared to Base and direct yaw moment control system, the proposed algorithm can effectively reduce tyre dissipation energy in the moderate driving situation. Moreover, the proposed algorithm enhances limit handling performance compared to Base and direct yaw moment control system. In addition to comparison with Base and direct yaw moment control, comparison the proposed algorithm with the control algorithm based on the known tyre force information has been conducted. The results show that the performance of the proposed algorithm is similar with that of the control algorithm with the known tyre force information.     

A comparison of various algorithms to extract Magic Formula tyre model coefficients for vehicle dynamics simulations

Tyre models are a prerequisite for any vehicle dynamics simulation. Tyre models range from the simplest mathematical models that consider only the cornering stiffness to a complex set of formulae. Among all the steady-state tyre models that are in use today, the Magic Formula tyre model is unique and most popular. Though the Magic Formula tyre model is widely used, obtaining the model coefficients from either the experimental or the simulation data is not straightforward due to its nonlinear nature and the presence of a large number of coefficients. A common procedure used for this extraction is the least-squares minimisation that requires considerable experience for initial guesses. Various researchers have tried different algorithms, namely, gradient and Newton-based methods, differential evolution, artificial neural networks, etc. The issues involved in all these algorithms are setting bounds or constraints, sensitivity of the parameters, the features of the input data such as the number of points, noisy data, experimental procedure used such as slip angle sweep or tyre measurement (TIME) procedure, etc. The extracted Magic Formula coefficients are affected by these variants. This paper highlights the issues that are commonly encountered in obtaining these coefficients with different algorithms, namely, least-squares minimisation using trust region algorithms, Nelder–Mead simplex, pattern search, differential evolution, particle swarm optimisation, cuckoo search, etc. A key observation is that not all the algorithms give the same Magic Formula coefficients for a given data. The nature of the input data and the type of the algorithm decide the set of the Magic Formula tyre model coefficients.     

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 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.     

T构桥振动过大病害的动力测试及分析

针对某T构桥在运营过程中振动过大现象,选取了另一座上部结构相同而基础形式略有不同的实桥进行对比。对2座桥各关键部位的振动情况进行了测试,对于病害桥和对比桥的振动响应数据分别进行了幅值特征和频谱特征比较,并结合模态分析对结构振害进行了诊断,主要从构造对比、结构缺陷和静力刚度几个方面分析桥梁纵向振动过大的病害原因,即:钢管桩的局部刚度过弱。为进一步的振动控制设计提供了依据。所提出的振害诊断方法具有较好的可实施性,可为同类型结构提供参考。     

Experimental investigations on the damping effect due to passengers on flexural vibrations of railway vehicle carbody and basic studies on the mimicry of the effect with simple substitutions

The effect of passengers on a railway vehicle is usually considered as additional mass in designing a carbody. However, previous studies by means of stationary excitation tests or running tests using actual vehicles indicate that passengers behave not as mass but as damping. In this paper, the authors examined the passengers' damping effect under controlled excitation conditions on a roller rig through a series of excitation tests using a commuter-type vehicle. Large and multi-modal reductions of flexural vibrations of the carbody were observed when passengers existed. Influences of the number of passengers, distributions and postures of passengers were investigated. The authors also tried to mimic the damping effect by passengers using flexible tanks filled with fluids. Three kinds of fluids which have different viscosities have been tested. As a result of the excitation tests, good vibration reduction effects were observed by applying those tanks, and it has been found that the flexible tanks filled with fluids bring about vibration reduction effect (including multi-modal reduction) which is equal to or rather better than the case of similar mass of passengers in the carbody; the difference of viscosity gave little affect on the damping abilities. From these measurement results, a possibility of realising effective damping devices against flexural vibrations of railway vehicle carbodies representing passengers damping effect, in a simple, economical and environmental friendly way, has been demonstrated.     

水泥混凝土路面板角弯沉的测点偏移影响及修正

为了分析弯沉测量结果上的差异,以水泥混凝土路面常见的2种弯沉测试方法为例,分析了板角弯沉测试时测点偏移对弯沉测试结果的影响,引入了测点偏移影响系数的概念,建立了允许偏移范围内实测弯沉的修正方法。结果表明,测点偏移对弯沉测试结果影响非常显著;测点向板内侧偏移时,2种测试方法均可引入测点纵向和横向偏移影响系数用来修正实测弯沉值,影响系数与荷载向板内移动的距离以及地基板相对刚度半径有关。因此,可以将测点偏移情况下的弯沉测试值转换为标准测点位置的弯沉值,方便了实测数据的统计处理,拓展了弯沉测试方法的应用范围,提高了弯沉测试的效率。