In-plane Dynamics of Tires on the Road Based on an Experimentally Verified Rolling Ring Model

The dynamic behavior of tires rolling on the road is predicted based on a ring model that is experimentally verified to well represent a real tire. The road contact is kinematically represented by two displacement constraints, one in radial and one in tangential direction. The displacement constraints are enforced via the receptance theory. The receptance matrix developed for the rolling tire is found to be Hermitian. Numerical results show that the natural (or eigen-) frequencies of the rolling tire with road contact are, as expected, higher than those of the tire with no contact. The influence of the rotating speed to the eigen-frquencies of the tire is also shown. Analytic expressions for the mode shapes of a rolling tire with ground contact are derived.     

Vehicle Energy Dissipation Due to Road Roughness

SUMMARY

Road roughness and surface texture are known to affect tire rolling resistance; however, little emphasis has been placed on the consequent changes in total vehicle energy dissipation due to road roughness. Thus, tire rolling resistance, in isolation from vehicle contributed losses such as dissipation in the suspension, appears to be a weakness in present evaluation procedures as they relate to fuel economy and pollution level testing: Recent work by Funfsinn and Korst has shown that substantial and measurable increases in energy losses occur for vehicles traveling on rough roads. The present investigation uses vehicle axle accelerations as a means of examining various road surfaces. Correlation with computer simulations has allowed the development of a deterministic road roughness model which permits the prediction of energy dissipation in both the tire and suspension as functions of road roughness, tire pressure, and vehicle speed. Comparison to the experiments of Korst and Funfsinn results in good agreement and shows that total rolling loss increases of up to 20 percent compared to ideal smooth roads are possible. The aerodynamic drag coefficient is also found to increase while driving on rough roads.     

Experimental Study of System Optimization for Suppression of Vehicle Vibration

SUMMARY

The improvements of ride comfort and vehicle maneuverability in the vehicle design can be achieved by using an active suspension. However, the problems in such a control are the complex control logic because of the control laws incompatible with the improvements of ride comfort and maneuverability, and the cost increase because of various sensors to be attached. Therefore, we examined the control abilities of ride comfort and maneuverability on a unique control law using frequency shaped LQ, and controlled the characteristic of the contact between tire and road without a road displacement sensor     

轮胎在水平路面上的自由滚动接触分析

利用轮胎的模态参数直接对轮胎在水平路面上的滚动建立了便于解析计算的仿真模型。该模型可模拟轮胎稳态的滚动过程并可计算出不小同工况下的滚动特性、有效滚动半径、载荷与下沉量的关系以及印迹内变形和分布力。计算结果揭示了以往模型难以描述的微观现象,与以往文献的试验研究结果定性一致,充分显示了模型的合理性。     

Simplified Analysis of Steady-State Turning Behaviour of Motor Vehicles Part 2: Stability of the Steady-State Turn∗

SUMMARY

A finite element model suitable for camber thrust analysis is formed. By inclining and pressing this finite element model onto the road plane, the forces prevailing in the contact patch of an inclined standing tire are calculated and the asymmetry-dependent mechanism of camber thrust generation is analyzed. By rotating the inclined standing tire at a constant vertical deflection, the roll-distance-dependent mechanism of camber thrust generation is analyzed.     

Index

A method is presented for the dynamic analysis of contact deformation for rolling tire on a road. The tire is modeled as an inextensible ring on elastic foundation with damping. Under known radial deflection, the ground contact region is predicted by solving simplified ring motion equation, treating ground contacting as a boundary condition. Furthermore, the effect of internal damping and rotating speed is analyzed on contact region.     

A Simple Analysis Method for Contact Deformation of Rolling Tire

A method is presented for the dynamic analysis of contact deformation for rolling tire on a road. The tire is modeled as an inextensible ring on elastic foundation with damping. Under known radial deflection, the ground contact region is predicted by solving simplified ring motion equation, treating ground contacting as a boundary condition. Furthermore, the effect of internal damping and rotating speed is analyzed on contact region.     

Two-Dimensional Contact Area of a Pneumatic Tire Subjected to a Lateral Force

A mathematical model of a two-dimensional contact patch of pneumatic tires rolling over a rigid flat road surface at arbitrary slip and camber angles has been developed. The model is simple in concept, contains few parameters and is applicable to any tire simulation models. In addition to tire geometric parameters and vertical deflection, the carcass camber angle is introduced in the model. This angle is alone responsible for the asymmetric shape of the tire contact patch when the tire undergoes a lateral force. The computed contact patches agree well with the measured patches of an automotive tire at different slip and camber angles. Lastly, the influence of the contact patch geometry on the tire cornering and aligning properties has been discussed through a computational example. It has been shown that the effect of tire contact patch geometry on the steady state behavior is rather remarkable.     

Adaptive Control of 4WS System by Using Neural Network

SUMMARY

An adaptive control system of the model following type is proposed for drive motion control of a four wheel steering (4WS) car with using neural network (NN) which has mastered nonlinear friction force between tire and road surface. A model of one rigid body is adopted which represents appropriately two kinds of car motion caused by steering action, namely the lateral displacement and the yawing rotation, and an equation of motion is described in a simplified form to make a system equation for motion control possible. Nonlinear relation between the cornering force of tire and the slip angle is obtained by numerical analysis with the tire model proposed by E. Fiala, taking friction coefficient and car speed as the parameters. The result is used as the teaching signal for NN. Three NN are used in the control system composed of both the feed-forward and the feedback circuits in order to realize adaptive control. Validity and usefulness of the proposed adaptive control system with NN are verified by three kinds of computer simulation.     

Ride Dynamics of Articulated Vehicles–A Literature Survey

SUMMARY

This paper presents a review of the available literature describing the methods of modelling the vibrational response of articulated vehicles to the road inputs at the tire contact points. It states and discusses the mathematical techniques that have been put forward for obtaining road input characteristics, for modelling the vehicles in a range of degrees of freedom, and for performing the analysis necessary to obtain the vibrational response. Finally the indices that have been proposed for ride comfort and ride safety are given and the manner in which various researchers relate these to the vibrational characteristics of the vehicles is described.     

汽车轮胎滚动阻力试验机测试方法分析

为了对汽车轮胎滚动阻力测试方案的可行性进行预先评估,基于检测设备的结构模型,提出了一种运用位移量对轮胎滚动阻力进行仿真分析的新方法。在简述滚动阻力有限元测试模型构建过程的基础上,通过改变轮胎的外部使用参数,分析传感器板在不同工况下位移场的分布情况,制定了设备的测试方案。以传感器的安装位置作为目标检测点,建立轮胎滚动阻力位移场与控制参数之间的关系曲线。最后将采集的数据经过平均滤波处理,与实验室的实测数据进行了趋势性对比。结果表明：采用该测试方法,轮胎滚动阻力随着轮胎负载和速度的增加而增大,随着气压的变大而减小;仿真结果和试验数据在相同工况下的变化趋势基本一致;该测试方法合理、可行。     

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.     

Adaptive Control of Vehicle Suspension

SUMMARY

An adaptive control scheme for a two-degree-of-freedom vehicle model with active suspension is proposed. The performance goal is to minimize the variance of vehicle body acceleration under inequality constraints imposed on the variance of either tire or suspension deflection. An active suspension is adapted to the changes in vehicle velocity and the type of road (or terrain) surface which is assumed to be reconstructable from the accelerometer measurements. The control gain factors are obtained by the iterative method taking advantage of stochastic linear control theory. The performance of the system is evaluated and compared to that of an active system with constant gain factors and a passive system with adjustable parameters.     

Numerical method for simulating tire rolling noise by the concept of periodically exciting contact force

For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling speed.     

载重子午轮胎与路面相互作用的分析

根据全钢载重子午线轮胎12.00R20的实际结构,考虑轮胎的几何非线性、材料非线性、接触非线性以及大变形等力学特性,应用有限元的方法建立轮胎的三维模型,橡胶材料采用Yeoh模型,橡胶-帘线复合材料采用加强筋模型,并通过轮胎径向刚度的测试验证了模型的有效性.在数值模拟中分析了轮胎在一定充气压力时,在不同垂直载荷和牵引速度的作用下,与地面在接触区域的变形情况、应力分布、摩擦应力分布等滚动接触规律.结果表明,轮胎与地面接触应力分布存在明显的非均匀性,轮胎的接地面积和地面总反力随着滚动速度的升高而增大.     

基于FSI方法的轮胎横向花纹沟泵吸噪声研究

运用abaqus对具有横向花纹槽的轮胎滚动进行仿真,提取轮胎沟槽表面在轮胎接地过程中随时间的变形曲线。建立单个横向花纹沟和其周围的空气域模型,在沟槽表面加载变形曲线,利用FSI方法分析了横向花纹沟尺寸对轮胎花纹沟泵吸噪声的影响。从分析结果可知,轮胎花纹沟泵吸噪声随着沟槽长度的增大而减小,随着沟槽宽度的增大而增大,但随沟槽深度的变化不明显。本文结果与相关文献的试验结果一致,表明FSI方法分析轮胎花纹沟泵吸噪声可行。     

Vehicle Energy Dissipation Due to Road Roughness

Road roughness and surface texture are known to affect tire rolling resistance; however, little emphasis has been placed on the consequent changes in total vehicle energy dissipation due to road roughness. Thus, tire rolling resistance, in isolation from vehicle contributed losses such as dissipation in the suspension, appears to be a weakness in present evaluation procedures as they relate to fuel economy and pollution level testing: Recent work by Funfsinn and Korst has shown that substantial and measurable increases in energy losses occur for vehicles traveling on rough roads. The present investigation uses vehicle axle accelerations as a means of examining various road surfaces. Correlation with computer simulations has allowed the development of a deterministic road roughness model which permits the prediction of energy dissipation in both the tire and suspension as functions of road roughness, tire pressure, and vehicle speed. Comparison to the experiments of Korst and Funfsinn results in good agreement and shows that total rolling loss increases of up to 20 percent compared to ideal smooth roads are possible. The aerodynamic drag coefficient is also found to increase while driving on rough roads.     

Road Surface Correction o f Tire Test Data

SUMMARY

Most tire data used for vehicle simulations is measured on laboratory test facilities. An investigation showed that the frictional properties of these laboratory machines can be quite different from actual road conditions. This paper describes a method to correct laboratory tire test data to be more like road data in order to achieve a higher degree of correlation between instrumented test- and simulation results.     

台试与路试轮胎滚动阻力关联性研究

分析了台试与路试轮胎滚动阻力影响因素的内在联系；建立了台试与路试轮胎滚动阻力关联性模型；揭示了台试与路试轮胎滚动阻力之间的差异；解决了通过台试试验求解道路滚动阻力问题。     

Tire Modeling for Vertical Properties Including Enveloping Properties Using Experimental Modal Parameters

Summary Tire modal parameters reflect the natural properties of the tire. This paper models tire performance using experimental tire modal parameters to calculate the static vertical tire stiffness on both drum and flat road surfaces and the distribution of vertical and shear forces. The model was used to investigate tire enveloping properties. In addition to the radial and tangential displacements, the rotational angular displacement of the contact element is considered. This study examined the obstacle's effect on tire static vertical properties, the axle load responses under rectangle obstacles with a fixed axle height, and the effects of tire pressure on enveloping properties.