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

SUMMARY

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.     

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。     

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.     

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.     

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。     

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.     

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。     

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.     

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.     

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。     

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.     

Study on Tire Dynamic Cornering Properties Using Experimental Modal Parameters

Based on the modeling of tire vertical characteristics and steady cornering properties, the model of tire nonsteady cornering is established in this paper using tire modal parameters extracted experimentally. In order to consider the influence of tire rolling effect on its cornering properties, the induced transfer function is introduced. The analytical formulae for calculation of transfer-function of lateral force and self-aligning torque with respect to lateral displacement and yaw angle are derived. The nonsteady cornering characteristics of tire under different loads can be calculated. The results of calculation are consistent with the experimental ones in the literature. The influence of rolling speed on tire cornering properties including the static case is analyzed. The nonsteady cornering properties in high frequency range are given by the model. The study demonstrates the consistency between steady and nonsteady tire modeling by using modal parameters.     

Study on Tire Dynamic Cornering Properties Using Experimental Modal Parameters

Based on the modeling of tire vertical characteristics and steady cornering properties, the model of tire nonsteady cornering is established in this paper using tire modal parameters extracted experimentally. In order to consider the influence of tire rolling effect on its cornering properties, the induced transfer function is introduced. The analytical formulae for calculation of transfer-function of lateral force and self-aligning torque with respect to lateral displacement and yaw angle are derived. The nonsteady cornering characteristics of tire under different loads can be calculated. The results of calculation are consistent with the experimental ones in the literature. The influence of rolling speed on tire cornering properties including the static case is analyzed. The nonsteady cornering properties in high frequency range are given by the model. The study demonstrates the consistency between steady and nonsteady tire modeling by using modal parameters.     

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.     

基于路面影响因子的轮毂电机驱动车辆自适应转矩控制

为实现轮毂电机驱动越野车辆在附着条件多变、路面起伏不定的复杂环境中动力性和稳定性的多目标优化,提出一种基于路面影响因子的自适应转矩控制策略。以滚动阻力差异、空气阻力归一化比例、坡度阻力归一化比例、路面附着差异方差以及最小路面附着系数5个特征参数作为输入,并基于模糊理论方法搭建路面影响因子五参数辨识模型。基于辨识出的路面影响因子,开发整车动力性和稳定性多目标优化自适应转矩控制策略,构建了三层式控制架构：顶层引入路面影响因子对加速度紧迫程度进行判定,采用模型预测控制算法得到期望总驱动力;中层为目标决策层,以最优滑转率为目标决策驱动防滑力矩,并基于路面行驶阻力,决策期望前馈补偿力矩;下层为转矩分配层,以需求总驱动力及轮胎利用率作为控制目标,引入路面影响因子优化两者权重系数,以多约束条件的混合优化算法对转矩进行自适应控制。利用Matlab/Simulink-CarSim联合仿真平台进行仿真,基于实车进行验证。结果表明,在低附着路面,在0.2 s内快速完成滑转率抑制;在对开路面,侧向位移接近0;在大扭曲路面,避免腾空车轮出现大滑转率,滑转率最高0.2。     

The Circumferential Contact Problem for the Belted Radial Passenger Car Tire

The belted radial passenger car tire is idealized as a prestressed circular ring connected to a hub through a distribution of linear springs modeling the sidewall. A second distribution of such springs exterior to the ring represents the tread rubber. The tire is supposed to be at rest, loaded at its hub, and pressed onto a flat, rigid, frictiontess roadway. In this situation the linear differential equations of the model are solved using a singular perturbation technique. Given the load at the hub, the solutions furnish the length of tread in contact with the road, the radial and circumferential displacement of all points on the ring, and the distribution of pressure over the region of contact.     

轻型货车轮胎接地压力分布实测

利用自主开发的轮胎接地压力测试仪,进行了轻型货车不同花纹和不同使用年限轮胎,在不同轮胎胎压和不同负荷作用下,轮胎的接地压力分布规律测量。实测结果发现:轻型货车轮胎与路面的接触形状更接近于矩形;新胎比旧胎的接地压力要均匀些;轮胎胎压与平均接地压力、轮胎负荷与平均接地压力、轮胎负荷与有效接地面积基本上呈线性关系。     

Constrained Optimal Control of Semi-Active Suspension Systems with Preview

Controllers for semi-active suspensions have to account for constraints on damper range, tire force and suspension travel. Two approaches to incorporate these constraints in the design of controllers to minimize peak values in the chassis acceleration are considered. It is assumed that information on the oncoming road elevations (preview) is available. In the soft constraint approach, the constraints on tire force and suspension travel are included in a quadratic performance index. Two clipped optimal control laws, which deal with preview in a different way, are presented. Simulation results with a 2-DOF vehicle model on some rounded pulses show that these laws do not work satisfactorily with respect to the constraints. Therefore, the control problem is reformulated as a constrained optimization problem with hard constraints on tire force and suspension travel. Simulations with the same model on the same rounded pulses show that the hard constraint approach handles the constraints more properly.