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.     

轮胎滚动速度效应对轮胎侧偏动特性的影响

在利用试验模态参数建立轮胎侧偏非稳态模型基础上，本文重点分析了轮胎滚动速度效应对侧偏动特性的影响。解析模型计算结构的变化趋势和文献的试验研究结果一致。表明计入轮胎滚动所带来的速度对侧偏动特性的影响是不可忽略的，它会对不同速度下行驶汽车的操稳性及横向振动产生影响。滚动速度效应对轮胎侧偏特性影响的成功建械表明了利用模态参数对轮胎建模的优越性。     

利用模态参数对轮胎纯侧偏特性建模

在轮胎静生趣特怀建模的基础上，探讨了利用轮胎模态参数对轮胎纯侧偏特性的建模。通过侧向激振试验提取了轮胎的侧向模态参数并计算了轮胎在不同载荷下的偏离特性，计算结果与以往轮胎的试验结果具有很好的一致性。计算结果转化为无量纲形式并与经验模型进行了比较，建模和计算结果充分说明了模型的合理并显示了建模方法的优越性。     

Establishment of Model for Tire Steady State Cornering Properties using Experimental Modal Parameters

Modeling of tire cornering properties using experimental modal parameters is studied. With tire lateral experimental modal parameters, the distribution of side force and lateral deformation under total adhesive and sliding conditions are obtained. Side force, self-aligning, cornering stiffness and relaxation length under different loads and friction coefficients are also calculated. The calculated results are in correspondence to experimental results in the references qualitatively. The non-dimensional side force obtained from the calculated results is compared with the Fiala model, its modified expression by experiments and also the widely used empirical Magic Formula model. The calculated results tally well with the fitted results obtained using Magic Formula model. It can be seen that the tire steady state cornering model using experimental modal parameters proposed in this paper is better for an in-depth study of tire natural characteristics, and the labored experimental work can be avoided.     

Establishment of Model for Tire Steady State Cornering Properties using Experimental Modal Parameters

Modeling of tire cornering properties using experimental modal parameters is studied. With tire lateral experimental modal parameters, the distribution of side force and lateral deformation under total adhesive and sliding conditions are obtained. Side force, self-aligning, cornering stiffness and relaxation length under different loads and friction coefficients are also calculated. The calculated results are in correspondence to experimental results in the references qualitatively. The non-dimensional side force obtained from the calculated results is compared with the Fiala model, its modified expression by experiments and also the widely used empirical Magic Formula model. The calculated results tally well with the fitted results obtained using Magic Formula model. It can be seen that the tire steady state cornering model using experimental modal parameters proposed in this paper is better for an in-depth study of tire natural characteristics, and the labored experimental work can be avoided.     

利用试验模态参数建立轮胎非稳态侧偏模型

在对轮胎垂直特性和稳态侧偏特性建模的基础上，利用由轮胎模态试验提取的试验模态参数建立了轮胎非稳态侧偏模型，该模型考虑了印迹的动态变形和胎宽的影响，对印迹进行离散化并初步计入了速度对非稳态性的影响，推导出侧向力和回正力矩关于侧向位移和摆动角的传递函数的解析公式，可以计算不同载荷下的非稳态特性，计算结果与文献中的试验结果相符，建模和计算结果说明利用试验模态参数可以方便地建立轮胎的非稳态特性，计算结果与     

轮胎胎面特性对侧偏模型预测精度影响分析

胎面花纹是影响轮胎性能的重要因素。文中以模态参数模型的稳态侧偏模型为基础，从理论推导和实际计算两方面说明胎而花纹刚度的重要性，其对侧偏模型计算结果的影响要大大高于对垂直模型的影响。因此，在确定轮胎解析模型中胎面花纹参数时应首先考虑其对侧偏模型的影响。     

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.     

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。     

轮胎非稳态转向特性非线性仿真模型

本文以轮与路面之间的滑移速度为出发点，在稳态指数统一模型的基础上，建立了轮胎非稳态转向特性非线性仿真模型。在实验研究中，发现了动态过程回正力臂和附加的回正力矩的滞后特性。仿真和试验结果对比表明，该模型足以反映轮胎非线性转向特性，可用于前轮及汽车操纵动力学仿真方面的研究。     

基于自适应模型预测的智能汽车横向轨迹跟踪控制

当路面附着情况和车辆行驶状态不断变化时,基于恒定侧偏刚度的模型预测控制(MPC)不能考虑轮胎非线性特性的影响,难以保证车辆轨迹跟踪的适应性。为此,提出一种考虑轮胎侧向力计算误差的自适应模型预测控制(AMPC),以提高智能汽车在不确定工况下的轨迹跟踪性能。分析了路面附着系数和垂向载荷对轮胎侧向力的影响,基于平方根容积卡尔曼滤波(SCKF)算法,设计了利用侧向加速度和横摆角速度作为测量变量的前后轮胎侧向力估计器。利用轮胎侧向力线性计算值与估计值的差值计算得到侧偏刚度修正因子,设计了前后轮胎侧偏刚度的自适应修正准则,进而提出了一种基于时变修正刚度的AMPC控制方法。基于CarSim与MATLAB/Simulink联合仿真和硬件在环测试平台,对AMPC控制的有效性和实时性进行了验证。研究结果表明：在不同的路面附着情况和车辆行驶状态下,AMPC控制都能够降低横向位置偏差和航向角偏差,有效提高车辆的轨迹跟踪精度,其控制效果明显优于基于恒定侧偏刚度的标准MPC控制。尤其在低附着工况下,标准MPC控制会因为线性轮胎力的计算误差过大而导致车辆在轨迹跟踪时严重失稳,而AMPC控制通过估计轮胎力修正侧偏刚度依然能够保证车辆稳定有效的跟踪参考轨迹。所提出的AMPC控制在保证控制精度的同时具有良好的实时性,对智能汽车控制系统的设计与优化具有重要参考价值。     

轮胎非稳态侧偏特性在空间域内的仿真研究

本文根据胎体复杂变形的轮胎非稳态侧偏特性理论模型在空间域内的表达式,推导出侧向力和回正力矩关于转动角与侧向位移的积分表达式,将其离散化并实现了非稳态侧偏特性在空间域内的仿真,最后给出了轮胎在几种典型输入时的仿真结果。     

轮胎非稳态侧偏特性的建模

分析了轮胎侧偏特性的建模机理，从胎面的印迹侧向变形和胎体的侧向平移变形出发，计算出运动状态下轮胎印迹瞬时变形的数学表达式，建立了考虑胎面弹性的轮胎非稳态侧偏特性模型。最后，将该理论模型与试验结果进行了对比。     

考虑胎体复杂变形的轮胎非稳态侧偏特性理论模型

本文从肥体的一般变形模式出发，根据胎体的侧向弯曲变形及扭转变形计算出胎面的侧向瞬时变形，从而建立了小幅运动时轮胎非稳态侧偏特性理论模型。考虑胎体的复杂变形之后，模型能真实地反映轮台力学特性和物理实质。     

利用试验模态参数对轮胎包容特性的建模及试验验证

利用试验模态参数建立轮胎模型,计算了轮胎的静包容特性,计算结果与文献中所揭示的包容现象及变化规律有很好的定性一致。在此基础上对轮胎包容特性的建模进行了定量分析,包括模态阶数的截取和胎侧非线性的刚度。将计算结果与平板式轮胎试验台上进行的试验结果相比较,表明记入以上两方面考虑的因素下,计算结果与试验结果在各方面均很好吻合。定量分析的结果表明,不考虑胎侧非线性时,对轮胎垂直刚度的计算结果会远远高于试验结果。     

适用于汽车转弯制动仿真的轮胎力学模型

通过对轮胎试验结果的分析,用统计拟合方法建立了一种适用于转弯制动联合工况仿真的轮胎力学模型。所建模型与实际情况接近,计算简便,在用理论分析建模困难时,而采用试验数据进行统计建模不失为一种有效的途径。     

利用试验模态参数对轮胎垂直特性建模

本文用试验模态参数建立轮胎模型。通过对轮胎的和径向和切向激振试验获取模态参数，将地面对轮胎的作用当作输入。采用迭代算法计算了静态垂直特性，即垂直刚度、印迹长度及摩擦力在纵向的分布。然后计算了考虑轮胎预载的３００Ｈｚ内的垂直振动特性。采用模态综合方向将车轮、悬架及车身组合成的一个系统，计算出了该系统的垂直振动特性。研究显示了这种方法的可靠性和优越性。     

动态载荷下轮胎侧偏特性的理论及试验研究

提出了在动载和时变印迹长度下轮胎的接触历程概念,导出了计算动载时轮胎接地印迹内各点接触历程的入迹方程,阐明轮胎动载侧偏力学特性建模机理,克服了动载侧偏特性理论建模的一个基本障碍,建立了考虑胎体平移弹性小幅动载时的理论模型,并提出了轮胎动载侧偏特性的半经验模型,进行了相应的试验研究,给出了试验结果与模型计算结果的比较。     

A simplified model for evaluating tire wear during conceptual design

In the field of vehicle dynamics, commercial software can aid the designer during the conceptual and detailed design phases. Simulations using these tools can quickly provide specific design metrics, such as yaw and lateral velocity, for standard maneuvers. However, it remains challenging to correlate these metrics with empirical quantities that depend on many external parameters and design specifications. This scenario is the case with tire wear, which depends on the frictional work developed by the tire-road contact. In this study, an approach is proposed to estimate the tire-road friction during steady-state longitudinal and cornering maneuvers. Using this approach, a qualitative formula for tire wear evaluation is developed, and conceptual design analyses of cornering maneuvers are performed using simplified vehicle models. The influence of some design parameters such as cornering stiffness, the distance between the axles, and the steer angle ratio between the steering axles for vehicles with two steering axles is evaluated. The proposed methodology allows the designer to predict tire wear using simplified vehicle models during the conceptual design phase.     

轮胎附着极限下差动制动对汽车横摆力矩的影响

本文以纵滑－侧偏联合工况的稳态轮胎模型为基础，分析了汽车极限转向条件下制动作用于不同车轮时对汽车横摆力矩的影响，并通过整车动力学仿真进行了验证，研究结果为利用差动制动控制提高汽车的高速操纵稳定性提供了动力学依据。