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.     

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。     

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。     

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.     

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     

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。     

轮胎静包容特性的试验研究

对轮胎静包容特性进行了试验研究。试验分为两种：静止状态进行测量(称静包容特性)和低速滚动连续测量(称准静态包容特性)。试验还在固定轴高和固定垂直轴荷的两种方法下进行了包容特性测量，试验工况分为不同形状和尺寸的障碍物，以及不同胎压。试验测试结果准确度高，可为模型计算结果提供试验验证。     

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.     

轮胎包容特性分析及其在汽车振动系统建模中的应用

本文分析了轮胎与路面的接触特点，将汽车承载系统简化为二自由度垂直振动系统，建立了同时考虑轮胎几何滤波效应与弹性滤波效应的弹性滚子接触模型。基于刚性滚子模型和弹性滚子模型，仿真出滚子包容后的有效路形。     

利用模态分析技术获取轮胎的模态参数

由模态试验获取轮胎自由悬置的模态参数，应用模态分析技术进行轮胎力学研究，用模态综合法实现轮胎自由悬置到固定支承的转化，从而从理论上给出轮胎固定支承时的模态参数。计算结果与试验结果基本吻合。     

轮胎动特性试验模态分析

本文探讨了对轮胎进行模态试验的方法，并对两种不同特性的轮胎进行了两个方向的激振试验，并在每向激振情况下提取了各阶的径向和切向模态振型。对比所获得的模态参数，可看出两种轮胎的模态参数明显地表征了它们的不同宏观特征。     

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。     

Simulation of Vehicle and Power Steering Dynamics Using Tire Model Parameters Matched to Whole Vehicle Experimental Results

This paper uses simulation to investigate how vehicle loading conditions (driver only, passengers, cargo, and fuel) affect power steering system and overall vehicle dynamics. Our purpose of the study was to evaluate the power steering system model for possible use in the National Advanced Driving Simulator (NADS). The effects of changing loading conditions on inertial properties of passenger cars have been found experimentally using a Vehicle Inertia Measurement Facility (VIMF). This paper presents simulation results using a vehicle handling model combined with a power steering system model and a nonlinear tire model. A crucial part of this project was the adjustment of certain parameters of Pacejka's tire model in order to match simulation results with experimental measurements of vehicle and power steering variables in transient maneuvers.     

Simulation of Vehicle and Power Steering Dynamics Using Tire Model Parameters Matched to Whole Vehicle Experimental Results

This paper uses simulation to investigate how vehicle loading conditions (driver only, passengers, cargo, and fuel) affect power steering system and overall vehicle dynamics. Our purpose of the study was to evaluate the power steering system model for possible use in the National Advanced Driving Simulator (NADS). The effects of changing loading conditions on inertial properties of passenger cars have been found experimentally using a Vehicle Inertia Measurement Facility (VIMF). This paper presents simulation results using a vehicle handling model combined with a power steering system model and a nonlinear tire model. A crucial part of this project was the adjustment of certain parameters of Pacejka's tire model in order to match simulation results with experimental measurements of vehicle and power steering variables in transient maneuvers.     

利用遗传算法识别汽车轮胎魔术公式参数

汽车轮胎动力学模型的准确度对汽车运动仿真的精度影响很大。汽车轮胎魔术公式是一种精度较高的轮胎模型。利用遗传算法的非线性优化特点,对汽车轮胎纯滑移魔术公式参数进行识别,并讨论算法参数对参数识别的影响。识别结果,纵向力和侧向力的相对残差在5%左右,回正力矩的相对残差在10%左右。     

轮胎橡胶摩擦特性的试验研究

在自主研制的摩擦试验机上进行了轮胎橡胶摩擦特性试验,以揭示摩擦因数随压力和滑摩速度而变化的规律.尽管由于试验机的原因,测出的数据有较大的波动,但经过适当的处理后,在试验工况范围内,仍然得出合理而有规律性的结果.连同试验方法都有一定的参考价值,但仍有待进一步研究.     

Magic Formula轮胎模型参数辨识的一种混合优化方法

Magic Formula(MF)轮胎模型能够准确描述轮胎的侧偏特性,广泛应用于车辆动力学的研究。由于MF轮胎模型参数多,且高度非线性,从大量的试验数据中准确辨识这些参数相当困难。提出一种基于遗传算法和数值优化算法的混合优化方法,采用由粗到精的辨识过程,先利用遗传算法得出近似最优解,再利用数值优化算法辨识出精确的参数。利用辨识出的参数计算轮胎的侧偏特性,计算结果与试验数据吻合良好,表明该方法是辨识MF轮胎模型参数的有效手段。     

分布式电驱动车辆纵-横-垂向力协同控制

针对现有研究多采用经验工况划分、主动悬架力简单分配等轮胎力解耦控制方法,难以实现车辆性能最优化的问题,提出了分层式轮胎纵-横-垂向力协同优化控制系统,在制定上层行驶期望目标和下层执行控制策略的同时,重点研究了中层轮胎纵-横-垂向力优化分配。建立了融合轮胎负荷率和垂向力动态系数的统一优化目标函数,综合考虑了车辆行驶期望目标、轮胎附着极限和执行器特性等约束条件,最终解决了轮胎纵、横、垂向力的协同优化控制难题。基于Matlab/Simulink和CarSim的联合仿真结果表明,提出的分层协同控制系统能同时有效控制车辆行驶姿态和改善车辆操纵稳定性能。