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。     

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。     

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。     

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。     

Prediction of tire natural frequency with consideration of the enveloping property

A lumped tire model was developed with consideration of the enveloping property in order to predict the natural tire frequency. Tire stiffness was classified into vertical, sidewall, and enveloping stiffnesses, and the tire characteristics were analyzed in detail experimentally and via finite element analysis. In addition, the effective masses of the tire tread and belt were extracted directly from design specifications taking into account the sizes and material properties of different rubber blocks. Using the design parameters of the tires, natural frequencies were calculated from the derived model and were compared with experimental results. Finally, based on good agreement with experimental results, sensitivity analysis was performed to verify the effect of tire stiffnesses on the natural frequencies.     

Finite element modeling of static tire enveloping characteristics

To investigate static tire enveloping characteristics, a three dimensional (3-D) finite element model is proposed. The vertical stiffness of the tire is studied on a flat surface with and without cleat. Tire rubber materials and cord layers are represented independently using “rebar” elements available in MSC Marc Mentat. Comparisons of numerical and experimental results are given to show the validity of the proposed model. It is shown that after a certain displacement, the results of the proposed model agree well with experimental results. In addition, the model results show that regardless of the type of the cleat placed under the rim center (hub center), all vertical force curves intersect after a certain displacement, which indicates typical static enveloping characteristics. Moreover, another typical characteristic of the radial tires that is unlike those of bias-ply constructions confirms that the contact patch does not expand laterally after a level vertical load is applied to the tire, which is directly related to fuel consumption and tire tread life.     

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。     

轮胎自由与约束悬置的模态试验与综合分析

为了证实约束对轮胎模态参数带来的影响，探讨如何从自由悬置的轮胎模态参数转化为固定悬置的参数，分别对自由悬置与固定悬置的轮胎进行激振试验，提取模态参数，并用模态综合法完成自由悬置结果到固定悬置结果的转化。模态综合计算的结果与试验相符，证明了利用自由悬置模态参数建模，利用模态综合的方法考虑约束系统动特性对轮胎特性的影响是合理的。     

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.     

轮胎位移包容性研究及有效路面谱计算方法

本文提出一种有效路形测量的新方法,研究轮胎的位移包容性。提出以轮胎包容参数为变量把真实路面功率谱变换为有效路面功率谱的新方法。该研究是道路激励模拟的基础研究。     

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。     

路面载重车辆的荷载特征

在收集了我国公路上行驶的单、双后轴整车型的载重车辆轴载资料的基础上,参考国家现行轴限规定与轮胎型号等标准,从路面结构设计的角度上对轴载、轮胎气压、接地压力、轴型参数等荷载特征参数进行了整理分析,采用统计回归方法找到了特征参数的规律和相互关系,进而提出了供路面结构设计的轴型参数:双轮间距、轮距、轴距按额定轴载进行分级的建议表,以及以后轴额定轴载和轴载实载率为自变参量的轮胎接地压力的统一回归式和回归系数,讨论了现行沥青路面结构分析中双轮中心距取3倍荷载当量圆半径宜根据额定轴载和轴载实载率确定适用范围。此研究结果为提高路面结构分析精度提供了可靠的荷载特征参数依据。