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     

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。     

轮胎转偏特性分析与建模

分析了不同轮胎侧向输入量间的几何关系，在考虑胎体复杂变形的轮胎非稳态侧偏理论模型的基础上得到累胎非稳态转偏理论模型。还将无量纲的非稳态转偏理论模简化为有理分式形式，以利于定性分析和理解轮胎转偏特性。所建模型可用于汽车动力学仿真与分析。     

考虑胎宽时的轮胎非稳态侧偏特性模型

计算出运动状态下轮胎印迹纵向瞬时变开的数学表达式。在考虑胎宽影响的条件下，建立了车轮输入分别为转动角与侧向位移、侧偏角与转含蓄经时的轮胎非稳态侧偏模型（传递函数）。根据该模型计算出的频率响应特性与试验结果相符，为汽车方向操纵运动仿真，前轮摆振和汽车动态响应等研究提供了反映物理实质的轮胎非稳态侧偏理论模型。     

轮胎滚动速度对车辆侧偏特性的影响

考虑滚动速度对印迹内压力分布及轮胎与路面间摩擦系数的影响,建立了考虑胎体复杂变形的轮胎稳态侧偏理论模型.仿真分析了滚动速度对轮胎侧偏侧向力及回正力矩特性的影响,并对轮胎高,低速特性的差异给出了解释.指出,建立具有合理速度预测能力半经验模型时,应考虑对滚动速度的影响.     

非稳态条件下轮胎结构参数对侧向力与回正力矩的影响

通过非稳态条件下小幅运动（即假设印迹内无滑移发生）时的轮胎侧偏特性在空间域内的仿真，分析了轮胎结构对侧向力与回正力矩的影响，并介绍了非稳态条件下轮胎侧偏特性的仿真表达式及纯转向运动时的仿真数值算法。     

轮胎非稳态侧偏特性的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肉的表达式，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。     

汽车轮胎侧偏特性影响因素的试验研究

应用轮胎静力学特性试验机，研究了低速条件下3种不同胎面花纹轮胎在干燥路面上的侧偏特性，主要分析了胎面花纹、轮胎负荷和轮胎气压等因素对轮胎侧偏特性的影响。结果表明：轮胎的Fy-α关系曲线形状与胎面花纹形式、轮胎负荷和胎压等均无关。而Mz-α关系曲线变化趋势与胎面花纹无关，却与轮胎负荷和气压有关；在相同试验条件下，顺向花纹轮胎具有更优异的附着性能和侧偏特性。     

大侧偏角下侧偏松弛长度特性的研究

本文在稳态指数统一模型和一阶线性微分方程的基础上，研究了大侧偏角下动态过程中侧偏松弛长度的特性。侧偏松弛长度是由轮胎的侧向弹性决定的。在大侧偏角下，侧偏松弛长度不再是一个常数，而是随着侧向有效滑移率的改变而改变，而且它们之间呈现非线性特性。深入了解侧偏松弛长度的特性对研究轮胎动态特性和建立轮胎动态模型具有重要的作用。     

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。     

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。     

A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis

Pacejka's Magic Formula Tyre Model is widely used to represent force and moment characteristics in vehicle simulation studies meant to improve handling behaviour during steady-state cornering. The experimental technique required to determine this tyre model parameters is fairly involved and highly sophisticated. Also, total test facilities are not available in most countries. As force and moment characteristics are affected by tyre design attributes and tread patterns, manufacturing of separate tyres for each design alternative affects tyre development cycle time and economics significantly. The objective of this work is to identify the interactions among various tyre design attributes-cum-operating conditions and the Magic Formula coefficients. This objective is achieved by eliminating actual prototyping of tyres for various design alternatives as well as total experimentation on each tyre through simulation using finite element analysis. Mixed Lagrangian–Eulerian finite element technique, a specialized technique in ABAQUS, is used to simulate the steady-state cornering behaviour; it is also efficient and cost-effective. Predicted force and moment characteristics are represented as Magic Formula Tyre Model parameters through non-linear least-squares fit using MATLAB. Issues involved in the Magic Formula Tyre Model representation are also discussed. A detailed analysis is made to understand the influence of various design attributes and operating conditions on the Magic Formula parameters. Tread pattern, tread material properties, belt angle, inflation pressure, frictional behaviour at the tyre–road contact interface and their interactions are found to significantly influence vehicle-handling characteristics.     

A two-dimensional tire model on uneven roads for vehicle dynamic simulation1

This study proposes a comprehensive analytical tire model for handling and ride comfort in low frequency ranges. A contact algorithm that is developed in this study provides a two-dimensional contact pressure distribution on even and uneven road surfaces with reasonable computational cost. Shear stresses and strains during cornering and braking are estimated by direct measurement of tread deformations. The model is validated against experimental force and moment data for general handling simulations. Cleat tests are also conducted and validated under different forward velocity and vertical load conditions for a tire vibration study.     

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.     

轮胎侧偏特性研究的特点及其发展

首先,分析并阐述了车辆动力学特性与轮胎力学特性的关系。然后,对轮胎力学特性进行了分类,介绍了轮胎侧偏特性研究的特点,描述了轮胎稳态和非稳态侧偏特性研究的历史及其发展。最后,指出了轮胎侧偏特性研究的意义和轮胎模型的研究方向。     

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.