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。     

轮胎动态侧偏特性对汽车摆振的影响

轮胎的侧偏力学特性是影响汽车前轮摆振的最关键因素之一，文中在箕是汽车研究所提出了轮胎动态侧偏特性试验方法的基础上，建立了侧向力与回正力矩的精确表达式，并从能量反馈和负阻尼效应研究了轮胎动态侧偏特性参数对汽车偏摆振的影响。     

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。     

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     

制动—驱动工况下的轮胎侧偏特性理论研究

本文通过考虑制动和驱动工况下的轮胎印迹内垂直载荷分布的不同，建立了比以往模型更完善的制动－驱动工况下的轮胎侧偏特性理论模型，以６．５０Ｒ１６轮胎为例，分析了滑移率，侧偏角和垂直载荷分布形状参数等对其侧特性的影响。     

轮胎侧偏动力特性的实验研究

本文研究了常侧偏角和时变轮胎载荷激励下轮胎的传递特性,测量了轮胎侧偏力、回正力矩和外倾力矩对轮胎载荷的传递函数,并考虑了轮胎参数的影响。用数据处理方法消除了实验台、测量装置和轮辋的惯性力的影响。     

基于虚拟样机的轮胎侧偏特性分析

设计了满足轮胎侧偏、外倾及加载功能的轮胎试验机,对其连杆机构进行了运动学仿真,评估了轮胎侧偏角、外倾角与油缸行程的运动关系.在试验机的虚拟样机模型上对轮胎进行了数值计算,获得不同使用条件下轮胎的侧偏特性,并与试验数据进行了趋势性对比.结果表明,该试验机具备复杂工况下轮胎侧偏性能测试能力.     

基于HSRI模型的参数自适应质心侧偏角观测器的设计

首先对全维车速观测器进行降维处理,以减少观测器的在线计算量,并设计了非线性级联车速观测器.接着,对路面附着系数和轮胎侧偏刚度进行参数自适应估计,以提高质心侧偏角的估计精度,并基于HSRI轮胎模型设计了参数自适应非线性质心侧偏角观测器.在估算轮胎侧偏刚度时采用无侧向车速的车辆模型,以避免车辆动力学模型与侧向车速观测器的耦合作用,并引入带双重遗忘因子的递推最小二乘法,以保持算法的修正能力和解除不同估计参数之间误差的耦合作用.最后采用Simulink与Carsim动力学仿真软件进行联合仿真验证,结果表明所设计的参数自适应非线性质心侧偏角观测器是有效的,估计精度满足ESC控制的工程要求.     

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。     

轮胎侧偏动特性对汽车操纵稳定性的影响

在建立轮胎侧偏动特性微分方程的基础上 ,利用 8自由度车辆模型进行仿真 ,分析了轮胎侧向力滞后对车辆操纵稳定性的影响 ,给出了各工况下的仿真结果。结果表明 ,轮胎侧偏动特性对车辆高速时的操纵稳定性具有一定的影响作用。     

Longitudinal Tire Dynamics

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

A semi-empirical dynamic tire model for combined-slip forces

This article presents a semi-empirical combined-slip tire model including transient behavior. It is assumed that the transient behavior is a result from the dynamic deformation of the tire carcass and that the interaction between the lateral and longitudinal slip, and forces can be explained by the deformation of the rubber treads. The deformation of the tire carcass makes the tread slip deviate from the wheel-rim motion in a way that may be described by differential equations. A method based on brush-model tire mechanics is used to construct the combined-slip forces as nonlinear scalings of corresponding pure-slip forces.     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

轮胎制动力—滑移率特性的动态模型研究

轮胎制动力及滑移率对制动力矩的响应存在着显著的低频衰减振荡现象，这从制动力－滑移率特性曲线上看，表现为一系列的以稳态点为中心的旋涡状过渡曲线。这是稳态的轮胎模型所不能描述的。本文在稳态ｂｒｕｓｈ轮胎模型基础上，通过印迹前端蹼处胎冠一阶变形模型，建立了轮胎制动力－滑移率的动态模型，并根据转鼓试验台上的轮胎制动试验，验证了该模型的仿真效果。     

Estimation of maximum road friction coefficient based on Lyapunov method

With the real time and accurate information of motor torque and rotation speed of the four-in-wheel-motordrive electric vehicles, a slip based algorithm for estimating maximum road friction coefficient is designed using Lyapunov stability theory. Modified Burckhardt tire model is used to describe longitudinal slip property of the tire. By introducing a new state variable, a nonlinear estimator is proposed to estimate the longitudinal tire force and the maximum road friction coefficient simultaneously. With the appropriate selection of estimation gain, the convergence of the estimation error of the tire longitudinal force and maximum road friction coefficient is proved through Lyapunov stability analysis. In addition, the error is exponentially stable near the origin. Finally the method is validated with Carsim-Simulink co-simulation and real vehicle tests under multi working conditions in acceleration situation which demonstrate high computational efficiency and accuracy of this method.     

车辆轮胎动力学仿真模型分析

分析了各种常用轮胎模型的特点和利用范围,介绍了ADAMS中轮胎试验台(tiretesting)这一轮胎参数可视化工具,利用这一工具分析比较一种物理轮胎模型与一种经验-半经验轮胎模型间关于侧向力与纵向力、纵向力与纵向滑移率、回正力矩与纵向滑移率的力学特性,针对一种魔术公式轮胎模型验证了侧向力和纵向滑移率、纵向力和纵向滑移率在不同载荷下的力学关系特性。     

Tire Lateral Force Estimation Using Kalman Filter

As for the tire analysis, lateral tire force is a fundamental factor that describes the stability of vehicle handling. Attempts to analyze the vehicle stability have been made based on various objective test methods and some specific factors such as yaw, lateral acceleration and roll angle. However, the problem to identify which axle is lack of the tire grip at a certain situation still remains. Since indoor tire force measurement system cannot represent a real road and vehicle conditions, tire force measurement through a real vehicle test is inevitable. Due to the high price of the tire force measurement device, tire force estimator can be an alternative toward cost reduction and device failure. In this paper, nonlinear planar full car model combined with tire model is proposed. Then, using discrete-time extended Kalman-Bucy filter (EKBF), individual tire lateral force are estimated with modified relaxation length model.     

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.