稳态条件下用于车辆动力学分析的轮胎模型

本文对稳态条件下可用于车辆动力学分析的轮胎理论模型和半经验模型,包括纵滑侧偏特性、纯纵滑特性和纯侧偏特性模型,进行了综合与分析,并讨论了各种模型间的相互关系。为车辆动力学分析提供了具体的轮胎模型和选用依据。     

稳态条件下用车车辆动力学分析的轮胎模型

本文对稳态条件下可用于车辆动力学分析的轮胎理论模型和半经验模型，包括纵滑侧偏特性、纯纵滑特性和纯侧偏特性模型，进行了综合与分析，并讨论了各种模型间的相互关系。为车辆动力学分析提供了具体的轮模型和选用依据。     

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。     

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。     

轮则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则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和方向。     

稳态轮胎偏滑力学的发展与展望

介绍了近70年来关于稳态轮胎纯理论模型的研究成果。描述了稳态轮胎半经验模型的发展过程及其现状和主要特点。在此基础上，总结出轮胎稳态力学研究工作发展过程的特点以及轮胎偏滑力学的发展趋势，指出了今后研究的重点。     

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.     

考虑胎体复杂变形的轮胎非稳态转向特性半经验模型

本文在考虑胎体复杂变形的轮胎非稳态侧偏特性理论模型的基础上，提出了一种半经验模型。经过试验验证，在与汽车平面运动有关的低频范围内，其理论值与试验值吻合较好。与已有产半经验模型相比，该模型精度较高，可直接反映轮胎模型参数和结构参数间的关系，便于在车辆动力学仿真与轮胎特性改进中应用。     

轮胎半经验模型中摩擦系数切换问题

介绍了2种简单的摩擦系数模型(库仑摩擦定律、静摩擦力模型)，并将其与轮胎统一刷子理论模型结合起来分析轮胎的摩擦问题。在此基础上引入了满足轮胎刷子理论模型边界条件的轮胎稳态半经验模型，给出了应用轮胎半经验模型实现摩擦状态切换的方法。通过轮胎在2种滚动速度下的侧偏试验，证明了轮胎半经验模型可实现2种速度下的摩擦系数切换。     

轮胎动力学特性仿真分析研究

分析了各种常用轮胎模型的特点与应用范围,根据汽车操纵动力学研究的需求,在Matlab环境下运用魔术公式建立了轮胎动力学模型,并对汽车轮胎力与纵向滑移率,纵向力、侧向力及回正力矩与纵向滑移率、侧偏角、外倾角、垂直载荷的关系等轮胎特性进行了仿真分析,实验结果表明,魔术公式轮胎动力学模型可以较好地模拟轮胎的动力学特性,适用于车辆动力学研究领域。     

Analysis of Tire Effect on the Simulation of Vehicle Straight Line Motion

In the dynamic simulation of vehicle straight line motion, a vehicle model usually drifts from its intended straight path even in the case of no external input. This is particularly true when a tire model based on experimental data is used. The purpose of this paper is to provide an enhancement of a basic understanding of a tire/vehicle system behavior in the straight line motion and to identify the effect of the tire on that motion. Through the analysis of a two degrees of freedom vehicle model, tire characteristic which causes a lateral drift in the straight line motion is identified. Then the results are confirmed from vehicle test and the simulations with a more complex full-car model.     

Analysis of Tire Effect on the Simulation of Vehicle Straight Line Motion

In the dynamic simulation of vehicle straight line motion, a vehicle model usually drifts from its intended straight path even in the case of no external input. This is particularly true when a tire model based on experimental data is used. The purpose of this paper is to provide an enhancement of a basic understanding of a tire/vehicle system behavior in the straight line motion and to identify the effect of the tire on that motion. Through the analysis of a two degrees of freedom vehicle model, tire characteristic which causes a lateral drift in the straight line motion is identified. Then the results are confirmed from vehicle test and the simulations with a more complex full-car model.     

Prediction procedure for wear distribution of transient rolling tire

As a research method, finite element analysis (FEA) with ABAQUS can help researchers to study throughout the whole process of abnormal tire wear. For precise tread wear simulation, this paper introduces a tire finite element model building method. Then, the model is verified by comparing its simulation results with experiment data. Based on the verified model, tire high-speed rolling procedure is presented by combining steady-state transport analysis and dynamic analysis. To predict the wear distribution, micro tread wear calculation method is described. Finally, the wear prediction procedure of tread mesh evolving is introduced and tire polygonal wear pattern is simulated by this procedure.     

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.     

Analysis of the Dynamic Response of a Rolling String-Type Tire Model to Lateral Wheel-Plane Vibrations

A theory has been developed for the analysis and prediction of the dynamic frequency response of lateral force and moment acting upon a pneumatic tire when the wheel is moved laterally and swivelled about the vertical axis. The theory establishes the force and moment response of a tire model which consists of a stretched circular string with mass, elastically supported to the wheel-center-plane. The analysis is confined to small deviations from rectilinear motion such that it is permissible to assume that sliding does not occur in the contact area. In this manner, the equations are kept linear.

The theory which gives an exact analysis of the dynamic response of the model adopted shows satisfactory qualitative agreement with experiments. The change in the moment response due to tire inertia reduces the tendency to shimmy at higher frequencies and higher speeds. The lateral force response, however, changes in an unfavorable fashion which, for castered wheels, may result in a decrease of the effective damping about the king-pin at higher speeds and frequencies.     

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.     

Adaptive Control of 4WS System by Using Neural Network

An adaptive control system of the model following type is proposed for drive motion control of a four wheel steering (4WS) car with using neural network (NN) which has mastered nonlinear friction force between tire and road surface. A model of one rigid body is adopted which represents appropriately two kinds of car motion caused by steering action, namely the lateral displacement and the yawing rotation, and an equation of motion is described in a simplified form to make a system equation for motion control possible. Nonlinear relation between the cornering force of tire and the slip angle is obtained by numerical analysis with the tire model proposed by E. Fiala, taking friction coefficient and car speed as the parameters. The result is used as the teaching signal for NN. Three NN are used in the control system composed of both the feed-forward and the feedback circuits in order to realize adaptive control. Validity and usefulness of the proposed adaptive control system with NN are verified by three kinds of computer simulation.     

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.     

Adaptive Control of 4WS System by Using Neural Network

SUMMARY

An adaptive control system of the model following type is proposed for drive motion control of a four wheel steering (4WS) car with using neural network (NN) which has mastered nonlinear friction force between tire and road surface. A model of one rigid body is adopted which represents appropriately two kinds of car motion caused by steering action, namely the lateral displacement and the yawing rotation, and an equation of motion is described in a simplified form to make a system equation for motion control possible. Nonlinear relation between the cornering force of tire and the slip angle is obtained by numerical analysis with the tire model proposed by E. Fiala, taking friction coefficient and car speed as the parameters. The result is used as the teaching signal for NN. Three NN are used in the control system composed of both the feed-forward and the feedback circuits in order to realize adaptive control. Validity and usefulness of the proposed adaptive control system with NN are verified by three kinds of computer simulation.