Magic Formula轮胎模型动力学性能研究

进一步研究Magic Formula轮胎模型的动力学性能。在Adams软件中建立Magic Formula轮胎模型,并进行纯制动、纯转向和制动转向联合三种工况下的仿真。仿真得到纵向力与纵向滑移率、侧向力与侧偏角、侧向力与纵向力和回正力矩与滑移率等关系曲线,并进行分析。结果表明,Adams软件完成了Magic Formula轮胎模型多种工况下的仿真工作,Magic Formula轮胎模型可以较好地模拟轮胎动力学特性。     

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。     

整车不足转向特性影响因素研究

文章分析了悬架KC特性、轮胎力学特性对车辆不足转向特性的影响,其中悬架侧倾转向、侧向力转向、回正力矩转向及轮胎侧偏刚度对整车不足转向特性有重要贡献,而轮胎垂向载荷及复合工况下纵向滑移率则对轮胎侧偏刚度有明显影响,进而改变整车不足转向特性,为底盘开发提供了重要的理论依据。     

用于动力学模拟的STI轮胎模型分析

介绍了用于汽车驾驶模拟器动力学模拟的STI（Systems Technologies Inc）轮胎半经验模型,建立了该轮胎模型的复合滑移率、横向刚度和纵向刚度以及横向力和纵向力的计算方程,并利用Vc＋＋6．0编程计算得到的理论值与实验值对比,对该模型进行了分析和验证。分析结果表明,该轮胎模型用于车辆动力学模拟时有较好的精度。     

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。     

轮胎力滞后对分布式驱动电动汽车瞬态响应的影响

分布式驱动电动汽车具有的电机直驱和工况响应快速的特点，会进一步激发轮胎瞬态特性。为了简要分析轮胎力滞后对分布式驱动电动汽车侧向、横摆瞬态响应的影响规律，进而优化其控制器模型，本文首先通过轮胎力学建模和高速轮胎试验台验证，得到轮胎力滞后的实用表达；其次，建立考虑轮胎侧-纵向力滞后的车辆动力学模型，通过频域、时域图分析，揭示轮胎力滞后对汽车横摆瞬态响应的影响规律；最后，通过Simulink仿真验证，将四个车轮互异&时变轮胎力滞后以状态空间形式写进控制器模型，可用于提高控制器模型的预测精度。     

轮胎侧倾力学特性模型

轮胎的力学特性对汽车的运动与车轮定位参数的合理选择有重要的影响。本在轮胎结构模型的基础上导出轮胎侧倾时的侧向力，回正力矩与滚动阻力特性表达式。讨论了轮胎对汽车运动性能仿真及车轮定位参数匹配的影响等有问题。     

轮胎纵滑非稳态特性测量方法研究

为解决轮胎纵滑非稳态特性的高精度测量行业难题，本文结合国际先进测试机构的经验，提出更合理的纵向滑移率正弦扫频测量法。首先，通过物理模型与理论推导，引入纵向松弛长度概念来表征轮胎纵滑非稳态特性。其次，分析现有刚度法、定频法存在的不足，并进行扫频法的原理推导与试验设计。然后，使用MTS Flat Trac CT+高速轮胎六分力试验台进行扫频法的纵向松弛长度测试；同时，以刚度法为参考进行扫频法的精度验证，对比显示两种方法的测量值非常接近，两者偏差在8%以内。最后得出结论：扫频法更加省时省力，可替代刚度法进行轮胎纵滑非稳态特性的合理准确测量。     

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。     

用于汽车制动、驱动与转向运动模拟的轮胎力学统一模型

提出了一种包括任意垂直载荷分布的轮胎在纵滑与侧偏联合工况下的力与力矩的统一模型。该模型可归结为无量纲合力与无量纲综合滑移率的关系,因此简化了试验结果的归纳与整理,并可从较易行的单纯侧偏试验结果中推断出侧偏与纵滑联合工况下的无量纲力学特性,从而为汽车在转向、制动、驱动及其联合工况下动力学的模拟研究奠定基础。文中同时给出了一些轮胎台架试验结果和汽车转弯制动试验结果,并与按模型计算的结果作了比较。     

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.     

轮胎附着极限下差动制动对汽车横摆力矩的影响

本文以纵滑－侧偏联合工况的稳态轮胎模型为基础，分析了汽车极限转向条件下制动作用于不同车轮时对汽车横摆力矩的影响，并通过整车动力学仿真进行了验证，研究结果为利用差动制动控制提高汽车的高速操纵稳定性提供了动力学依据。     

Electronic stability control for electric vehicle with four in-wheel motors

The electric vehicle with four direct-driven in-wheel motors is an over actuated system. A three-level control strategy of electronic stability control (ESC) is proposed to achieve optimal torque distribution for four in-wheel motors. The first level is a gain-scheduled linear quadratic regulator which is designed to generate the desired yaw moment command for ESC. Control allocation is the second level which is used to distribute the desired longitudinal tire forces according to the yaw moment command while satisfying the driver’s intent for acceleration and deceleration. The associated weighting matrix is designed using the work load ratio at each wheel to prevent saturating the tire. The third level is slip ratio control (SRC) which is employed at each wheel to generate the desired longitudinal tire force based on a combined-slip tire model. Simulation results show that the proposed method can enhance the ESC performance for the test maneuvers. Since the tire model is often unknown for practical implementation, the effectiveness of the SRC is studied using the sine with dwell test. It is found that the SRC is not crucial for achieving performance similar to the proposed method with SRC, if the slip ratio can be maintained in the stable region using traction control system/anti-lock braking system.     

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.     

Non-singular slip (NSS) method for longitudinal tire force calculations in a sudden braking simulation

In a dynamic vehicle simulation, longitudinal tire force is primarily based on the longitudinal slip (ratio). In the longitudinal slip formula, state variables are used in the denominator. This causes a divergence problem for numerical simulations of vehicle dynamics. To avoid this numerical singularity, a differential slip calculation method was developed for use in dynamic vehicle simulations. However, this method also causes a singularity when the wheel velocity approaches zero in a pure slip state, such as during sudden braking. In this paper, a new longitudinal slip calculation method, which can overcome singularities in all velocity conditions, is proposed. For this purpose, the Taylor series is adapted to the slip formula and the idea of virtual wheel rotation stiffness is introduced for the development of the slip equation. The physical phenomenon at the zero slip state is analyzed. Finally, the proposed slip formula is used to solve the numerical singularity problem, and the non-singular slip (NSS) calculation method is proposed. The proposed NSS method is applied to tire model performance test (TMPT) simulations to validate its performance.     

Selfexcited Vibrations of the Tire

In this paper a mechanical work of external forces and torques, acting on the tire has been considered. A theory has been developed for the prediction of necessary conditions for selfexciting vibrations. The theory establishes, that the mechanical work of external forces and torques must be positive, or, what is equivalent, that the tire has to transmit energy from external environment to vehicle. The work of forces and torques has been considered as a convolution of functions, which next has been submitted to Laplace transformation. The condition of selfexcitation of vibrations, obtained from above in the frequency domain, establishes, that the imaginary part of all eigenvalues of frequency response matrix must be negative. As an example, the ranges of selfexcited vibrations of the tire have been calculated. The tire has been treated as a stretched circular string. Four different models have been considered. Three of them have been massles (kinematic), namely Pacejka's model, Von Schlippe's model and single-point model. As fourth model the dynamic Pacejka's model has been considered. The influences of longitudinal deflections on the shimmy tendency have been studied for all models

Frequency response characteristics have been numerically computed and compared for all models. A critical speed and a critical reduced frequency of first and second kind have been defined. Admissible, negative, imaginary parts of the eigenvalues of frequency response matrix have been established. These admissible values of imaginary parts of eigenvalues assure, that the energy absorbing does not excite shimmy vibrations.     

基于动态目标调整的汽车全轮纵向力分配的研究

针对现有汽车稳定性控制系统中,汽车全轮纵向力分配算法在极端工况下出现轮胎力饱和.导致滑移率控制器过多介入而出现控制振荡和对控制目标的调整不合理等问题,提出了一种新的主动动态目标调整的全轮纵向力分配算法.该算法在极端工况下,根据车辆运动状态和路面附着状态,对直接横摆力矩控制目标M_(xd)和纵向驱动/制动力控制目标F_(xd)进行主动动态的调节.仿真结果表明,采用该算法解决了现有全轮纵向力分配算法的上述问题.