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.     

用于公路车-桥系统振动分析的精细化轮胎模型

为了解决当前公路车桥耦合振动模型中轮胎模型过于简化、车轮-路面接触力与桥梁响应计算结果不够精确的问题,提出了一种精细化轮胎模型.首先基于车辆橡胶轮胎的几何、力学特征,建立了径向弹簧力学模型并进行了理论推导;然后考虑轮胎与路面接触面的刚度分布特征和高速状况下轮胎的惯性力,提出了轮胎接触面分布刚度的计算方法,保证了轮胎接触...     

Method for measuring force transmitted from road surface to tires and its applications

The force transmission from road surface to a rolling tire has been successfully measured by force measurements on suspension parts and correction for interia forces of suspension parts. The results of the measurement have shown that the force from road to tire has a sharp directivity, which is inclined rearward in side view, within the frequency range between 5 and 15 Hz. And the inclination angle of the direction of action has been found to be dependent on the vehicle velocity. As the application of the finding, the optimal wheel center locus inclination in side view has been studied, to minimize the longitudinal force transmission. And the optimum angle has been confirmed to exist.     

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。     

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.     

轮胎动刚度和阻尼特性的研究

本文通过轮胎动态实验，采用多元逐步回归技术对实验结果进行了分析，给出了轮胎弹性力与轮胎变形，激振频率之间，以及轮胎阻尼力与轮胎变形速率，激振频之间的关系，分析了充气压力，振幅及滚动速度对轮胎刚度和阻尼特性的影响。     

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.     

Performance of Low-bandwidth,Semi-active Damping Concepts for Suspension Control

Abstract

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

深水桥梁结构的地震反应分析

南水北调工程丹江口二桥主桥为四跨预应力混凝土变截面连续箱粱,其2号主墩基础入水深度超过40 m,在动力荷载作用下水对该类结构的动力特性和地震反应的影响不可忽略。以丹江口二桥为例,用有限元程序ANSYS建立了该桥的有限元模型,模拟了该桥的动力特性和地震反应,利用分析结果探讨了水对该桥动力特性的影响。输入地震波后,由于水的附加质量引起的惯性力和动水阻力的影响,结构的位移和内力较之不考虑水的情况会有所增加,但由于桩质点运动的速度和加速度较小,导致附加质量引起惯性力和动水阻力较小,所以给结构带来的影响较小。分析结果为同类结构的抗震分析提供了参考。     

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.     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

Performance of Low-bandwidth, Semi-active Damping Concepts for Suspension Control

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

汽车侧翻和滚翻事故建模研究

分析汽车在侧翻和滚翻过程中的受力状态和轮胎或车身与路面的相互作用方式,建立汽车侧翻和滚翻的运动学和动力学模型,揭示汽车临界侧翻碰撞力与持续作用时间等参数的关系,推导侧翻车辆侧向速度的范围,确定滚筒模型中关键参数的选取方法。事故案例表明模型在实际应用中效果良好、定量准确、直观性强。     

滚动轮胎瞬态和稳态强迫响应分析

采用移动载荷的概念,分别推导了点力激励的响应及分布力激励的响应列式,计算了胎体上点在点载荷作用下的时间历程。为轮胎滚动模型提供基础。     

轮胎泵气噪声有限元仿真分析

轮胎花纹槽泵气噪声是轮胎噪声的主要部分之一。在假设轮胎胎面结构与空气完全耦合的条件下建立轮胎横向花纹槽噪声的有限元模型,在施加与速度相关的强制位移条件下对空气中花纹槽泵气噪声进行仿真仿真,验证轮胎花纹槽泵气噪声的机理,同时通过线性迭加轮胎周向单个横向花纹槽的方法,给出轮胎花纹槽整体噪声的频域曲线。     

Numerical method for simulating tire rolling noise by the concept of periodically exciting contact force

For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling speed.     

The Wheel Shimmy Problem: Its Relationship to Wheel and Road Irregularities

The equations of motion are derived for a single wheel steerable pneumatic tire system. Included in this system are a built-in wheel wobble and wheel-tire irregularities which produce oscillation of the normal load. Special emphasis is placed on the dynamic characterization of the tire cornering force and aligning torque. The results show that the built-in wheel wobble causes a steady shimmy which is large when the wheel rotation frequency is close to the natural shimmy frequency. The results also show that a normal load oscillation which has a frequency approximately twice the natural shimmy frequency causes a decrease in shimmy stability.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.