Wheel Vibrations and Transient Tire Forces

This paper presents a survey of the state-of-the-art in predicting the wheel vibrations in a complex dynamic vehicle suspension system and their influence on the forces transduced in a high frequency area from the tire to the vehicle's body. Secondly it presents also the transient evolution of tire models used for prediction and understanding high frequency movements in the tire's contact area, producing the guiding forces and torques during vehicle handling.     

Wheel Vibrations and Transient Tire Forces

SUMMARY

This paper presents a survey of the state-of-the-art in predicting the wheel vibrations in a complex dynamic vehicle suspension system and their influence on the forces transduced in a high frequency area from the tire to the vehicle's body. Secondly it presents also the transient evolution of tire models used for prediction and understanding high frequency movements in the tire's contact area, producing the guiding forces and torques during vehicle handling.     

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.     

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.     

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

SUMMARY

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.     

一种汽车ESP仿真模型的研究

基于Pacejka的"魔术公式"轮胎模型,建立了包括汽车纵向与横向移动、横摆、侧倾和4个车轮的转动的8自由度动力学模型.设计了由汽车仿真模型和驱动系统、四通道制动系统、制动踏板、转向盘与油门踏板等实物以及控制器(ESP)等部分组成的半实物仿真平台.以侧向加速度与横摆角速度为仿真控制变量对模型进行仿真测试.仿真与实车测试数据相当接近,为ESP的研究提供了有效的模型.     

Energy analysis of the Von Schlippe tyre model with application to shimmy

Shimmy is an engineering example of self-excited vibrations. Much research on shimmy has considered the tyre as a positive feedback or negative damping to introduce instability of the entire system. In this context, we focus on the behaviour of the tyre under periodic excitations. The Von Schlippe tyre model is selected and the energy flow method is applied to illustrate the energy transfer by the tyre during shimmy. The energy flow method evaluates the tyre performance with a prescribed sinusoidal motion and provides a novel evaluation method for tyre models. With the help of straight contact line assumption in the Von Schlippe tyre model, the relative motion between the contact line and the wheel centre is studied to understand the path dependency of the energy transfer. It turns out that the tyre is extracting energy from the forward motion to induce unstable lateral and yaw vibrations when the motion or orientation of the contact line has a phase lead with respect to the wheel centre.     

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。     

前轮定位参数与轮胎特性对前轮摆振影响的研究

前轮定位参数对前轮摆振的影响是极其复杂的,它不仅影响了前轮的几何特性,并且对摆振系统的运动,约束与受力状况均产生重要影响。本文建立了包括全部前轮定位参数的前轮摆振数学模型;并在轮胎试验的基础上,比较系统、全面地研究了前轮定位参数对前轮摆振的影响规律。本文还研究了轮胎蛇形运动频率对汽车动力学摆振的影响。     

Approximate Dynamic Shimmy Response of Pneumatic Tires*

An improved approximation of the theory of the dynamic frequency response of side force and aligning torque acting upon the rolling wheel when the latter is moved laterally and swivelled about the vertical axis, is presented. The method is particularly suitable for application in vibration problems of steering and suspension systems of automobiles and aircraft where relatively high speed and high frequency phenomena play a role. The theoretical results show satisfactory agreement with experimental data. Calculations indicate that the inertia of the tire decreases the tendency to shimmy at higher frequencies and speeds of travel. For castered wheels however, tire inertia may have an adverse effect due to its unfavorable influence upon the side force response to swivel motions.     

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.     

A 3D Brush-type Dynamic Tire Friction Model

The use of advanced dynamic friction models can improve the brush-type tire friction models. This paper presents a 3D dynamic brush model based on the LuGre friction model. The model describes the dynamics of longitudinal and lateral tire friction forces, as well as the self aligning torque dynamics. It has been originally derived in a distributed-parameter form, and then transformed to a simpler lumped-parameter form with only three internal states. Both uniform and non-uniform normal pressure distributions are considered. The model has analytical solution for steady-state conditions. The steady-state behavior is validated with respect to “magic” formula static model, which served as an “ideal” benchmark. The lumped model dynamic behavior is validated by comparing its time-responses with original distributed model responses. The model parameterization with respect to normal force and other tire/road parameters is considered as well.     

A 3D Brush-type Dynamic Tire Friction Model

The use of advanced dynamic friction models can improve the brush-type tire friction models. This paper presents a 3D dynamic brush model based on the LuGre friction model. The model describes the dynamics of longitudinal and lateral tire friction forces, as well as the self aligning torque dynamics. It has been originally derived in a distributed-parameter form, and then transformed to a simpler lumped-parameter form with only three internal states. Both uniform and non-uniform normal pressure distributions are considered. The model has analytical solution for steady-state conditions. The steady-state behavior is validated with respect to “magic” formula static model, which served as an “ideal” benchmark. The lumped model dynamic behavior is validated by comparing its time-responses with original distributed model responses. The model parameterization with respect to normal force and other tire/road parameters is considered as well.     

Simulation of Vehicle and Power Steering Dynamics Using Tire Model Parameters Matched to Whole Vehicle Experimental Results

This paper uses simulation to investigate how vehicle loading conditions (driver only, passengers, cargo, and fuel) affect power steering system and overall vehicle dynamics. Our purpose of the study was to evaluate the power steering system model for possible use in the National Advanced Driving Simulator (NADS). The effects of changing loading conditions on inertial properties of passenger cars have been found experimentally using a Vehicle Inertia Measurement Facility (VIMF). This paper presents simulation results using a vehicle handling model combined with a power steering system model and a nonlinear tire model. A crucial part of this project was the adjustment of certain parameters of Pacejka's tire model in order to match simulation results with experimental measurements of vehicle and power steering variables in transient maneuvers.     

某车型高速行驶方向盘摆振分析

研究高速行驶方向盘摆振影响因素与测试方法。针对某款乘用车方向盘摆振的现象进行原因分析,通过对其进行道路再现试验,测试分析轮胎至方向盘的灵敏度,可知该车对轮胎异相位的激励非常灵敏;以副车架为参考点,建立模型,通过ODS分析进一步验证摆振产生原因。该研究为高速行驶方向盘摆振问题的解决提供依据。     

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     

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。     

Computational Vibration Analysis of Vehicle Shimmy by a Power-Work Method

This paper presents the simulation of vehicle shimmy for a mid-size truck with focus on a computational analysis tool that measures the power and corresponding work in dissipating the excitation energy. After a review of shimmy theory the power and work equations and their response classification in vibrating systems are introduced. Next, model validation compares the full vehicle model to an actual test vehicle. Finally, two designs that suppress shimmy in the test vehicle are analyzed in the model by the power-work method, showing components that effectively dissipate the shimmy energy.