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.     

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.     

A study on the effect of different tyre imperfections on steering wheel vibration

Multibody dynamics and tyre models have made possible detailed analysis not only for ride and handling, but also for determining their effects on tyre nonuniformities. The aim of this paper is to analyse the steering wheel vibration, both shimmy and shake, excited by different tyre imperfections by using the commercial simulation package ADAMS/car 2005R2 and FTire. Different settings with respect to imperfection locations, amount, and the combined effects of defects have been studied. An interesting beat phenomenon is observed when all the wheels have imperfections. A procedure to determine the type of imperfections in the tyre from the results of the test rig has also been proposed.     

汽车操纵稳定性与前轮摆振的非线性仿真分析

以某轿车为例,建立3自由度整车系统动力学模型,利用常微分方程稳定性理论和数值仿真计算,详细研究整车的稳态转向特性和系统失稳后的前轮摆振特性。阐明汽车的操纵稳定性与前轮摆振特性同属汽车整车稳定性问题,前者是负刚度系统,后者是负阻尼系统。在一定的参数组合下,具有不同转向特性的汽车都或多或少地存在摆振现象,这与实际情况相符,建议适当增加转向系阻尼和刚度以减小甚至消除摆振的发生。     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis.

Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are calculated, and the implications are discussed.

It is concluded that typical levels of structural compliance in models (a) and (c) contribute significantly to the steering behaviour properties of large motorcycles, and their observed behaviour can be understood better in terms of the new results than of those existing previously. Some conclusions relating to optimal structural stiffness properties are also drawn.     

某大客车转向轮摆振及影响因素的分析

考虑侧偏角和侧偏力之间的非线性关系,建立4自由度某大客车转向轮摆振模型。运用非线性动力学理论,确定转向轮发生自激摆振的Hopf分岔点：通过MATLAB＆Simulink软件建立大客车转向轮摆振仿真模型。通过仿真结果检验理论分析,并得到车速、转向系参数、横拉杆参数、质心位置、主销后倾角与转向轮自激摆振幅值或频率的关系曲线．找出影响自激摆振的敏感参数及敏感参数的适取范围,能有效减小或消除客车的自激摆振。     

Achievable Dynamic Response for Automotive Active Suspensions *

A complete set of constraints is derived for the road disturbance transfer functions in a quarter car model of an automotive active suspension, for typical choices of measured outputs. It is shown that any road disturbance responses which are achievable using “full state feedback” can be achieved, to within an arbitrary small tolerance, using a dynamic compensator measuring suspension deflection only. Also considered are the disturbance responses to loads acting on the sprung mass, and a complete set of constraints is derived for these. It is shown that road disturbance and load disturbance responses can be determined independently if suspension deflection and sprung mass velocity are measured. Indeed, any responses achievable separately with “full measurements” can be approximated together to an arbitrary small tolerance. Certain integral relationships are shown to follow from the derived transfer function constraints. These relationships imply fundamental limitations for certain responses (e.g. tyre deflection) no matter what measurements are available for feedback.     

关于车辆方向盘摆振的补偿方法及补偿系统研究

研究电动助力转向系统对方向盘摆振补偿的功能,通过对影响方向盘摆振因素的分解,当整车基本参数确定的情况下可以采用EPS进行摆振补偿.通过摆振补偿功能开发到某车型实车测试验证,有效解决高速制动等工况下方向盘摆振问题.该研究为车辆方向盘摆振问题的解决提供采用EPS补偿万式提供方法及系统.     

干摩擦力矩对某独立悬架汽车前轮摆振影响研究

为了探究前轮摆振的影响因素,将运动副间隙处的干摩擦等效到前轮主销处．应用拉格朗日方程建立了3自由度摆振系统模型,并用Matlab对其进行了仿真计算。结果表明,汽车在较大的初始激励下才会激发摆振;较大的干摩擦力矩有利于抑制摆振。     

解放CA1170P2K1L2型载货汽车动力转向机构的故障排除

介绍了解放CAll70P2Kll2型载货汽车动力转向机构的组成及工作原理。根据长期使用实践，对该动力转向机构可能产生的故障、产生故障的原因及故障排除方法介绍如下：一是转向沉重；二是左右转向轻重不同；三是行驶中前轮摆头；四是转向盘自由行程过大；五是转向轮回正困难；六是油泵噪声大；七是动力转向系统过热。     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

SUMMARY

A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis.

Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are calculated, and the implications are discussed.

It is concluded that typical levels of structural compliance in models (a) and (c) contribute significantly to the steering behaviour properties of large motorcycles, and their observed behaviour can be understood better in terms of the new results than of those existing previously. Some conclusions relating to optimal structural stiffness properties are also drawn.     

转向柱后倾角对三轮汽车前轮自激摆振特性影响

为获得转向柱后倾角对三轮汽车摆振影响,以国产某型三轮汽车作为样车,对其转向系统进行了简化,建立了二自由度前轮摆振系统动力学模型。基于以上模型,运用数值计算方法,得到了随车速变化的前轮摆振系统振动特性及转向柱后倾角变化对其的影响。结果表明,减小转向柱后倾角,能有效减小三轮汽车前轮自激摆振的速度区间。而当车速较高,前轮摆振系统发生自激振动时,减小转向柱后倾角能有效地降低前轮自激摆振极限环幅值和频率,甚至消除自激摆振现象。     

Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model

McPherson suspension modelling poses a challenging problem due to its nonlinear asymmetric behaviour. The paper proposes a planar quarter-car analytical model that not only considers vertical motion of the sprung mass (chassis) but also: (i) rotation and translation for the unsprung mass (wheel assembly), (ii) wheel mass and its inertia moment about the longitudinal axis, and (iii) tyre damping and lateral deflection. This kinematic–dynamic model offers a solution to two important shortcomings of the conventional quarter-car model: it accounts for geometry and for tyre modelling. The paper offers a systematic development of the planar model as well as the complete set of mathematical equations. This analytical model can be suitable for fast computation in hardware-in-the-loop applications. Furthermore, a reproducible Simulink implementation is given. The model has been compared with a realistic Adams/View simulation to analyse dynamic behaviour for the jounce and rebound motion of the wheel and two relevant kinematic parameters: camber angle and track width variation.     

Comparative study of vehicle tyre–road friction coefficient estimation with a novel cost-effective method

This paper qualitatively and quantitatively reviews and compares three typical tyre–road friction coefficient estimation methods, which are the slip slope method, individual tyre force estimation method and extended Kalman filter method, and then presents a new cost-effective tyre–road friction coefficient estimation method. Based on the qualitative analysis and the numerical comparisons, it is found that all of the three typical methods can successfully estimate the tyre force and friction coefficient in most of the test conditions, but the estimation performance is compromised for some of the methods during different simulation scenarios. In addition, all of these three methods need global positioning system (GPS) to measure the absolute velocity of a vehicle. To overcome the above-mentioned problem, a novel cost-effective estimation method is proposed in this paper. This method requires only the inputs of wheel angular velocity, traction/brake torque and longitudinal acceleration, which are all easy to be measured using available sensors installed in passenger vehicles. By using this method, the vehicle absolute velocity and slip ratio can be estimated by an improved nonlinear observer without using GPS, and the friction force and tyre–road friction coefficient can be obtained from the estimated vehicle velocity and slip ratio. Simulations are used to validate the effectiveness of the proposed estimation method.     

EQ2102越野汽车前轮摆振影响因素试验分析及改进措施

针对东风EQ2102型独立悬架越野汽车的前轮摆振问题进行了道路试验分析,研究了前轮失衡量、转向系统阻尼和刚度对前轮摆振的影响。试验及分析表明,该车摆振主要为强迫振动,通过控制激振源、增大转向系统阻尼可抑制摆振。提出了采用阻尼轴承代替主销滚针轴承来增大转向阻尼的解决方案,同时评估了阻尼轴承对汽车操纵稳定性的影响。     

线控转向系统转向盘力回馈控制模型的研究

根据轮胎和传统转向系的力学特性提出了利用车轮转角和车速计算得到转向盘回馈力的思路,并以此建立了线控转向系统转向盘回馈力控制模型,仿真和试验表明该模型能够满足路感要求。     

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.     

Chaotic Motion of Wheels

Abstract

Trolleys have wheels which can choose the direction of their rolling. Studying the motion of a wheel like this, we can often find periodic motions (“shimmy”) or even chaotic ones. It has also been experienced that the chaotic motions sometimes disappear quite unexpectedly. A strongly simplified model of these systems is analysed in the paper by means of the methods of bifurcation theory. Analytical and numerical results are shown to characterize the system, including simulation results. Similar behaviour can be found in more complicated systems as well, like the trailers or the nose-gears of aeroplanes. The development of the so-called transient chaotic motion is explained in these systems.