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.     

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.     

Handling Analysis of a Motorcycle with Added Cambering of the Front Frame

SUMMARY

Through linear analysis, the handling characteristics of the motorcycle with fixed control of added cambering of front frame are investigated under the variation of fixed and free controls of steering axis. The cornering responses and stability characteristics of the motorcycle are presented with the aid of the handling diagram. From numerical results for a typical motorcycle, it is found that the influence of the cambering of front frame on the cornering response of fixed steering control is opposite to that of free steering control. Moreover, the design philosophy of a so-called semi-direct steering mechanism, which cambers the front frame for cornering, is studied.     

Experimental and numerical analysis of the influence of tyres’ properties on the straight running stability of a sport-touring motorcycle

The behaviour of a motorcycle on the road is largely governed by tyre properties. This paper presents experimental and numerical analyses dealing with the influence of tyre properties on the stability of weave and wobble in straight running. The final goal is to find optimal sets of tyre properties that improve the stability of a motorcycle. The investigation is based on road tests carried out on a sport-touring motorcycle equipped with sensors. Three sets of tyres are tested at different speeds in the presence of weave and wobble. The analysis of telemetry data highlights significant differences in the trends of frequency and damping of weave and wobble against speed. The experimental analysis is integrated by a parametric numerical analysis. Tyre properties are varied according to the design of experiments method, in order to highlight the single effects on stability of lateral and cornering coefficient of front and rear tyres.     

Steady Turning of Two-Wheeled Vehicles

When driving along a circular path, the driver of a motorcycle controls the vehicle mainly by means of steering torque. If low steering torque is necessary, the driver feels that the vehicle is manoeuvrable. In this paper, a mathematical model concerning steering torque is developed; it takes into account the actual kinematic behaviour of the vehicle and the properties of motorcycle tyres. Tyre forces act at the contact points of toroidal tyres, which are calculated according to kinematic analysis. Non-linear equations are solved using an iterative approach. Several numerical results are presented, and the influence of tyre properties and some geometrical and inertial properties of the vehicle on steering torque are discussed.     

Steady Turning of Two-Wheeled Vehicles

When driving along a circular path, the driver of a motorcycle controls the vehicle mainly by means of steering torque. If low steering torque is necessary, the driver feels that the vehicle is manoeuvrable. In this paper, a mathematical model concerning steering torque is developed; it takes into account the actual kinematic behaviour of the vehicle and the properties of motorcycle tyres. Tyre forces act at the contact points of toroidal tyres, which are calculated according to kinematic analysis. Non-linear equations are solved using an iterative approach. Several numerical results are presented, and the influence of tyre properties and some geometrical and inertial properties of the vehicle on steering torque are discussed.     

Study of the Pneumatic Tyre Behaviour on Dry and Rigid Road by Finite Element Method

SUMMARY

The paper presents a physical tyre model capable of describing the complete pneumatic tyre behaviour during steady and transient states. Given the radial deflection, the longitudinal and lateral slip, the camber angle, the inner pressure and the mechanical parameters describing the tyre structure, the model returns the vertical load, the longitudinal and lateral forces, the self aligning torque. Particular attention has been devoted to the computation (by f.e.m.) of tyre carcass and tread deformations; it is explained how side force increases by moderate braking at constant slip angle. An experimental verification validates the model, although more studies could be needed to improve model effectiveness.     

Shear Force Development by Pneumatic Tyres in Steady State Conditions: A Review of Modelling Aspects

SUMMARY

Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems.

The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the behaviour of a particular tyre.

Conclusions relate to the structural and frictional mechanisms present in the shear force generation process, the contributions of carcass and tread elastic properties and of geometrical and frictional factors to the determination of the distributions of force through the contact region, the relationship between accuracy and computational load and the selection of methods for modelling tyre forces in a road vehicle dynamics context. Reference to the most pertinent literature in the field is made and possibilities for the further development of the state of the art are mentioned.     

On the wobble mode of a bicycle

Wheel shimmy and wobble are well-known dynamic phenomena at automobiles, aeroplanes and motorcycles. In particular, wobble at the motorcycle is an (unstable) eigenmode with oscillations of the wheel about the steering axis, and it is no surprise that unstable bicycle wobble is perceived unpleasant or may be dangerous, if not controlled by the rider in time. Basic research on wobble at motorcycles within the last decades has revealed a better understanding of the sudden onset of wobble, and the complex relations between parameters affecting wobble have been identified. These fundamental findings have been transferred to bicycles. As mass distribution and inertial properties, rider influence and lateral compliances of tyre and frame differ at bicycle and motorcycle, models to represent wobble at motorcycles have to prove themselves, when applied to bicycles. For that purpose numerical results are compared with measurements from test runs, and parametric influences on the stability of the wobble mode at bicycles have been evolved. All numerical analysis and measurements are based on a specific test bicycle equipped with steering angle sensor, wheel-speed sensor, global positioning system (GPS) 3-axis accelerometer, and 3-axis angular velocity gyroscopic sensor.     

A theoretical model of speed-dependent steering torque for rolling tyres

ABSTRACT

It is well known that the tyre steering torque is highly dependent on the tyre rolling speed. In limited cases, i.e. parking manoeuvre, the steering torque approaches the maximum. With the increasing tyre speed, the steering torque decreased rapidly. Accurate modelling of the speed-dependent behaviour for the tyre steering torque is a key factor to calibrate the electric power steering (EPS) system and tune the handling performance of vehicles. However, no satisfactory theoretical model can be found in the existing literature to explain this phenomenon. This paper proposes a new theoretical framework to model this important tyre behaviour, which includes three key factors: (1) tyre three-dimensional transient rolling kinematics with turn-slip; (2) dynamical force and moment generation; and (3) the mixed Lagrange–Euler method for contact deformation solving. A nonlinear finite-element code has been developed to implement the proposed approach. It can be found that the main mechanism for the speed-dependent steering torque is due to turn-slip-related kinematics. This paper provides a theory to explain the complex mechanism of the tyre steering torque generation, which helps to understand the speed-dependent tyre steering torque, tyre road feeling and EPS calibration.     

如何延长汽车轮胎的使用寿命

介绍了汽车轮胎在使用中不正常磨损的几种情况：一是轮胎冠两肩超常磨损；二是轮胎胎冠中部超常磨损；三是轮胎胎侧呈侧呈锯齿状磨损；四是胎冠呈波浪状或碟片状磨损；五是转向轮胎冠内（外）侧超常磨损等。分析了轮胎不正常磨损的原因。介绍了轮胎的正确使用、定期检查与维护。     

Handling Analysis of a Motorcycle with Added Cambering of the Front Frame

Through linear analysis, the handling characteristics of the motorcycle with fixed control of added cambering of front frame are investigated under the variation of fixed and free controls of steering axis. The cornering responses and stability characteristics of the motorcycle are presented with the aid of the handling diagram. From numerical results for a typical motorcycle, it is found that the influence of the cambering of front frame on the cornering response of fixed steering control is opposite to that of free steering control. Moreover, the design philosophy of a so-called semi-direct steering mechanism, which cambers the front frame for cornering, is studied.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

SUMMARY

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

Dynamic analysis and control of an anti-lock brake system for a motorcycle with a camber angle

This paper analyses the dynamic response of a motorcycle with an anti-lock brake system (ABS) and camber or steering angle. Most studies have assumed that motorcycles brake in a straight line – that is, without a steering or camber angle. In this work, the performance of an ABS modulator is designed and analysed at first. Then, a controller is designed for motorcycle turning. The controller uses angular acceleration and the pressure value in brake calipers on the front and rear wheels, camber angle and lateral acceleration as commands to control brake pressure on each wheel to prevent wheel locking. The equation of motion for a motorcycle is based on Weir's equations. This motorcycle model combines a mathematical equation of the ABS modulator, tyre model and controller in simulations.     

Additional 4WS and Driver Interaction

SUMMARY

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

The Dynamics of Single Track Vehicles

SUMMARY

The paper contains a brief review of the more subjective aspects of the steering behaviour of single track vehicles, a review of the more significant published work in the field, and an assessment of the current state of understanding and likely ways in which further progress can be made

Attention is drawn to the many areas of agreement between theory and practice and to some areas of disagreement. The greatest need now seems to be for the incorporation of more complex tyre models into vehicle handling models.     

Analysis of vehicle rollover dynamics using a high-fidelity model

Recent data show that 35% of fatal crashes in sport utility vehicles included vehicle rollover. At the same time, experimental testing to improve safety is expensive and dangerous. Therefore, multi-body simulation is used in this research to improve the understanding of rollover dynamics. The majority of previous work uses low-fidelity models. Here, a complex and highly nonlinear multi-body model with 165 degrees of freedom is correlated to vehicle kinematic and compliance (K&C) measurements. The Magic Formula tyre model is employed. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to link suspension K&C characteristics with rollover propensity. Research so far reveals that the tyre properties that have the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness and tyre vertical stiffness. Key K&C characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force.     

On the influence of tyre and structural properties on the stability of bicycles

In recent years the Whipple Carvallo Bicycle Model has been extended to analyse high speed stability of bicycles. Various researchers have developed models taking into account the effects of front frame compliance and tyre properties, nonetheless, a systematic analysis has not been yet carried out. This paper aims at analysing parametrically the influence of front frame compliance and tyre properties on the open loop stability of bicycles. Some indexes based on the eigenvalues of the dynamic system are defined to evaluate quantitatively bicycle stability. The parametric analysis is carried out with a factorial design approach to determine the most influential parameters. A commuting and a racing bicycle are considered and numerical results show different effects of the various parameters on each bicycle. In the commuting bicycle, the tyre properties have greater influence than front frame compliance, and the weave mode has the main effect on stability. Conversely, in the racing bicycle, the front frame compliance parameters have greater influence than tyre properties, and the wobble mode has the main effect on stability.     

中型载货汽车轮胎异常磨损的原因分析及解决措施

中型载货汽车轮胎常发生异常磨损现象，磨损形式是横向花纹轮胎呈锯齿状磨损，从胎冠上方向下看，胎肩处花纹块呈前高后低状，也有少部分呈前低后高状，形状似锯齿；纵向花纹轮胎一侧胎肩磨损明显大于另一侧。分析了此现象产生的原因，并提出了相应的解决措施。