The effect of the inflation pressure of tyres on motorcycle weave stability: experiments and simulation

Increasing the stability of a motorcycle requires an understanding of the optimal conditions of the tyre. The inflation pressure is one of the main parameters that directly affects the tyre properties, which in turn influences motorcycle stability and safety. This paper focuses on the effect of the inflation pressure of the tested tyres on motorcycle weave stability. Experimental data are collected from tests carried out in straight running at constant speed. The data analysis is based on stochastic subspace identification methods. Simulations are performed using an advanced motorcycle multi-body code with parameters measured from the tested vehicle. Finally, the comparison between simulations and experimental tests is discussed. The research results show an agreement between experimental tests and simulations where weave stability increases with inflation pressure for the specified range of tyre pressure.     

Time-optimal control of the race car: influence of a thermodynamic tyre model

The robustness of an existing numerical method for the time-optimal control of the race car is demonstrated through its application to a model of a Formula 1 car equipped with a simplified thermodynamic tyre model. The tyre model includes a temperature- and frequency-dependent model of road/tyre friction. A lumped parameter approach is used to model the thermodynamics of the various parts of the tyre such as the tread, carcass and inflation gas. The influence of tyre, track surface and ambient temperatures on time-optimal manoeuvring is presented.     

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

This paper deals with in-curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre–road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analysed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle-node bifurcation parameters.     

Identification of the mechanical properties of bicycle tyres for modelling of bicycle dynamics

Advanced simulation of the stability and handling properties of bicycles requires detailed road–tyre contact models. In order to develop these models, in this study, four bicycle tyres are tested by means of a rotating disc machine with the aim of measuring the components of tyre forces and torques that influence the safety and handling of bicycles. The effect of inflation pressure and tyre load is analysed. The measured properties of bicycle tyres are compared with those of motorcycle tyres.     

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 novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces

Direct yaw moment control (DYC), which differentially brakes the wheels to produce a yaw moment for the vehicle stability in a steering process, is an important part of electric stability control system. In this field, most control methods utilise the active brake pressure with a feedback controller to adjust the braked wheel. However, the method might lead to a control delay or overshoot because of the lack of a quantitative project relationship between target values from the upper stability controller to the lower pressure controller. Meanwhile, the stability controller usually ignores the implementing ability of the tyre forces, which might be restrained by the combined-slip dynamics of the tyre. Therefore, a novel control algorithm of DYC based on the hierarchical control strategy is brought forward in this paper. As for the upper controller, a correctional linear quadratic regulator, which not only contains feedback control but also contains feed forward control, is introduced to deduce the object of the stability yaw moment in order to guarantee the yaw rate and side-slip angle stability. As for the medium and lower controller, the quantitative relationship between the vehicle stability object and the target tyre forces of controlled wheels is proposed to achieve smooth control performance based on a combined-slip tyre model. The simulations with the hardware-in-the-loop platform validate that the proposed algorithm can improve the stability of the vehicle effectively.     

The influence of frame compliance and rider mobility on the scooter stability

This article investigates the effect of frame compliance and rider mobility on the scooter stability. Particular attention is given to the wobble mode, because it may easily become unstable in the vehicle speed range. This article includes a synthetic discussion of previous works, presents a new mathematical model, and discusses the results of both numerical and experimental analyses of the vehicle stability by varying the vehicle characteristics and motion conditions.

The mathematical model describes the out-of-plane dynamics of the scooter and consists of a twelve-degree-freedom linear model. It describes the main scooter features and, in particular, includes the frame compliance, rider mobility, and an advanced tire model. The torsion and bending compliance of both the front fork and swingarm are modelled using lumped rotational springs; similarly, the rider mobility is described by means of two soft springs which connect the rider body to the chassis. The tire model describes in detail the carcass geometry and its compliance. The full scooter model is available on the website www.dinamoto.it and has been derived using ‘MBSymba’, which is a package for the symbolic modelling of multibody systems.

The scooter stability has been investigated at both low and high speeds; in particular, the effect of vehicle compliance and rider mobility on the weave and wobble modes have been examined. Numerical simulations show that the bending flexibility of the front fork stabilizes wobble mode at high speed and has a contrary effect at low speed, whereas the torsion flexibility of the fork does not appear to have a remarkable influence; the bending flexibility of the swingarm slightly stabilizes the weave mode at very high speeds whereas the torsion flexibility of the swingarm has a contrary effect. The effect of rider mobility is to stabilize the weave mode at high speed and the wobble mode at low speed. Several experimental tests have been carried out in the same speed range and a good correlation between simulations and tests has been found. The variation of some important vehicle parameters has been investigated; in particular, tests were repeated for different values of the rear-frame inertia, the rear-chassis stiffness, the front-tire characteristics, the normal trail, and the steer inertia.     

Velocity and normal tyre force estimation for heavy trucks based on vehicle dynamic simulation considering the road slope angle

A precise estimation of vehicle velocities can be valuable for improving the performance of the vehicle dynamics control (VDC) system and this estimation relies heavily upon the accuracy of longitudinal and lateral tyre force calculation governed by the prediction of normal tyre forces. This paper presents a computational method based on the unscented Kalman filter (UKF) method to estimate both longitudinal and lateral velocities and develops a novel quasi-stationary method to predict normal tyre forces of heavy trucks on a sloping road. The vehicle dynamic model is constructed with a planar dynamic model combined with the Pacejka tyre model. The novel quasi-stationary method for predicting normal tyre forces is able to characterise the typical chassis configuration of the heavy trucks. The validation is conducted through comparing the predicted results with those simulated by the TruckSim and it has a good agreement between these results without compromising the convergence speed and stability.     

The effect of engine spin direction on the dynamics of powered two wheelers

The effect of engine spin direction on the dynamics of powered two wheelers is investigated in terms of steady-state points (equilibria), vibration modes (stability), manoeuvre time (performance/manoeuvrability) and handling. The goal is to assess and quantify the advantage sometimes claimed for the ‘counter-rotating’ engine configuration, where the engine spins in the opposite direction with respect to wheels, against the ‘conventional’ configuration, where the engine spins in the same direction of wheels.     

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.     

Yaw damper modelling and its influence on railway dynamic stability

This paper deals with the modelling of yaw dampers and determining the influence of the modelling of this component on the results obtained when predicting the dynamic stability of a vehicle. The first part of the work analyses the influence of the yaw damper characteristics on railway dynamic stability. Following this, a physical model of the damper is developed which allows its performance to be reproduced accurately in the whole range of operating conditions the damper is envisaged to operate in. Once obtained, it was found that the computational cost of the model was relatively high. Therefore, a simplified model has been developed. The simplified model allows obtaining accurate results without excessively increasing the time required to perform the simulations. Analysing the results obtained with this model, it has been concluded that with respect to previous model based on conventional approaches, it improves the accuracy of dynamic calculation for the stability assessment. Also, it has been found that the accurate modelling of the yaw damper is critical when dealing with the vehicle's dynamic performance. In the last part of the paper, a special type of yaw damper was studied as well as its effect on the dynamic behaviour of the vehicle.     

Effect of vertical and lateral coupling between tyre and road on vehicle rollover

The vehicle stability involves many aspects, such as the anti-rollover stability in extreme steering operations and the vehicle lateral stability in normal steering operations. The relationships between vehicle stabilities in extreme and normal circumstances obtain less attention according to the present research works. In this paper, the coupling interactions between vehicle anti-rollover and lateral stability, as well as the effect of road excitation, are taken into account on the vehicle rollover analysis. The results in this paper indicate that some parameters influence the different vehicle stabilities diversely or even contradictorily. And it has been found that there are contradictions between the vehicle rollover mitigation performance and the lateral stability. The direct cause for the contradiction is the lateral coupling between tyres and road. Tyres with high adhesion capacity imply that the vehicle possesses a high performance ability to keep driving direction, whereas the rollover risk of this vehicle increases due to the greater lateral force that tyres can provide. Furthermore, these contradictions are intensified indirectly by the vertical coupling between tyres and road. The excitation from road not only deteriorates the tyres’ adhesive condition, but also has a considerable effect on the rollover in some cases.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis

Pacejka's Magic Formula Tyre Model is widely used to represent force and moment characteristics in vehicle simulation studies meant to improve handling behaviour during steady-state cornering. The experimental technique required to determine this tyre model parameters is fairly involved and highly sophisticated. Also, total test facilities are not available in most countries. As force and moment characteristics are affected by tyre design attributes and tread patterns, manufacturing of separate tyres for each design alternative affects tyre development cycle time and economics significantly. The objective of this work is to identify the interactions among various tyre design attributes-cum-operating conditions and the Magic Formula coefficients. This objective is achieved by eliminating actual prototyping of tyres for various design alternatives as well as total experimentation on each tyre through simulation using finite element analysis. Mixed Lagrangian–Eulerian finite element technique, a specialized technique in ABAQUS, is used to simulate the steady-state cornering behaviour; it is also efficient and cost-effective. Predicted force and moment characteristics are represented as Magic Formula Tyre Model parameters through non-linear least-squares fit using MATLAB. Issues involved in the Magic Formula Tyre Model representation are also discussed. A detailed analysis is made to understand the influence of various design attributes and operating conditions on the Magic Formula parameters. Tread pattern, tread material properties, belt angle, inflation pressure, frictional behaviour at the tyre–road contact interface and their interactions are found to significantly influence vehicle-handling characteristics.     

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

In this first part of a two-part article, a previously described and validated finite-element model of a racing-car tyre is developed further to yield detailed information on carcass deflections and contact pressure and shear stress distributions for a steady rolling, slipping, and cambered tyre. Variations in running conditions simulated include loads of 1500, 3000 and 4500 N, camber angles of 0° and ?3°, and longitudinal slips from 0% to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest. Results generated are in broad agreement with limited experimental results from the literature and they provide considerable insight into how the tyre deforms and how the contact stresses are distributed as functions of the running conditions. Generally, each rib of the tyre behaves differently from the others, especially when the wheel is cambered. The results form a basis for the development of a simpler physical tyre model, the purpose of which is to retain accuracy over the full operating range while demanding much less computational resource. The physical tyre model is the topic of the second part of the article.     

Investigation into untripped rollover of light vehicles in the modified fishhook and the sine manoeuvres,part II: effects of vehicle inertia property,suspension and tyre characteristics

In this paper, as a continuation of part I of [N. Zhang, G.M. Dong, and H.P. Du, Investigation into untripped rollover of light vehicles in the modified fishhook and the sine manoeuvres, part I: vehicle modelling, roll and yaw instability, Veh. Syst. Dyn. 46 (2008), pp. 271–293], detailed parametric studies are conducted and compared between the fishhook and sine manoeuvres using the presented nine-degree-of-freedom vehicle model, in order to understand the rollover resistance capability of a light passenger vehicle with various parameters. First, effects of driving conditions are studied in the two manoeuvres. Secondly, effects of suspension characteristics are studied, in which the influence of suspension spring stiffness and shock absorber damping, anti-roll bar is discussed. Thirdly, effects of vehicle inertia properties, such as moment of inertia of vehicle sprung mass, sprung mass weight and location of centre of gravity, are investigated. Finally, effects of tyre characteristics are also investigated by altering the scaling factor λ _Fz0. An in-depth understanding has been gained on the significant effects of key system parameters on the kinetic performance of vehicles under the fishhook and the sine manoeuvres. Parametric studies show that the combination of step input (fishhook) and frequency input gives a clear indication of the vehicle dynamic stability during cornering.     

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicle's lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.     

The influence of compliant chassis components on motorcycle dynamics: an historical overview and the potential future impact of carbon fibre

This paper details the influence of compliant chassis components on motorcycle dynamics. Initially, research which has previously been carried out in terms of motorcycle dynamics and in particular the impact of compliant chassis components on motorcycle dynamics is discussed. This paper then considers the consequences of these findings with regard to the use of modern materials such as carbon fibre reinforced plastics and the impact they will potentially have on motorcycle dynamics and its simulation.