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.     

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.     

Identification of the characteristics of motorcycle and scooter tyres in the presence of large variations in inflation pressure

Stability and safety of road vehicles are largely affected by tyre properties. Single-track vehicles are characterised by weakly damped modes of vibration (weave and wobble) and therefore this phenomenon is even more important. This article focuses on the study of both steady-state and transient properties of motorcycle and scooter tyres in the presence of very low and very high inflation pressures. The steady-state properties are defined as lateral forces (side-slip and camber forces) and yaw torques (self-aligning and twisting). The transient properties are described in terms of relaxation length, which represents the distance needed to reach a certain percentage of the steady-state value of the tyre force. Experimental tests are carried out on a specific rotating disk machine. Three sets of tyres are analysed. Steady-state properties are measured by increasing step by step the values of camber and side-slip angles. Transient properties are studied carrying out tests with harmonic side-slip excitation and measuring the phase lag between the excitation (input) and the tyre force (output). Experimental results show important variations in tyre properties with inflation pressure with general trends of all the tested tyres and particular features related to the tyre's geometry. After the analysis and discussion of experimental results, the measured data are fitted by means of a specific version of the Magic Formula. The dependence of the Magic Formula's coefficients on inflation pressure is analysed and interpolation curves are given.     

Tyre pressure monitoring using a dynamical model-based estimator

In the last few years, various control systems have been investigated in the automotive field with the aim of increasing the level of safety and stability, avoid roll-over, and customise handling characteristics. One critical issue connected with their integration is the lack of state and parameter information. As an example, vehicle handling depends to a large extent on tyre inflation pressure. When inflation pressure drops, handling and comfort performance generally deteriorate. In addition, it results in an increase in fuel consumption and in a decrease in lifetime. Therefore, it is important to keep tyres within the normal inflation pressure range. This paper introduces a model-based approach to estimate online tyre inflation pressure. First, basic vertical dynamic modelling of the vehicle is discussed. Then, a parameter estimation framework for dynamic analysis is presented. Several important vehicle parameters including tyre inflation pressure can be estimated using the estimated states. This method aims to work during normal driving using information from standard sensors only. On the one hand, the driver is informed about the inflation pressure and he is warned for sudden changes. On the other hand, accurate estimation of the vehicle states is available as possible input to onboard control systems.     

Experimental analysis of tyre-enveloping characteristics at low speed

In this study, experiments are conducted to investigate tyre-enveloping characteristics. Four different types of tyres are tested. Parameters such as different tyre inflation pressures, vertical loads and types of obstacles (cleats) are considered. In addition to vertical stiffnesses of all tyres, vertical and horizontal force variations while traversing different obstacles at low speed are studied. The effects of inflation pressure and vertical load on variations of force and moment are investigated. Static test results showed that after a certain vertical displacement, all curves in force–deflection diagrams plotted with and without cleat intersect regardless of cleat and tyre types, depending on the inflation pressure of the tyre, which can be called typical static tyre-enveloping characteristics. Test results at low speed show that there is a considerable influence of the vertical load on vertical and lateral force responses of a tyre.     

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.     

Application of the Pacejka Magic Formula Tyre Model on a Study of a Hydraulic Anti-Lock Braking System for a Light Motorcycle

The object of the study is to apply the Pacejka magic formula tyre model on a study of a hydraulic anti-lock braking system, especially applied to a light motorcycle. A sliding mode PWM controller is designed and tested. Both simulation and experimental studies of an anti-lock braking system are undertaken. The paper presents an analytical approach for estimating the longitudinal adhesive coefficient between a tyre and the road through the magic formula tyre model, the parameters of which are identified by a genetic algorithm. A dynamic analysis of a light motorcycle is carried out in detail. The experimental results show that the antilock braking system designed in the study is effective to prevent wheels locking during emergency braking. The proposed simulation results match experimental data well.     

Application of the Pacejka Magic Formula Tyre Model on a Study of a Hydraulic Anti-Lock Braking System for a Light Motorcycle

The object of the study is to apply the Pacejka magic formula tyre model on a study of a hydraulic anti-lock braking system, especially applied to a light motorcycle. A sliding mode PWM controller is designed and tested. Both simulation and experimental studies of an anti-lock braking system are undertaken. The paper presents an analytical approach for estimating the longitudinal adhesive coefficient between a tyre and the road through the magic formula tyre model, the parameters of which are identified by a genetic algorithm. A dynamic analysis of a light motorcycle is carried out in detail. The experimental results show that the antilock braking system designed in the study is effective to prevent wheels locking during emergency braking. The proposed simulation results match experimental data well.     

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.     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

Environmental effects on Pacejka’s scaling factors

A set of scaling factors has been introduced by Pacejka [Pacejka, H.B., 2002, Tyre and Vehicle Dynamics (Oxford: Butterworth Heinemann Editions)] into his Magic Formula tyre model to take into account the influence of a number of external overall parameters such as road roughness, weather conditions, suspension characteristics and so on. These scaling factors are important for a correct prediction of tyre–road contact forces, but are not a function of the tyre itself. Changing the point of view, one could say that scaling factors should remain constant for different tyres on the same circuit, with the same weather conditions and with the same car. After characterizing different tyres through indoor tests (that do not consider external overall parameters) and after having identified Pacejka’s coefficients with scaling factors equal to one, several outdoor experimental tests have been carried out to assess the influence of vehicle and road surface conditions on scaling factors. These experimental data allowed us to identify, through a minimization approach, the ‘best’ set of Pacejka’s scaling factors for that vehicle and for that tyre on that track. Scaling factors for equal track and vehicle but different tyres were compared to check whether their values remained constant. To access the validity of scaling factors, a comparison between experimental data, collected on an instrumented passenger car, and MB simulations considering unity and identified scaling factors’ values, were carried out. All experimental data shown in this article come from tests carried out within the VERTEC project, a European founded research project (Task 2.a and 2.b) that puts together knowledge coming from vehicle manufacturers (Volvo, Porsche and Centro Ricerche Fiat CRF), tyre manufacturers (Pirelli and Nokian Tyres), control logic manufacturers (Lucas Varity GmbH), road maintenance experts (Centres d’Études Techniques de l’Équipement CETE), transport research organizations (Transport Research Laboratory TRL, Swedish National Road and Transport Research Institute VTI) and universities (Helsinki University of Technology HUT, Politecnico di Milano and University of Florence UNIFI).     

Longitudinal wheel slip during ABS braking

Anti-lock braking system (ABS) braking tests with two subcompact passenger cars were performed on dry and wet asphalt, as well as on snow and ice surfaces. The operating conditions of the tyres in terms of wheel slip were evaluated using histograms of the wheel slip data. The results showed different average slip levels for different road surfaces. It was also found that changes in the tyre tread stiffness affected the slip operating range through a modification of the slip value at which the maximum longitudinal force is achieved. Variation of the tyre footprint length through modifications in the inflation pressure affected the slip operating range as well. Differences in the slip distribution between vehicles with different brake controllers were also observed. The changes in slip operating range in turn modified the relative local sliding speeds between the tyre and the road. The results highlight the importance of the ABS controller's ability to adapt to changing slip–force characteristics of tyres and provide estimates of the magnitude of the effects of different tyre and road operating conditions.     

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

In-plane tyre modal behaviour determines the response of tyres to ride excitations and braking/traction manoeuvres. In many studies, the interest is limited to relatively low frequencies and a detailed investigation into the ability of models to accurately simulate higher-order responses is unnecessary. In cases where an in-plane model is to be used for the generation of the contact deformation and stresses, or where modal reduction methods are implemented, a detailed knowledge of the modal response is desirable. The present work forms a study on the ability of a number of frequently used modelling approaches to generate realistic modal data throughout a wide frequency range. The analytical ring on elastic foundation model is used as a benchmark throughout the paper. Its predictions are compared with those of two discretised models, namely a truss- and a beam-based model. The sensitivity of the ring’s response to a number of physical parameters is discussed. The results are used to inform the comparison between the analytical ring and the discretised models, providing explanations for any discrepancies observed. The limited applicability of the truss model is pointed out, while the accuracy of the beam-based model is enhanced by a circumferential inextensible string element. Both the ring and the enhanced beam models are further improved with the addition of a nonlinear string-based sidewall that accounts for the change in sidewall stiffness with inflation pressure. The findings may offer a reference when setting up in-plane models, including the stage of planning modal tests for parameter identification.     

Numerical investigation of engine-to-slip dynamics for motorcycle traction control applications

This work discusses the motorcycle engine-to-slip dynamics which are strictly related to the traction control design. A street motorcycle is analysed by means of an advanced mathematical model which also includes the tyre flexibility and the transmission compliance. The effects of the following parameters on engine-to-slip dynamics are investigated: vehicle speed, engaged gear ratio, sprocket absorber flexibility and road properties. Guidelines for increasing the maximum achievable closed-loop bandwidth are given.     

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.     

Lateral dynamics of motorcycles towing single-wheeled trailers

A motorcycle towing a single-wheel trailer may provide useful transport for light cargo on narrow tracks and off-road use, particularly in rural areas of developing countries. Four designs of such trailers are described. Linear models are derived for the lateral dynamics of an off-road motorcycle towing this type of trailer straight ahead at constant speed. The trailers were tested behind an instrumented motorcycle. Linear autoregressive models were fitted to the experimental data using system identification techniques. Analytical and experimentally derived models largely agreed on frequency, damping and shape of the weave, wobble and trailer sway normal modes. The trailers made the motorcycle’s steering heavier but the analytical models did not predict this. The location of the articulation axes between the motorcycle and the trailer were found to be critical for stability. The best trailer design handled well with loads up to 200 kg and speeds up to 70 km/h.