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.     

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.     

Geometric-based tyre vertical force estimation and stiffness parameterisation for automotive and unmanned vehicle applications

Advanced empirical, and physical-based tyre models have proven to be accurate for simulating tyre dynamics; however, these tyre models typically require expensive and intensive tyre parameterisation. Recent research into wheeled unmanned ground vehicles requiring vertical force analysis has shown good results using a simple linear spring model for the tyre which demonstrate the continued use for simple tyre models; however, parameterisation of the tyre still remains a challenge when load test equipment is not available. This paper presents a cost-effective tyre vertical stiffness parameterisation procedure using only measured tyre geometry and air pressure for applications where high-fidelity tyre models are unnecessary. Vertical forces calculated through an air volume optimisation approach are used to estimate tyre vertical stiffness. Nine tyres from the literature are compared to evaluate the performance of the vertical force estimation and stiffness parameterisation algorithms. Experimental results on a pair of ATV tyres are also presented.     

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.     

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.     

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.     

轮胎侧偏特性研究的特点及其发展

首先,分析并阐述了车辆动力学特性与轮胎力学特性的关系。然后,对轮胎力学特性进行了分类,介绍了轮胎侧偏特性研究的特点,描述了轮胎稳态和非稳态侧偏特性研究的历史及其发展。最后,指出了轮胎侧偏特性研究的意义和轮胎模型的研究方向。     

杭州市电动自行车交通管理现状及源头管理对策

电动自行车的普及，在给交通参与者带来出行便利的同时，也给道路交通安全和交通秩序管理带来了一系列问题。主要以杭州市的电动自行车发展和交通管理现状为例，探讨如何从源头管理方面以合法、合理的手段解决电动自行车发展带来的问题。     

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.     

The bricycle: a bicycle in zero gravity can be balanced or steered but not both

A bicycle or inverted pendulum can be balanced, that is kept nearly upright, by accelerating the base. This balance is achieved by steering on a bicycle. Simultaneously one can also control the lateral position of the base: changing of the track line of a bike or the position of hand under a balanced stick. We show here with theory and experiment that if the balance problem is removed, by making the system neutrally stable for balance, one cannot simultaneously maintain balance and control the position of the base. We made a bricycle, essentially a bicycle with springy training wheels. The stiffness of the training wheel suspension can be varied from near infinite, making the bricycle into a tricycle, to zero, making it effectively a bicycle. The springy training wheels effectively reduce or even negate gravity, at least for balance purposes. One might expect a smooth transition from tricycle to bicycle as the stiffness is varied, in terms of handling, balance and feel. Not so. At an intermediate stiffness, when gravity is effectively zeroed, riders can balance easily but no longer turn. Small turns cause an intolerable leaning. Thus there is a qualitative difference between bicycles and tricycles, a difference that cannot be met halfway.     

Tyre rolling kinematics and prediction of tyre forces and moments: part II – simulation and experiment

There are two aims for the second part of this paper: verifying the theory presented in the first part through parameter variation and comparison between simulation and experiment, and to study the effect of the belt structure on the cornering properties of radial tyres. Research has been carried out with a passenger car radial tyre and two different kinds of truck or bus radial tyres using both simulation and experiment. This second part of the paper shows that belt structure plays an important role in the generation of tyre forces and moments in addition to the effects of the tread stiffness and friction coefficients. The theory and method presented in this paper opens a new robust way to predict the tyre forces and moments from the tyre design and provides a reliable model for a generation mechanism.     

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.     

抗滑水轮胎技术的新发展

轮胎在湿路面上的行驶性能关系到汽车的安全性。阐述了国外开发的三种新型抗滑水轿车轮胎的设计思想，结构特点以及主要性能，介绍了提高轮胎在潮湿带水路面上行驶性能的新技术及其新发展，对开发国产高性能轿车轮肥具有现实的参考借鉴意义。     

A mechanism to enhance bicycle conspicuity and visibility and increase detection distances: New insights into bicycle safety

Poor sensory conspicuity and poor visibility of bicycles are key factors that correlate strongly with bicycle-vehicle accidents. Although researchers have explored how to improve detection distances, i.e., the distances from which bicycles can be recognized by other road users, there is a dearth of research on ways to signal bicyclists' presence on the road. This study investigates how to enhance, at minimum cost, the level of visibility and sensory conspicuity of bicycles; it also considers ways to signal their presence to other road users, without necessitating any active behavior by bicyclists themselves. In the first study, the level of visibility of 6 rear-end components of bicycles was analyzed according to Adrian's model; the sensory conspicuity of these same components was analyzed via respondent perceptions in conditions of sunlight, twilight with no car headlights, twilight with car headlights, and night with car headlights. The level of visibility and sensory conspicuity of the 6 rear-end components were compared with considering angular size of the components under 4 lighting conditions. The level of visibility of the rear fender was good under sunlight and night-time conditions; in other conditions, the level of visibility was directly affected by painting the fender a silver color with reflectivity and also by the fender's angular size. However, the rear tire, among the 6 components tested, had a higher visible area when used with a short fender; it also produced rotational effects during riding conditions with no extra effort by the cyclists. In the second study, adhesive tape with specific patterns and 6 different color combinations were applied to the rear tire of a bicycle under the same lighting conditions, with the aim of creating a strong signal of the bicycle's presence for other road users. Among the 6 combinations, white stripes overlaid on the color red provide an optimal combination in terms of detection distance. The mean detection distance of white stripes on red in sunlight was 138.67 m, 94.67 m in twilight without car headlights, 94 m in twilight with car headlights, and 53.67 m at night with car headlights. In addition, this combination strongly signals the presence of the bicycle to other road users with no extra effort by the cyclists, thereby reducing the likelihood of drivers looking but failing to see bicycles. In sum, the study recommends that bicyclists install white stripes overlaid on red, in order to increase visibility and conspicuity and signal the presence of their bicycles, thereby reducing the likelihood of cyclist-vehicle collisions.     

Development of an experimental methodology to evaluate the influence of a bamboo frame on the bicycle ride comfort

In the current environment of increased emphasis on sustainable transport, there is manifold increase in the use of bicycles for urban transport. One concern which might restrict the use is the ride comfort and fatigue. There has been limited research in addressing the difficulty in bicycle ride comfort quantification. The current study aims to develop a methodology to quantify bicycle discomfort so that performance of bicycles constructed from bamboo and aluminium alloy can be compared. Experimentally obtained frequency response functions are used to establish a relation between the road input and the seat and rider response. A bicycle track input profile based on standard road profiles is created so as to estimate the acceleration responses. The whole-body-vibration frequency weighting is applied to quantify the perception of vibration intensity so that eventual discomfort ranking can be obtained. The measured frequency response functions provide an insight into the effect of frame dynamics on the overall resonant behaviour of the bicycles. The beneficial effect of frame compliance and damping on lower modes of vibration is very clear in the case of bamboo frame, in turn affecting seat and rider response. In the bamboo frame, because of multiple resonances, the frequency response of the handlebar is smaller at higher frequencies suggesting effective isolation. Further improvements may have come from the joints made from natural composites. Overall, based on the comparative analysis and the methodology developed, bamboo frame shows significant improvement in ride comfort performance compared with the aluminium frame.     

轮胎制动与驱动特性的理论模型

轮胎印迹内垂直载荷的分布与形式的选择，对建立轮胎制动与驱动特性的理论模型有很大影响。根据轮胎制动和驱动时印迹内垂直载荷分布特性，以及轮胎的前后变形特性，建立了轮胎制动、驱动特性的理论模型。应用该理论模型的计算结果，与试验结果具有很好的一致性。     

车轮荷载下土壤静力学特性分析

利用有限元软件ANSYS建立三维有限元模型,模拟车轮和土壤的静态接触,进行非线性有限元分析,研究车轮荷载下土壤的静力学特性。采用基于Drucker-Prager的弹塑性模型来模拟真实土壤,并考虑摩擦作用。分别采用刚性轮模型和超弹性轮胎模型模拟车轮,并将2种情况进行对比。结果表明：在车轮荷载作用下,土壤的竖向位移和等效应力在轮胎与土壤接触的区域最大;土壤的竖向位移和等效应力随土壤深度的增加而减小;土体在刚性轮作用下的变形和应力要远大于其在超弹性轮作用下的值,表明虽然刚性轮几何形状简单,模型设置容易,但是与超弹性轮胎模型相比,这种模拟精确度低。     

胎面轮廓形状优化技术研究--提高轮胎耐磨耗性能

胎面轮廓形状对轮胎的耐磨耗性能影响很大，因此对其进行优化很有意义。针对胎面轮廓形状比较复杂的特点，文中采用多个变量来定义胎面轮廓。同时，在现有磨耗理论的基础上，通过对胎面轮廓形状的优化初步给出了评价轮胎耐磨耗性能的指标。在此基础上，采用自编的多目标优化程序对胎面轮廓进行优化，并将计算结果与原胎数据进行了比较，结果表明，不论是从胎面的磨耗速度还是从胎面磨耗的均匀性来说优化胎都要优于原始。     

A nonlinear model of bicycle shimmy

This paper presents a nonlinear model accurately describing, both qualitatively and quantitatively, the onset and dynamics of bicycle shimmy. Methods of nonlinear dynamics, such as numerical continuation and bifurcation analysis, show that the model exhibits two stable periodic motions found experimentally in on-road tests: the weave and wobble (or shimmy) mode. The modelling results are compared with experimental data collected by riding a racing bicycle downhill at high speeds with hands on the handlebar. The model predicts with surprising accuracy the amplitudes and frequencies of the oscillations, the longitudinal velocity at which they occur, as well as the substantial independence of wobble frequency and amplitude from the forward speed. The lateral acceleration of the upper tube of the frame near the steering axis reaches 5–10?g, both in the model and in the data. The analysis shows that wobble onset and amplitude is particularly sensitive to changes in the torsional stiffness of the frame and strongly depends on tyre lateral force and aligning torque at the wheel–road contact point. It also allows to quantify the additional viscous rotary damping that should be added to the steering assembly to prevent wobble.     

A review on bicycle and motorcycle rider control with a perspective on handling qualities

This paper is a review study on handling and control of bicycles and motorcycles, the so-called single-track vehicles. The first part gives a brief overview on the modelling of the dynamics of single-track vehicles and the experimental validation. The second part focusses on a review of modelling and measuring human rider control. The third part deals with the concepts of handling and manoeuvrability and their experimental validation. Parallels are drawn with the literature on aircraft handling and pilot models. The paper concludes with the open ends and promising directions for future work in the field of handling and control of single-track vehicles.