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.     

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.     

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.     

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.     

Dynamic modelling and experimental validation of three wheeled tilting vehicles

The present paper describes the study of the stability in the straight running of a three-wheeled tilting vehicle for urban and sub-urban mobility. The analysis was carried out by developing a multibody model in the Matlab/SimulinkSimMechanics environment. An Adams-Motorcycle model and an equivalent analytical model were developed for the cross-validation and for highlighting the similarities with the lateral dynamics of motorcycles. Field tests were carried out to validate the model and identify some critical parameters, such as the damping on the steering system. The stability analysis demonstrates that the lateral dynamic motions are characterised by vibration modes that are similar to that of a motorcycle. Additionally, it shows that the wobble mode is significantly affected by the castor trail, whereas it is only slightly affected by the dynamics of the front suspension. For the present case study, the frame compliance also has no influence on the weave and wobble.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Eigensystem of Tangential Contact in Tyre Models

Summary In this paper, a simplified model of tangential contact between tyre and rigid surface is investigated. By linearization the eigensystem of the contact equations is obtained and parameter variations are carried out. It is shown, that some vehicle model parameters have great influence on the eigensystem of tangential contact and can determine the highest eigenfrequency of the system vehicle and tyre. Root loci are used to investigate the influence of parameters like vehicle velocity and gridwidth of the discretization. Based on the eigensystem, stability areas of numerical methods in solving the partial differential equations of tangential contact are calculated. Numerical solutions using stiff and nonstiff integrators are compared with respect to the stability areas, computational effort and accuracy. The results are discussed with a view to further development.     

Eigensystem of Tangential Contact in Tyre Models

Summary In this paper, a simplified model of tangential contact between tyre and rigid surface is investigated. By linearization the eigensystem of the contact equations is obtained and parameter variations are carried out. It is shown, that some vehicle model parameters have great influence on the eigensystem of tangential contact and can determine the highest eigenfrequency of the system vehicle and tyre. Root loci are used to investigate the influence of parameters like vehicle velocity and gridwidth of the discretization. Based on the eigensystem, stability areas of numerical methods in solving the partial differential equations of tangential contact are calculated. Numerical solutions using stiff and nonstiff integrators are compared with respect to the stability areas, computational effort and accuracy. The results are discussed with a view to further development.     

In-Plane and Out-of-Plane Dynamics of Pneumatic Tyres

During the last decade research has been conducted on the dvnamics of the tvre considered as a vehiclecomponent. Asurvey is given of these developments where tyre mass plays an important role. The underlying theoretical considerations concerning the massless tyre have been discussed as well. Two groups of tyre response have been distinguished: the lateral (out-of-plane) response and the vertical/longitudinal (in-plane) response to motions of the wheel. In both categories tyre compliance, slip and inertia have influence. The dynamic properties of the rolling tyre have been presented in the form of transfer functions and/or differential equations. The frequency of the imposed oscillations is assumed to be below ca. 40 Hz. Non-linear effects and modelling have been briefly touched on.     

In-Plane and Out-of-Plane Dynamics of Pneumatic Tyres

SUMMARY

During the last decade research has been conducted on the dvnamics of the tvre considered as a vehiclecomponent. Asurvey is given of these developments where tyre mass plays an important role. The underlying theoretical considerations concerning the massless tyre have been discussed as well. Two groups of tyre response have been distinguished: the lateral (out-of-plane) response and the vertical/longitudinal (in-plane) response to motions of the wheel. In both categories tyre compliance, slip and inertia have influence. The dynamic properties of the rolling tyre have been presented in the form of transfer functions and/or differential equations. The frequency of the imposed oscillations is assumed to be below ca. 40 Hz. Non-linear effects and modelling have been briefly touched on.     

FSAE赛车前悬架运动学仿真及参数优化

运用Catia软件建立某FSAE赛车前悬架三维模型,并将Catia中的坐标转换成Adams软件中的坐标,建立Adams前悬架模型。针对该FSAE赛车前悬架进行双轮跳动运动学仿真,并对悬架传递比和前轮定位参数进行参数优化。     

考虑心理潜变量的城市电动自行车用户出行决策行为

为探究电动自行车用户对不同城市电动自行车规范管理政策的行为响应机理,采用问卷调查方法收集用户的社会人口特征、出行特征、心理特征以及在不同政策下的决策,基于心理接受度等潜变量构建了多指标多因素模型, 得出了潜变量的拟合值,将潜变量作为解释变量引入到行为决策模型中,构成了混合选择模型来分析社会人口变量、出行特征变量和心理潜变量对电动自行车用户出行决策的影响。结果表明:①电动自行车用户的心理特征显著影响其出行决策行为,对政策接受度更高的用户会表现出更强的正面行为倾向;②经济因素是导致出行者继续使用超标违规电动自行车或违反政策的主要原因;③提供报废补贴能中和收入对决策的影响,促进低收入家庭购买符合标准的电动自行车;④政策的实施会促进电动自行车交通向小汽车交通的转移。      

Using an integrated model of TPB and TAM to analyze the pandemic impacts on the intention to use bicycles in the post-COVID-19 period

Due to the rapid increase in bicycle usage during the pandemic, this study aims to ascertain the effects of COVID-19 and the role of psychosocial factors on the intention to cycle in the future. An integrated model of the theory of planned behavior (TPB) and technology acceptance model (TAM) was modified and utilized with a sample of 473 cyclists in Yogyakarta, Indonesia. The results confirm that the awareness change because of the advent of COVID-19, especially related to the environment, negative impacts of motorized vehicles (including road safety burden), and climate change issues, has the strongest power to influence bicycle use intention. The positive effect of COVID-19 also significantly influenced subjective norms and perceived behavioral control. Meanwhile, attitudes toward cycling and its perceived usefulness did not significantly contribute to bicycle use intention. Attitudes to use bicycles also could not mediate the relationship between COVID-19 and the intention to use bicycles. Based on the study findings, a set of policy initiatives was proposed, including cycling campaigns related to environmental issues, promoting bicycle use by public figures, providing a segregated bike lane, and introducing bicycle-specific programs, such as bicycle usage in cultural events.     

民生警务背景下电动自行车治理困境与应对策略

大量的电动自行车违法行为给交通管理增加了繁重的压力的同时,也给民生警务改革、构建和谐警民关系带来了难题。在此背景下,文章首先阐述了新修订的《浙江省电动自行车管理条例》主要内容,接着分析了目前电动自行车治理存在民众对新《条例》认知不足、违法者不认同执法、电动自行车驾驶员安全意识不高和违规电动自行车生产销售等问题,最后有针对性地从宣传引导、加强执法协作和强化监管等方面提出了相应的对策建议。