Bicycle wheel wobble: a case study in dynamics

This paper examines reasons why wheel wobble occurs in common production bicycles. In particular, the effects of frame size, rider position and riding style are examined with reference to a range of mathematical models of bicycles which are available in the published literature. Much of the motivation for this work comes from the personal cycling experience of one of the authors and the difficulty in resolving the true cause of wheel wobble from the wide range of advice offered of a variety of cycling experts. It is hoped that recourse to a mathematical analysis will give objective direction as to how wheel wobble can be alleviated through rider intervention

Bicycle wheel wobble: a case study in dynamics

This paper examines reasons why wheel wobble occurs in common production bicycles. In particular, the effects of frame size, rider position and riding style are examined with reference to a range of mathematical models of bicycles which are available in the published literature. Much of the motivation for this work comes from the personal cycling experience of one of the authors and the difficulty in resolving the true cause of wheel wobble from the wide range of advice offered of a variety of cycling experts. It is hoped that recourse to a mathematical analysis will give objective direction as to how wheel wobble can be alleviated through rider intervention

Parametric analysis of the stability of a bicycle taking into account geometrical, mass and compliance properties

Some studies of bicycle dynamics have applied the Whipple Carvallo bicycle model (WCBM) for the stability analysis. The WCBM is limited, since structural elements are assumed to be rigid bodies. In this paper, the WCBM is extended to include the front assembly lateral compliance, and analysis focuses on the study of the open loop stability of a benchmark bicycle. Experimental tests to identify fork and wheel properties are performed, this data is used in the stability analysis for ranking the influence of design parameters. Indexes from the eigenvalues analysis are applied in a full factorial approach. The results show that introducing front assembly compliance generates a wobble mode with little effect on self-stability. The forward displacement of the centre of mass of the rear frame and the increment in trail lead to large increments in the self-stability, whereas increments in front wheel radius and wheelbase reduce stability

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

Bicycles, Motorcycles and Models

Published versio

Model Based Analysis of Shimmy in a Racing Bicycle

In this paper we are presenting a model of a racing bicycle, developed in Modelica language within the Dymola environment. The main purpose is to investigate the dynamic response of the bicycle and its modes of vibration, referring in particular to shimmy. This phenomenon occurs at high speeds and consists of sudden oscillations of the front assembly around the steering axis. Lateral accelerations on the horizontal tube of the frame can reach 5-10 g with a frequency that varies between 5-10 Hz. Even if it is quite uncommon, shimmy is a topic of great relevance, because it may be extremely dangerous for the rider. Thanks to this model, we can show that the main elements which contribute to the rise of the oscillations are the lateral compliance of the frame and the tyres’ deformation

Stability analysis of bicycles by means of analytical models with increasing complexity

The basic Whipple-Carvallo bicycle model for the study of stability takes into account only geometric and mass properties. Analytical bicycle models of increasing complexity are now available, they consider frame compliance, tire properties, and rider posture. From the point of view of the designer, it is important to know if geometric and mass properties affect the stability of an actual bicycle as they affect the stability of a simple bicycle model. This paper addresses this problem in a numeric way by evaluating stability indices from the real parts of the eigenvalues of the bicycle's modes (i.e., weave, capsize, wobble) in a range of forward speeds typical of city bicycles. The sensitivity indices and correlation coefficients between the main geometric and mass properties of the bicycle and the stability indices are calculated by means of bicycle models of increasing complexity. Results show that the simpler models correctly predict the effect of most of geometric and mass properties on the stability of the single modes of the bicycle. Nevertheless, when the global stability indices of the bicycle are considered, often the simpler models fail their prediction. This phenomenon takes place because with the basic model some design parameters have opposite effects on the stability of weave and capsize, but, when tire sliding is included, the capsize mode is always stable and low speed stability is chiefly determined by weave stability

The effect of tyre and rider properties on the stability of a bicycle

To work towards an advanced model of the bicycle-rider-environment system, an open-loop bicycle-rider model was developed in the commercial multibody dynamics software ADAMS. The main contribution of this article to bicycle dynamics is the analysis of tyre and rider properties that influence bicycle stability. A system identification method is used to extract linear stability properties from time domain analysis. The weave and capsize eigenmodes of the bicycle-rider system are analysed. The effect of tyre properties is studied using the tyre’s forces and torques that have been measured in several operating conditions. The main result is that extending simplified models with a realistic tyre model leads to a notable decrease in the weave stability and a stabilization of the capsize mode. This effect is mainly caused by the twisting torque. Different tyres and tyre inflation pressures have little effect on the bicycle’s stability, in the case of riding straight at a constant forward speed. On the other hand, the tyre load does have a large effect on bicycle stability. The sensitivity study of rider properties shows that body stiffness and damping have a small effect on the weave and capsize mode, whereas arm stiffness destabilizes the capsize mode and arm damping destabilizes the weave mode

Suppression of Burst Oscillations in Racing Motorcycles

Burst oscillations occurring at high speed and under firm acceleration are suppressed with a mechanical steering compensator. Burst instabilities in the subject racing motorcycle are the result of interactions between the wobble and weave modes under high-speed cornering and firm-acceleration conditions. Under accelerating conditions the wobble-mode frequency decreases, while the weave mode frequency increases so that destabilizing interactions occur. The design analysis is based on a time-separation principle, which assumes that bursting occurs on time scales over which speed variations can be neglected. Therefore, under braking and acceleration conditions linear time-invariant models corresponding to constant-speed operation can be utilized in the design process. The inertial influences of braking and acceleration are modelled using d’Alembert-type forces that are applied at the mass centres of each of the model’s constituent bodies. The resulting steering compensator is a simple mechanical network that comprises a conventional steering damper in series with a linear spring. This network is a mechanical lag compensator

A Multibody Dynamics Model of a Motorcycle with a Multi-link Front Suspension

The development of motorcycles has been around for over a century. Nowadays, it has become one of the most popular means of transportation in the world. It is well known that the telescopic fork is the most widely used front suspension for motorcycles, because the first motorcycle was a bicycle with a small engine attached to the frame. However, there are a number of shortcomings inherent in this design. Therefore, a novel multi-link suspension has been designed for the front assembly of the motorcycle in this research. In order to compare the performance between telescopic fork and multi-link front suspension motorcycles, linear and nonlinear models were built and simulated under a variety of different conditions. Furthermore, an appropriate method of comparison between conventional and multi-link models was developed, and the assessment standard of performance for conventional and multi-link models was explored in this research