Identification of the Structural Modes of High Performance Bicycles in the Perspective of Wobble Control

Abstract

Most of researches in the field of bicycle dynamics deal with auto-stabilization and rider control by means of steer-torque and lean-torque. Bicycle models composed by rigid bodies with thin wheels making point contact with the road and rolling without any slip are suited for carrying out these studies. Numerical analysis of stability by means of these models leads to the capsize, castering and weave modes, which make it possible to understand many aspects of bicycle dynamics. However, some high performance bicycles at high speed show dangerous wobble oscillations. Cyclists’ experience and recent researches highlight that wobble phenomena are related both to tire properties and to fork and frame compliance. Since structural compliance in dynamic conditions generates vibrations, this paper focuses on the study of structural vibrations of high performance bicycles with the modal analysis approach. To isolate the effects of frame and fork compliance, four particular bicycles are considered, they are built assembling a pair of wheels, two forks (fork A and B) with the same shape but different structures and materials and two frames (frame A and B) with the same shape but different structures. Preliminary road tests showed that bicycles made with components A are more prone to wobble oscillations. In order to have a better comprehension of the different influence of fork and frame compliance, first the two forks (with the front wheel) are modally tested with the steer tube locked to a very stiff structure, then, the whole bicycles are tested. Modal analysis is carried out with the impulse method, for the analysis of each bicycle 60 FRFs are measured. The results of modal analysis are presented and the influence of identified modes on bicycle stability is discussed. An important issue of modal analysis of vehicles is the correlation between modal tests carried out in the laboratory and bicycle behavior on the road. When the vehicle is tested in the laboratory, additional constraints are added to guarantee equilibrium, but centrifugal forces are not present, because the vehicle is stationary. Since the analysis of the equations of linearized dynamics shows that the stiffness matrix includes a part due to centrifugal effects, the additional stiffness terms due to constraints in laboratory tests can be assumed to be equivalent to the centrifugal terms of the stiffness matrix at a certain speed. Details and limits of this equivalence are presented and discussed in the paper.

On-road measurements of high speed bicycle shimmy, and comparison to structural resonance

“…Apart from that disparity in boundary condition, it is expected that their given mode 1 roughly approximates the one studied here. By constraining the saddle, and optionally simulating the mass loading of the rider's hands on the handlebars, the experiments of [14] should more closely match the vibrations we have observed both on the road, and in the laboratory.…”

“…Torsional compliance of the frame is likely to be a large contributor to this lateral elastic flexibility, but the lightly constructed front fork and wheel may also play a part, even if the main motion of the steering assembly is the rotation around the fork (head tube) axis, consequent to the head tube lateral oscillation with fixed front contact point. [14] specifically examined structural frequencies of the bicycle, so it is appropriate to point out similarities and differences from the present work. The central difference is the lack of mass loading at the saddle: rider mass is easily 10X or 15X the bicycle mass, thus very nearly fixing the saddle in the high frequency modes being studied.…”

“…The central difference is the lack of mass loading at the saddle: rider mass is easily 10X or 15X the bicycle mass, thus very nearly fixing the saddle in the high frequency modes being studied. The lack of such inertia or constraint leads to a higher (11.5 Hz) first-mode frequency in [14], and shifts the nodes away from the saddle. Apart from that disparity in boundary condition, it is expected that their given mode 1 roughly approximates the one studied here.…”

Identification of lumped stiffness parameters for a motorcycle model in investigating weave and wobble

“…The crucial part of the lumped stiffness approach is the identification of the parameters [10]. In the literature, most models using the lumped stiffness approach make assumptions about the position of the joints for modeling flexibility.…”

An experimental-numerical method for the prediction of on-road comfort of city bicycles

“…A valid alternative to shaker tests is the identification of the frequency response functions (FRFs) of the bicycle-rider system with the impulsive method [11,12] and the prediction of vibrations on the road using an experimentally-derived bicycle model and normalised road profiles [13].…”