Identification of the structural modes of high performance bicycles in the perspective of wobble control.

Most of researches in the field of bicycle dynamics deal with auto-stabilization and rider control by means of steertorque and lean-torque. Bicycle models composed by rigid bodies with the wheels making knife-edge rolling point contact with the road 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 laboratory and bicycle behavior on the road. When the vehicle is tested in 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.