On the influence of tyre and structural properties on the stability of bicycles

Abstract

In recent years the Whipple Carvallo Bicycle Model (WCBM) has been extended to analyze high speed stability of bicycles. Various researchers have developed models taking into account the effects of front frame compliance and tire properties, nonetheless, a systematic analysis has not been yet carried out. This paper aims at analyzing parametrically the influence of front frame compliance and tire 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 tire 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 tire properties, and the wobble mode has the main effect on stability.

Analysis of the Phenomena Causing Weave and Wobble in Two-Wheelers

“…Lumped parameter models are described in [15]. This kind of modelling is also found in other sources, especially when a more complex non-rigid model is developed [16][17][18][19][20][21].…”

“…There are several parameters affecting a motorcycle's wobble stability; a complete list can be found in [2,3,17,21]. For this work, besides the fork bending compliance, two tyre parameters are of particular importance: the relaxation length and the cornering stiffness.…”

“…For this work, besides the fork bending compliance, two tyre parameters are of particular importance: the relaxation length and the cornering stiffness. Some research [3,16,17,20] has underlined that a tyre model with cornering stiffness is necessary in order to simulate the wobble mode. This also suggests an important consideration: the principal cause of the wobble is given by the tyre's response.…”

“…The other important tyre parameter influencing wobble is the relaxation length [3,13,23]. Several works [3,16,17,20,24] investigated its effect on wobble damping, underlying how the relaxation length destabilises the wobble mode, since it generates a delay between the wheel steering and the tyre-lateral force generation. As a consequence, Sharp [3] (p. 323) clarifies that both tyre sideslip and tyre relaxation properties are fundamental for a proper representation of a motorcycle's dynamic properties.…”

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

“…The rider with his/her mass, stiffness and damping characteristics has a large effect on bicycle dynamics, even if the control actions (Kooijman and Schwab, 2013) are neglected and a completely passive behavior is assumed. For this reason, some researchers have integrated the bicycle model with rider models composed of rigid bodies (the limbs) connected by means of joints (the articulations) and by lumped stiffness and damping elements (Schwab et al, 2012;Doria and Tognazzo, 2014). These models make it possible to simulate the passive response of the rider both in the hands-off and in the hands-on configuration.…”