Influence of tire side forces on bicycle self-stability

Abstract

Lateral forces are known to be important in motorcycle stability. These forces also affect the stability of bicycles. In this study, we focus on the influence of tire lateral forces on bicycle self-stability. On the basis of the work of Whipple, we develop a linear bicycle model, including front and rear wheel lateral forces, in symbolic equations of motion. Modal analysis and dynamic simulation of the bicycle model are conducted and used to examine self-stability. The lateral stability of a bicycle is characterized by two oscillatory vibration modes, namely, wobble and weave, and one non-oscillatory capsize mode. Tire sideslip force modeling reveals the wobble mode, and relaxation modeling reveals the rear wobble mode. At low speed, the unstable capsize mode dominates. At medium speed, the weave mode vibratory motion dominates. At high speed, the wobble mode dominates. The influence of lateral forces on self-stability is identified using the developed model. A nonlinear multibody bicycle model is used to confirm the results of the linear analysis.

State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches

“…The effect of a linear Fig. 9 Two distinct bicycle models which include a leaned and steering rider: (a) rider with forward leaned body and stretched arms and (b) rider with upright body and flexed arms [197] tyre model on the stability of the bicycle was presented by Souh [213]. He showed the unstable wobble mode in a linear model and verified his results on a non-linear dynamic model of the system.…”

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

“…The stability of bicycles has drawn the attention of scientists since the development of the first modern bicycles. The first dynamic models for understanding the bicycle dynamics were written independently by two scientists at the end of the nineteenth century: Whipple (1899) and Carvallo (1899). The Whipple-Carvallo bicycle model (WCBM) consists in the linearized equations of motion of the bicycle and the rider.…”

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

“…Extended bicycle models that hold true at high speed were presented in [5][6][7]. Some bicycle models including tire properties were presented in [8]. In these papers, the researchers highlighted the influence of tire properties and compliances of structural elements on high speed dynamics and stability.…”

“…In [6] some results regarding the effect of cornering stiffness on the open loop stability were presented and the effect of the position of the deformation axis was studied as well. The effects on the open loop stability of parametric variations in cornering stiffness, relaxation length and camber stiffness were considered in [8], but different models were adopted for studying the influence of the various properties, and the comparison with other results is difficult.…”