Analysis of the Influence of Tyre Cross-Sectional Parameters on the Stability of a Nonlinear Bicycle Model with Elliptic Toroidal Wheels

In this work, the stability of a bicycle with elliptic toroidal wheels is analysed in detail. The influence of the tyre cross-sectional parameters on the self-stability velocity range of the steady forward motion is studied. The bicycle multibody model is based on a well-acknowledged bicycle benchmark, which has been extensively used in several works. The nonlinear equations of motion, constituting a Differential-Algebraic Equations (DAE) system, are derived and linearized along the steady forward motion. The robustness of the linearization approach allows obtaining the resulting Jacobian matrix as a function of the tyre cross-sectional parameters. Therefore, a sensitivity analysis of the eigenvalues with the wheels’ geometric parameters is performed. Different scenarios are considered, and the influence of the tori aspect ratios and the elliptic cross-sections are illustrated with various stability regions.