Motorcycle Steering Oscillations due to Road Profiling

Abstract

A study of the effects of regular road undulations on the dynamics of a cornering motorcycle is presented. This work is based on an enhanced version of the motorcycle model described in “A Motorcycle Model for Stability and Control Analysis” (R. S. Sharp and D. J. N. Limebeer, 2001, Multibody Syst. Dyn., Vol. 6, No. 2, pp. 123–142). We make use of root-locus and frequency response plots that were derived from a linearized version of this model; the linearization is for small perturbations from a general steady-cornering equilibrium state. The root-locus plots provide information about the damping and resonant frequencies of the key motorcycle modes at different machine speeds, while the frequency response plots are used to study the propagation of road forcing signals to the motorcycle steering system. Our results are based on the assumption that there is road forcing associated with both wheels and that there is a time delay between the front and rear wheel forcing signals—this is sometimes referred to as wheelbase filtering. As has been explained before, control systems are used in the nonlinear simulation code to establish and maintain the machine’s speed and roll angle at preset values (for flat road running). These controllers are used to find the machine’s equilibrium state and not to emulate a rider’s control actions. The results show that at various critical cornering conditions, regular road undulations of a particular wavelength can cause severe steering oscillations. At low speeds the machine is susceptible to road forcing signals that excite the lightly damped wobble and front suspension pitch modes. At higher speeds it is the weave and front wheel hop modes that become vulnerable to road forcing. We believe that the results and theory presented here explain many of the stability related road accidents that have been reported in the popular literature and are therefore of practical import. The models used in this research make use of the multibody modelling package AUTOSIM (Autosim 2.5+ Reference Manual, 1998, Mechanical Simulation Corporation) and are available at the web site http://www.ee.ic.ac.uk/control/motorcycles/. The motorcycle and tire parameters can be found at the end of the code.