Energy harvesting from friction-induced vibrations in vehicle braking systems in the presence of rotary unbalances

A severe limitation of energy harvesting from friction-induced vibrations in vehicle brakes is that the voltage generated is significant only at low vehicle speeds. The present work suggests a strategy to overcome this limitation by the utilisation of ambient vibrations resulting from rotary unbalances of vehicle components. A realistic model for vibrations in the brake pad of a disc brake under the action of rotary unbalance is used. The brake pad vibration is modelled using a non-smooth stick–slip oscillator in the presence of Stribeck friction. A weightless shaft of rectangular cross-section rotating at constant angular speed and having an unbalanced mass concentrated at its centre is used to model rotary unbalances. It is shown that the rotary unbalance provides parametric excitation to the brake pad mass undergoing friction-induced self-excited vibration leading to synchronising patterns via Neimark–Sacker bifurcation. Such synchronisation is successful in ensuring steady voltage generation over a much wider speed bandwidth. The qualitative nature of the different solution regimes interspersed with periodic intervals are determined by Lyapunov exponents. The technique used to arrive at the Lyapunov exponents in the present discontinuous model is outlined, and MATLAB code for the same is provided in the appendix.