Friction-induced vibrations between the brake disc and pad represent a significant source of noise and vibrations in automotive systems. To mitigate these vibrations, this study investigates the influence of brake force on friction-induced vibrations and explores corresponding active suppression methods. Both simulation and experimental results indicate that the Hopf bifurcation curve can be used to prevent friction-induced vibrations; specifically, such vibrations can be avoided by maintaining the brake pressure below the Hopf bifurcation threshold. To optimize the trade-off between energy recovery efficiency and vibrations suppression, the energy recovery efficiency is defined as the objective function, while the Hopf bifurcation curve or the stick-slip curve is imposed as a constraint. Based on this framework, an IPSO-FC-based strategy is proposed to allocate regenerative and friction braking torques effectively. The results demonstrate that utilizing the Hopf bifurcation curve, rather than the stick-slip curve, significantly expands the feasible operational region and enhances regenerative braking efficiency. Furthermore, the extent of improvement in regenerative braking efficiency is shown to depend on the specific driving cycle.
Zheng et al. (2026) studied this question.