Phase-flip in a nonlinear jumping full-car model with time delays

• Nonlinear jumping full-car models with time delays were proposed • In-phase, out-of-phase, and phase-lag synchronization between wheels are observed • Phase flips from in-phase /phase-lag to out-of-phase synchronization are observed • Out-of-phase synchronization significantly reduces vertical acceleration . Understanding nonlinear vehicle dynamics is important for enhancing vehicle performance, such as safety and ride comfort, as well as for the development of autonomous driving. Various types of nonlinearities exist in the vehicle dynamics. Among these nonlinearities, jumping nonlinearities can cause dangerous behaviors in vehicles, including steering instability and overturning. In this study, a nonlinear jumping full-car model with time delays is proposed, which is considered to be a combination of four nonlinear quarter-car models or two nonlinear half-car models. Time delays play important roles in dynamic systems. We introduced such delays in a full-car model using active suspension. Numerical simulations were performed under periodic excitations, that is, simultaneous and non-simultaneous sine excitations. The numerical results revealed novel behaviors in the nonlinear jumping full-car model. First, the bifurcation from periodic to quasi-periodic was observed under non-simultaneous excitations. This shows that the phase differences in the excitations can induce more complex vibrations in the full-car model. Second, time delays can induce different types of synchronization in the nonlinear full-car model, that is, in-phase, out-of-phase, and phase-lag motions. A phase-flip was observed in the presence of time delays. Furthermore, time delays can significantly decrease the vertical acceleration of the sprung mass by inducing an out-of-phase motion. This indicates that time delays can be tuned to induce out-of-phase motion to reduce vibrations. These insights were validated using noise-contaminated excitations, indicating that they are feasible for vibration reduction in practical situations.