Dynamics analysis of the hybrid powertrain under multi-frequency excitations with two time scales

Aiming at the dynamic behavior of hybrid powertrain under multi-frequency excitations with two time scales, this paper has carried out related research work. A nonlinear dynamic model of hybrid powertrain is established by taking engine excitation, load excitation and electromagnetic excitation into consideration. Considering the order gap between the excitation frequency and the natural frequency, slow variables are introduced to transform this model into a fast-slow model. Through introducing the De Moivre equation, slow variables are unified into a single one. The dynamic equations under different excitation frequencies and amplitudes are obtained. Bifurcation theory is applied to study the bifurcation behavior when the equilibrium point is unstable, and the conditions for the generation of fold bifurcation are derived. By means of numerical analysis, the influence of excitation frequency and amplitude on dynamics behavior is investigated by curve of equilibrium point, transformed phase portrait and time history. The simulation results show that fold bifurcation may lead to jumping phenomenon of the system trajectory and bursting oscillation is generated correspondingly. Additionally, the bifurcation characteristics of the hybrid powertrain may change with the excitation frequency and amplitude, making the pattern of bursting oscillation more complicated. The conclusion provides a reference for further analysis of dynamic behavior of hybrid powertrain.