Abstract
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.
Highlights
The hybrid electric vehicle (HEV) has been widely used by combining the conventional internal combustion engine (ICE) propulsion system and the pure electric propulsion system, which solved the problem of the large pollution of traditional vehicle and the poor battery life of electric vehicle (EV).[4,5]
Comparing with the traditional powertrain, the addition of motor in hybrid powertrain causes the essential change of the structure and working principle, making the dynamic characteristics totally different
On account of the variety of working modes and the unknown operating conditions of HEV, the hybrid powertrain is always subjected to a variety of excitations
Summary
Liu[19] investigated the dynamic characteristics of the gear transmission system under multi-frequency excitation based on Hopf bifurcation theory, and revealed the mathematical mechanism of instability.[20] The influence of parameters, including friction coefficient and modal damping, on the dynamic response changing from the stable period to the unstable chaotic motion was revealed by largest Lyapunov exponent. 2. At present, the dynamic characteristics of the periodically excited dynamic system with two time scales, especially in physics, chemistry, biology, and mechanics, are mostly limited to single excitation.[26,27,28,29,30,31] In view of such research gap, this paper establishes the multi-time scale model of hybrid powertrain under multi-frequency excitations, and the corresponding dynamic characteristics is investigated.
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