Torsional dynamics and stability of automotive driveline considering cubic nonlinearity

Abstract

Since the half-shaft is the main flexible part of the automotive driveline, the torsional dynamics of the simplified driveline considering the cubic nonlinearity of the half-shaft is discussed in the paper. The approximate solutions of the torsional shock response and the resonance response of the driveline are derived using the method of multiple scales. The stability and bifurcation condition of the responses are judged based on the Routh–Hurwitz criterion and the bifurcation theory, respectively. It is shown that the negative cubic nonlinear stiffness is propitious to suppress the torsional shock of the driveline while the positive is on the contrary. Meanwhile, the ability of the suppression of the torsional shock can be improved with the decrease in the linear stiffness. The resonance curve of the driveline may lose its stability when the value of the cubic nonlinear stiffness reaches the threshold. By properly designing the negative cubic nonlinear stiffness of the half-shaft, the instability of the resonance can be suppressed and the ability of the suppression of the torsional shock can also be improved.

Stability analysis of shock response of EV powertrain considering electro-mechanical coupling effect

“…The drive-shaft model, which contains the flexibility of the half shaft and the conversion ratio of the transmission and the final drive, is shown in Figure 1, where J 0 m is the moment of inertia of the motor rotor; J L is the sum of the moment of inertia of the wheel and the moment of inertia of the vehicle being equivalent to the wheel; f 0 m , f L are the motor rotor angle and the wheel angle, respectively; k is the stiffness of the powertrain; c is the damping coefficient of the powertrain 4,7 ; i 0 and i 1 are the speed ratio of the transmission and the final drive, respectively; T 0 m is the torque of drive motor, and T L is the torque of vehicle load.…”

“…3 In the meantime, resonance is an important part that should be considered when studying torsional vibration as it may destroy the powertrain when the frequency of the outer excitation equals or near the resonance frequency of the powertrain. 4 Generally, there are two kinds of methods that are usually used to control the torsional vibration of the powertrain: add some dampers to the powertrain 5 or design active control methods. Compared with the resonance, shock 6,7 is a kind of transient behavior, such as judder 8,9 or shuffle, 10 which usually happens during start/stop 11 or tip in/out.…”

“…However, if the parameters of the electric vehicle powertrain are properly designed, the fold bifurcation can be eliminated, and the unstable dynamics of the resonance can also be controlled. 4 Even though the torsional dynamics of the electric vehicle powertrain have been widely studied, there are still several issues that must be discussed properly, such as the stability of the shock response of the electric vehicle powertrain when considering electro-mechanical coupling effect. If the parameters of the electric part or the mechanical part are not chosen properly, the electric vehicle powertrain may not work stably after the impact.…”