This paper investigates the nonlinear dynamics of light-duty commercial vehicle electric drivetrains via a 12-DOF lumped parameter model derived from Lagrange’s equations, including a permanent magnet synchronous motor (PMSM), dual Cardan universal joints, a spiral bevel gear pair, and discretized shafts. Key excitations include PMSM torque ripple, joint-induced speed fluctuation, shaft eccentricity, and backlash-induced gear meshing with transmission error. Steady-state responses are characterized using time- and frequency-domain analyses, phase portraits, and Poincaré sections. Parametric studies with bifurcation diagrams and largest Lyapunov exponents (LLE) elucidate dynamic evolution. Results show that shafts exhibit predominantly periodic responses governed by motor rotational frequency and harmonics, while the gear pair displays irregular oscillations from backlash impacts. Period-doubling transitions and multistability are identified with variations in motor speed, backlash, and joint angle. Among these parameters, backlash shows the strongest influence on system stability and markedly advances the onset of chaotic responses. A high-fidelity LS-DYNA finite element model validates natural frequencies and time-domain trends. This work offers insights for analyzing and mitigating nonlinear vibration and chaos in electric drive systems.
Bai et al. (Tue,) studied this question.