A coupled torsional-transition nonlinear dynamic model of a two-stage helical gear (TSHG) reduction system for electric vehicles (EVs) is presented in this paper. The model consists of 16 degrees of freedom (DOF), which includes factors such as the nonlinearity of backlash, time-varying mesh stiffness (TVMS), mesh damping, supporting bearings, static transmission error (STE), and the torsional damping and stiffness of the intermediate shaft, in which the fourth-order Runge–Kutta numerical integration method was applied to solve the differential equations. With the help of bifurcation diagrams, time-domain histories diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps, root-mean-square (RMS) curves, peak-peak values (PPVs), and Lyapunov exponents, the effects of pinion rotational speed, backlash, torsional stiffness, and torque fluctuation on the dynamic behavior of TSHG system are investigated. The stability properties of steady-state responses are investigated using Lyapunov exponents. The results reveal various types of dynamic evolution mechanisms and nonlinear phenomena such as periodic-one responses, quasiperiodic responses, jumps phenomena, and chaotic responses. The research presents useful results and information to vibration control and dynamic design of the TSHG transmission system used in EVs.

中文翻译：

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电动汽车两阶段斜齿轮减速机的扭转过渡非线性振动与动力学模型

提出了电动汽车（EV）两级斜齿轮减速系统的扭转过渡非线性动力学模型。该模型包含16个自由度（DOF），其中包括反冲的非线性，时变网格刚度（TVMS），网格阻尼，支撑轴承，静态传递误差（STE）以及扭转阻尼和刚度等因素在中间轴上，应用四阶Runge-Kutta数值积分方法求解微分方程。借助分叉图，时域历史图，幅度频谱，相平面图，庞加莱图，均方根（RMS）曲线，峰峰值（PPV）和Lyapunov指数，小齿轮转速，齿隙，扭转刚度，研究了转矩波动对TSHG系统动力学行为的影响。使用Lyapunov指数研究稳态响应的稳定性。结果揭示了各种类型的动态演化机制和非线性现象，例如周期一响应，准周期响应，跳跃现象和混沌响应。该研究为电动汽车用TSHG传动系统的振动控制和动态设计提供了有益的结果和信息。