Abstract In this study, a hybrid model is proposed for the flexible helical planetary gear by coupling the lumped-parameter dynamic models for the sun and planets, and reduced FEMs (finite element models) for the ring and carrier. To consider the planet centrifugal forces, the formula for planet acceleration is newly derived. Moreover, a method is also proposed to include centrifugal, inertia, and Coriolis forces in the reduced FEM of the carrier which possesses rigid rotating motion, so that the model is applicable to high-speed operations. The meshing points vary in the circumference direction in the condensed ring model. The translational and angular displacements (including the rigid and vibration displacements) are chosen as the generalized coordinates. The time-variant meshing stiffness and profile error excitation directly vary with the gear angular displacements. Thus, the proposed model can also be used for the variable-speed process. Considering the structure details, the FEM of the electric motor is also constructed to obtain the motor torque. Electromechanical dynamic analysis is conducted for the planetary gear of electric vehicles during stable and variable speed processes, and some improvement methods are proposed, investigated and evaluated.

中文翻译：

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电动汽车行星齿轮系统混合动力建模与分析

摘要 在这项研究中，通过耦合太阳和行星的集中参数动力学模型以及环和载体的简化 FEM（有限元模型），提出了柔性斜齿轮行星齿轮的混合模型。为了考虑行星离心力，新推导出行星加速度公式。此外，还提出了一种将离心力、惯性力和科里奥利力包含在具有刚性旋转运动的载体的简化有限元中的方法，使该模型适用于高速运行。在稠环模型中，啮合点沿圆周方向变化。选择平移和角位移（包括刚性和振动位移）作为广义坐标。时变啮合刚度和轮廓误差激励直接随齿轮角位移而变化。因此，所提出的模型也可用于变速过程。考虑到结构细节，还构建了电机的 FEM 以获得电机扭矩。对电动汽车行星齿轮在稳速和变速过程中进行机电动力学分析，并提出、研究和评估了一些改进方法。