人字齿行星传动中的内、外啮合时变刚度是造成齿轮传动振动的主要激励源。根据轮齿啮合接触原理推导了人字齿行星齿轮啮合传动的时变刚度动态梯形图，得到了内、外啮合刚度的分布规律，二者不具有时间同步性。采用集中质量法建立了人字齿行星齿轮传动的扭转非线性动力学模型，在欧拉型积分和牛顿迭代法等数值方法基础上对系统的非线性振动方程组进行了求解，结果显示内啮合在多个转速区域出现显著振动，最大振幅发生在转速5900 r／min处，外啮合动载特性较为稳定，均载系数为K＝1．38。借助相图、Poincaré映射、FFT频谱分析等手段对系统拟周期振动特性进行分析，表明振动吸引子在相空间中发生扭曲翻转形成封闭超环面，频域则由多个离散次谐波响应构成。%Internal and external time⁃varying meshing stiffnesses are the primary excitations which result in unsta⁃bility in herringbone planetary gear train. Based upon meshing principle, the dynamical trapezoidal wave of meshing stiffness is performed with respect to variation movement of tooth contact areas, the behaviors of the meshing stiff⁃ness are exhibited, where both of them are independent and asynchronous along the times. The torsional nonlinear dynamical model including backlash are built by utilizing lumped⁃mass method, The governing equations are inves⁃tigated by means of Euler integral as well as Newton iteration algorithm, the analytical solutions demonstrate that in⁃ternal mesh indicates significant perturbations at some rotational speeds, the maximum vibration displacement takes place at 5 900 r/min, the external mesh movement is more stable with the mean dynamical coefficient at K=1.38. In conjunction with the phase portrait, Poincaré maps and FFT spectral analysis, the quasi⁃periodic vibration is studied with the conclusion that the attractors in state space warps and flips forming a close hypertorus toroidal sur⁃face, the frequency spectrum consists of quantities of independent sub harmonic frequencies.
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