本文对齿轮由于变刚度啮合所产生的振动问题采用摄动方法进行分析．首次导出变刚度啮合齿轮副角动量守恒定理及相应的有阻尼和无阻尼两种情况下的摄动方程；并用离散富氏变换数值计算获得轮齿节点处的刚度、位移、速度、加速度以及相应的频谱．其结果不但为进一步进行齿轮噪声振动分析和疲劳寿命分析等提供了必要的理论根据及相应的计算方法；而且对齿轮工程设计有重要的参考价值． This paper analyzes the vibration problem caused by gear meshing due to variable meshing. For the first time, the theorem of conservation of angular momentum of variable meshing gear pair and corresponding perturbation equations with both damping and no damping are deduced. The stiffness, displacement, velocity and acceleration at the tooth nodes are obtained by discrete Fourier transformation. The spectrum. The results not only provide necessary theoretical basis and corresponding calculation method for further analysis of gear noise and fatigue life, but also have important reference value for gear engineering design.