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通过对由齿轮、轴与轴承所组成的齿轮传动系统中弯曲振动、扭转振动和横向振动问题的分析，并考虑到齿轮质量偏心和轮齿啮合摩擦力对系统振动的影响，应用拉格朗日方程，建立了一对渐开线直齿轮传动系统振动的数学模型。得到了15自由度的时变系数振动微分方程组，为系统的振动分析奠定了基础。并给出一特定传动条件下的动态响应数值计算结果。
Based on the analysis of flexural vibration, torsional vibration and transverse vibration in the gear system composed of gear, shaft and bearing, and considering the influence of gear mass eccentricity and gear meshing friction on the system vibration, Lagrange Equation, established a pair of involute spur gear transmission system vibration mathematical model. The 15-DOF vibration-induced differential equations are obtained, which lays the foundation for the vibration analysis of the system. And gives the numerical results of dynamic response under a specific transmission condition.