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基于矩阵摄动方法研究了设计参数对行星齿轮传动系统模态能量的灵敏度。此处所计及的设计参数包括太阳轮与行星轮、内齿圈与行星轮的啮合刚度、行星轮的支承刚度以及各构件的转动惯量。系统模态能量与系统的振动强度密切相关,高的模态能量预示着当系统受到来自齿轮啮合动载荷激励时将发生较大的振动。采用集中参数法建立了行星齿轮传动系统的动力学模型,并采用矩阵摄动方法对模态能量特征灵敏度问题进行了推导和求解。结合具体实例,分析了各设计参数对系统模态能量的灵敏度,并通过实验验证了一些设计参数选择对系统振动强度的影响。实验结论与理论分析相吻合,在一定程度上验证了设计过程中采用模态能量灵敏度分析法预估参数选择对系统振动强度的影响是可行了。
Based on the matrix perturbation method, the sensitivity of design parameters to the modal energy of planetary gear drive system is studied. The design parameters considered here include the sun gear and planet gear, the meshing stiffness of the ring gear with the planet gear, the bearing stiffness of the planet gear, and the moment of inertia of each member. The modal energy of the system is closely related to the vibration intensity of the system. The high modal energy indicates that a large vibration will occur when the system is excited by the meshing dynamic load. The dynamic model of planetary gear drive system is established by the method of concentration parameter. The matrix perturbation method is used to derive and solve the sensitivity of modal energy characteristics. Combined with concrete examples, the sensitivity of each design parameter to the modal energy of the system is analyzed, and the influence of some design parameters on the vibration intensity of the system is verified through experiments. The experimental conclusion is consistent with the theoretical analysis, to a certain extent, it is feasible to use the modal energy sensitivity analysis method to predict the influence of the parameter selection on the system vibration strength in the design process.