变位直齿轮副齿顶修形参数设计

该文以变位直齿轮副的齿顶修形为研究对象，考虑齿轮啮合的非线性接触、修正基体刚度以及延长啮合的影响，建立了考虑齿顶修形的变位直齿轮副时变啮合刚度解析模型，并通过有限元方法验证了该模型的正确性；以对刚度进行快速傅里叶变换（FFT）得到的前五阶幅值之和最小为设计目标，获得了齿顶修形的最优参数范围，并通过有限元模型进行应力分析，反证了该范围的正确性。研究结果表明:基于啮合刚度FFT前5阶幅值之和最小的设计方法可以更为高效地计算并锁定最优修形参数的范围，通过有限元进行应力分析可进一步验证齿顶修形的最优参数；齿轮齿顶修形后，刚度谐波量和应力均明显减小，有助于降低齿轮系统的振动和噪声。研究结果可为变位直齿轮副齿顶修形设计提供理论方法与依据。

PARAMETER DESIGN OF TIP RELIEF FOR SPUR GEAR PAIR WITH ADDENDUM MODIFICATION

An analytical model is developed for a spur gear pair with an addendum modification to concern the tip relief when calculating time-varying mesh stiffness, by considering the effects of nonlinear contact stiffness, of revised fillet-foundation stiffness and of extended tooth contact. The proposed model is verified by the finite element (FE) method. The ranges of optimum parameters for tip relief are acquired by making the sum of the first five-step amplitude of fast Fourier transform (FFT) for mesh stiffness minimum. Furthermore, stress analysis is conducted to prove the optimal modification parameters based on the FE method. Results showed that the design method based on the sum of the first five-step amplitude of FFT for mesh stiffness minimum can determine efficiently the optimal modification parameter range and the stress analysis based on the finite element method can further verify the optimal parameters of tip relief. The fluctuation of stiffness and stress decrease obviously after tip relief, which can contribute to the reduction of vibration and noise in the meshing process of gear pairs. The results can provide a theoretical basis for the tip relief design of a spur gear pair with an addendum modification.