基于近场动力学的齿根裂纹扩展特性研究

Research on Crack Growth Characteristics of Dedendum Based on Peridynamics

摘要: 为优化齿根裂纹扩展问题的分析，在标准渐开线齿轮对上，基于近场动力学理论建立齿轮接触啮合断裂模型，模拟近场动力学下齿轮齿根断裂啮合过程。近场动力学理论通过空间积分的方法，避免了传统有限元在分析裂纹尖端问题时的奇异性。首先建立一对健康的渐开线齿轮模型并通过近场动力学接触理论确定齿根在啮合过程中应力最大点，从而确定裂纹起始点并预制裂纹；通过近场动力学方法可以有效避免裂纹扩展过程中不断重新划分网格的问题。然后通过基于节点位移的应力强度因子反推法得到裂纹扩展后的应力强度因子。最后依据Paris公式对齿根疲劳裂纹剩余寿命进行评估。从近场动力学裂纹扩展结果上看，近场动力学方法下裂纹扩展方向、疲劳周期与有限元中结果是一致的。该研究结果可以提供一种新的方法进行齿轮接触疲劳分析。

Abstract: In order to optimize the analysis of tooth root crack propagation problem, a gear contact meshing fracture model was established based on the peridynamicstheory on the standard involute gear pair, and the meshing process of tooth root fracture was simulated under the peridynamics. The peridynamics theory avoids the singularity of the traditional finite element method in analyzing the crack tip problem by using the method of space integration. Firstly, a pair of healthy involute gear models was established and the maximum stress point of tooth root during meshing was deter-mined by the peridynamics contact theory. Then the crack initiation point was determined and the crack was prefabricated. The peridynamics method can effectively avoid the problem of constantly remeshing during crack propagation. Then, the stress intensity factor after crack propagation is obtained by the inverse stress intensity factor method based on node displacement. Finally, the re-sidual life of root fatigue crack was evaluated according to Paris formula. According to the results of peridynamics crack propagation, the direction of crack propagation and fatigue period under the peridynamics method are consistent with those obtained in the finite element method. The re-search results can provide a new method for gear contact fatigue analysis.