Abstract: The conventional gear bending fatigue test data processing method was based on the traditional frequency theory such as the LSE, and the probabilistic-stress-life(P-S-N) curve was prone to fitting distortion under the conditions of small samples. The bending fatigue tests of 8620H steel surface carburized gears were carried out based on the group method. Bayesian theory was applied to the analysis of bending fatigue test data under the conditions of small samples, and the HBM of the gear bending fatigue test data was established. Gibbs sampling was applied to acquire the posterior distribution of the parameters and the gear bending fatigue P-S-N curve. At the same time, the relative slope ratio of the S-N curve at 50% and 99% reliability was used as the evaluation index to compare the fitting effectiveness of the LSE model and the HBM model. The results show that the relative slope ratio α of the HBM model fluctuates with the change of the test sample data volume. The rate of change is 1/40 of that of the traditional LSE model, and the results of the HBM model are better than that of the traditional LSE model under the conditions of a small sample. This model may be extended and applied to data analysis such as gear contact fatigue tests.

Key words: small sample data, gear bending fatigue test, hierarchical Bayesian model(HBM), least squares method(LSE)

摘要： 常规齿轮弯曲疲劳试验数据处理方法是基于最小二乘法（LSE）等传统频率理论的，在小样本条件下可靠度应力寿命（P-S-N）曲线易发生拟合失真。基于成组法开展了8620H钢表面渗碳齿轮的弯曲疲劳试验，将贝叶斯理论应用于小样本条件下弯曲疲劳试验数据分析，建立了齿轮弯曲疲劳试验数据的分层贝叶斯（HBM）模型，并通过Gibbs采样获得了参数的后验分布，得到齿轮弯曲疲劳P-S-N曲线。同时以50%和99%可靠度下S-N曲线相对斜率比为评价指标，对比了LSE模型与HBM模型拟合效果，结果表明：随着试验样本数据量的变化，HBM模型的相对斜率比α波动变化率为传统LSE模型的1/40，小样本条件下HBM模型结果优于传统的LSE模型结果。HBM模型可推广应用至齿轮接触疲劳试验等数据分析中。

关键词: 小样本数据, 齿轮弯曲疲劳试验, 分层贝叶斯模型, 最小二乘法