Calculation Method and Software Development of Gear Fatigue Strength under Small Samples Based on Monte-Carlo Simulation

doi:10.3969/j.issn.1004-132X.2023.02.008

Abstract

Abstract: The Dixon-Mood（D-M）method used in gear fatigue strength evaluation needed a certain amount samples of tests， and the results might contain deviations. Thus an effective estimation method（the CQUboot method）of gear fatigue strength was proposed based on the Monte-Carlo simulation. D-M method and CQUboot method were verified and compared by a large number of bending fatigue strength tests. Compared with the results of 20～22 samples recommended in GB/T 14230—2021 Test Method of Tooth Bending Strength for Gear Load Capacity， while the sample number reduces to 12， the maximum errors of the D-M method are as 15.76%～24.99%， while that of the CQUboot method is as 8.02%～12.98%. With 12.66% as the maximum allowable error of fatigue strength estimation， the D-M method at least needs 10～18 samples， while the CQUboot method only needs 8 samples.

Key words: gear fatigue strength, Dixon-Mood method, Monte-Carlo simulation, test verification, software development

摘要： 齿轮疲劳极限评估Dixon-Mood（D-M）法的试验样本需求量较大，标准差估计值存在较大偏差，因此基于Monte-Carlo模拟提出小样本的齿轮疲劳极限分析方法（CQUboot），并结合大量弯曲疲劳极限试验对D-M法和CQUboot法进行了对比分析。与GB/T 14230—2021《齿轮弯曲疲劳强度试验方法》推荐的20～22个样本计算结果相比，样本量降至12时，D-M法的最大误差为15.76%～24.99%，CQUboot法为8.02%～12.98%；以12.66%为疲劳极限预估允许的最大误差时，D-M法至少需要10～18个样本点，CQUboot法只需8个样本点。

关键词: 齿轮疲劳极限, Dixon-Mood法, Monte-Carlo模拟, 试验验证, 软件开发

CLC Number:

TH132.417

LI Yang, LIU Huaiju, WEI Peitang, MAO Tianyu, CHEN Difa. Calculation Method and Software Development of Gear Fatigue Strength under Small Samples Based on Monte-Carlo Simulation[J]. China Mechanical Engineering, 2023, 34(02): 185-192.

李扬, 刘怀举, 魏沛堂, 毛天雨, 陈地发. 基于Monte-Carlo模拟的小样本下齿轮疲劳极限计算方法及软件开发[J]. 中国机械工程, 2023, 34(02): 185-192.

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