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

China Mechanical Engineering ›› 2023, Vol. 34 ›› Issue (02): 185-192.DOI: 10.3969/j.issn.1004-132X.2023.02.008

Previous Articles Next Articles

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

LI Yang;LIU Huaiju;WEI Peitang;MAO Tianyu;CHEN Difa

State Key Laboratory of Mechanical Transmissions，Chongqing University，Chongqing，400044

Online:2023-01-25 Published:2023-02-16

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

李扬;刘怀举;魏沛堂;毛天雨;陈地发

重庆大学机械传动国家重点实验室，重庆，400044

通讯作者: 刘怀举（通信作者），男，1986年生，教授、博士研究生导师。研究方向为机械传动智能设计与抗疲劳制造。发表论文100余篇。E-mail：huaijuliu@cqu.edu.cn。
作者简介:李扬，男，1999年生，硕士研究生。研究方向为机械传动智能设计与软件开发。E-mail：202107131116t@cqu.edu.cn。
基金资助:
国家自然科学基金（52175041）；国家科技重大专项（2019-Ⅶ-0017-0158）

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.

References

［1］LIU Heli， LIU Huaiju， ZHU Caichao， et al. Influence of Load Spectrum on Contact Fatigue Damage of a Case Carburized Wind Turbine Gear［J］. Engineering Failure Analysis， 2021， 119：105005.
［2］LIU Heli， LIU Huaiju， ZHU Caichao， et al. Study on Gear Contact Fatigue Failure Competition Mechanism Considering Tooth Wear Evolution［J］. Tribology International， 2020， 147：106277.
［3］ZHANG Boyu， LIU Huaiju， ZHU Caichao， et al. Simulation of the Fatigue-wear Coupling Mechanism of an Aviation Gear［J］. Friction， 2021， 9（6）：1616-1634.
［4］DIXON W. The Up-and-down Method for Small Samples［J］. Journal of the American Statistical Association， 1965， 60（312）：967-978.
［5］DIXON W J， MOOD A M. A Method for Obtaining and Analyzing Sensitivity Data［J］. Journal of the American Statistical Association， 1948， 43（241）：109-126.
［6］ROU V， DOUDARD C， CALLOCH S， et al. Simulation-based Investigation of the Reuse of Unbroken Specimens in a Staircase Procedure：Accuracy of the Determination of Fatigue Properties［J］. International Journal of Fatigue， 2020， 131：105288.
［7］LITTLE R. Estimating the Median Fatigue Limit for Very Small Up-and-down Quantal Response Tests and for SN Data with Runouts［M］. West Conshohocken, USA:ASTM International， 1972.
［8］LITTLE R E. Manual on Statistical Planning and Analysis for Fatigue Experiments［M］. West Conshohocken, USA:ASTM International， 1975.
［9］BROWNLEE K， JR HODGES J， ROSENBLATT M. The Up-and-down Method with Small Samples［J］. Journal of the American Statistical Association， 1953， 48（262）：262-277.
［10］SVENSSON T. Random Features of the Fatigue Limit［J］. Extremes， 1999， 2（2）：165-176.
［11］张天飞，蔡瑞娇，董海平，等. 升降法试验下标准差σ估计的Monte Carlo分析［J］. 火工品， 2004（2）：43-47.
ZHANG Tianfei， CAI Ruijiao， DONG Haiping， et al. Study on σ Estimation in Up-down Sensitivity Test with Monte Carlo Method［J］. Initiators and Pyrotechnics， 2004（2）：43-47.
［12］SVENSSON T， LORN S， DE MAR J， et al. Statistical Models of the Fatigue Limit［R］. SP Sveriges Tekniska Forskningsinstitut， 2000.
［13］IX-ISO. Metallic Materials-fatigue Testing-statistical Planning and Analysis of Data：ISO 12107—2012［S］.Genevce：International Organization for Standardization， 2012.
［14］郑州中机轨道交通装备科技有限公司，中机生产力促进中心，郑州机械研究所有限公司，等. 齿轮弯曲疲劳强度试验方法:GB/T 14230—2021［S］. 北京：中国标准出版社， 2021.
Zhengzhou Zhongji Rail Transit Equipment Technology， China Productivity Center for Machinery， Zhengzhou Machinery Research Institute， et al. Test Method of Tooth Bending Strength for Gear Load Capacity：GB/T 14230—2021［S］. Beijing：Standards Press of China， 2021.
［15］中国钢铁工业协会. 金属材料疲劳试验数据统计方案与分析方法：GB/T 24176—2009［S］. 北京：中国标准出版社， 2009.
China Iron and Steel Association. Metallic Materials-fatigue Testing-statistical Planning and Analysis of Data：GB/T 24176—2009［S］. Beijing：Standards Press of China， 2009.
［16］MLLER C， WCHTER M， MASENDORF R， et al. Accuracy of Fatigue Limits Estimated by the Staircase Method Using Different Evaluation Techniques［J］. International Journal of Fatigue， 2017， 100：296-307.
［17］ZHAO Y X， YANG B. Probabilistic Measurements of the Fatigue Limit Data from a Small Sampling Up-and-down Test Method［J］. International Journal of Fatigue， 2008， 30（12）：2094-2103.
［18］MAO Tianyu， LIU Huaiju， WEI Peitang， et al. An Improved Estimation Method of Gear Fatigue Strength Based on Sample Expansion and Standard Deviation Correction［J］. International Journal of Fatigue， 2022， 161：106887.
［19］郑州中机轨道交通装备科技有限公司，中机生产力促进中心，郑州机械研究所有限公司，等. 直齿轮和斜齿轮承载能力计算第3部分：轮齿弯曲强度计算：GB/T 3480. 3—2021［S］. 北京：中国标准出版社， 2021.
Zhengzhou Zhongji Rail Transit Equipment Technology， China Productivity Center for Machinery， Zhengzhou Machinery Research Institute， et al. Calculation of Load Capacity of Spur and Helical Gears-Part 3：Calculation of Tooth Bending Strength：GB/T 3480. 3—2021［S］. Beijing：Standards Press of China， 2021.
［20］DENGO C， MENEGHETTI G， DABALA M. Experimental Analysis of Bending Fatigue Strength of Plain and Notched Case-hardened Gear Steels［J］. International Journal of Fatigue， 2015， 80：145-61.
［21］LIN S K， LEE Y L， LU M W. Evaluation of the Staircase and the Accelerated Test Methods for Fatigue Limit Distributions［J］. International Journal of Fatigue， 2001， 23（1）：75-83.

[1]	ZHAO Ning1；LUO Xinzhen1；LI Wenying1；YUAN Zhaoyun2. Suitability about FEM Standard on AS/RS with Monte-Carlo Simulation [J]. China Mechanical Engineering, 2020, 31(18): 2153-2160.
[2]	ZHANG Zhigang;YU Xiaoxia;ZHENG Yanjie;LI Teng. Modeling, Simulation and Tests of Friction Characteristics for Synchronizers [J]. China Mechanical Engineering, 2019, 30(07): 825-831.
[3]	Li Guihua, Wang Hui, Xiong Zhao, Gao Liang, Cao Tingfen, . Surface Error Analysis of Large Reflecting Mirror under Assembly Fastening Forces [J]. China Mechanical Engineering, 2015, 26(9): 1173-1178.
[4]	Yu Zhimin, Liu Zijian, Dong Sike, Li Simin, Ai Yandi. Tolerance Modeling Based on Monte-Carlo Simulation and Response Surface Method [J]. China Mechanical Engineering, 2015, 26(4): 427-434.
[5]	CA Zhong-Xi, LIU Lin, WANG Shao-Hui, LI Meng-Zhe, CAO Jun-Hui. Process Control and CAD Software Development for Continuous Flexible Forming [J]. China Mechanical Engineering, 2011, 22(8): 943-947.
[6]	He Xuehong;Zhang Min;Xie Liyang;Zuo Koucheng. Accuracy Analysis and Simulation of 3-TPT Parallel Machine Tool [J]. J4, 2008, 19(11): 0-1269.

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

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

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 6

Recommended Articles

Metrics