精密长寿命齿轮的制造成本高、周期长，针对这种齿轮的疲劳试验更是费时费力。为了简单、准确地得到齿轮的寿命信息，基于最小次序统计量的概念建立齿轮的概率寿命预测模型，模型建立不同齿数的齿轮之间的概率寿命关系，其将特定齿轮的寿命数据作为输入变量，可以转化得到其他齿轮的概率寿命。在恒定应力水平下进行齿轮弯曲疲劳试验，在试验过程中说明了齿轮失效的监测与判据方法，同时将齿轮的失效机理分析与断口分析相结合，解释了齿轮的失效模式，最后借助试验数据详细阐述了模型的使用方法。利用随机截尾数据统计方法对模型进行验证，证明模型具有良好的预测能力和处理小样本数据的优势。
Manufacture of the precision and long life gears has a characteristic of high cost and long cycle, furthermore, fatigue test for the gears is time-consuming and laborious. In order to get the life information of gears accurately and conveniently, the concept of minimum order statistics is used to establish a model for predicting the probabilistic life of gears. Then the probabilistic life relationship of gears with different number of teeth is established. The life data of specific gear are taken as input variable for the model, after translating by model the probabilistic life of other gears can be obtained. At the same time, a gear bending fatigue test is carried out at a constant stress level, and in the course of the test, the method of monitoring and evaluating for gear failure is explained. Next, two kinds of analysis of failure mechanism and fracture for gear are combined to show the failure mode, and test data are employed to show the instructions of the model. The model is finally validated by a statistical method of random censoring data, and the advantages of model with good prediction ability and dealing with small amount of data are proved.
[1] BHAUMIK S K, SUJATA M, KUMAR M S, et al. Failure of an intermediate gearbox of a helicopter[J]. Engineering Failure Analysis, 2007, 14:85-100.
[2] DEEN K M. Investigating the failure of bevel gears in an aircraft engine[J]. Case Studies in Engineering Failure Analysis, 2013, 1:24-31.
[3] FERNANDES P. Tooth bending fatigue failures in gears[J]. Eng. Fail. Anal., 1996, 3:219-225.
[4] GLODEZ S, ABERSEK B. A computational model for determination of service life of gears[J]. International Journal of Fatigue, 2002, 24:1013-1020.
[5] GLODEZ S, ABERSEK B. Evaluation of the service life of gears in regard to surface pitting[J]. Engineering Fracture Mechanics, 2004, 71:429-438.
[6] ABERSEK B, FLASKER J. Review of mathematical and experimental models for determination of service life of gears[J]. Engineering Fracture Mechanics, 2004, 71:439-453.
[7] 段明德, 位宝磊, 游延伟. 基于无偏灰色马尔可夫组合模型的齿轮寿命预测[J]. 机械传动, 2015, 39(2):16-19. DUAN Mingde, WEI Baolei, YOU Yanwei. Prediction of gear life based on unbiased grey Markov combined model[J]. Mechanical Transmission, 2015, 39(2):16-19.
[8] 秦大同, 周志刚, 杨军, 等. 随机风载作用下风力发电机齿轮传动系统动态可靠性分析[J]. 机械工程学报, 2012, 48(3):1-8. QIN Datong, ZHOU Zhigang, YANG Jun, et al. Time-dependent reliability analysis of gear transmission system of wind turbine under stochastic wind load[J]. Journal of Mechanical Engineering, 2012, 48(3):1-8.
[9] 周志刚, 徐芳. 考虑强度退化和失效相关性的风电齿轮传动系统动态可靠性分析[J]. 机械工程学报, 2016, 52(11):80-87. ZHOU Zhigang, XU Fang. Dynamic reliability analysis of gear transmission system of wind turbine considering strength degradation and dependent failure[J]. Journal of Mechanical Engineering, 2016, 52(11):80-87.
[10] 谢里阳. 机械可靠性理论、方法及模型中若干问题评述[J]. 机械工程学报, 2014, 50(14):27-35. XIE Liyang. Issues and commentary on mechanical reliability theories, methods and models[J]. Journal of Mechanical Engineering, 2014, 50(14):27-35.
[11] 安宗文, 张宇, 刘波. 风电齿轮箱零件寿命分布函数的确定方法[J]. 电子科技大学学报, 2014, 43(6):950-954. AN Zongwen, ZHANG Yu, LIU Bo. A method to determine the life distribution function of components for wind turbine gearbox[J]. Journal of University of Electronic Science and Technology of China, 2014, 43(6):950-954.
[12] PETERSON R E. Stress concentration factors[D]. New York:John Wiley, 1974.
[13] 叶慈南. 完全样本情形下威布尔分布参数的估计[J]. 应用概率统计, 2003, 19(3):259-266. YE Cinan. Weibull distribution parameter estimation in complete sample case[J]. Chinese Journal of Applied Probability and Statistics, 2003, 19(3):259-266.
[14] KATERI M. On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data[J]. Statistics and Probability Letters, 2008, 78:2971-2975.
[15] 朱孝录. 齿轮的试验技术与设备[M]. 北京:机械工业出版社, 1988. ZHU Xiaolu. Gear test technology and equipment[M]. Beijing:China Machine Press, 1988.
