基于系统PSN曲线的齿轮箱疲劳可靠度评估

马洪义; 谢里阳

doi:10.13700/j.bh.1001-5965.2017.0378

基于系统PSN曲线的齿轮箱疲劳可靠度评估

doi: 10.13700/j.bh.1001-5965.2017.0378

马洪义,
谢里阳^,

东北大学现代设计与分析研究所, 沈阳 110819

基金项目:

国家自然科学基金 51335003

详细信息

作者简介:
马洪义男, 博士研究生。主要研究方向:机械系统可靠度评估

谢里阳男, 博士, 教授, 博士生导师。主要研究方向:机械系统可靠度评估、疲劳与断裂失效分析

通讯作者:
谢里阳, E-mail: lyxie@mail.neu.edu.cn

中图分类号: V215.5⁺2;TH132.4
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出版历程
- 收稿日期: 2017-06-05
- 录用日期: 2017-07-07
- 网络出版日期: 2018-05-20

Assessment of gearbox fatigue reliability based on system PSN curve

MA Hongyi,
XIE Liyang^,

Institute of Modern Design and Analysis, Northeast University, Shenyang 110819, China

Funds:

National Natural Science Foundation of China 51335003

More Information

Corresponding author: XIE Liyang, E-mail:lyxie@mail.neu.edu.cn

摘要

摘要:
蒙特卡罗方法可以准确评估复杂机械系统疲劳共因失效概率，但效率偏低，因此提出系统PSN曲线的概念和基于此概念的系统可靠度蒙特卡罗评估方法。在给定的恒幅载荷下，基于同一零件的疲劳寿命在不同应力水平下的概率分位点具有一致性的原则，对系统中零件PSN曲线进行随机抽取；根据线性累积损伤法则和相应的系统可靠度模型，得到齿轮传动的恒幅载荷下的疲劳寿命分布，拟合恒幅载荷与寿命分布之间的关系得到系统PSN曲线。将系统视为一个零件，完成"零件"-"系统"-"零件"的寿命分析过程。通过损伤等效原则，将随机载荷下的复杂串联系统可靠度评估问题转化为恒幅载荷下零件的可靠度评估问题。
- 疲劳可靠度 /
- 系统PSN曲线 /
- 串联系统 /
- 共因失效 /
- 蒙特卡罗
Abstract:
To improve the efficiency of Monte Carlo simulation applied to evaluating the common cause failure probability of complex mechanical system, the concept of system fatigue life PSN curve was set up first, and then a Monte Carlo method for system reliability assessment based on this concept was proposed. With a given constant load, based on the correspondence of probability percentiles between specimen fatigue lives associated with different cyclic stress levels, every single PSN curve of component can be extracted stochastically. According to the linear cumulative damage rule and the corresponding system reliability model, the fatigue life distribution of gear-series-system was acquired. System PSN curve can be obtained by fitting constant load and life distribution. The system can be treated as a component, and the life analysis process of component-system-component has been completed. By means of damage equivalence principle between random load and constant load, the problem of reliability assessment of a complicated series system under random load can be converted to the problem of reliability assessment of component under constant load.
- fatigue reliability /
- system PSN curve /
- series system /
- common cause failure /
- Monte Carlo

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图 1 齿轮箱传动原理图

Figure 1. Schematic of gearbox transmission

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图 2 零件PSN曲线

Figure 2. PSN curves of components

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图 3 齿轮传动系统可靠度仿真流程

Figure 3. Gear transmission system reliability simulation process

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图 4 基于零件PSN，随机载荷下齿轮系统寿命概率分布

Figure 4. Gear system life probability distribution under random load based on component PSN

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图 5 各级恒幅扭矩下齿轮系统寿命及统计矩

Figure 5. Gear system life and statistical moment under various constant torque

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图 6 齿轮系统各级扭矩下对数寿命分布正态拟合

Figure 6. Normal fitting of gear system logarithmic life distribution under various torque

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图 7 齿轮系统PSN曲线

Figure 7. Gear system PSN curves

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图 8 齿轮串联系统寿命分布

Figure 8. Life distribution of gear series system

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表 1 齿轮箱零件参数

Table 1. Gearbox component parameters

参数	太阳轮	行星轮	内齿圈	齿轮4	齿轮5	齿轮6	齿轮7
Z	21	38	99	84	23	92	24
M_n	10	10	10	8	8	5	5
α_n/(°)	20	20	20	20	20	20	20
β/(°)	7.5	7.5	7.5	14	14	14	14
α_t′/(°)	22.6	22.6	22.6	21.5	21.5	21.5	21.5

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表 2 齿面接触应力

Table 2. Gear surface contact stress

啮合齿轮	太阳轮/行星轮	行星轮/内齿圈	齿轮1/齿轮2	齿轮3/齿轮4
σ_H/MPa	0.052 1	0.022 5	0.030 9	0.031 6

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表 3 各级恒幅扭矩下齿轮系统寿命统计及统计矩

Table 3. Gear system life andstatistics moment under various constant torque

输入轴扭矩/(10⁸ N·mm)	寿命标准差/cycle	寿命均值/cycle
2	3.3×10⁵	6.6×10⁵
3	6.2×10⁴	1.1×10⁵
5	4.2×10³	1.2×10⁴
6	2.2×10³	5.9×10³

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表 4 3种方法寿命特征值比较

Table 4. Comparison of characteristic life of three methods

方法	系统寿命均值/(10⁴cycle)	系统寿命标准差/(10⁴cycle)	以a为参照的均值相对误差/%	以a为参照的标准差相对误差/%
a	9.8	4.0	0	0
b	9.5	3.5	3.1	12.5
c	11	5.3	12.2	32.5

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