﻿ 基于二重威布尔混合分布的某型燃机燃油泵组件可靠性分析
 舰船科学技术  2024, Vol. 46 Issue (3): 126-130    DOI: 10.3404/j.issn.1672-7649.2024.03.022 PDF

1. 海军工程大学 动力工程学院，湖北 武汉 430033;
2. 中国人民解放军95778部队，云南 昆明，650000

Reliability analysis of fuel pump component for a gas turbine based ona double Weibull hybrid distribution
CHEN Yang1, LI Jun2, XIONG Jing-yang1
1. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2. No.95778 Unit of PLA, Kunming 650000, China
Abstract: The fuel pump component is mechatronics. The fault data obtained in the use of the products contains different failure mechanisms, so a single distribution cannot describe the product failure mechanism accurately, while the hybrid distribution can couple multiple failure distributions, thus can fully describe the product failure mechanism. For the first time, the double-three-parameter Weibull hybrid distribution model is applied to the fault analysis of ship engine accessories. Based on the fault data of a fuel pump component of one certain type of gas turbine, the fault model and model initialization parameters are determined by data analysis histogram. The linear curve fitting method is used to estimate the parameters of the double-three-parameter Weibull hybrid distribution. The research methods and results can provide a feasible method for the reliability analysis and optimization of fuel pump components.
Key words: fuel pump component     mixed three-parameter Weibull distribution     data analysis histogram     parameter estimation
0 引　言

1 燃油泵组件工作原理

 图 1 燃油泵组件结构剖面图 Fig. 1 Sectional view of fuel pump component

 图 2 燃油泵组件工作原理图 Fig. 2 Working diagram of fuel pump component
2 燃油泵组件故障模型评估

 图 3 故障数据 Fig. 3 Fault data

 ${K}=1+3.3{\rm{l}}_{{\rm{g}}}{{n}} 。$ (1)

 $\Delta {t}=({L}-{S})/{K} 。$ (2)

 ${t}_{i}=\frac{\mathrm{某}\mathrm{组}\mathrm{下}\mathrm{限}\mathrm{制}+\mathrm{某}\mathrm{组}\mathrm{上}\mathrm{限}\mathrm{值}}{2}。$ (3)

 ${w}_{i}=\frac{{\mathrm{\Delta }{r}}_{i}}{n} 。$ (4)

 $\stackrel-{t}=\sum _{i=1}^{k}{w}_{i}\times{t}_{i} 。$ (5)

 ${S}=\sqrt{\frac{1}{n-1}\sum _{i=1}^{k}\Delta {r}_{i}({t}_{i}-\stackrel-{t}{)}^{2}} 。$ (6)

 图 4 累积频率分布图 Fig. 4 Cumulative frequency distribution

 图 5 失效频率直方图 Fig. 5 Failure frequency histogram

3 基于Matlab对故障分布函数参数求解

 ${F}\left({t}\right)={P}\left\{{1-e}^{-\frac{{(t-\gamma 1)}^{m1}}{\eta 1}}\right\}+\left(1-P\right)\left\{1-{e}^{-\frac{{(t-\gamma 2)}^{m2}}{\eta 2}}\right\}。$ (7)

 ${F}_{1}\left({t}\right)=1-{e}^{-\frac{{(t-\gamma 1)}^{m1}}{\eta 1}} ，$ (8)
 ${{F}_{2}\left(t\right)=1-e}^{-\frac{{(t-\gamma 2)}^{m2}}{\eta 2}}。$ (9)

 ${F}\left({t}\right)=P{F}_{1}\left(\mathrm{t}\right)+\left(1-P\right){F}_{2}\left(t\right)。$ (10)

Matlab中对于非线性数据进行拟合时，为了能够在最短的时间内获得收敛解，需要对未知参数进行初始化，以未知参数的初值作最小二乘拟合，未知参数初始化值直接影响到能否获得收敛解以及拟合曲线的品质。因此如何拟定合适的初始参数是参数求解的关键。

 图 6 曲线对比分析图 Fig. 6 Similar curve comparison and analysis chart

{P γ1 η1 m1 γ2 η2 m2}={0.27 0 463.3 0.61 534.1 861.2 3.375}；残差平方=1.3463×10−4，将参数代入式（7）得到失效分布函数：

 ${F}\left({t}\right)=0.27 \cdot \left({1-e}^{-{\left(\frac{t}{463.3}\right)}^{0.61}}\right)+0.73 \cdot \left(1-{e}^{-({\frac{t-534.1}{861.2})}^{3.375}}\right) 。$

 图 7 拟合曲线与故障数据分析对比图 Fig. 7 Comparison and analysis between fitting curve and fault data chart
4 燃油泵组件可靠性分析

 $\begin{split} {f}\left({t}\right) = & 3.6\times{10}^{-4} \times {\left(\frac{t}{463.3}\right)}^{-0.39} \times {e}^{-{\left(\frac{t}{463.3}\right)}^{0.61}} + 2.86 \times {10}^{-3}\times\\ & \left(\frac{t-534.1}{861.2}\right)^{2.375}\times{e}^{-\left(\frac{t-534.1}{861.2}\right)^{3.375}}，\\[-10pt] \end{split}$ (11)

 ${{MTBF}}=\theta={{P}}\times\theta_1+(1-{\mathrm{P}})\times\theta_2。$ (12)

 ${{MTBF}} =1\;142.5\;{\mathrm{h}} 。$

 $\scriptsize\mathrm{\lambda }\left(\mathrm{t}\right) = \frac{3.6 \times {10}^{-4} \times \left( \frac{t}{463.3} \right)^{-0.39} \times {e}^{-\left( \frac{t}{463.3} \right)^{0.61}}+2.86 \times {10}^{-3} \times \left( \frac{t-534.1}{861.2} \right)^{2.375} \times {e}^{-\left(\frac{t-534.1}{861.2}\right)^{3.375}}}{0.27 \times {e}^{-{\left(\frac{t}{463.3}\right)}^{0.61}}+0.73 \times {e}^{-\left(\frac{t-534.1}{861.2}\right)^{3.375}}} 。$ (13)

 图 8 燃油泵组件的失效率曲线 Fig. 8 Failure rate curve of fuel pump component

1）对燃油泵组件中柱塞泵密封环等易损件进行定期拆解更换；

2）改进密封环的材质，在不降低其密封性能的基础上，提高耐磨度；

3）优化燃油泵组件内部润滑结构，提高润滑效果；

4）指导使用人员增加对上游燃油滤清器的清洗频率，减少进入泵燃油组件内部燃油中的杂质。

5 结　语

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