基于Wiener过程的涡轮盘榫槽裂纹扩展可靠性分析

王宁晨; 胡殿印; 刘茜; 鄢林; 王荣桥

doi:10.13224/j.cnki.jasp.20220402

基于Wiener过程的涡轮盘榫槽裂纹扩展可靠性分析

doi: 10.13224/j.cnki.jasp.20220402

王宁晨¹,
胡殿印^{1, 2, 3},
刘茜^{2, 3, 4,*, ,},
鄢林⁴,
王荣桥^{2, 3, 4}

1.
北京航空航天大学航空发动机研究院，北京 100191
2.
北京航空航天大学航空发动机结构强度北京市重点实验室，北京 100191
3.
中小型航空发动机联合研究中心，北京 100191
4.
北京航空航天大学能源与动力工程学院，北京 100191

基金项目: 国家自然科学基金（51875020，52022007，52105138）；国家科技重大专项（J2019-Ⅳ-0009-0077，J2019-Ⅳ-0016-0084）

详细信息

作者简介:
王宁晨（1998-），男，硕士生，主要从事航空发动机结构强度及可靠性研究

通讯作者:
刘茜（1994-），女，博士，主要从事航空发动机疲劳可靠性、不确定性量化、复合材料损伤分析研究。E-mail：liuxi@buaa.edu.cn

中图分类号: V232.3
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出版历程
- 收稿日期: 2022-06-04
- 网络出版日期: 2022-09-09

Reliability analysis of crack growth in turbine disk mortise based on Wiener process

WANG Ningchen¹,
HU Dianyin^{1, 2, 3},
LIU Xi^{2, 3, 4,*
, ,},
YAN Lin⁴,
WANG Rongqiao^{2, 3, 4}

1.
Research Institute of Aero-Engine，Beihang University，Beijing 100191，China
2.
Beijing Key Laboratory of Aero-Engine Structure and Strength， Beihang University，Beijing 100191，China
3.
United Research Center of Mid-Small Aero-Engine，Beijing 100191，China
4.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China

摘要

摘要:
建立了考虑裂纹扩展退化过程的时变模型，并应用于涡轮盘榫槽裂纹扩展的概率寿命分析。首先，引入双时间尺度函数的Wiener过程，建立了GH4720Li高温合金的裂纹扩展时变模型，并通过紧凑拉伸试件的裂纹扩展试验进行验证。接着，以涡轮盘榫槽齿根关键部位为对象，建立了榫槽齿根角裂纹的权函数应力强度因子求解方法，并与真实涡轮盘榫槽裂纹扩展有限元分析结果进行对比。最后，结合权函数与裂纹扩展时变模型，建立了涡轮盘榫槽疲劳裂纹扩展可靠性分析方法。分析结果表明，涡轮盘榫槽结构裂纹扩展退化的寿命呈现较大的分散性，均值为14177循环，标准差为1090.09循环，99.87%可靠度下的裂纹扩展寿命预测为10312循环。
- 疲劳裂纹扩展 /
- 涡轮盘榫槽 /
- 时变模型 /
- 通用权函数 /
- 可靠性分析
Abstract:
A time-varying model considering crack growth degradation process was established and applied to the probabilistic life analysis of crack growth in the turbine disk mortise. Firstly, a time-varying crack growth model of GH4720Li superalloy was established by introducing the Wiener stochastic process with double time scale functions. And it was verified by crack growth test of compact tensile specimens. Then, taking the root of the turbine disk’s mortise tooth as the key object, the weight function method for solving the stress intensity factor of the crack in the root of the turbine disk’s mortise tooth was established and compared with the finite element analysis results of the crack growth in the turbine disk mortise. Finally, combining the weight function and the time-varying crack growth model, the reliability analysis method for fatigue crack growth degradation of the turbine disk mortise was established. Analysis results showed that the crack growth degradation life of the turbine disk’s mortise presented a large dispersion, with an average value of 14177 cycles and a standard deviation of 1090.09 cycles. The prediction of crack growth life was 10312 cycles when the reliability was 99.87%.
- fatigue crack growth /
- turbine disk mortise /
- time-varying model /
- general weight function /
- reliability analysis

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图 1 CT试件疲劳裂纹扩展a-N曲线

Figure 1. a-N curves of fatigue crack growth for CT specimens

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图 2 CT试件da/dN-ΔK关系图

Figure 2. Relationship between da/dN and ΔK for CT specimens

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图 3 CT试件对数裂纹扩展速率曲线

Figure 3. Curves of logarithmic crack growth rate for CT specimens

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图 4 CT试件对数裂纹扩展速率标准差

Figure 4. Standard deviation of logarithmic crack growth rate for CT specimens

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图 5 裂纹扩展时变模型中值曲线

Figure 5. Median curve of time-varying fatigue crack growth model

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图 6 裂纹扩展时变模型残差

Figure 6. Residual of time-varying fatigue crack growth model

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图 7 涡轮盘榫槽有限元分析结果

Figure 7. Results of finite element analysis of turbine disk mortise

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图 8 榫槽角裂纹示意图

Figure 8. Diagram of corner crack in a mortise

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图 9 应力强度因子计算结果对比

Figure 9. Comparison of calculation results of stress intensity factor

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图 10 权函数法裂纹扩展模拟结果对比

Figure 10. Comparison of simulation results of crack growth by weight function method

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图 11 裂纹扩展概率寿命评估流程

Figure 11. Assessment process of probabilistic crack growth life

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图 12 裂纹扩展概率寿命及裂纹扩展寿命累积分布

Figure 12. Probabilistic crack growth life and cumulative distribution of crack growth life

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表 1 参考载荷及应力强度因子

Table 1. Reference loadings and stress intensity factors

载荷	示意图	应力分布	参考应力强度因子
均布		$ \sigma \left( x \right) = {\sigma _0} $	$K_{0\;A/B}^{} = {\sigma _0}\sqrt {\dfrac{ { {\text{π} }b} }{Q} } F_{0\;A/B}^{}$
线性		$\sigma \left( x \right) = {\sigma _0}\left( {1 - \dfrac{x}{a} } \right)$	$K_{1A/B}^{} = {\sigma _0}\sqrt {\dfrac{ { {\text{π} }b} }{Q} } F_{1A/B}^{}$
2次		$\sigma \left( x \right) = {\sigma _0}{\left( {1 - \dfrac{x}{a} } \right)^2}$	$K_{2A/B}^{} = {\sigma _0}\sqrt {\dfrac{ { {\text{π} }b} }{Q} } F_{2A/B}^{}$

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表 2 参考载荷下拟合参数$ p_k^{ij} $

Table 2. Fitting parameter $ p_k^{ij} $ under reference loadings

载荷	$ p_k^{ij} $	点A					点B
载荷	$ p_k^{ij} $	α_i0	α_i1	α_i2	α_i3	α_i4	β_i0	β_i1	β_i2	β_i3	β_i4
均布 i=0	p₁^ij	1.995	−1.603	18.444	−25.500	18.013	2.387	−1.542	20.039	−26.521	22.052
	p₂^ij	−1.088	1.830	−18.775	29.690	−21.158	−1.624	1.590	−19.949	27.390	−22.745
	p₃^ij	0.300	−0.674	6.408	−10.756	7.669	0.459	−0.529	6.562	−9.234	7.673
	p₄^ij	−0.030	0.079	−0.715	1.237	−0.880	−0.046	0.057	−0.704	1.008	−0.839
线性 i=1	p₁^ij	0.494	−0.797	11.320	−16.511	11.841	1.990	−0.780	11.741	−14.271	13.364
	p₂^ij	−0.185	0.765	−10.810	18.061	−13.243	−1.353	0.695	−11.065	13.685	−13.129
	p₃^ij	0.042	−0.256	3.522	−6.278	4.645	0.386	−0.210	3.506	−4.389	4.288
	p₄^ij	−0.004	0.029	−0.379	0.700	−0.520	−0.039	0.021	−0.367	0.463	−0.459
2次 i=2	p₁^ij	0.268	−0.645	8.770	−13.295	9.453	1.749	−0.578	8.682	−10.353	10.179
	p₂^ij	−0.083	0.625	−8.421	14.500	−10.524	−1.192	0.519	−8.202	9.950	−10.021
	p₃^ij	0.016	−0.209	2.749	−5.027	3.679	0.342	−0.158	2.602	−3.194	3.277
	p₄^ij	−0.001	0.023	−0.296	0.559	−0.410	−0.034	0.016	−0.272	0.337	−0.351

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表 3 不同可靠度下裂纹扩展寿命

Table 3. Crack growth life at different reliabilities

可靠度/%	寿命/循环
50.00	14205
99.00	11465
99.87	10312
99.99	8301

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