Reliability analysis of turbine disk low-cycle fatigue life based on quasi-monte carlo method under mixed uncertainty
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摘要:
综合考虑航空发动机轮盘工作状态下几何、材料等混合不确定性因素，建立低周疲劳概率寿命模型，对比分析多种不确定性模型，建立几何不确定性概率表征模型，采用深度神经网络代理模型与拟蒙特卡洛模拟结合算法，构建一种区间拟蒙特卡洛抽样方法用于考虑几何、材料混合不确定性的可靠性分析方法，实现疲劳寿命概率预测及可靠性分析，计算得到寿命可靠度的上下界，99.87%可靠度下寿命下界为1.61×104次循环，寿命上界为2.53×104次循环，为涡轮盘高可靠性设计提供方法支撑。
Abstract:To account for mixed uncertainties, including geometric and material factors, under the operating conditions of aero-engine turbine disks, this study developed a probabilistic low-cycle fatigue life model. A comparative analysis of various uncertainty models was conducted, and a probabilistic representation model for geometric uncertainty was established. Through the integration of a deep neural network surrogate model with quasi-Monte Carlo simulation algorithms, an interval quasi-Monte Carlo sampling approach was formulated for reliability analysis incorporating geometric and material mixed uncertainties. This enabled probabilistic fatigue life prediction and reliability analysis, thereby quantifying the upper and lower bounds of life reliability. At a reliability level of 99.87%, the lower bound of fatigue life was 1.61×104 cycles and the upper bound was 2.53×104 cycles, These results provide methodological support for high-reliability turbine disk design.
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Key words:
- turbine disk /
- mixed uncertainty /
- low-cycle fatigue life /
- quasi-Monte Carlo /
- reliability
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图 5 关键几何尺寸按相对影响排序
Figure 5. Ranking of critical geometrical dimensions by relative influence
表 1 FGH96合金力学性能参数
Table 1. Mechanical properties of FGH96 alloy
温度/℃ 弹性模量/GPa 泊松比 线性膨胀系数/10−6 ℃ 400 174 0.311 13.0 500 179 0.311 13.4 600 168 0.311 13.9 700 164 0.311 14.4 
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表 2 关键几何参数
Table 2. Critical geometrical parameters
参数 几何意义 d1/（°） 盘心角度 h9/mm 中心孔半径 w1/mm 轮缘半厚度 w3/mm 左侧厚度
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表 3 不同分布拟合的K-S检验统计量（Dn）
Table 3. Kolmogorov-Smirnov test statistics （Dn） for different distribution fits
参数 正态分布 伽马分布 威布尔分布 d1 0.087218 0.097228 0.105659 h9 0.092015 0.096983 0.087002 w1 0.088971 0.100667 0.092811 w3 0.142282 0.159366 0.201176
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表 4 盘心400 ℃确定性模型参数
Table 4. Parameters of the deterministic model for the 400 ℃ disk center
$ {\sigma }^{\prime}_{{\mathrm{f}}} $/MPa $ {\varepsilon }^{\prime}_{{\mathrm{f}}} $ b c E/MPa 2286 12.27 − 0.0948 − 0.8616 174000
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表 5 裂纹萌生寿命模型参数（盘心温度为400 ℃）
Table 5. Parameters of the crack initiation life model at 400 ℃
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表 6 不同可靠度下疲劳寿命
Table 6. Fatigue life at different reliability levels
疲劳寿命 50%可靠度寿命/
104循环周次90%可靠度寿命/
104循环周次99%可靠度寿命/
104循环周次99.87%可靠度寿命/
104循环周次寿命上界 3.03 2.87 2.68 2.53 寿命下界 2.03 1.89 1.73 1.61
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