Damage analysis of turbine blade considering creep and fatigue under load spectrum
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摘要:
基于可描述蠕变三阶段的归一化参数蠕变模型，通过编写usercreep子程序，实现了对涡轮叶片包含多工况的典型试验载荷谱下的蠕变模拟。对单个及多个循环的载荷谱分别进行蠕变模拟，结果显示在蠕变作用下，应力集中部位随着蠕变应变的增长会发生应力松弛现象，单个载荷谱循环下，高工况产生的蠕变应变占比超过90%。在试验载荷谱运行下，引发叶片失效的主要因素为蠕变与疲劳。结合Miner线性损伤累积法则，对涡轮叶片在寿命预测的基础上进行损伤分析。而在实际应用中，试验载荷远高于实际运行使用强度，因此为了更贴合实际地评估叶片的平均故障间隔时间，利用损伤等效系数对叶片的当量运行时间进行评估，并建立估算流程，针对本文研究的涡轮叶片及试验载荷谱，可以将其换算为实际运行强度下的时长为26 283.6 h。
Abstract:Using the three-stage normalized parametric creep model, the creep behavior of a turbine blade under a typical multi-condition test load spectrum was simulated through the usercreep subroutine. The results indicated that as creep strain increased, stress relaxation occurred in stress concentration regions. Under high operating conditions, significant creep strain accumulation and stress relaxation were observed. Under a single load spectrum cycle, the creep strain induced by high operating conditions accounted for more than 90%. Based on Miner’s linear damage accumulation rule, a damage analysis of the turbine blade was conducted as part of the life prediction process. In practical applications, the test load was significantly higher than the actual operating intensity. Therefore, to more accurately evaluate the mean time to failure (MTTF) of the blade, an equivalent damage factor was employed to assess the equivalent operating time of the blade and establish an estimation process. For the turbine blade and test load spectrum, the equivalent duration under actual operating conditions was calculated to be 26 283.6 h.
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图 2 K444材料持久寿命方程拟合数据点
Figure 2. Fitting experiments data of K444 endurance life equation
图 7 单个循环结束后叶片Mises等效蠕变应变分布
Figure 7. Mises equivalent creep strain distribution of blade after single cycle
图 8 单个循环结束后叶片Mises等效应力分布
Figure 8. Mises equivalent stress distribution of blade after single cycle
图 9 M1和M2点应变和应力随时间变化曲线
Figure 9. Strain and stress curve with time of points M1 and M2
图 10 100个循环结束后叶片Mises等效应力和蠕变应变分布
Figure 10. Mises equivalent stress and creep strain distributions after 100 cycles
图 13 各工况下累积损伤等效系数随循环数增长曲线
Figure 13. Curve of cumulative damage equivalent coefficient increase with cycle number
表 1 K444材料应力-持久寿命方程拟合系数
Table 1. Fitting coefficients of K444 stress-endurance life equation
g1 g2 g3 g4 g5 134.9009 − 0.0099 − 142.2438 62.5064 − 9.4111 
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表 2 K444材料蠕变模型拟合参数
Table 2. Parameter fitting results of K444 creep model
i ai bi ci di 1 15.4923 − 24.8095 − 18.1057 26.4454 2 − 10.2401 13.4548 18.7700 − 22.5927 3 − 90.8229 130.6416 136.6764 − 198.1386 4 − 107.1287 160.7775 232.7360 − 335.5564 5 25.6918 − 30.8656 − 25.9412 33.2279
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表 3 K444合金低循环疲劳寿命模型参数
Table 3. Parameters of low cycle fatigue life model of K444
参数 温度/℃ 20 600 800 900 E/GPa 203 173 157 148 $ {\sigma }^{\prime}_{\text{f}} $/MPa 1205 1354 1405 1431 $ {\varepsilon }^{\prime}_{\text{f}} $ 1.15 10.12 13.21 14.76 b − 0.0599 − 0.1401 − 0.1678 − 0.1816 c − 0.4189 − 0.6384 − 0.7141 − 0.7520
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表 4 各工况产生的等效蠕变应变及其占比
Table 4. Equivalent creep strain and proportion under each working condition
% 工况 等效蠕变应变 在总蠕变应变中的占比 A 0.17095 93.795 B 0.01107 6.074 C 0.00019 0.104 D 0.00002 0.011 E 0.00003 0.016
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表 5 局部子模型法应力分析结果
Table 5. Results of stress analysis by local submodel method
网格 模型 应力云图 最大
应力/MPa原网格 
858 1次
加密
906 2次
加密
1008 3次
加密
1106
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表 6 各工况下持久寿命累积损伤等效系数
Table 6. Cumulative damage equivalent coefficient of endurance life under various working conditions
工况 单个载荷谱
运行时间/h100个循环下的累积
损伤等效系数350个循环下的
累积损伤等效系数A 2.70 0.0874 0.2143 B 1.03 0.0082 0.0196 C 0.33 2.584×10−4 5.858×10−4 D 0.33 2.166×10−5 4.819×10−5 E 0.93 1.489×10−5 3.379×10−5
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表 7 不同工况间相对损伤等效系数
Table 7. Equivalent coefficient of relative damage with different working conditions
工况 总运行
时间/h每小时产生的
损伤等效系数各工况相对工况A的
相对损伤等效系数A 945 2.268×10−4 1 B 360.5 5.437×10−5 0.240 C 115.5 5.072×10−6 0.022 D 115.5 4.172×10−7 1.840×10−3 E 325.5 1.038×10−7 4.577×10−4
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表 8 各工况下疲劳寿命累积损伤等效系数
Table 8. Cumulative damage equivalent coefficient of fatigue life under various working conditions
工况 单个载荷谱
循环次数100个循环下的
累积损伤等效系数350个循环下的
累积损伤等效系数A 4 0.0374 0.1769 B 2 0.0272 0.0767 C 0 D 0 E 2 1.341×10−3 3.042×10−3
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表 9 不同工况间相对疲劳损伤等效系数
Table 9. Equivalent coefficient of relative fatigue damage with different working conditions
工况 总循环
次数每次循环产生的
损伤等效系数各工况相对工况A的
相对损伤等效系数A 1400 1.264×10−4 1 B 700 1.096×10−4 0.867 C 0 0 D 0 0 E 700 4.346×10−6 0.0344
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表 10 实际燃气轮机运行时长统计
Table 10. Data of actual gas turbine operating time
工况 年度平均
运行时长/h工况 年度平均
运行时长/h高工况A 0.6 低工况H 16.6 高工况B 12.1 低工况I 15.5 中工况D 19.2 低工况J 10.3 中工况E 44.2 低工况K 12.3 低工况F 101.9 低工况L 48.5 低工况G 62.5
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表 11 试验载荷谱与实际运行对应工况损伤等效系数
Table 11. Equivalent damage coefficient of working conditions under test load spectrum and actual operation
参数 工况 实际运行 试验载荷谱
运行运行时长/h A 0.6 945 B 12.1 360.5 C 0 115.5 D 19.2 115.5 E 44.2 325.5 累积损伤
等效系数高工况 7.940×10−4 0.2345 中工况 2.902×10−5 8.198×10−5 平均损伤
等效系数高工况 6.252×10−5 1.650×10−4 中工况 1.986×10−7 1.859×10−7 全工况 1.081×10−5
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表 12 快速加载工况不同时刻损伤等效系数分析
Table 12. Analysis of equivalent damage coefficient at different times under fast loading condition
参数 数值 初始时刻 200个载荷谱循环 350个载荷谱循环 Mises等效应力/MPa 706.89 612.83 Mises等效蠕变应变/% 0.466 0.424 疲劳寿命/循环 3151 7514 累积损伤等效系数 3.174×10−4 0.0436 0.0636 平均损伤等效系数 3.174×10−4 2.178×10−4 1.816×10−4
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