Very⁃high cycle fatigue strength estimation method for aero⁃engine reliability design
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摘要:
提出了一种面向可靠性设计的四参数随机疲劳极限模型，可针对小样本数据实现超高周疲劳（VHCF）应力⁃寿命（
S⁃N ）曲线处理。通过对航空用钛合金常规样本数超高周疲劳数据的拟合分析和对比验证了模型的准确性。同时，以某型航空发动机压气机叶片用TC17钛合金为研究对象，分别对室温（RT）和400 ℃小样本超高周疲劳数据进行了处理，得到了典型置信度和可靠度条件下的超高周疲劳强度估计值。结果表明：本文提出的四参数随机疲劳极限模型，能够通过少量的长寿命区试验数据获得材料超高周范围内发动机设计所需的疲劳强度估计值；相较于常用的升降法，基于本模型进行试验安排可大幅降低68%的试验量，为发动机材料的超高周疲劳强度评价提供方法支持。-
关键词:
- 超高周疲劳（VHCF） /
- 随机疲劳极限（RFL）模型 /
- 概率⁃应力⁃寿命（P⁃S⁃N）曲线 /
- 疲劳数据处理 /
- 钛合金
Abstract:A four⁃parameter random fatigue limit model for reliability design was proposed，which can realize very⁃high cycle fatigue stress⁃life （
S ⁃N ） curve processing for small sample of data.The accuracy of the model was verified by fitting analysis and comparison of very⁃high cycle fatigue data of conventional samples of titanium alloys for aviation.At the same time，TC17 titanium alloy for a specific type of aero⁃engine compressor blade was taken as the research object，and the very⁃high cycle fatigue data of small samples were processed at room temperature （RT） and 400 ℃，respectively.The very⁃high cycle fatigue strength under typical confidence and survival probability was investigated by this mode.The results showed that the four⁃parameter random fatigue limit model proposed can obtain the value of the estimated fatigue strength required for engine design in very‑high cycle regime.With a small amount of long⁃life area data，the proposed model provides a reliable method for very⁃high cycle fatigue strength evaluation of engine materials by an economical cost. -
图 2 TA11钛合金超高周疲劳P⁃S⁃N曲线（常规样本数）
Figure 2. P⁃S⁃N curve of TA11 alloy in VHCF region （moderate samples number）
图 3 旋转弯曲疲劳试样形状和尺寸图（单位：mm）
Figure 3. Specimen shape and size for rotating bending fatigue（unit:mm）
图 5 TC17合金超高周疲劳强度概率分布对比
Figure 5. Comparison of probability distribution of very‑high cycle fatigue strength of TC17 alloy
表 1 TA11超高周疲劳RFL模型参数估计值（常规样本）
Table 1. Estimated values of RFL model parameters for TA11 alloy in VHCF rgime （moderate sample number）
样本数 a b S0 σ 26 14.84 -0.770 4 471.9 16.94 
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表 2 不同估计方法对超高周疲劳强度估计值对比
Table 2. Comparison of estimated VHCF strength by different methods
数据来源 超高周（108）疲劳强度估计值 γ=50%P=50% γ=95%P=50% γ=50%P=99.87% γ=95%P=97.72% γ=95%P=99.87% 四参数RFL 471 465 414 420 396 升降法 462 451 427 439 376 相对误差/% -2.08 -3.07 2.89 4.18 -5.20
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表 3 TC17合金室温超高周旋转弯曲疲劳试验数据
Table 3. Rotating bending fatigue test data of TC17 alloy at room temperature in very‑high cycle fatigue
应力/MPa 循环次数 700 3.75×104 4.46×104 1.27×105 675 1.33×105 1.54×105 650 4.67×105 1.83×107 625 1.29×106 600 5.81×106 6.95×106 4.75×107 575 4.51×107 >1.00×108 550 >1.00×108
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表 4 TC17合金400 ℃高温超高周旋转弯曲疲劳试验数据
Table 4. Rotating bending fatigue test data of TC17 alloy at 400 ℃ in very‑high cycle fatigue
应力/MPa 循环次数 600 5.38×105 1.34×107 575 6.19×106 3.85×107 550 2.78×107 7.37×105 540 7.27×106 2.00×107 520 2.62×107 >1.00×108 500 6.98×106 >1.00×108 480 >1.00×108
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表 5 TC17合金基于正态分布四参数RFL模型参数估计
Table 5. Parameter estimation of four⁃parameter RFL model based on normal distribution for TC17 alloy
试验温度 样本数n a b S0 σ 室温 14 56.80 -8.955 526.4 23.86 400 ℃ 13 187.9 -34.54 410.9 29.18
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表 6 TC17合金在给定置信度、可靠度下的超高周疲劳强度估计值（基于正态分布）
Table 6. Estimated value of very‑high cycle fatigue strength of TC17 alloy under specified confidence and reliability （based on normal distribution）
试验温度 超高周（108）疲劳强度估计值 γ=50%，P=50% γ=95%，P=50% γ=50%，P=99.87% γ=95%，P=97.72% γ=95%，P=99.87% 室温 593.7 581.4 510.9 510.3 470.9 400 ℃ 534.3 517.2 427.9 423.0 370.7
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表 7 本方法与常规超高周疲劳测试方法成本对比
Table 7. Cost comparison between the proposed method and the conventional very⁃high cycle fatigue testing method
采用方法 样本数 测试时间/h 常规的升降法 30~45 3 616 本方法 15 1 128
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