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摘要:
载荷谱的分散性是影响机群疲劳可靠性寿命的重要因素，阵风载荷是运输类飞机重要的损伤来源。为研究运输类飞机阵风载荷谱的损伤分散性，基于离散阵风模型，对调研得到的多个运输机型号的实测阵风速度超越数数据进行了统计分析；假定指定阵风速度下的超越数服从对数正态分布，建立了阵风速度超越数的分散性模型。采用Monte Carlo方法抽样得到单机阵风速度超越数曲线，得到单机随风载荷过载谱，计算得到单机阵风载荷谱损伤，对机群的阵风载荷谱损伤分散进行了研究，结合3个机型的使用剖面进行了算例分析。结果表明：运输类飞机的阵风载荷谱损伤服从对数正态分布，分散性取值与使用剖面密切相关。
Abstract:Load spectrum variation matters to fatigue reliability service life of a fleet. For transport aircraft, gust load is one of the critical damage sources. To study the damage variation of gust load spectra, two parts have been investigated. In the first process, gust velocity exceedance measured in service of several transport aircraft are statistically analyzed based on discrete-gust model. It is assumed that incremental exceedance of specific gust velocity follows lognormal distribution, and a model of gust velocity exceedance variation is built. In the second process, the damage variation of gust load spectra is studied. With the help of Monte Carlo simulation, gust velocity exceedance curves of aircraft in a fleet are acquired, after which damage of gust load spectra can be calculated. To examine the validity of the methodology, numerical examples are calculated, in which flight profiles of 3 specific transport aircraft are used. The results show that damage variation of gust load spectra of transport aircraft follows lognormal distribution and the values of scatter factor are relevant to flight profiles.
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Key words:
- gust load /
- load spectrum /
- load variation /
- damage /
- aircraft structure
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表 1 实测阵风速度超越数数据信息
Table 1. Information of measured gust velocity exceedance data
组织 型号 飞机起落次数 飞行时间/h 航程/n mile KSSU B747[21] 24 358 121 893 56 747 773 A320[22] 10 066 30 817 13 052 670 B737-400[23] 11 721 19 105 5 244 686 B767-200ER[24] 1 285 9 164 3 798 859 FAA B777-200ER[25] 10 047 67 000 30 502 553 BE1900D[26] 903 585 136 440 ERJ145XR[27] 47 273 88 305 34 747 170 MD82/83[28] 3 978 7 120 2 672 975 注：1n mile=1.852 km；B747的原始数据以增量超越数ΔN的形式给出。由于重心过载计数的门槛值为0.18g，导致小Ude值的ΔN计数并不准确，本文将该部分数据剔除。 
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表 2 A400M飞机基本参数
Table 2. Basic parameters of A400M aircraft
参数 翼展/m 长度/m 高度/m 机翼面积/m2 使用空重/kg 数值 41.4 42.0 14.5 221.5 66 500
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表 3 A400M飞机典型使用剖面
Table 3. Typical flight profile of A400M aircraft
任务段 高度/(103 ft) 质量/kg 指示空速/(n mile·h-1) Ma 距离/n mile 初期爬升 0.25 137 615 324.1 0.286 0.3 0.48 137 103 333.3 0.288 0.3 0.70 137 103 342.6 0.288 1.3 1.2 137 103 370.4 0.34 1.5 爬升 1.5 137 103 407.4 0.342 9.9 6.0 137 103 407.4 0.370 51.9 20.0 129 250 463 0.547 74.6 巡航 30.0 121 250 472.2 0.68 1 044 30.0 107 000 472.2 0.68 721.4 30.0 102 588 472.2 0.68 1 079.4 下降 20.0 102 588 463 0.54 72.4 6.0 102 588 407.4 0.3 11.7 接近 1.5 101 910 325.9 0.277 3.6 1.4 101 910 262.9 0.229 0.5 1.3 101 910 262.9 0.228 0.2 0.65 102 588 262.9 0.225 3.8
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表 4 简化的A400M飞机使用剖面
Table 4. Simplified flight profile of A400M aircraft
任务段 高度/(103 ft) 距离/n mile 质量/kg ve/(m·s-1) CLα 1 离场 0.87 3.4 137 171 97.9 4.70 2 爬升1 1.5 9.9 137 103 113.2 4.73 3 爬升2 6 51.9 137 103 113.2 4.76 4 爬升3 20 74.6 137 103 126.1 5.08 5 巡航 30 2 844.8 117 872 127.0 5.46 6 初期下降 20 72.4 102 588 128.1 5.07 7 后期下降 6 11.7 102 588 113.2 4.69 8 接近 1.089 8.1 102 211 80.8 4.66
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表 5 P3C飞机基本参数
Table 5. Basic parameters of P3C aircraft
参数 翼展/m 长度/m 高度/m 机翼面积/m2 使用空重/kg 数值 30.37 35.61 10.27 120.8 27 216
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表 6 P3C飞机任务段典型参数值
Table 6. Typical parameter values of mission segment of P3C aircraft
任务段 高度/(103 ft) 距离/n mile 质量/kg ve/(m·s-1) CLα 1 爬升1 8.9 134.8 61 917 108.0 4.77 2 巡航1 17.9 717.6 58 086 107.5 4.87 3 下降1 11.9 73.2 54 642 133.5 4.96 4 搜索 6 575.8 51 804 128.6 4.83 5 下降2 3.5 34.7 49 088 133.8 4.83 6 攻击 1 270.8 47 875 154.3 4.90 7 爬升2 16.3 192.1 45 911 106.6 4.84 8 巡航2 31.7 1 071.6 41 691 118.7 5.41 9 下降3 15.8 37.4 38 223 132.0 5.03
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表 7 B767-200飞机基本参数
Table 7. Basic parameters of B767-200 aircraft
参数 翼展/m 长度/m 高度/m 机翼面积/m2 使用空重/kg 数值 47.6 48.5 15.8 283.3 80 423
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表 8 B767-200飞机任务段典型参数值
Table 8. Typical parameter values of mission segment of B767-200 aircraft
任务段 高度/(103 ft) 距离/n mile 质量/kg ve/(m·s-1) CLα 1 离场 0.87 2.7 111 132 95.2 4.68 2 初期爬升 1.5 7.8 110 678 128.6 4.80 3 爬升 6 66.0 109 318 151.2 5.20 4 巡航 20 249.0 107 503 152.3 5.98 5 初期下降 30 60.0 106 142 182.1 5.57 6 下降 20 7.1 106 142 128.6 4.80 7 接近 6 4.9 106 142 83.3 4.66
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表 9 使用剖面的载荷谱损伤分布特性检验
Table 9. Distribution characteristic test of load spectra damage of flight profile
型号 r 对数正态分布 威布尔分布 指数分布 A400M 0.974 0.904 0.914 P3C 0.986 0.919 0.989 B767-200 0.997 0.951 0.963
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表 10 使用剖面的载荷谱损伤分布参数
Table 10. Distribution parameters of load spectra damage of flight profile
型号 μlg D σlg D Dave A400M 5.004 0.175 1.00×105 P3C 6.34 0.287 2.19×106 B767-200 5.989 0.161 9.75×105
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表 11 A400M飞机任务段损伤分布特性检验
Table 11. Distribution characteristic test of load spectra damage of mission segments of A400M aircraft
任务段 高度/(103 ft) r 对数正态分布 威布尔分布 指数分布 离场 0.87 0.999 0.957 0.91 爬升1 1.5 0.997 0.95 0.884 爬升2 6 0.998 0.968 0.99 爬升3 20 0.999 0.956 0.918 巡航 30 0.999 0.955 0.992 初期下降 20 0.999 0.958 0.959 后期下降 6 1.000 0.967 0.993 接近 1.089 0.998 0.955 0.733
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表 12 P3C飞机任务段损伤分布特性检验
Table 12. Distribution characteristic test of load spectra damage of mission segments of P3C aircraft
任务段 高度/(103 ft) r 对数正态分布 威布尔分布 指数分布 爬升1 8.9 1.000 0.966 0.989 巡航1 17.9 1.000 0.967 0.989 下降1 11.9 1.000 0.968 0.993 搜索 6 1.000 0.968 0.983 下降2 3.5 1.000 0.966 0.922 攻击 1 0.997 0.952 0.866 爬升2 16.3 1.000 0.967 0.985 巡航2 31.6 0.999 0.957 0.993 下降3 15.8 1.000 0.968 0.989
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表 13 B767-200飞机任务段损伤分布特性检验
Table 13. Distribution characteristic test of load spectra damage of mission segments of B767-200 aircraft
任务段 高度/(103ft) r 对数正态分布 威布尔分布 指数分布 离场 0.87 0.997 0.953 0.843 初期爬升 1.5 1.000 0.965 0.951 爬升 6 1.000 0.967 0.992 巡航 20 0.999 0.958 0.993 初期下降 30 1.000 0.965 0.951 下降 20 1.000 0.966 0.977 接近 6 0.997 0.95 0.71
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表 14 A400M飞机任务段的载荷谱损伤分布参数
Table 14. Distribution parameters of damage of load spectra of mission segments of A400M aircraft
任务段 高度/(103ft) μlg D σlg D dseg.ave 离场 0.87 0.364 3.892 7.80×103 爬升1 1.5 0.366 4.505 3.20×104 爬升2 6 0.28 3.635 4.32×103 爬升3 20 0.19 4.313 2.05×104 巡航 30 0.19 4.313 2.05×104 初期下降 20 0.285 3.403 2.53×103 后期下降 6 0.286 3.012 1.03×103 接近 1.089 0.369 3.815 6.53×103
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表 15 P3C飞机任务段的载荷谱损伤分布参数
Table 15. Distribution parameters of damage of load spectra of mission segments of P3C aircraft
任务段 高度/(103 ft) μlg D σlg D dseg.ave 爬升1 8.9 0.282 4.44 2.75×104 巡航1 17.9 0.282 5.148 1.40×105 下降1 11.9 0.285 4.324 2.11×104 搜索 6 0.285 5.092 1.24×105 下降2 3.5 0.364 4.529 3.38×104 攻击 1 0.373 6.201 1.59×106 爬升2 16.3 0.288 4.368 2.33×104 巡航2 31.7 0.189 3.751 5.64×103 下降3 15.8 0.286 3.754 5.67×103
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表 16 B767-200飞机任务段的载荷谱损伤分布参数
Table 16. Distribution parameters of damage of load spectra of mission segments of B767-200 aircraft
任务段 高度/(103 ft) μlg D σlg D dseg.ave 离场 0.87 0.369 4.644 4.40×104 初期爬升 1.5 0.364 4.774 5.94×104 爬升 6 0.287 5.338 2.18×105 巡航 30 0.193 4.564 3.66×104 初期下降 15 0.29 5.541 3.48×105 下降 3 0.362 4.703 5.04×104 接近 1 0.371 4.726 5.32×104
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