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Calculation and analysis of the scatter of load spectrum damage based on Fokker F27 airplanes
LI Tang, HE Xiaofan , LIU Wenting
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:To assess the reliability life of a fleet, the scatter of the load spectrum must be considered. In this paper, 56 individual load spectra are compiled based on the acceleration-exceedance curves corresponding to a fleet of Fokker F27. With the application of the SWT formula and linear accumulative damage rule, the flight damage and the ground-air-ground (GAG) damage, as well as the total damage per flight have been analyzed. Next, the probabilistic coordinate regression is conducted to examine the distribution parameters of the three types of the damage of load spectra respectively. The goodness fit shows that the flight damage follows the Weibull distribution whilst the GAG damage follows the lognormal distribution, and the total damage comprehensively including flight damage and GAG damage follows a lognormal distribution. In addition, the lognormal standard deviation of the total damage is 0.073 7.
Key words: load spectrum     damage     scatter     distribution     airplane structure

1) 载荷因子-超越数曲线族.

2) 数据筛选.

①筛选原则:飞机的使用方法基本相同,每次飞行时间基本相当,飞行次数和飞行时间比较接近[19].

②筛选结果

Fokker F27载荷因子数据记录于1961年至1976年间,采用英国Mechanism Ltd的“Fatigue meter”按“Peak between mean”方法进行计数,这种计数方法会造成峰、谷值累积超越数不相等.文献[18]给出的Fokker F27飞机的谷值累积超越数低于峰值累积超越数,为了编制飞机的载荷谱,需要将谷值对应的载荷超越数曲线外推至与峰值累积超越数相同.为此,参考文献[20]采用一般对数多项式方程拟合谷值-累积超越数曲线.

 图 1 Fokker F27飞机载荷因子-超越数曲线族Fig. 1 Load factor-exceedence curves of Fokker F27 airplanes
1.3 地-空-地循环

1) 分级离散.

2) 分配载荷.

3) 随机配对.

4) 关于地-空-地循环载荷的考虑.

 图 2 Fokker F27飞机载荷谱(局部)Fig. 2 Load spectrum of Fokker F27 (part)
2 损伤计算 2.1 损伤计算方法

S-N曲线参数m的值与材料、结构特性以及载荷情况相关.文献[8]给出了综合考虑飞机结构多个关键部位不同材料及细节形式可能的m值范围的m值优化方法.并且给出了对应一般飞机载荷历程下的m值在4左右的结论,在本文计算中取m=4.

SWT公式转换载荷循环应力比R=－1后,S-N曲线的参数C为定值.式(8)可以进一步整理得

1) 对载荷因子谱进行雨流计数[24],抽取全循环和半循环.

2) 按2.1中的方法对每个循环进行当量损伤计算.

3) 按线性累积损伤理论计算得到总的当量损伤. 2.3 损伤计算结果

 序号 飞行损伤 GAG损伤 总损伤 R′ 序号 飞行损伤 GAG损伤 总损伤 R′ 1 2.260 92 4.738 67 7.150 82 0.66 29 2.640 20 4.966 72 7.819 87 0.64 2 2.022 64 4.712 97 6.929 74 0.68 30 2.433 92 4.921 53 7.576 96 0.65 3 2.433 09 4.981 41 7.635 89 0.65 31 2.544 55 5.051 28 7.847 18 0.64 4 3.676 21 5.161 59 8.987 90 0.57 32 3.015 15 5.391 84 8.705 04 0.62 5 1.334 38 4.306 19 5.816 38 0.74 33 3.226 22 5.355 06 8.843 99 0.61 6 2.684 09 5.143 76 8.091 34 0.64 34 2.570 67 4.957 39 7.743 86 0.64 7 3.248 09 5.053 99 8.474 81 0.60 35 2.340 00 4.841 22 7.403 33 0.65 8 3.507 96 5.227 79 8.944 08 0.58 36 1.673 27 4.532 24 6.352 54 0.71 9 1.763 95 4.506 14 6.446 32 0.70 37 2.295 39 4.770 95 7.227 62 0.66 10 2.060 88 4.759 31 7.075 14 0.67 38 2.406 23 5.055 34 7.740 25 0.65 11 3.702 98 5.666 42 9.817 19 0.58 39 1.102 17 4.101 38 5.491 29 0.75 12 1.650 95 4.557 20 6.377 79 0.71 40 2.961 40 5.308 64 8.576 66 0.62 13 2.624 21 5.651 72 8.559 10 0.66 41 3.489 28 5.483 19 9.253 54 0.59 14 3.384 38 5.526 41 9.211 39 0.60 42 1.964 93 4.720 67 6.907 48 0.68 15 2.978 24 5.205 65 8.433 29 0.62 43 1.192 81 4.173 51 5.557 14 0.75 16 1.615 05 4.467 83 6.185 25 0.72 44 2.042 37 4.692 49 6.940 91 0.68 17 0.917 87 3.933 00 4.969 60 0.79 45 3.505 12 5.888 97 9.845 06 0.60 18 2.229 95 4.767 07 7.171 19 0.66 46 4.081 16 6.103 99 10.599 20 0.58 19 2.087 41 4.702 72 6.945 58 0.68 47 2.238 77 4.782 61 7.212 73 0.66 20 2.364 34 4.921 53 7.487 62 0.66 48 2.206 49 5.059 39 7.545 02 0.67 21 3.918 71 5.934 56 10.133 10 0.59 49 2.084 56 4.665 70 6.915 85 0.67 22 2.483 73 4.950 74 7.633 31 0.65 50 1.722 51 4.475 22 6.314 65 0.71 23 2.042 92 4.839 91 7.108 22 0.68 51 2.651 47 5.901 11 9.020 28 0.65 24 1.877 10 4.825 54 6.891 29 0.70 52 2.176 73 5.212 57 7.756 22 0.67 25 0.865 69 3.897 28 4.860 94 0.80 53 2.811 87 5.593 17 8.857 28 0.63 26 2.727 74 5.255 57 8.227 59 0.64 54 2.364 71 4.974 73 7.689 75 0.65 27 1.999 03 4.677 17 6.829 86 0.68 55 1.917 98 5.037 79 7.208 01 0.70 28 2.537 31 4.948 08 7.699 73 0.64 56 1.275 48 4.389 49 5.855 79 0.75

1) 对数正态分布:

2) 威布尔分布(双参数):

3) 指数分布:

1) 标准正态分布:

2) 威布尔分布(双参数):

3) 指数分布:

1) 飞行载荷损伤分布特性.

 分布 相关系数 对数正态 0.980 42 威布尔 0.990 76 指数 0.948 95

 图 3 飞行载荷损伤威布尔分布Fig. 3 Weibull distribution of flight load damage

2) 地-空-地载荷损伤分布.

 分布 相关系数 对数正态 0.991 82 威布尔 0.971 78 指数 0.947 98

 图 4 GAG损伤对数正态分布Fig. 4 Lognormal distribution of GAG load damage

3) 每次飞行载荷损伤分布.

 分布 相关系数 对数正态 0.992 31 威布尔 0.982 82 指数 0.944 54

 图 5 机群载荷谱损伤对数正态分布Fig. 5 Lognormal distribution of fleet load spectrum damage

3.3 对比分析

1) Fokker F27机群飞机每次飞行的飞行载荷当量损伤服从威布尔分布,Fokker F27机群飞机每次飞行的损伤与地-空-地循环的损伤服从对数正态分布.

2) Fokker F27机群每次飞行损伤的对数正态标准差为0.073 7.

3) Fokker F27飞机机群地-空-地循环损伤占总损伤的比例在57%~80%的范围.

#### 文章信息

LI Tang, HE Xiaofan, LIU Wenting

Calculation and analysis of the scatter of load spectrum damage based on Fokker F27 airplanes

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 551-558.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0195