Cumulative damage analysis of ice-induced structural fatigue for polar ships navigating in ice-covered regions
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摘要: 极地船舶在冰区航行中经常与各种类型的海冰发生不同程度的碰撞，充足的疲劳强度储备至关重要。本文提出了基于实测冰载荷的极地船舶结构冰激疲劳的累积损伤分析方法。以“雪龙”号极地考察船为研究对象，通过对我国第8次北极科学考察中的冰厚和航速等现场测量数据进行统计分析，在冰厚0.5～2.5 m、航速2～12 kn范围内构造冰激疲劳工况，并将二者的联合概率分布作为疲劳工况的发生概率；基于支持向量机方法反演识别出典型工况下的冰载荷时程，通过动力学分析确定关键位置及相应的热点应力，并采用雨流计数法统计应力循环次数；最后通过S-N曲线和Miner线性累积损伤理论进一步计算该航次内的疲劳损伤度，验证了“雪龙”号在冰区航行的安全性。本文对极地船舶结构的抗冰设计和安全评估具有一定的参考意义。Abstract: Polar ships always collide with various types of sea ice in varying degrees during their voyages in ice-covered regions, so sufficient fatigue strength reserves are essential. This paper proposes a cumulative damage analysis method for ice-induced fatigue on polar ship structures based on field measured ice loads. Firstly, according to the statistical analysis of the field data of ice thickness and sailing speed of RV Xue Long during the China’s 8th Arctic Scientific Expedition, ice-induced fatigue conditions are constructed within the ice thickness range of 0.5−2.5 m and the sailing speed range of 2−12 kn. The joint probability distribution of the two parameters is taken as the occurrence probability of fatigue conditions. Then, the time histories of ice loads under typical conditions are identified based on the support vector machine method. The key positions and corresponding hot spot stresses are determined by dynamic analysis. The rainflow counting algorithm is adopted to count the number of stress cycles. Finally, the fatigue damage during the voyage is further calculated by S-N curve and Miner linear cumulative damage theory, which verifies the ice navigation safety of RV Xue Long. This paper has certain reference significance for the ice-resistant design and safety evaluation of polar ship structures.
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图 2 我国第8次北极科学考察中的实测冰厚（a）及其概率密度（b）
Fig. 2 Measured ice thickness (a) and its probability density (b) during China’s 8th Arctic Scientific Expedition
图 3 我国第8次北极科学考察中的实测航速（a）及其概率密度（b）
Fig. 3 Measured sailing speed (a) and its probability density (b) during China’s 8th Arctic Scientific Expedition
图 4 冰激疲劳工况的具体划分及相应的出现概率
Fig. 4 Specific division of ice-induced fatigue conditions and corresponding occurrence probability
图 6 典型工况下的冰载荷反演识别结果
Fig. 6 Ice load identification results under typical working conditions
图 7 典型工况下的疲劳损伤分布及关键位置
Fig. 7 Fatigue damage distribution and key positions under typical working conditions
S-N曲线类型 lg K m C 12.540 3.0 D 12.182 3.0 
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表 2 冰厚子工况的划分及相应的出现概率
Tab. 2 Division of ice thickness sub-conditions and corresponding occurrence probability
冰厚范围/m 出现概率 冰厚范围/m 出现概率 0.5～0.7 3.72 ×10−2 1.5～1.7 2.00 × 10−1 0.7～0.9 2.13 × 10−2 1.7～1.9 1.44 × 10−1 0.9～1.1 7.71 × 10−2 1.9～2.1 9.31 × 10−2 1.1～1.3 1.54 × 10−1 2.1～2.3 3.46 × 10−2 1.3～1.5 2.21 × 10−1 2.3～2.5 1.86 × 10−2
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表 3 航速子工况的划分及相应的出现概率
Tab. 3 Division of sailing speed sub-conditions and corresponding occurrence probability
航速范围/kn 出现概率 航速范围/kn 出现概率 2～3 3.19 × 10−2 7～8 2.10 × 10−1 3～4 4.26 × 10−2 8～9 6.65 × 10−2 4～5 1.09 × 10−1 9～10 3.19 × 10−2 5～6 2.37 × 10−1 10～11 1.06 × 10−2 6～7 2.55 × 10−1 11～12 5.30 × 10−3
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表 4 艏部结构模型的材料属性
Tab. 4 Material properties of bow structure model
参数 数值 单位 密度 7 850 kg/m3 弹性模量 206 GPa 屈服强度 355 MPa 泊松比 0.3 —
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表 5 典型工况下关键位置的节点编号及热点应力
Tab. 5 Node numbers and hot spot stresses of key positions under typical working conditions
关键
位置节点
编号热点应力/MPa 工况一
（hi = 1.73 m, Vs= 6.9 kn ）工况二
（hi = 1.13 m, Vs= 3.3 kn）1 15983 225.20 64.60 2 26613 225.00 64.57 3 15984 223.70 64.19 4 15687 221.70 63.62 5 15979 221.70 63.60 6 28244 221.60 63.59 7 26611 221.10 63.43 8 26507 208.80 59.90
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表 6 主要典型工况下关键位置处的累积疲劳损伤度
Tab. 6 Cumulative fatigue damage at key positions under main typical working conditions
工况编号 冰厚/m 航速/kn 出现概率 累积作用时间/min 关键位置处的累积疲劳损伤度 15983 15687 26507 1 1.73 6.9 5.32 × 10−2 1226 1.99 × 10−3 1.84 × 10−3 1.36 × 10−3 2 1.13 3.3 2.66 × 10−3 61 5.20 × 10−8 4.73 × 10−8 3.27 × 10−8 3 1.73 3.7 1.06 × 10−2 244 1.18 × 10−5 1.07 × 10−5 7.24 × 10−6 4 1.71 4.1 2.39 × 10−2 551 4.10 × 10−5 3.70 × 10−5 2.48 × 10−5 5 1.64 6.3 3.46 × 10−2 797 8.86 × 10−4 8.20 × 10−4 6.06 × 10−4 6 1.59 5.6 5.32 × 10−2 1226 7.72 × 10−4 7.18 × 10−4 4.82 × 10−4 7 1.56 7.2 5.85 × 10−2 1348 1.37 × 10−3 1.27 × 10−3 9.60 × 10−4 8 1.52 4.5 2.13 × 10−2 491 3.76 × 10−5 3.40 × 10−5 2.28 × 10−5 9 1.48 3.1 1.60 × 10−2 369 1.05 × 10−5 9.54 × 10−6 6.47 × 10−6 10 1.45 6.2 6.12 × 10−2 1410 1.93 × 10−4 1.74 × 10−4 1.16 × 10−4 11 1.44 5.1 5.85 × 10−2 1348 5.63 × 10−5 5.10 × 10−5 3.45 × 10−5 12 1.32 7.1 3.99 × 10−2 919 3.80 × 10−5 3.44 × 10−5 2.33 × 10−5 13 1.29 5.2 2.66 × 10−2 613 8.35 × 10−6 7.58 × 10−6 5.17 × 10−6 14 1.28 7.5 4.79 × 10−2 1104 2.26 × 10−5 2.05 × 10−5 1.40 × 10−5 15 1.23 6.7 3.46 × 10−2 797 1.30 × 10−5 1.18 × 10−5 8.02 × 10−6 16 1.18 4.7 1.86 × 10−2 429 4.05 × 10−6 3.68 × 10−6 2.51 × 10−6 17 1.05 6.5 2.39 × 10−2 551 2.45 × 10−6 2.22 × 10−6 1.52 × 10−6 18 1.03 7.8 1.33 × 10−2 306 1.19 × 10−6 1.08 × 10−6 7.42 × 10−7
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