Uncertainty analysis of propulsion shafting vibration
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摘要:
目的 针对传统的船舶推进轴系确定性振动分析存在安全性与可靠性不足的问题,开展轴系在不确定性激励下的振动响应分析。 方法 采用基于非概率凸模型过程的非随机振动分析方法,以区间上下界的形式描述不确定性激励和振动响应,降低对大量激励样本数据的依赖。与相关文献的计算结果对比,验证所编求解二自由度系统响应边界程序的正确性,并基于在此,探究轴系的不确定振动问题。 结果 当轴系受到螺旋桨[−30 N,30 N]的横向激励力激励时,在轴承处产生了量级约为10−6 m的位移响应,表明轴系受到某一区间的激励,则必会产生某一区间的响应。 结论 将基于非概率凸模型过程的非随机振动分析方法应用于船舶推进轴系不确定性振动分析领域,可求得轴系受到不确定性激励时的振动位移响应边界,并可在激励样本较少的情况下为提高轴系系统动态响应预测的稳健性提供有益参考。 Abstract:Objective In view of the insufficient safety and reliability of the traditional deterministic vibration analysis of ship propulsion shafting system, the vibration response analysis of the shafting system under uncertain excitation conditions is carried out. Methods Using non-random vibration analysis based on non-probabilistic convex model process, the uncertain excitation and vibration response are described in the form of the upper and lower bounds of the interval to reduce dependence on a large amount of excitation sample data. Compared with the calculation results in the relevant literature, the validity of the program for solving the response bound of the two-degrees-of-freedom (2-DOFs) system is verified, and the uncertain vibration problem of the shafting system is then explored on this basis. Results The results show that when the shafting system is excited by [−30 N, 30 N] propeller laterally, a displacement response of the magnitude of about 10−6 m is generated at the bearing. It is also indicate that the shafting system is excited in a certain interval, so a certain interval response must be produced. Conclusions Applying the non-probabilistic convex model process and non-random vibration analysis to the field of the uncertain vibration analysis of ship propulsion shafting system, the vibration displacement response bound of the shafting under uncertain excitation conditions can be obtained with fewer excitation samples, thereby providing useful references for improving the robustness of the dynamic response prediction of ship propulsion shafting systems. -
表 1 船舶推进轴系模型尺寸及材料参数
Table 1. Model sizes of ship propulsion shafting system and material parameters
参数 轴段Li 1 2 3 4 轴段截面直径/ mm 110 轴段长度 / m 0.01 0.59 1.60 0.80 轴段杨氏模量 /Pa 2.1×1011 轴段密度/ (kg·m−3) 7 800 表 2 不同方法计算的船舶轴系横向固有频率对比
Table 2. Comparison of lateral natural frequency of ship shafting obtained by different methods
阶数 不同方法计算的横向固有频率/Hz 误差/% Matlab ANSYS 1 22.629 22.625 0.02 2 39.868 39.859 0.02 3 69.424 69.432 0.01 4 168.520 168.664 0.08 5 286.707 287.313 0.21 6 446.862 448.642 0.40 7 665.472 669.630 0.62 表 3 船舶推进轴系所受激励的4种工况
Table 3. Four working conditions of ship propulsion shafting system under different excitations
工况 激励力区间/N 自相关系数函数 工况1 ${ {\boldsymbol{F} }_{} }^{\rm{I} }(t) = [ - {\text{30} },{\text{30} }]$ $\rho {\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 1 $ 工况2 ${\boldsymbol{F} }_1^{\rm{I} }(t) = [ - {\text{30} },{\text{30} }]$${\boldsymbol{F} }_2^{\rm{I} }(t) = [ - 15,15]$ ${\rho _1}{\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 1 $${\rho _2}{\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 3 $ 工况3 ${{\boldsymbol{F}}^{\rm{I} } }(t) = [ - {\text{30} },{\text{30} }]$ $\rho {\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 1 $ 工况4 ${\boldsymbol{F} }_1^{\rm{I} }(t) = [ - {\text{30} },{\text{30} }]$${\boldsymbol{F} }_2^{\rm{I} }(t) = [ - 30,30]$ ${\rho _1}{\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 1 $${\rho _2}{\text{ = } }{{\rm{e}}^{ - \lambda \left| \tau \right|} }$,$ \lambda = 1 $ 表 4 横向位移响应对比
Table 4. Comparison of lateral displacement response
位置 横向位移响应/m 工况1 工况2 轴承1 [−0.868×10−6,0.868×10−6] [−0.885×10−6,0.885×10−6] 轴承2 [−1.203×10−6,1.203×10−6] [−2.900×10−6,2.900×10−6] 螺旋桨 [−6.528×10−6,6.528×10−6] [−6.538×10−6,6.538×10−6] 表 5 纵向位移响应对比
Table 5. Comparison of longitudinal displacement response
位置 纵向位移响应/m 工况3 工况4 轴承1 [−3.083×10−6,3.083×10−6] [−4.343×10−6,4.343×10−6] 轴承2 [−3.059×10−6,3.059×10−6] [−4.326×10−6,4.326×10−6] 螺旋桨 [−3.092×10−6,3.092×10−6] [−4.350×10−6,4.350×10−6] -
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