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船舶推进轴系振动的不确定性分析

周慧慧 李增光 李天匀 朱翔 李清盛

周慧慧, 李增光, 李天匀, 等. 船舶推进轴系振动的不确定性分析[J]. 中国舰船研究, 2023, 18(2): 235–242, 250 doi: 10.19693/j.issn.1673-3185.02539
引用本文: 周慧慧, 李增光, 李天匀, 等. 船舶推进轴系振动的不确定性分析[J]. 中国舰船研究, 2023, 18(2): 235–242, 250 doi: 10.19693/j.issn.1673-3185.02539
ZHOU H H, LI Z G, LI T Y, et al. Uncertainty analysis of propulsion shafting vibration[J]. Chinese Journal of Ship Research, 2023, 18(2): 235–242, 250 doi: 10.19693/j.issn.1673-3185.02539
Citation: ZHOU H H, LI Z G, LI T Y, et al. Uncertainty analysis of propulsion shafting vibration[J]. Chinese Journal of Ship Research, 2023, 18(2): 235–242, 250 doi: 10.19693/j.issn.1673-3185.02539

船舶推进轴系振动的不确定性分析

doi: 10.19693/j.issn.1673-3185.02539
基金项目: 国家自然科学基金资助项目(51839005,51879113)
详细信息
    作者简介:

    周慧慧,女,1995年生,硕士生。研究方向:结构振动。E-mail:2445655193@qq.com

    李增光,男,1982年生,博士,高级工程师

    李天匀,1969年生,博士,教授。研究方向:结构振动与噪声控制。E-mail:ltyz801@hust.edu.cn

    通信作者:

    李天匀

  • 中图分类号: U664.21;U661.44

Uncertainty analysis of propulsion shafting vibration

知识共享许可协议
船舶推进轴系振动的不确定性分析周慧慧,等创作,采用知识共享署名4.0国际许可协议进行许可。
  • 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。
  • 图  非概率凸模型过程

    Figure  1.  Non-probabilistic convex model process

    图  非概率凸模型过程中自协方差函数的求取

    Figure  2.  Auto-covariance function obtained via convex model process

    图  平稳凸模型过程

    Figure  3.  Stationary convex model process

    图  $l$维多自由度系统

    Figure  4.  $l$-dimensional multi-DOFs system

    图  二自由度系统示意图

    Figure  5.  Schematic diagram of a 2-DOFs system

    图  本文计算的二自由度系统动态位移响应边界x1(t)和x2(t)的结果

    Figure  6.  Calculation results of dynamic displacement response bound x1(t) and x2(t) for a 2-DOFs system in this paper

    图  文献[19]计算的二自由度系统动态位移响应边界x1(t)和x2(t) 结果

    Figure  7.  Calculation results of dynamic displacement response bound x1(t) and x2(t) for a 2-DOFs system in Ref. [19]

    图  船舶轴系弹性支撑梁模型

    Figure  8.  Model of beam with elastic support for ship shafting

    图  螺旋桨横向激励作用下轴系非随机振动分析示意图

    Figure  9.  Non-random vibration analysis of shafting under lateral excitation of propeller

    图  10  两个轴承处的横向位移响应

    Figure  10.  Lateral displacement response at the two bearings

    图  11  螺旋桨处的横向位移

    Figure  11.  Lateral displacement at the propeller

    图  12  两个轴承处的瞬态响应

    Figure  12.  Transient response at the two bearings

    图  13  螺旋桨处的瞬态响应曲线对比

    Figure  13.  Comparison of transient response at the propeller

    图  14  4种工况对应的轴系所受激励示意图

    Figure  14.  Excitation of shafting corresponding to the four working conditions

    表  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
    1234
    轴段截面直径/ mm 110
    轴段长度 / m0.010.591.600.80
    轴段杨氏模量 /Pa2.1×1011
    轴段密度/ (kg·m−3)7 800
    下载: 导出CSV

    表  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/%
    MatlabANSYS
    122.62922.6250.02
    239.86839.8590.02
    369.42469.4320.01
    4168.520168.6640.08
    5286.707287.3130.21
    6446.862448.6420.40
    7665.472669.6300.62
    下载: 导出CSV

    表  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 $
    下载: 导出CSV

    表  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]
    下载: 导出CSV

    表  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]
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-09-24
  • 修回日期:  2021-12-01
  • 网络出版日期:  2023-04-06
  • 刊出日期:  2023-04-28

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