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

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

周慧慧^{1, 2,},
李增光³,
李天匀^{1, 2, 4, ,},
朱翔^{1, 2, 4},
李清盛^{1, 2}

1.
华中科技大学船舶与海洋工程学院，湖北武汉 430074
2.
船舶与海洋水动力湖北省重点实验室，湖北武汉 430074
3.
中国舰船研究设计中心，上海 201108
4.
高新船舶与深海开发装备协同创新中心，上海 200240

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
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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

Uncertainty analysis of propulsion shafting vibration

ZHOU Huihui^{1, 2
,},
LI Zengguang³,
LI Tianyun^{1, 2, 4
, ,},
ZHU Xiang^{1, 2, 4},
LI Qingsheng^{1, 2}

1.
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, Wuhan 430074, China
3.
China Ship Development and Design Center, Shanghai 201108, China
4.
Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

船舶推进轴系振动的不确定性分析由周慧慧，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

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。
- 推进轴系 /
- 轴系振动 /
- 不确定性激励 /
- 动态响应边界 /
- 非概率凸模型 /
- 非随机振动分析
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.
- marine propulsion shafting system /
- shafting vibration /
- uncertain excitation /
- dynamic response bound /
- non-probabilistic convex model /
- non-random vibration analysis

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图 1 非概率凸模型过程

Figure 1. Non-probabilistic convex model process

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图 2 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

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图 3 平稳凸模型过程

Figure 3. Stationary convex model process

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图 4 $l$维多自由度系统

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

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图 5 二自由度系统示意图

Figure 5. Schematic diagram of a 2-DOFs system

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图 6 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

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图 7 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]

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图 8 船舶轴系弹性支撑梁模型

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

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图 9 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

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图 10 两个轴承处的横向位移响应

Figure 10. Lateral displacement response at the two bearings

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图 11 螺旋桨处的横向位移

Figure 11. Lateral displacement at the propeller

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图 12 两个轴承处的瞬态响应

Figure 12. Transient response at the two bearings

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图 13 螺旋桨处的瞬态响应曲线对比

Figure 13. Comparison of transient response at the propeller

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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

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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L_i
参数	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

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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/%
阶数	Matlab	ANSYS	误差/%
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

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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 $

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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
位置	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]

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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
位置	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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