﻿ 开孔球形耐压壳力学特性及疲劳分析
 舰船科学技术  2017, Vol. 39 Issue (3): 7-11 PDF

1. 江苏科技大学 机械工程学院，江苏 镇江 212003;
2. 中国船舶科学研究中心，江苏 无锡 214082

Mechanical properties and fatigue analysis of spherical pressure shell with openings
ZHU Yong-mei1, MA Qing-li1, DAI Yong-jian1, ZHANG Jian1,2
1. School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. Chinese Ship Scientific Research Center, Wuxi 214082, China
Abstract: In this paper, the mechanical properties and fatigue life of spherical pressure shell under 7000m depth are studied. Firstly, the strength and stability of the spherical pressure shell are analyzed . Secondly, based on the full spherical pressure shell, the openings is designed and strengthened according to the specification of the submersible design.Finally, the strength and stability and the fatigue life of the spherical shell with openings with renforment are analyzed. Calculation results show that the pressure spherical shell with opening with coaming reinforement compared with the spherical shell with no opening, the strength decreases by 9.4%, the stability decreases by 19% and the service life was reduced by 32.4%. The research results can provide reference for the design of deep sea spherical pressure shell with openings.
Key words: pressure spherical shell     opening     strength     stability     fatigue life
0 引　言

1 完整球形耐压壳的强度和平稳性分析 1.1 理论分析

 $\mathop \sigma \nolimits_{in} = \frac{{3p\mathop {(2 + \frac{t}{R})}\nolimits^3 }}{{2[\mathop {(2 + \frac{t}{R})}\nolimits^3 - \mathop {(2 - \frac{t}{R})}\nolimits^3 ]}}{\text{，}}$ (1)
 $\sigma = \frac{P}{{2\frac{t}{R}}}{\text{，}}$ (2)

 $\mathop \Delta \nolimits_\sigma = \frac{{\left| {\mathop \sigma \nolimits_{in} - \left. \sigma \right|} \right.}}{{\mathop \sigma \nolimits_{in} }} \times 100\% {\text{。}}$ (3)

 $\mathop P\nolimits_{cr1} = \frac{{2Et}}{{R(1 - \mathop \mu \nolimits^{\rm{2}} )}}\left( {\sqrt {\frac{{({\rm{1 - }}\mathop \mu \nolimits^{\rm{2}} )}}{{\rm{3}}}} \frac{t}{R} - \frac{{\mu \mathop t\nolimits^2 }}{{2\mathop R\nolimits^2 }}} \right){\text{，}}$ (4)

Zolly 公式[6]是船级社球形耐压壳稳定性设计规范的共性理论基础，此公式基于薄壳理论。则薄壳稳定性问题的解析解为：

 $\mathop P\nolimits_{cr2} = \frac{{2E\mathop t\nolimits^2 }}{{\mathop R\nolimits^2 }}\sqrt {\frac{1}{{3(1 - \mathop \mu \nolimits^2 )}}} {\text{，}}$ (5)

 $\Delta = \frac{{\left| {{P_{cr1}} - \mathop P\nolimits_{cr2} } \right|}}{{\mathop P\nolimits_{cr1} }} \times 100\% {\text{。}}$ (6)

 图 1 薄壳、中厚壳力学模型计算结果 Fig. 1 The calculation results of mechanical model of thin thick shell and Medium thick shell
1.2 数值模型

 $\mathop p\nolimits_s = k\mathop \rho \nolimits_\omega gh/0.9{\text{，}}$ (7)

 $t = \frac{{\mathop { P}\nolimits_s \times R}}{{2\mathop \sigma \nolimits_\phi }}{\text{。}}$ (8)

1.3 完整球形耐压壳有限元分析

 图 2 完整球壳静力学分析结果 Fig. 2 Results of static analysis of complete spherical shell

 图 3 完整球壳屈曲分析结果 Fig. 3 Results of buckling analysis of complete spherical shells

2 开孔耐压球壳的初步设计

 图 4 开孔球壳围壁加强示意图 Fig. 4 Schematic diagram of the enclosure wall of the opening spherical shell
3 开孔耐压球壳的强度和平稳性分析及实验验证 3.1 开孔加强球形耐压壳有限元分析

 图 5 开孔加强球壳静力学分析结果 Fig. 5 The static analysis results of strengthened spherical shell with opening

 图 6 开孔加强球壳屈曲分析结果 Fig. 6 The results of buckling analysis of strengthened spherical shell with opening

3.2 实验验证结果

 图 7 试验模型 Fig. 7 Test model

 图 8 试验结果 Fig. 8 Test result
4 疲劳分析计算结果

 $\frac{{{\text{应力循环次数}}}}{{{\text{最大疲劳损伤值}}}} = \frac{{\rm{1}}}{{{\rm{3}}{\rm{.926}} \times \mathop {{\rm{10}}}\nolimits^{{\rm{ - 4}}} }} = {\rm {2 \ 547} \text{次}}{\text{。}}$

 $\frac{{{\text{应力循环次数}}}}{{{\text{最大疲劳损伤值}}}} = \frac{{\rm{1}}}{{{\rm{5}}{\rm{.810}} \times \mathop {{\rm{10}}}\nolimits^{{\rm{ - 4}}} }} = {\rm {1 \ 722} \text{次}}{\text{。}}$

5 结　语

1）在 7 km 水深中，完整球形耐压壳的最大应力为 717.1 MPa，开孔加强后的球形耐压球壳的最大应力为 792 MPa。此结果说明开孔加强后的耐压球壳与完整球壳的强度相比仅下降了 9.4%，表明围壁加强的方式是有效的。

2）根据屈曲模态分析的结果，完整球形耐压壳的一阶屈曲模态值为 7.57，开孔加强后的球形耐压壳的一阶屈曲模态值为 6.12。即完整球形壳和开孔加强球壳都在近 600 MPa 载荷下，球壳才会出现失稳状态。上述表明在 7 km 水深中，材料强度是影响完整球形耐压壳与开孔加强后的耐压壳的寿命的主要因素，且开孔加强后的耐压球壳稳定性与完整球壳相比下降了 19%。

3）以强度为基准，分别对完整球形耐压壳和开孔加强后的球形耐压壳进行疲劳分析，得出使用寿命分别为 2 547 次和 1 722 次。说明对开孔的球形耐压壳进行围壁加强后，使用寿命与完整球形耐压壳相比下降了 32.4%。表明开孔加强设计对球形耐压壳的疲劳寿命影响较大。研究成果可为深海球形耐压壳开孔开窗设计提供参考。

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