﻿ 基于聚四氟乙烯的水下航行器壳体优化设计
 舰船科学技术  2017, Vol. 39 Issue (12): 40-43 PDF

Underwater vehicle shell optimal design based on PTFE
LAI Hui, DU Xiang-dang, FAN Ying-hao, WANG Fang-chao
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
Abstract: According to the buoyancy redundancy requirements of a special ROV, the optimal design model of the shell is established by taking the maximum internal volume of ROV as the objective function and the relevant design parameters as the design variables. The global search solver globalsearch and the local optimization solver fmincon are used to solve the problem. The optimized internal volume of the shell is improved by 9.46%, and the corresponding mass is reduced by 42.38%, which meets the design requirements.
Key words: ROV     shell     optimal design     strength     stability     PTFE
0 引　言

1 水下航行器强度和稳定性模型

ROV运动环境在直径36 m的盛满烷基苯溶液的球形罐体内，要求ROV外形限制在直径300 mm、高度500 mm的空间内，壳体使用非金属材料——聚四氟乙烯。ROV壳体受到的静态载荷主要有：液体的外压；壳体内部安装的推进装置、电池、电路板、配重等载荷的不均匀分布，在各载荷面处浮力和重力的差值产生的剪切与弯矩；在空气环境中吊装或者悬挂时受到的剪切与弯矩。以上各种载荷中，最大载荷是最大深度时所受液体的外压，因此本文中选取最深处环境液体压力 ${P_j} = 0.36\;{\rm{MPa}}$ 为载荷进行计算。

1.1 壳体强度计算模型

1）跨度终点处壳板的横向平均应力：

 $\sigma _2^0 = K_2^0{p_j}R/t \text{。}$ (1)

2）肋骨处板壳的纵向相当应力：

 ${\sigma _{leg}}\left| {_{x = l/2} = (0.91{K_1} - 0.3{K_r}){P_j}R/t} \right. \text{。}$ (2)

3）肋骨上的应力：

 ${\sigma _r} = {K_r}{P_j}R/t \text{。}$ (3)

1.2 壳体稳定性计算模型

1）肋间壳板稳定性

 $\begin{split}p_{cr}^{\prime} & = \displaystyle\frac{E}{{{n_2} + 0.5{\alpha ^2} - 1}}\left[ {\displaystyle\frac{{{t^3}}}{{12(1 - {\mu ^2}){R^3}}}{{({n^2} + {\alpha ^2} - 1)}^2}} +\right.\\ & \left. { \displaystyle\frac{t}{R}\frac{{{\alpha ^4}}}{{{{({n^2} + {\alpha ^2})}^2}}}} \right] \text{。}\end{split}$ (4)

2）总体稳定性

 ${(p_{cr}')_g} = \frac{E}{{1 + \displaystyle\frac{{\alpha _1^2}}{{2({n^2} - 1)}}}}\left[\frac{t}{R}\frac{{\alpha _1^4}}{{{{({n^2} + \alpha _1^2)}^2}({n^2} - 1)}} + \frac{{I({n^2} - 1)}}{{{R^3}l}}\right] \text{。}$ (5)

 ${P_{cr}} = {\eta _1}{\eta _2}{P'_{cr}} \text{，}$ (6)
 ${({P_{cr}})_g} = {\eta _1}{\eta _2}{({P'_{cr}})_g} \text{。}$ (7)

2 参数优化设计 2.1 优化数学模型的建立

1）设计变量

 图 1 壳体中部矩形肋骨结构图 Fig. 1 Rectangular rib structure chart in the middle of the shell

2）目标函数

 $V = \pi {(R - t)^2} \cdot h - \pi [{(R - t)^2} - {(R - t - b)^2}] \cdot a \cdot (\left\lceil {\frac{h}{l}} \right\rceil + 1) \text{。}$ (8)

3）约束条件

 $\sigma _2^0 \leqslant 0.85{\sigma _s} \text{，}$ (9)

 ${\sigma _{leg}}\left| {_{x = l/2}} \right. \leqslant {\sigma _s} \text{，}$ (10)

 ${\sigma _r} \leqslant 0.55{\sigma _s} \text{，}$ (11)

 ${P_j} \leqslant {P_{cr}} \text{，}$ (12)

 $\left( {1.1 \sim 1.3} \right){P_j} \leqslant {(P_{cr}^{})_g} \text{，}$ (13)

 ${N_{noli}} \leqslant 0 \text{，}$

 $\begin{array}{l}{R_1} \leqslant R \leqslant {R_2} \text{，}\\{l_1} \leqslant l \leqslant {l_2} \text{，}\\{t_1} \leqslant t \leqslant {t_2} \text{，}\\{a_1} \leqslant a \leqslant {a_2} \text{，}\\{b_1} \leqslant b \leqslant {b_2} \text{，}\end{array}$ (14)

 $\text{约束条件}\left\{ \begin{array}{l}\text{非线性约束}:{N_{noli}} \leqslant 0 \text{，}\\\text{优化变量约束}:\left\{ \begin{array}{l}100 \leqslant R \leqslant 150 \text{，}\\100 \leqslant l \leqslant 300 \text{，}\\3 \leqslant t \leqslant 15 \text{，}\\3 \leqslant a \leqslant 50 \text{，}\\3 \leqslant b \leqslant 20 \text{。}\end{array} \right.\end{array} \right.$ (15)

ROV实际的外形相关尺寸作为优化初始值： ${R_0} = 150$ $l_0^{} = 156.67$ ${t_0} = 10$ ${a_0} = 30$ ${b_0} = 12$

2.2 优化求解

 $\frac{{0.032\;4 - 0.029\;6}}{{0.029\;6}} \times 100\% = 9.46\% \text{，}$ (16)

 $10.202\;7 - 5.878\;8 = 4.323\;9\; {\rm kg} \text{，}$ (17)
 $\frac{{4.323\;9}}{{10.202\;7}} \times 100\% = 42.38\% \text{。}$ (18)

3 有限元分析

 图 2 壳体的Mises应力图 Fig. 2 Mises stress chart of the shell

 图 3 壳体稳定性分析图 Fig. 3 Stability analysis chart of shell
4 结　语

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