﻿ 基于几何相似性的载人潜水器无动力潜浮运动预报
 舰船科学技术  2024, Vol. 46 Issue (11): 6-9    DOI: 10.3404/j.issn.1672-7649.2024.11.002 PDF

1. 中国船舶科学研究中心，江苏 无锡 214082;
2. 深海技术科学太湖实验室，江苏 无锡 214082;
3. 深海载人装备国家重点实验室，江苏 无锡 214082

Prediction of unpowered descend and ascend motion of human occupied vehicle based on geometric similarity
HU Zhonghui1,2,3, QU Wenxin1,2,3, LIU Shuai1,2,3, YE Cong1,2,3
1. China Ship Scientific Research Center, Wuxi 214082, China;
2. Taihu Laboratory of Deepsea Technological Science,Wuxi 214082, China;
3. State Key Laboratory of Deep-sea Manned Vehicles, Wuxi 214082, China
Abstract: Unpowered descend and ascend can greatly save the energy of Human Occupied Vehicle(HOV), improve the underwater operation time of HOV, is one of the important bases of underwater operation ability of HOV. Based on the force relationship of HOV and geometric similarity theory, this paper obtains the relationship between speed and underwater gravity of HOV, and establishes the prediction model of unpowered descend and ascend motion. Taking “Jiaolong” HOV as an example, the prediction model established was used to forecast 7 000 m unpowered descend and ascend motion. Through comparative analysis, it can be seen that the prediction accuracy of the prediction model established in this paper is higher than the based on the standard motion model, which verifies the feasibility and effectiveness of the model established in this paper. It provides a reliable technical means to predict unpowered descend and ascend motion.
Key words: human occupied vehicle     geometric similarity     descend and ascend motion     unpowered
0 引　言

1 基于几何相似性的运动预报模型 1.1 受力分析

 图 1 受力分析 Fig. 1 Force analysis

 $G + B + {F_d} = Ma 。$ (1)

 $M = {M_0} + {M_c} + {M_{ad}} 。$ (2)

 $B = \rho \cdot g \cdot \left( {1 - k} \right) \cdot V 。$ (3)

1.2 预报模型

1）深海载人潜水器的无动力潜浮运动为弱机动，属于垂直面运动；

2）载人潜水器在无动力下潜/上浮运动过程中，其运动均可近似为平稳运动，即近似认为下潜/上浮平稳阶段载人潜水器的加速度为0；

3）计算过程中，只考虑载人潜水器平稳下潜阶段和平稳上浮阶段。

 $\left\{ \begin{gathered} {{G}_s} = -{{F}_d}，\\ {{G}_s} = G + B。\\ \end{gathered} \right.$ (4)

 ${F_d} \propto S{v^2}。$ (5)

 $S \propto {l^2} ，$ (6)
 $V \propto {l^3}。$ (7)

 $S \propto {V^{2/3}}。$ (8)

 $S \propto G_s^{2/3} 。$ (9)

 $v \propto {\left( {G + B} \right)^{1/6}}。$ (10)

 $\left\{ \begin{gathered} v = b \cdot {\left( {Mg + B} \right)^{1/6}} + c ，\\ M = {M_0} + {M_c} + {M_{ad}} ，\\ B = \rho \cdot g \cdot \left( {1 - k} \right) \cdot V 。\\ \end{gathered} \right.$ (11)

2 模型参数辨识方法

 $\left\{ \begin{gathered} x = {\left( {Mg + B} \right)^{1/6}}，\\ y = v。\\ \end{gathered} \right.$ (12)

 $y = b \cdot x + c。$ (13)

 $R = \sum\limits_{i = 1}^n {{{\left( {{y_i} - b \cdot {x_i} - c} \right)}^2}} 。$ (14)

 $\left\{ \begin{gathered} \sum\limits_{i = 1}^n {\left( {{y_i} - b \cdot {x_i} - c} \right){x_i}} = 0 ，\\ \sum\limits_{i = 1}^n {\left( {{y_i} - b \cdot {x_i} - c} \right)} = 0 。\\ \end{gathered} \right.$ (15)

 $\left\{ \begin{gathered} b = \frac{{n\displaystyle\sum {{x_i}{y_i}} - \displaystyle\sum {{x_i}} \displaystyle\sum {{y_i}} }}{{n\displaystyle\sum {x_i^2 - {{\left( {\displaystyle\sum {{x_i}} } \right)}^2}} }} ，\\ c = \frac{{\displaystyle\sum {x_i^2\displaystyle\sum {{y_i}} } - \displaystyle\sum {{x_i}{y_i}} \displaystyle\sum {{x_i}} }}{{n\displaystyle\sum {x_i^2 - {{\left( {\displaystyle\sum {{x_i}} } \right)}^2}} }}。\\ \end{gathered} \right.$ (16)
3 计算验证

3.1 参数辨识

 图 2 下潜过程中水中重力随深度变化曲线 Fig. 2 Gravity in water varies with depth during diving

 图 3 上浮过程中水中重力随深度变化曲线 Fig. 3 Gravity in water varies with depth during floating

 V = \left\{ {\begin{aligned} & {0.3171 \cdot {{\left( {Mg - B} \right)}^{1/6}} - 0.621,{\rm{下潜阶段}}}，\\ & {0.3842 \cdot {{\left( {Mg - B} \right)}^{1/6}} - 0.9442,{\rm{上浮阶段}}}。\end{aligned}} \right. (17)
3.2 潜浮运动预报

 图 4 下潜速度预报曲线 Fig. 4 Diving speed forecast curve

 图 5 上浮速度预报曲线 Fig. 5 Floating speed forecast curve

 图 6 下潜速度预报误差对比 Fig. 6 Comparison of error in prediction of diving speed

 图 7 上浮速度预报误差对比 Fig. 7 Comparison of error in prediction of floating speed

4 结　语

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