﻿ 一种水下机器人自主布放回收装置水动力分析
 舰船科学技术  2022, Vol. 44 Issue (16): 83-88    DOI: 10.3404/j.issn.1672-7649.2022.16.016 PDF

The hydrodynamic analysis and research of a launching device of an underwater robot
CHEN Yi-zong, SUN Mao-kai, WANG Sheng-hai, HAN Guang-dong, LIU Ke-xin, CHEN Hai-quan
College of Marine Engineering, Dalian Maritime University, Dalian 116026, China
Abstract: Based on three-dimensional potential flow theory and Ansys-AQWA software, the motion response characteristics of catamaran under different environmental loads are obtained. The kinematics model of catamaran and underwater vehicle is established, and the kinematics analysis is carried out by using Matlab /Simulink to calculate the rocking condition of the underwater vehicle. The results show that the catamaran can complete the deployment and recovery of the AUV smoothly and normally under the nearshore sea conditions, and the rocking degree of the AUV is acceptable, which can meet the requirements of engineering design.
Key words: catamaran unmanned ship     launching and recovery device     dynamics analysis     hydrodynamic analysis     AQWA
0 引　言

1 计算原理和方法 1.1 坐标系

 图 1 船体坐标系 Fig. 1 Hull coordinate system

1.2 速度势

 $q(x,y,z,t) = {Re} \{ u(x,y,z){e^{ - i\omega t}}\} ，$ (1)
 $F(x,y,z,t) = f(x,y,z){e^{ - i\omega t}} ，$ (2)

 ${\nabla ^2}\phi (x,y,z) = 0 ，$ (3)

 $\frac{{\partial \phi _j^R}}{{\partial n}} - \frac{{{\omega ^2}}}{g}\phi _j^R = 0 ，$ (4)

 ${\left. {\frac{{\partial \phi _j^R}}{{\partial n}}} \right|_S} = {n_j}，$ (5)

 ${\left. {\frac{{\partial \phi _j^R}}{{\partial n}}} \right|_{Z = - H}} = 0，$ (6)

 $\mathop {\lim }\limits_{x \to \infty } \sqrt R \left( {\frac{{\partial \varPhi }}{{\partial R}} - ik\varPhi } \right) = 0 。$ (7)

 $\varPhi (x,y,z,t) = {\varPhi ^I}(x,y,z,t) + {\varPhi ^D}(x,y,z,t) + {\varPhi ^R}(x,y,z,t) ，$ (8)

 ${\Phi ^I} = - \frac{{Ag}}{\omega }\frac{{\cosh k(z + h)}}{{\cosh kh}}\exp [ik(x\cos \beta + y\sin \beta )]，$ (9)

1.3 动力学建模

 图 2 简化模型图 Fig. 2 Simplified model diagram

 \begin{aligned} & {x_p} = {x_2} + l\cos \alpha \sin \beta ，\\ & {y_p} = {y_2} + l\sin \alpha ，\\ & {z_p} = {z_2} - l\cos \alpha \cos \beta ，\end{aligned} (10)

 \begin{aligned} & {{\dot x}_p} = {{\dot x}_2} + l\cos \alpha \cos \beta \dot \beta - l\sin \alpha \sin \beta \dot \alpha ，\\ & {{\dot y}_p} = {{\dot y}_2} + l\cos \alpha \dot \alpha ，\\ & {{\dot z}_p} = {{\dot z}_2} + l\cos \beta \sin \alpha \dot \alpha + l\cos \alpha \sin \beta \dot \beta ，\end{aligned} (11)

 \begin{aligned} & T = \frac{1}{2}{m_p}({{\dot x}_p}^2 + {{\dot y}_p}^2 + {{\dot z}_p}^2) ，\\ & V = {m_p}g{z_p}，\end{aligned} (12)

 $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_j}}}} \right) - \frac{{\partial T}}{{\partial {{\dot q}_j}}} + \frac{{\partial V}}{{\partial {q_j}}} = 0，$ (13)

 $\begin{split} &\;\ddot \alpha = \frac{{ - \cos \beta (g + {{\ddot z}_2})\sin \alpha - \cos \alpha ({{\ddot y}_2} + l{{\dot \beta }^2}\sin \alpha ) + {{\ddot x}_2}\sin \alpha \sin \beta }}{l} ，\\ &\;\ddot \beta = - \frac{{\cos \beta {{\ddot x}_2} - 2l\dot \alpha \dot \beta \sin \alpha + (g + {{\ddot z}_2})\sin \beta }}{{l\cos \alpha }} 。\\[-15pt] \end{split}$ (14)

2 水动力分析 2.1 双体船介绍及建模

 图 3 双体船模型 Fig. 3 Catamaran model

 图 4 网格划分 Fig. 4 Mesh division

2.2 频域运动响应

 $R(\omega ,\beta ,t) = A{Re} [\left| {\left. {H(\omega ,\beta )} \right|{e^{i(\omega t + \varphi )}}} \right.]，$ (15)

 图 5 各自由度下的运动响应 Fig. 5 Motion response under each degree of freedom

2.3 时域分析

 $S(\omega ) = \alpha {g^2}{\omega ^{ - 5}}\exp \left[ { - \frac{5}{4}{{\left( {\frac{\omega }{{{\omega _p}}}} \right)}^{ - 4}}} \right]{\gamma ^{\exp \left[ { - 0.5{{\left( {\frac{{\omega - {\omega _p}}}{{\sigma {\omega _p}}}} \right)}^2}} \right]}} 。$ (16)

 图 6 不同浪向角和波高下的响应曲线 Fig. 6 Response curves under different wave direction angles and wave heights

1）双体船的运动响应与弹簧振子的简谐运动类似，曲线整体呈现规律性。双体船在不同方向下的3个运动的响应幅值随着波浪高度的增加而逐渐变大。

2）在不同海况条件下，根据作用在双体船的浪向角不同，最大的运动响应分别是横摇和纵摇。当浪向角为90°时，双体船的横摇运动响应最大，其横摇的运动响应最大可以达9.821°；当浪向角为180°时，双体船的纵摇运动响应最大，最大可达13.429°。

3 布放回收装置动力学分析

 图 7 不同浪向角下面外角、面内角、横向位移变化曲线 Fig. 7 Variation curves of external angle, in-plane angle and transverse displacement under different wave direction angles

 图 8 不同收绳速度以及不同绳长横向位移曲线 Fig. 8 Transverse displacement curves of different retracting speeds and rope lengths

4 结　语

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