﻿ 仿驼背鲸改进减摇鳍的升力系数数值计算及分析
 舰船科学技术  2023, Vol. 45 Issue (10): 27-30    DOI: 10.3404/j.issn.1672-7649.2023.10.006 PDF

1. 广西大学，广西 南宁 530004;
2. 广西质量工程职业技术学院，广西 南宁 530009;
3. 北部湾大学，广西 钦州 535011

Numerical calculation and analysis of lift coefficient of humpback whale like fin stabilizer
LIN Hong1,2, LIU Jun-yong3
1. Guangxi University, Nanning 530004, China;
2. Guangxi Vocational and Technical College of Quality and Engineering, Nanning 530009, China;
3. Beibu Gulf University, Qinzhou 535011, China
Abstract: Due to the complex ocean environment and variable climate, ships may experience certain impacts on their navigation due to the influence of ocean currents during navigation, resulting in multi degree of freedom movement. As the most influential mode of motion, roll motion poses great risks to the safe travel of ships. Therefore, with the development of bionics, the appearance of humpback whale like fin stabilizers can help reduce the motion amplitude of ships in the process of rolling. Therefore, in order to better apply the humpback whale like fin stabilizer to play its role in resisting the ocean responsible environment, this paper will start with the numerical calculation of lift coefficient, carry out in-depth analysis on it, and improve its fin angle lift coefficient variation, bringing more abundant theoretical basis for ships' ocean navigation.
Key words: improving fin stabilizers by imitating humpback whales     lift coefficient     numerical calculation
0 引　言

1 仿驼背鲸改进减摇鳍控制系统 1.1 仿驼背鲸改进减摇鳍工作原理

 ${K_C} = \frac{1}{2}\rho {V^2}{A_f}C_L^\alpha \left( {{\alpha _m} + \frac{{\dot \phi {l_f}}}{V}} \right){l_f}。$

1.2 仿驼背鲸改进减摇鳍控制系统基本组成

 图 1 仿驼背鲸改进减摇鳍系统控制框图 Fig. 1 Control block diagram of improved fin stabilizer system modeled after humpback whale
1.3 仿驼背鲸改进减摇鳍控制系统各部分传递函数 1.3.1 检测元件

 ${G_a}\left( s \right) = \frac{{400\;s}}{{{s^2} + 80\;{\rm{s}} + 4\;000}} \text{。}$
1.3.2 放大器与控制器

 ${G_{PID}}\left( s \right) = {K_P} + \frac{{{K_I}}}{s} + {K_D}s \text{。}$
1.3.3 舵速灵敏度调节器

 ${\alpha _{m\_\max 0}} = \left\{ {\begin{array}{*{20}{l}} 0,& V < 6 ，\\ {\alpha _{m0}},&6 \leqslant V \leqslant {V_0}，\\ {\alpha _{m0}}V_0^2/{V^2},&V \geqslant {V_0} 。\end{array}} \right.$

 ${G_s}\left( s \right) = \frac{{550}}{{{s^2} + 15s + 225}} \text{。}$

2 船舶横摇运动数学模型建立 2.1 船舶横摇升力系数受力分析

 图 2 船舶横摇运动 Fig. 2 Ship rolling motion

 $M\left( {{\alpha _f}} \right) = - Dh{\alpha _f} \text{，}$
 $M\left( {\dot\alpha _f } \right) = - 2N\ddot\alpha _f \text{，}$
 $M\left( {\ddot \alpha _f} \right) = - \Delta Ix\ddot\alpha _f \text{。}$

 $M\left( \phi \right) = - Dh\phi \text{。}$

 图 3 减摇鳍阻尼力矩随时间的变化曲线 Fig. 3 Variation curve of fin stabilizer damping torque with time
 $M\left( {\ddot \phi } \right) = - \left( {{I_x} + \Delta {I_x}} \right)\ddot \phi \text{。}$

 $M\left( {\dot \phi } \right) = - 2N\dot \phi \text{。}$
2.2 船舶横摇线性数学模型

 $\left( {{I_x} + \Delta {I_x}} \right){\ddot\varPhi} + 2N{\dot\varPhi } + Dh\varPhi = - \left( {\Delta {I_x}\ddot\alpha _{^{_f}} + 2N{\alpha _f} + Dh{\alpha _f}} \right) \text{。}$

 $\left( {{I_x} + \Delta {I_x}} \right)\ddot \phi + 2N\dot \phi + Dh\phi = - Dh{\alpha _f} \text{。}$

 ${G_\phi }\left( s \right) = \frac{{\phi \left( s \right)}}{{{\alpha _f}\left( s \right)}} = \frac{1}{{{K^2}{s^2} + 2\xi Ks + 1}} \text{。}$

 图 4 不同K值下的减摇鳍特征参数变化曲线 Fig. 4 Variation curves of fin stabilizer characteristic parameters under different K values
3 仿驼背鲸改进减摇鳍非线性升力系数分析

 $M\left( \phi \right) = - {C_1}\phi - {C_2}{\phi ^3} - {C_3}{\phi ^5} \text{。}$

 $M\left( {\dot \phi } \right) = - {B_1}\dot \phi - {B_2}\left| {\dot \phi } \right|\dot \phi \text{。}$

 $\left( {Ix + \Delta Ix} \right)\ddot \varphi + {B_2}\left| {\dot \varphi } \right|\dot \varphi + {C_1}\varphi + {C_2}{\varphi ^3} + {C_3}{\varphi ^5} = - Dh{\alpha _f} 。$
4 结　语

 [1] 赵云瑞, 高海波, 林治国, 等. 基于组合赋权-TOPSIS法的极地邮轮减摇鳍选型评价[J]. 中国舰船研究, 2021, 16(5): 121–126+149. ZHAO Yun-rui, GAO Hai-bo, LIN Zhi-guo, et al. Selection and evaluation of fin stabilizers for polar cruise ships based on combined weighting-TOPSIS method[J]. Chinese Journal of Ship Research, 2021, 16(5): 121–126 +149. [2] 李乐宇, 吴建威, 万德成. 基于CFD的带附体KCS船在波浪中的阻力及纵摇优化[J]. 中国舰船研究, 2022, 17(2): 63-72. LI Le-yu, WU Jian-wei, WAN De-cheng. Resistance and pitch optimization of KCS ship with appendages in waves based on CFD[J]. China Ship Research, 2022, 17(2): 63-72. DOI:10.19693/j.issn.1673-3185.02169 [3] 高宇辉, 李晖, 张华健, 等. 基于NFTSM的吊舱推进器与减摇鳍联合减摇控制[J]. 船舶工程, 2022, 44(6): 100-108. GAO Yu-hui, LI Hui, ZHANG Hua-jian, et al. Combined anti-rolling control of pod propeller and fin stabilizer based on NFTSM[J]. Ship Engineering, 2022, 44(6): 100-108. DOI:10.13788/j.cnki.cbgc.2022.06.17 [4] 黄雪平, 王振强. 减摇鳍控制策略优化[J]. 船舶标准化工程师, 2021, 54(5): 71-76. HUANG Xue-ping, WANG Zhen-qiang. Optimization of fin stabilizer control strategy[J]. Ship Standardization Engineer, 2021, 54(5): 71-76. DOI:10.14141/j.31-1981.2021.05.012 [5] 孙云, 金方银, 曾启盛, 等. 大型减摇鳍液压机组隔振装置设计与试验[J]. 机电设备, 2022, 39(4): 1-6. SUN Yun, JIN Fang-yin, ZENG Qi-sheng, et al. Design and test of vibration isolation device for large fin stabilizer hydraulic unit[J]. Electromechanical Equipment, 2022, 39(4): 1-6. DOI:10.16443/j.cnki.31-1420.2022.04.001