﻿ 基于升摇效果分析新型船舶舵减摇潜力
 舰船科学技术  2020, Vol. 42 Issue (8): 69-73    DOI: 10.3404/j.issn.1672-7649.2020.08.013 PDF

Analysis of the rudder reduction potential of a new type of ship based on the effect of shaking
LI Chen, CHEN Yong-bing, LI Wen-kui, ZHOU Gang
Electrical Engineering College, Naval University of Engineering,Wuhan 430033, China
Abstract: In order to explore the rudder reduction potential of a new type of ship, the actual hull parameters of the ship are introduced into the ship motion model, and the simulation is carried out through the established MATLAB simulation platform. Observe the influence of different rudder amplitude and rudder frequency on the ship's toll angle without considering the environmental disturbances such as waves. According to the variation law of the roll angle, the experimental scheme is designed to explore the maximum roll angle that can be generated under the limitation of hardware conditions, especially the rudder speed condition, and analyze the rudder roll-shake potential of the ship and the feasibility of the rudder roll for the ship. According to the experiment, the ship can generate a large roll angle through a reasonable steering strategy, reflecting its better rudder anti-rolling potential.
Key words: rudder reduction     rising ability     rudder amplitude     rudder frequency     rudder speed
0 引　言

1 船舶运动四自由度模型的建立

 \left\{\begin{aligned} &\left(m+{m}_{11}\right)\dot{u}={X}_{HH}+{X}_{HR}+{X}_{HP}+\left(m+{m}_{22}\right){\text{，}}\\ &\left(m+{m}_{22}\right)\dot{v}={Y}_{H}-(m+{m}_{11})ur{\text{，}}\\ &({I}_{x}+{m}_{44})\dot{p}={K}_{H}+{K}_{\varphi }+{K}_{\dot{\dot{\varphi }}}{\text{，}}\\ &\left({I}_{Z}+{m}_{66}\right)\dot{r}={N}_{H}{\text{。}}\end{aligned}\right. (1)

 \left\{\begin{aligned} &\dot{{{x}}_{0}}={\rm{{u}cos}}\varPsi -{\rm{{v}sin}}\psi{\text{，}}\\ &\dot{{r{y}}_{0}}={\rm{{u}sin}}\psi +{\rm{{v}cos}}\psi{\text{，}} \\ &\dot\psi=r{\text{，}}\\ &\dot{{\varPhi }}=p{\text{。}}\end{aligned}\right. (2)

1）对方程右侧的船舶受力进行分析[7]

 ${X_{HH}} = - \left( {13\;747.99{{u - 638}}{\rm{.1}}{{{u}}^{\rm{2}}}{\rm{ + 313}}{\rm{.8}}{{{u}}^3}} \right){\text{。}}$ (3)

 \left\{ \begin{aligned} &{{{{X}}_{{{HP}}}} = \left( {1 - {{t}}} \right)*2}{\text{，}}\\ &{T = {{{K}}_{{T}}}\rho {{\rm{n}}^2}{{D}}_{{P}}^4}{\text{，}}\\ &{{{{K}}_{{T}}} = 0.752\;4 - 0.558\;2{{J}} + 0.010\;34{{{J}}^2}}{\text{，}}\\ &{{{J}} = \frac{{\left( {1 - {{{W}}_{{{p}}0}}} \right){\rm{u}}}}{{{{n}}{{{D}}_{{p}}}}}} {\text{。}}\end{aligned} \right. (4)

 \left\{ \begin{aligned} &{{{{X}}_{{\rm{HR}}}} = {{{F}}_{\rm{N}}}\sin{\rm{\delta}} }{\text{，}}\\ &{{{{F}}_{{\rm{N}} = \left( {{{{C}}_{{\rm{NS}}}} + {{{C}}_{{\rm{NP}}}}} \right)\frac{1}{2}{\rm{\rho }}{{{V}}^2}{{{A}}_{{R}}}}}}{\text{，}}\\ &{{{{C}}_{{\rm{NS}}}} = {{\rm{\alpha }}_1}\left[ {{\rm{\delta }} + {{\rm{\alpha }}_2}\left( {{{v}} + {{{I}}_{\rm{R}}}{{r}}} \right)} \right]} {\text{。}}\end{aligned} \right. (5)

${K}_{\varphi }$ 为恢复力矩

 ${K_\phi } =m{\rm{ghsin}}{\rm{\phi}} {\text{。}}$ (6)

${K}_{\dot{\varphi }}$ 为横摇阻尼力矩

 \left\{ \begin{aligned} &{{K_{\dot \phi }} = - 2{{{N}}_{\dot {\rm{\phi}} }}p}{\text{，}}\\ &{{{{N}}_{\dot {\rm{\phi}} }} = {{\rm{u}}_{\dot {\rm{\phi}} }}\sqrt {{{{I}}_{{\rm{xl}}}}{{{{m}}gh}}} }{\text{，}}\\ &{{{{I}}_{{\rm{xl}}}} = {{I}_{\rm{x}}} + {m_{44}}}{\text{，}}\\ &{{{{u}}_{\dot {\rm{\phi}} }} = {{{u}}_{\dot {\rm{\phi }}}}\left( 0 \right)\left( {1 + 3.3{{{F}}_{{r}}}} \right)}{\text{，}}\\ &{{{{u}}_{\dot {\rm{\phi}} }}\left( 0 \right) = \frac{1}{2}\frac{{0.057{{L}}{{{B}}^4}}}{{{{W}}\left( {{{{B}}^2} + {{{D}}^4}} \right)}}{{\rm{\phi}} _{\rm{m}}}}{\text{。}} \end{aligned} \right. (7)

${K}_{H}$ 可以直接由水动力导数表示：

 $\begin{split} {K_H} =\;& ({{K}}_{{v}}'{{v'}} + {{K}}_{{r}}'{m{r'}} + {{K}}_{{\delta }}'{{\delta '}} + {{K}}_{{{vvv}}}'{{{{v'}}}^3} + \\ &{{K}}_{{{rrr}}}'{{{{r'}}}^3} + {{K}}_{{{\delta \delta \delta }}}'{{{{\delta '}}}^3} + {{K}}_{{m{vvr}}}'{{{m{v'}}}^2}{{r'}} + {{K}}_{{{vrr}}}'{{{{r'}}}^2}{{v'}} + \\ &{{K}}_{{{v\delta \delta }}}'{{{{\delta '}}}^2}{{v'}} + {{K}}_{{{\delta \delta r}}}'{{{\rm{\delta '}}}^2}{m{r'}} + {{K}}_{{{v\delta r}}}'{{v'\delta '}}{{{r}}'})\frac{1}{2}{{\rho }}{{{v}}^2}{{{L}}^3} {\text{。}}\end{split}$ (8)

2）附加质量的计算

2 船舶横摇角变化规律

2.1 摆舵频率对横摇的影响规律

 图 1 航速为18 kn，摆舵幅度为20°，频率为0.314 Hz下船舶舵角、横摇角、舵速的变化 Fig. 1 The ship’s rudder angle, roll angle and rudder speed change at a speed of 18 kn, a rudder amplitude of 20° and a rudder frequency of 0.314 Hz.

 图 2 航速为18 kn，摆舵幅度为20°，频率为0.471 Hz下船舶舵角、横摇角、舵速的变化 Fig. 2 The ship’s rudder angle, roll angle and rudder speed change at a speed of 18 kn, a rudder amplitude of 20° and a rudder frequency of 0.471 Hz.

 图 3 航速为18 kn，摆舵幅度为20°，频率为0.628 Hz下船舶舵角、横摇角、舵速的变化 Fig. 3 The ship’s rudder angle, roll angle and rudder speed change at a speed of 18 kn, a rudder amplitude of 20° and a rudder frequency of 0.628 Hz.

 图 4 航速为18 kn，摆舵幅度为20°，频率为0.78 5 Hz下船舶舵角、横摇角、舵速的变化 Fig. 4 The ship’s rudder angle, roll angle and rudder speed change at a speed of 18 knots, a rudder amplitude of 20° and a rudder frequency of 0.785 Hz.

1）对比图1~图4并结合表1可以发现，在船舶航速不变，摆舵幅度相同的情况下，摆舵产生的横摇角会随着摆舵频率出现先上升后下降的趋势。相应的船速、摆舵幅度下会对应一个摆舵频率使船舶产生横摇角呈现最大值：航速18 kn情况下，摆舵幅度为20°时，最大的横摇角出现在摆舵频率为0.653 Hz附近。

2）经过实验分析，船舶在摆舵幅度不变时，横摇角会随摆舵频率增大出现先增后减的变化并且有峰值的存在。其原因是船舶摆舵频率过小，产生的横摇力矩很小，不足以使船摆动；船舶摆舵频率过高，由于船舶惯性，船舶横摇反应滞后导致来不及响应，因此船舶横摇角也小。

2.2 摆舵幅度对横摇的影响规律

 图 5 航速18 kn，摆舵幅度10°下船舶舵角、最大横摇角、舵速的变化 Fig. 5 Changes in ship rudder angle, maximum roll angle and rudder speed at 18 kn and 10° yaw amplitude

 图 6 航速为18 kn，摆舵幅度20°下船舶舵角、最大横摇角、舵速的变化 Fig. 6 Changes in ship rudder angle, maximum roll angle and rudder speed at 18 kn and 20° yaw amplitude

 图 7 航速为18 kn，摆舵幅度35°下船舶舵角、最大横摇角、舵速的变化 Fig. 7 Changes in ship rudder angle, maximum roll angle and rudder speed at 18 kn and 35° yaw amplitude

2.3 船速对横摇角的影响规律

 图 8 保持船舶摆舵幅度10°、摆舵频率0.659 Hz不变，不同航速下船舶横摇角变化 Fig. 8 Keeping the ship’s rudder amplitude 10°, the rudder frequency 0.659 Hz unchanged at different speeds

3 在舵速限制下所具备的舵减摇潜力分析

1）在船舶航速27 kn、摆舵幅度为10°时，对于最大横摇角24.28°时，最大舵速为6.60°/s，符合船舶舵速要求；

2）在船舶航速27 kn、摆舵幅度为15°时，对于最大横摇角34.43°时，最大舵速为9.79°/s，符合船舶舵速要求；

3）在船舶航速27 kn、摆舵幅度为20°时，对于最大横摇角时，最大舵速为13.03°/s，超出船舶舵速要求。根据上述实验可知，船舶在最大舵速增大到13.03°/s的过程中，横摇角随舵速递增，因此实验在摆舵幅度20°，最大舵速为10°/s情况下，最大横摇角为13.13°/s。

4 结　语

1）本文将实际的船舶参数代入建立的船舶四自由度运动模型中，利用Matlab仿真平台进行仿真。发现船舶的操舵影响船舶横摇，且横摇角的大小与船舶摆舵幅度、摆舵频率以及进行操舵时船舶的航速有关。

2）船舶在静水条件下的升摇能力即代表船舶在海中航行时的舵减摇潜力。根据实验得到船舶横摇角变化规律：船舶横摇角随摆舵频率的增加，出现先增后减趋势，每个摆舵幅度下存在一个摆舵频率使横摇角达到峰值；船舶摆舵幅度越大，其能够产生的最大横摇角也越大，对应的舵速要求也越高；船舶航速越大，相同摆舵幅度和摆舵频率产生的横摇角越大。

3）对本船来说，在航速27 kn情况下船舶通过摆舵产生的最大横摇角可达30°以上，具备较好的舵减摇潜力。

 [1] 马亮. 船舶舵鳍联合减摇控制策略研究[D]. 大连: 大连海事大学, 2012. MA Liang. Research on ship rudder fin joint anti-rolling control strategy[D]. Dalian: Dalian Maritime University, 2012. [2] CROSSLAND P. The effect of roll stabilization controllers on warship operational performance[J]. Control Engineering Practice, 2003, 114(11): 423-431. [3] 郭大勇, 梁利华, 赖志昌, 等. 新型主动式减摇装置的仿真研究[J]. 自动化技术及应用, 2001(3): 20-22. GUO Da-yong, LIANG Li-hua, LAI Zhi-chang, et al. Simulation study of a new type of active anti-rolling device[J]. Automation Technology and Applications, 2001(3): 20-22. [4] 邹令辉. 基于最优控制的舵鳍联合减摇性能指标函数的分析研究[J]. 舰船科学技术, 2018(4): 40-4. ZOU Ling-hui. Analysis of the performance index function of rudder fin combined anti-rolling based on optimal control[J]. Ship Science and Technology, 2018(4): 40-4. [5] 袁远, 成志军, 金咸定. 船舶在波浪中运动的六自由度非线性耦合方程[J]. 上海交通大学学报, 2001, 35(4): 541-543. YUAN Yuan, CHENG Zhi-jun, JIN Xian-ding. Six-degree-of-freedom nonlinear coupled equation for ship motion in waves[J]. Journal of Shanghai Jiaotong University, 2001, 35(4): 541-543. DOI:10.3321/j.issn:1006-2467.2001.04.014 [6] 贾欣乐, 杨盐生. 船舶运动数学模型[M]. 大连: 大连海事大学出版社, 2003. [7] Sarch M G.. Fin stabilizers as maneuver control surfaces[D]. Monterey: Naval Postgraduate School, 2003. [8] 周昭明, 盛子寅, 冯悟时. 多用途货船的操纵性预报计算[J]. 船舶工程, 1983(6): 21-29. ZHOU Zhao-ming, SHENG Zi-kai, FENG Wu-shi. Maneuverability forecast calculation of multipurpose cargo ships[J]. Ship Engineering, 1983(6): 21-29.