﻿ 大型船舶装载和风浪条件下的稳性校核与分析
 舰船科学技术  2022, Vol. 44 Issue (18): 65-68    DOI: 10.3404/j.issn.1672-7649.2022.18.014 PDF

Stability check and analysis of large ships under loading and wind and wave conditions
ZHANG Zhi-min, CHEN Lei
Department of Automotive and Marine Engineering, Yantai Vocational College, Yantai 264670, China
Abstract: The stability of large ships, such as hoisting ships and crane ships, during loading will be affected by the change of the position of heavy objects and the disturbance force of wind, wave and current at sea. Once the large ships roll and other motions with large amplitude caused by the disturbance force, their own stability will be destroyed, and in serious cases, accidents such as ship capsizing will even occur. Aiming at the stability check and control of large-scale ships, this paper studies the wind and wave environmental force, ship motion model, ship stability restoring moment modeling and so on, and simulates the ship stability index with Matlab.
Key words: stability check     wind and wave conditions     motion model     roll
0 引　言

1 风浪条件下的船舶稳性干扰作用力分析

 $f\left( t \right) = {\theta _m} - B\sin \left( {{w_o}t + {\varphi} _{0}} \right) \text{。}$

 ${\theta _m} = \frac{{2\pi \zeta }}{\lambda }。$

 $\varGamma \left( t \right) = \sum\limits_{i = 1}^n {} B\cos \left( {{w_o}t + {\varphi _0} + {\varepsilon _i}} \right) \text{。}$

 图 1 一段时间内的波面函数曲线图 Fig. 1 Wavefront function curve over a period of time

 $F(t) = \sum\limits_{i = 1}^n {{{\rm{m}}} {a_x}\cos \left( {{w_0}t + {\varepsilon _i}} \right) + } \sum\limits_{i = 1}^n {{{\rm{m}}} {a_y}\cos \left( {{w_0}t + {\varepsilon _i}} \right)} \text{。}$

 ${F_f}(t) = \sum\limits_{t = 1}^n {\left( {\dfrac{{\sqrt {2s(t)\Delta w} \sin (wt + \theta )}}{2}} \right)} \text{。}$

2 大型船舶装载和风浪条件下的运动建模

 图 2 风浪条件下大型船舶运动坐标系 Fig. 2 Motion coordinate system of large ship under wind and wave conditions

 $\left\{\begin{gathered} l = x ，\\ m = y\cos \varphi - z\sin \varphi, \\ n = y\sin \varphi + z\cos \varphi 。\\ \end{gathered} \right.$

 $\left[ {\begin{array}{*{20}{l}} l \\ m \\ n \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{\cos \varphi }&{ - \sin \varphi } \\ 0&{\sin \varphi }&{\cos \varphi } \end{array}} \right]\left[ {\begin{array}{*{20}{l}} x \\ y \\ z \end{array}} \right] \text{。}$

 $\left[ {\begin{array}{*{20}{l}} l \\ m \\ n \end{array}} \right] = \left[ {\begin{array}{*{20}{l}} {\cos \theta \cos \beta }&{ - \cos \varphi \sin \beta }&{\cos \varphi } \\ {\cos \theta \sin \beta }&{\cos \varphi \cos \beta }&{\cos \beta } \\ { - \sin \theta }&{\sin \varphi \cos \theta }&{\cos \varphi \cos \theta } \end{array}} \right]\left[ {\begin{array}{*{20}{l}} x \\ y \\ z \end{array}} \right] \text{。}$

 $\left\{ {\begin{array}{*{20}{c}} {{F_X} = m\ddot x = m{a_X}} ，\\ {{F_Y} = m\ddot y = m{a_Y}}，\\ {{F_Z} = m\ddot z = m{a_Z}}。\end{array}} \right.$

 \left\{ {\begin{aligned} &{{{\dot x}_0} = {V_x}\cos \gamma \cos \beta + {V_y}\cos \gamma \sin \beta } ，\\ &{{{\dot y}_0} = {V_x}\sin \gamma \cos \beta + {V_z}\cos \gamma \cos \alpha }，\\ &{{{\dot z}_0} = - {V_x}\sin \beta + {V_y}\cos \beta \sin \alpha - {V_z}\cos \beta }，\\ &{\dot \alpha = {w_x} + {w_y}\tan \beta \sin \lambda }，\\ &\dot \beta = {w_x}\cos \alpha - {w_z}\sin \alpha ，\\ &\dot \gamma = {w_y}\sin \alpha /\cos \beta 。\\ \end{aligned}} \right.

3 大型船舶装载和风浪条件下的稳性校核分析 3.1 大型船舶随浪条件下的船舵作用力分析

 图 3 风浪条件下船舵的力学模型 Fig. 3 Mechanical model of rudder under wind and wave conditions

 $P = \sqrt {P_x^2 + P_y^2} \text{。}$

$l$ 为船舵剖面的弦长，定义船舵的压力中心为 ${x_t}$ ，分散系数按下式计算：

 $Cp = \frac{{{x_t}}}{l} 。$

1）连续性方程

 $\frac{{{\rm{d}}{\rho _{}}}}{{{\rm{d}}t}} + {\rho _{}}\Delta \cdot {v_c} = 0 \text{。}$

2）动量方程

 ${\rho _{}}\frac{{{\rm{d}}{v_c}}}{{{\rm{d}}t}} = {\rho _{}}f + \Delta \cdot \sigma \text{。}$

3）能量方程[3]

 $\rho \frac{{{\rm{d}}E}}{{{\rm{d}}t}} = - \rho \Delta \cdot {v_c} + Q - \Delta q \text{。}$

 $\frac{{\partial \left( {\rho {v_c}} \right)}}{{\partial t}} + div\left( {\rho {v_c}} \right) = - \frac{{\partial P}}{{\partial t}} + \frac{{\partial {F_{\tau x}}}}{{\partial x}} + \frac{{\partial {F_{\tau y}}}}{{\partial y}} + \frac{{\partial {F_{\tau z}}}}{{\partial z}} 。$

3.2 大型船舶随浪条件下的恢复力矩计算

 图 4 船舶倾角稳性过程的数学模型 Fig. 4 Mathematical model of ship inclination stability process

 ${F_S} = \frac{1}{2}{\rho _0}{A_O}{C_0}{v^2} \text{。}$

 ${M_o} = \frac{1}{2}{k_1}{k_2}{L_b}^2B(\delta + 0.8) \cdot {10^{ - 2}}\;{\rm{kN}} \cdot {\rm{m }} \text{。}$

 ${k_1} = 4.5{\left( {\frac{{{L_b}}}{{980}} - 0.2} \right)^2} + 0.82 \text{，} {k_2} = 9 - 0.96{\left( {\frac{{300 - {L_b}}}{{100}}} \right)^2} 。$

 ${M_S} = \frac{1}{2}L{\rho _0}{A_O}\cos \theta \text{，}$

 图 5 不同吃水深度下的船体稳性倾角变化数据 Fig. 5 Hull stability inclination variation data at different draft depths
4 结　语

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