﻿ 船舶拖航系统六自由度操纵运动仿真
 舰船科学技术  2016, Vol. 38 Issue (6): 57-62 PDF

1. 哈尔滨工程大学 船舶工程学院 船舶设计研究所, 哈尔滨 150001 ;
2. 海洋石油工程股份有限公司, 天津 300461

6-DOF maneuvering simulation of ship towing system
WU Cheng-cheng1, YUAN Li-hao1, ZAN Ying-fei1, WANG Xin2
1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China ;
2. Offshore Oil Engineering Co., Ltd., Tianjin 300461, China
Abstract: The 6-DOF maneuvering model is based on MMG (Ship Maneuvering Model Group) mathematical model and catenary model of towing rope, include a series of maneuvering motion equations of towing system. The ship towing system contains one tug, one barge and towrope. Maneuvering motion simulation of the towing system is carried out by numerical calculation. Taking a tug boat towing a jacket barge as example, the factors such as towing rope length, towing speed and environmental conditions are studied. The simulation obtains some useful conclusion for improve operational security.
Key words: waterway transportation     towing system     MMG     6-DOF     simulation
0 引言

1 拖航系统六自由度运动数学模型 1.1 基本假设

1.2 坐标系和操纵运动模型

 图 1 坐标系 Fig. 1 Coordinate system

 \left\{ \begin{aligned} & ({m_{\rm{t}}} \!+\! {\lambda _{11}}_{\rm{t}}){{\dot u}_{\rm{t}}} \!-\! ({m_{\rm{t}}} \!+\! {\lambda _{22}}_{\rm{t}}){r_{\rm{t}}}{v_{\rm{t}}} \!=\! {X_H}_{\rm{t}} \!+\! {X_P}_{\rm{t}} \!+\! {X_R}_{\rm{t}} \!+\! {X_W}_{\rm{t}} \!+\! \\[2pt] & \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\,\,{X_F}_{\rm{t}} \!+\! {X_{Ct}} \!+\! {X_{Tt}}\text{，}\\[2pt] & ({m_{\rm{t}}} + {\lambda _{22}}_{\rm{t}}){{\dot v}_{\rm{t}}} \!+\! ({m_{\rm{t}}} \!+\! {\lambda _{11}}_{\rm{t}}){r_{\rm{t}}}{u_{\rm{t}}} \!=\! {Y_H}_{\rm{t}} \!+\! {Y_P}_{\rm{t}} \!+\! {Y_R}_{\rm{t}} \!+\! {Y_W}_{\rm{t}} \!+\! \\[2pt] & \qquad\qquad\qquad\qquad\quad\quad\quad\,\,\,\,\,{Y_F}_{\rm{t}} \!+\! {Y_{Ct}} \!+\! {Y_{Tt}}\text{，}\\[2pt] & ({m_t} + {\lambda _{33}}_{\rm{t}}){{\dot \omega }_t} \!+\! {m_{\rm{t}}}({p_t}{v_t} \!-\! {q_t}{u_t}) \!=\! {Z_H}_{\rm{t}} \!+\! {Z_W}_{\rm{t}} \!+\! \\[2pt] & \qquad\qquad\qquad\qquad\qquad\quad\quad\,{Z_F}_{\rm{t}} \!+\! {Z_{Tt}}\text{，}\\[2pt] & ({I_{xt}} \!+\! {\lambda _{44}}_{\rm{t}}){{\dot p}_t} \!+\! ({I_{zt}} \!-\! {I_{yt}}){q_t}{r_t} \!=\! {L_{Ht}} \!+\! {L_{Rt}} + {L_{Wt}} \!+\! \\[2pt] & \qquad\qquad\qquad\qquad\qquad\quad {L_{Ft}} \!+\! {L_{Tt}}\text{，}\\[2pt] & ({I_{yt}} \!+\! {\lambda _{55}}_{\rm{t}}){{\dot q}_t} \!+\! ({I_{xt}} \!-\! {I_{zt}}){r_t}{p_t} \!=\! {M_{Ht}} \!+\! {M_{Pt}} \!+\! {M_{Rt}} \!+\! \\[2pt] & \qquad\qquad\qquad\qquad\qquad\quad {M_{Wt}} \!+\! {M_{Ft}} \!+\! {M_{Tt}}\text{，}\\[2pt] & ({I_z}_{\rm{t}} \!+\! {\lambda _{66}}_{\rm{t}}){{\dot r}_{\rm{t}}} \!=\! {N_H}_{\rm{t}} \!+\! {N_P}_{\rm{t}} \!+\! {N_R}_{\rm{t}} \!+\! {N_W}_{\rm{t}} \!+\! \\[2pt] & \qquad\qquad\quad\,\,{N_F}_{\rm{t}} \!+\! {N_{Ct}} \!+\! {N_{Tt}}\text{，} \end{aligned} \right. (1)

 \left\{ \begin{aligned} & ({m_b} \!+\! {\lambda _{11}}_b){{\dot u}_b}-({m_b} \!+\! {\lambda _{22b}}){r_b}{v_b} \!=\! {X_H}_b \!+\! {X_W}_b \!+\! {X_F}_b \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\qquad\quad {X_{Cb}} + {X_{Tb}}\text{，}\\ & ({m_b} \!+\! {\lambda _{22}}_b){{\dot v}_b} \!+\! ({m_b} \!+\! {\lambda _{11}}_b){r_b}{u_b} \!=\! {Y_H}_b \!+\! {Y_W}_b \!+\! {Y_F}_b \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\quad\quad\,\,\,{Y_{Cb}} + {Y_{Tb}}\text{，}\\ & ({m_b} \!+\! {\lambda _{33}}_b){{\dot \omega }_b} \!+\! {m_b}({p_b}{v_b} \!-\! {q_b}{u_b}) \!=\! {Z_H}_b \!+\! {Z_{Wb}} \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\qquad\quad {Z_F}_b + {Z_{Tb}}\text{，}\\ & ({I_{xb}} \!+\! {\lambda _{44}}_b){{\dot p}_b} \!+\! ({I_{zb}} \!-\! {I_{yb}}){q_b}{r_b} \!=\! {L_{Hb}} \!+\! {L_{Wb}} \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\quad\quad {L_{Fb}} + {L_{Tb}}\text{，}\\ & ({I_{yb}} \!+\! {\lambda _{55}}_b){{\dot q}_b} \!+\! ({I_{xb}} \!-\! {I_{zb}}){r_b}{p_b} \!=\! {M_{Hb}} \!+\! {M_{Wb}} \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\quad\quad {M_{Fb}} + {M_{Tb}}\text{，}\\ & ({I_z}_b \!+\! {\lambda _{66}}_b){{\dot r}_b} \!+\! ({I_{yb}} \!-\! {I_{xb}}){p_b}{q_b} \!=\! {N_H}_b \!+\! {N_W}_b \!+\! {N_F}_b \!+\! \\ & \qquad\qquad\qquad\qquad\qquad\quad\quad {N_{Cb}} + {N_{Tb}}\text{。} \end{aligned} \right. (2)

1.3 拖航系统水动力计算模型 1.3.1 船体水动力

 \left\{ \begin{aligned} {X_H} = & X(u) + {X_{vv}}{v^2} + {X_{vr}}vr + {X_{rr}}{r^2}\text{，}\\ {Y_H} = & {Y_v}v + {Y_r}r + {Y_{v\left| v \right|}}v\left| v \right| + {Y_{v\left| r \right|}}v\left| r \right| + \\ & {Y_{r\left| r \right|}}r\left| r \right| + {Y_{vvr}}{v^2}r + {Y_{vrr}}v{r^2}\text{，}\\ {N_H} = & {N_v}v + {N_r}r + {N_{v\left| v \right|}}\left| v \right|v + {N_{r\left| r \right|}}r\left| r \right| + \\ & {N_{vvr}}{v^2}r + {N_{vrr}}v{r^2}\text{。} \end{aligned} \right. (3)

 $({I_x} + {\lambda _{44}})\ddot \varphi + 2{L_{\dot \varphi }}\dot \varphi + \Delta \cdot GZ(\varphi ) + {Y_H} \cdot {z_H} = {L_H}\text{，}$ (4)

 $\left\{ \begin{array}{l} (m + {\lambda _{33}})\ddot z + {Z_{\dot z}}\dot z + {Z_z}z + {Z_{\ddot \theta }}\ddot \theta + {Z_{\dot \theta }}\dot \theta + {Z_\theta }\theta = {Z_\Sigma }\text{，}\\ ({I_y} \!+\! {\lambda _{55}})\ddot \theta \!+\! {M_{\dot \theta }}\dot \theta \!+\! {M_\theta }\theta \!+\! {M_{\ddot z}}\ddot z \!+\! {M_{\dot z}}\dot z + {M_z}z = {M_\Sigma }\text{。} \end{array} \right.$ (5)

1.3.2 拖船桨、舵水动力

 $\left\{ \begin{array}{l} {X_P} = (1-t)({T_L} + {T_R})\text{，}\\ {M_P} = {X_P} \cdot {z_P}\text{，}\\ {N_P} = b(1-t)({T_L}-{T_R})/2\text{。} \end{array} \right.$ (6)

 $\left\{ \begin{array}{l} {X_R} =-\left( {1-{t_R}} \right){F_N}\sin \delta\text{，} \\ {Y_R} = \left( {1 + {\alpha _H}} \right){F_N}\cos \delta\text{，} \\ {L_R} =-{Y_R}\times{z_R}\text{，}\\ {M_R} = {X_R}\times{z_R}\text{，}\\ {N_R} = {x_R}(1 + {\alpha _H}){F_N}\cos \delta \text{。} \end{array} \right.$ (7)

1.4 环境因素模型 1.4.1 风

 $\left\{ \begin{array}{l} {X_W} =-{R_a}\cos {\alpha _a}\text{，}\\ {Y_W} = {R_a}\sin {\alpha _a}\text{，}\\ {L_W} = {Y_W}{z_s}\text{，}\\ {M_W} = {X_W}{z_f}\text{，}\\ {N_W} = {Y_W}({l_G}-a)\text{。} \end{array} \right.$ (8)

1.4.2 浪

 \left\{ \begin{aligned} {X_{F2}} = & 0.5\rho gL\xi _W^2{C_{XW}}\cos \chi\text{，} \\ {Y_{F2}} = & 0.5\rho gL\xi _W^2{C_{YW}}\sin \chi \text{，}\\ {N_{F2}} = & 0.5\rho g{L^2}\xi _W^2{C_{NW}}\sin \chi \text{。} \end{aligned} \right. (9)

1.4.3 流

 \left\{ \begin{aligned} {X_{\rm{C}}} = & rV_C^{}\sin (\psi-{\psi _{\rm{C}}})({\lambda _{11}}-{\lambda _{22}})\text{，}\\ {Y_{\rm{C}}} = & rV_C^{}\cos (\psi-{\psi _{\rm{C}}})({\lambda _{22}}-{\lambda _{11}})\text{，}\\ {N_{\rm{C}}} = & 0\text{。} \end{aligned} \right. (10)
1.5 拖缆力计算模型

 \left\{ \begin{aligned} & H = \frac{{{T_0}(\sec {\theta _0}-1) }}{w}\text{，}\\ & \tan \theta = \frac{{{L_c}w}}{{2{T_0}}}\text{，}\\ & {l_c} = \frac{{2{T_0}}}{w}{\sin\text{h} ^{-1}}(\tan {\theta _0}) + \frac{{{T_0}{L_c}}}{{EA}}\text{，}\\ & {T_V} = \frac{1}{2}w{L_c}\text{。} \end{aligned} \right. (11)

 ${R_{\rm{t}}} = 1.224\frac{S}{{1 \; 000}}\frac{d}{{10}}{V^2}[1 + \frac{{1.122}}{{1 \; 000T}}\frac{d}{{10}}{(\frac{S}{{1 \; 000}})^2}]\text{。}$ (12)

2 拖航系统仿真计算 2.1 仿真程序

 图 2 仿真流程 Fig. 2 Flow-process diagram
2.2 仿真实例

3 拖航系统仿真计算结果分析 3.1 拖缆长度的影响

 图 3 直航时拖轮纵摇角对比曲线 Fig. 3 Typical graph of tug’s pitch angles

 图 4 直航时驳船纵摇角对比曲线 Fig. 4 Typical graph of barge’s pitch angles

3.2 拖航速度的影响

 图 5 速度变化前后拖缆力对比曲线 Fig. 5 Typical graph of towing force in different speeds

 图 6 速度变化前后拖轮纵摇对比曲线 Fig. 6 Typical graph of tug’s pitch angle in different speeds

 图 7 工况 3 首向角的变化曲线 Fig. 7 Heading angles of condition 3

 图 8 加速后首向角的变化曲线 Fig. 8 Heading angles of condition 3（speed up）

3.3 风、浪、流的共同作用下拖航运动

 图 9 风浪流作用下横摇角曲线 Fig. 9 Typical graph of roll angles

 图 10 风浪流作用下纵摇角曲线 Fig. 10 Typical graph of pitch angles

4 结语

 [1] BERNITSAS, M. M., KEKRIDIS, N .S. Simulation and Stability of Ship Towing[J]. Int. Shipbuild. Prog , 1985, 32 (369) :112–123. [2] LEITE, A J P, ARANHA, J A P, UMEDA, C ., et al. Current forces in tankers and bifurcation of equilibrium of turret systems:hydrodynamic model and experiments[J]. Appl.OceanRes , 1998, 20 :145–156. DOI:10.1016/S0141-1187(98)00002-9 [3] YASUKAWA, H, NAKMURA, N, HIRATA, N, et al. Maneuvering simulations of tow and towed ships in still water[C]//.In:Proceedings of the 1st International Conference on Towing and Salvage of Disabled Tankers (TSDT2007), Glasgow, UK. 200722-23 March. pp. 73-82. [4] FITRIADHY A, YASUKAWA H, KOH K K. Course stability of a ship towing system in wind[J]. Ocean Engineering , 2013, 64 :135–145. DOI:10.1016/j.oceaneng.2013.02.001 [5] MARCO S, GABRIELE B. Towing simulation in wind through a nonlinear 4-DOF model:Bifurcation analysis and occurrence of fishtailing[J]. Ocean Engineering , 2014, 88 :366–392. DOI:10.1016/j.oceaneng.2014.06.007 [6] LIANG K, DENG De-heng, HUANG Guo-liang. A study of towing system maneuvering motion dimulation[J]. Navigation of China , 2007 (2) :10–29. [7] SUN Hong-bo, WENG Yue-zong. 4-DOF modeling and simulation of marine towing system[J]. Navigation of China , 2012 (2) :39–44. [8] YAO jing-zheng, HAN duan-feng, ZHAO peng-ju. Research on the simulation of ship towing system[J]. Ship Building of China , 2011, 52 (3) :75–82. [9] FITRIADHY, A, YASUKAWA H. Course stability of a ship towing system[J]. Ship Technol. Res , 2011, 58 :4–24. DOI:10.1179/str.2011.58.1.001 [10] YASUKAWA, H, HIRONO, T, NAKAYAMA, Y, et al. Course Stability and Yaw Motion of a Ship in Steady Wind[J]. Marine Science and Technology , 2012, 3 :291–304.