﻿ 半潜式平台在外载荷下的位移计算与仿真
 舰船科学技术  2018, Vol. 40 Issue (8): 55-60 PDF

Movement calculation and simulation of semi-submersible platform under external interference
HAN Sen, JIA Bao-zhu, GU Yi-ming
Marine Engineering College, Dalian Maritime University, Dalian 116026, China
Abstract: In order to improve the ability of mooring-assisted dynamic positioning system to resist external interference, a method of calculating the movement of semi-submersible platform is proposed. The method can estimate the movement of the platform under the condition of knowing the external interference, so as to improve the control accuracy of the controller for feedforward compensation. Using this method, the difference of platform movement, mooring line tension and platform bow under the same external interference of the intersect and non-intersect mooring system is studied. The results show that the mooring system can be simplified into the intersect system when the correlation calculation is carried out, and the timeliness of controller can be improved. The research work can provide reference for the design of mooring-assistant dynamic positioning system controller.
Key words: mooring-assisted dynamic positioning system     semi-submersible platform     external interference     intersect mooring system
0 引　言

1 计算方法

 图 1 锚泊系统在外载荷下的位置变化图 Fig. 1 The position change of the mooring system under external interference

1.1 回复力计算

 $\begin{split}{X_{Wi}} = \rm{sgn} \left[ {\sin (\frac{\pi }{4} + \frac{\pi }{2}i)} \right] \times \frac{{{x_0}}}{2}\cos \psi +\;\;\;\;\;\;\;\;\;\;\;\; \\\rm{sgn} \left[ {\sin (\frac{\pi }{2}i - \frac{\pi }{4})} \right] \times \frac{{{y_0}}}{2}\sin \psi + \delta \cos \alpha \text{，}\end{split}$ (1)
 $\begin{split}{Y_{Wi}} = \rm{sgn} \left[ {\sin (\frac{\pi }{4} + \frac{\pi }{2}i)} \right] \times \frac{{{x_0}}}{2}\sin \psi +\;\;\;\;\;\;\;\;\;\;\;\;\;\\ \rm{sgn} \left[ {\sin (\frac{\pi }{2}i - \frac{\pi }{4})} \right] \times \frac{{{y_0}}}{2}\cos \psi + \delta \sin \alpha\text{。}\end{split}$ (2)

 $\Delta {L_j} = \sqrt {{{\left( {{X_{Wi}} - {X_j}} \right)}^2} + {{\left( {{Y_{Wi}} - {Y_j}} \right)}^2}} - L\text{。}$ (3)

 $T = {T_0} + g(\Delta L,\kappa ) = {T_0} + \sum\limits_{i = 1}^n {{a_i}{{(\Delta L)}^i}} \text{。}$ (4)

 ${\lambda _j} = \arctan \left( {\frac{{{Y_{Wi}} - {Y_j}}}{{{X_{Wi}} - {X_j}}}} \right)\text{。}$ (5)

 $F = \sqrt {\begin{split}{\left( {\sum\limits_{j = 1}^8 {{\rm{sgn}}\left[ {\sin (\frac{{3\pi }}{8} + \frac{\pi }{4}j)} \right] \times {{\rm{T}}_j}\cos {\lambda _j}} } \right)^2} + \\ {\left( {\sum\limits_{j = 1}^8 {{\rm{sgn}}\left[ {\sin (\frac{\pi }{4}j - \frac{\pi }{8})} \right] \times {{\rm{T}}_j}\sin {\lambda _j}} } \right)^2}{\text{，}}\end{split}}$ (6)
 $\begin{split}\beta = & \arctan \left( {\sum\limits_{j = 1}^8 {{\rm{sgn}}\left[ {\sin (\frac{\pi }{4}j - \frac{\pi }{8})} \right] \times {{\rm{T}}_j}\sin {\lambda _j}} /} \right.\\& \left. {\sum\limits_{j = 1}^8 {{\rm{sgn}}\left[ {\sin (\frac{{3\pi }}{8} + \frac{\pi }{4}j)} \right] \times {{\rm{T}}_j}\cos {\lambda _j}} } \right)\end{split}\text{。}$ (7)

M是首摇方向的平台力矩，则

 $M = \sum\limits_{j = 1}^8 {{T_j}d\left[ { - \cos {\lambda _j}\sin ({\mu _i} + \psi ) + \sin {\lambda _j}\cos ({\mu _i} + \psi )} \right]}\text{。}$ (8)

1.2 公式拟合

 图 2 锚泊线张力-位移曲线 Fig. 2 The tension-movement curve of mooring line

 $\begin{split}T = & {T_0} + g(\Delta L) = 1\;386\;989 + 1.085\;6 \times {10^{ - 5}}{(\Delta L)^9}+ \\ &2.152\;1 \times {10^{ - 4}}{(\Delta L)^8}- 3.929\;7 \times {10^{ - 3}}{(\Delta L)^7} - \\ &0.075\;248{(\Delta L)^6} + 0.626\;44{(\Delta L)^5}+ 7.245\;6 {(\Delta L)^4} - \\ &77.946{(\Delta L)^3} + 234\;9.4{(\Delta L)^2} + 971\;93\Delta L\text{，}\end{split}$ (9)

 图 3 锚泊线水平张力-位移曲线 Fig. 3 The horizontal tension-movement curve of mooring line

2 求解与验证

 图 4 方向示意图 Fig. 4 Direction diagram

 图 5 回复力方向与位移方向差异图 Fig. 5 The direction difference between the restoring force and movement

2.1 求解方法

 图 6 求解流程图 Fig. 6 The solution flow chart
2.2 可行性验证

 图 7 坐标差异图 Fig. 7 The coordinate difference chart

3 汇交和非汇交锚泊系统的差异

3.1 位移差异

 图 8 位移差异图 Fig. 8 The movement difference diagram

 Fr = \left\{ {\begin{aligned}&{3900000 \times \sin (0.053t),\quad\quad\quad\quad\,\quad\quad\quad\quad\quad t \leqslant30}\text{；}\\&{3950000 + 600000\sin \left[ {0.08 \times (t - 30)} \right],\;\;\;30 < t \leqslant 70}\text{；}\\&{3859138 - 2000000\sin \left[ {0.05 \times (t - 70)} \right],70 < t\leqslant 100 }\text{。}\end{aligned}} \right. (11)

 $\gamma = \left\{ {\begin{array}{*{20}{c}}{0.4 \times \sin (0.05t),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;t \leqslant 30}\text{；}\\{0.4 + 1.15\sin \left[ {0.04 \times \left( {t - 30} \right)} \right],\;30 < t \leqslant 70\;}\text{；}\\{1.55 - 1.2\sin \left[ {0.05 \times \left( {t - 70} \right)} \right] ,\;70 < t \leqslant 100 }\text{。}\end{array}} \right.$ (12)

 图 9 运动轨迹差异图 Fig. 9 The trajectory difference chart

3.2 锚泊线受力差异

 图 10 锚泊线受力差异图 Fig. 10 The tension difference of all mooring lines

 图 11 受力均匀性差异图 Fig. 11 The difference diagram of tension uniformity

3.3 平台的首向差异

 图 12 平台首向变化图 Fig. 12 The difference diagram of platform bow

4 结　语

1）本文给出的半潜式平台位移计算方法具备可行性及准确性。

2）采用锚泊定位的半潜式平台的位移方向与外载荷方向基本一致，其首向在外载荷的影响下变化也很小。

3）在对锚泊系统的受力及平台位移进行计算时，可使用汇交锚泊系统代替非汇交系统。

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