许秀军1,王立权1,房晓明2,李震1
(1.哈尔滨工程大学 机电工程学院, 哈尔滨 150001; 2.海洋石油工程股份有限公司 海洋工程技术中心,天津 300451)
摘要:
为建立准确的海上起重作业视景仿真系统,以“海洋石油201”起重船为研究对象,构建综合考虑海情海况、船舶动力定位系统、起重船压载系统等影响下的起重作业数学模型.综合应用虚拟现实技术、多通道数据交互技术、数值模拟技术以及半物理仿真技术,构建交互式三维动态虚拟场景.采用布利斯近似积分法对起重作业数学模型进行实时求解,在保证求解精度的基础上,实现了视景仿真系统的实时数据交互.仿真系统重点对起重作业过程中的船舶位移、船舶姿态角、吊物系统摆角和受力以及起重船受到的反作用力等参数的动态响应过程进行了仿真模拟,得到起重作业过程中船舶和吊物系统的运动规律.将仿真系统结果与海试数据进行对比,仿真系统偏差保持在10%以内,起重作业数学模型准确度满足仿真系统需求.视景仿真结果表明:仿真系统在保证精度的前提下,可以对海上起重作业的施工项目进行工程预演,能有效地降低海上起重作业风险,提高工程作业的安全性.
关键词: 起重船 多通道数学模型 吊物系统 数值模拟 交互式视景仿真
DOI:10.11918/j.issn.0367-6234.201705068
分类号:TH133; TP183
文献标识码:A
基金项目:国家科技重大专项(Z12SJENA0014)
Interactive visual simulation of offshore hoisting operation and numerical modelling
XU Xiujun1,WANG Liquan1,FANG Xiaoming2,LI Zhen1
(1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001,China; 2. Offshore Engineering Technology Center, Offshore Oil Engineering Co. Ltd. , Tianjin 300451, China)
Abstract:
To establish an accurate visual simulation system for offshore hoisting operations, the "Offshore Oil 201" crane ship was regarded as the research object, a mathematical model for hoisting operations was established with comprehensive considering the influence of sea conditions, the dynamic positioning system of the ship and the ballasting system of the crane ship. An interactive three-dimensional dynamic virtual scene was constructed by the comprehensive application of virtual reality technology, multi-channel data interaction technology, numerical solution technology and semi-physical simulation technology. The Bliss approximate integration was used to solve the mathematical model of the hoisting operation and the real-time data interaction of the visual simulation system was realized on the basis of guaranteeing the accuracy of the solution. The dynamic response of the ship displacements, the ship attitude angles, the swing angles and forces of the hoisting system and the reaction force of the crane ship were emphatically analyzed in the simulation system. The movement law of the ship and the hoisting system were obtained. The simulation system results were compared with the sea trial and the deviation of the simulation system was kept within 10%. The accuracy of the mathematical model of the hoisting operation is sufficient for the simulation system, and the simulation system can carry on the engineering rehearsal of the offshore hoisting operations with ensuring the system accuracy, which can effectively improve the safety of the offshore engineering operations.
Key words: crane ship multi-channel mathematical model hoisting system numerical simulation interactive Visual simulation
许秀军, 王立权, 房晓明, 李震. 海上起重作业交互式视景仿真与数值模拟[J]. 哈尔滨工业大学学报, 2018, 50(1): 160-168. DOI: 10.11918/j.issn.0367-6234.201705068.
![复制到剪切板](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/copy.gif)
XU Xiujun, WANG Liquan, FANG Xiaoming, LI Zhen. Interactive visual simulation of offshore hoisting operation[J]. Journal of Harbin Institute of Technology, 2018, 50(1): 160-168. DOI: 10.11918/j.issn.0367-6234.201705068.
![复制到剪切板](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/copy.gif)
基金项目 国家科技重大专项(Z12SJENA0014) 作者简介 许秀军(1988—),男,博士研究生;
王立权(1957—),男,教授,博士生导师 通信作者 王立权,wangliquan@hrbeu.edu.cn 文章历史 收稿日期: 2017-05-13
Contents -->Abstract Full text Figures/Tables PDF
海上起重作业交互式视景仿真与数值模拟
许秀军1, 王立权1
![通讯作者](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/REcor.gif)
![wangliquan@hrbeu.edu.cn](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/REemail.gif)
1. 哈尔滨工程大学 机电工程学院,哈尔滨 150001;
2. 海洋石油工程股份有限公司 海洋工程技术中心,天津 300451
收稿日期: 2017-05-13
基金项目: 国家科技重大专项(Z12SJENA0014)
作者简介: 许秀军(1988—),男,博士研究生;
王立权(1957—),男,教授,博士生导师
通信作者: 王立权,wangliquan@hrbeu.edu.cn
摘要: 为建立准确的海上起重作业视景仿真系统,以“海洋石油201”起重船为研究对象,构建综合考虑海情海况、船舶动力定位系统、起重船压载系统等影响下的起重作业数学模型.综合应用虚拟现实技术、多通道数据交互技术、数值模拟技术以及半物理仿真技术,构建交互式三维动态虚拟场景.采用布利斯近似积分法对起重作业数学模型进行实时求解,在保证求解精度的基础上,实现了视景仿真系统的实时数据交互.仿真系统重点对起重作业过程中的船舶位移、船舶姿态角、吊物系统摆角和受力以及起重船受到的反作用力等参数的动态响应过程进行了仿真模拟,得到起重作业过程中船舶和吊物系统的运动规律.将仿真系统结果与海试数据进行对比,仿真系统偏差保持在10%以内,起重作业数学模型准确度满足仿真系统需求.视景仿真结果表明:仿真系统在保证精度的前提下,可以对海上起重作业的施工项目进行工程预演,能有效地降低海上起重作业风险,提高工程作业的安全性.
关键词: 起重船 多通道数学模型 吊物系统 数值模拟 交互式视景仿真
Interactive visual simulation of offshore hoisting operation
XU Xiujun1, WANG Liquan1
![Corresponding author](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/REcor.gif)
![wangliquan@hrbeu.edu.cn](http://hit.alljournals.cn/html/hitxb_cn/2018/1/images/REemail.gif)
1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China;
2. Offshore Engineering Technology Center, Offshore Oil Engineering Co. Ltd., Tianjin 300451, China
Abstract: To establish an accurate visual simulation system for offshore hoisting operations, the "Offshore Oil 201" crane ship was regarded as the research object, a mathematical model for hoisting operations was established with comprehensive considering the influence of sea conditions, the dynamic positioning system of the ship and the ballasting system of the crane ship. An interactive three-dimensional dynamic virtual scene was constructed by the comprehensive application of virtual reality technology, multi-channel data interaction technology, numerical solution technology and semi-physical simulation technology. The Bliss approximate integration was used to solve the mathematical model of the hoisting operation and the real-time data interaction of the visual simulation system was realized on the basis of guaranteeing the accuracy of the solution. The dynamic response of the ship displacements, the ship attitude angles, the swing angles and forces of the hoisting system and the reaction force of the crane ship were emphatically analyzed in the simulation system. The movement law of the ship and the hoisting system were obtained. The simulation system results were compared with the sea trial and the deviation of the simulation system was kept within 10%. The accuracy of the mathematical model of the hoisting operation is sufficient for the simulation system, and the simulation system can carry on the engineering rehearsal of the offshore hoisting operations with ensuring the system accuracy, which can effectively improve the safety of the offshore engineering operations.
Key words: crane ship multi-channel mathematical model hoisting system numerical simulation interactive Visual simulation
海上起重工程船[1~3]是深海资源开发的重要装备之一,承担着海上平台起吊、安装以及货物卸载等多项任务.海上起重作业过程中,受到风载荷、波浪载荷以及动力定位系统、压载系统[4]等多种条件的影响,操作失误会影响被吊物安装作业精度,甚至导致作业失败,造成无法挽回的巨大损失.由于起重作业的外部环境复杂多变,很难得到实时准确的吊物系统响应模型,海上起重作业的运动响应一直是起重行业关注研究的重点.对海上起重作业过程进行准确的计算和仿真模拟,得到起重船和吊物系统的运动规律,尽可能降低实际的施工风险[5~6],对实际的海上工程作业具有重大意义.
Masoud等[7]考虑了海况对起重作业的影响,分析了吊物系统摇摆幅度的影响因素.王立权等[8]研究了深水起重作业的动力学响应特性; Trabka[9]利用三维球原理模型建立了吊物系统的摆动模型. Trabiat和Bockstedte等[10~11]研究了海上起重作业的控制方法和策略.所有这些研究,大多都是对于起重作业过程中吊物系统数学模型的研究,没有综合考虑实际起重作业过程中船舶动力定位系统、压载系统、起重船实时操纵、海况等条件与吊物系统之间的相互影响关系.
本文以“海洋石油201”船的起重作业过程实时仿真为目标,基于深水起重船特点及其工作环境实测数据,建立了一套海上起重作业的视景仿真系统.基于C++编程实现了仿真系统的软件开发与数据通讯,利用视景仿真平台Quest-3D搭建了三维虚拟场景的驱动,通过起重操纵与三维动态视景相结合实现了身临其境的沉浸感.
1 起重作业视景仿真系统介绍 1.1 海上起重作业介绍起重船结构如图 1所示.
Figure 1
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2018/1/PIC/hebgydxxb-50-1-160-1.jpg)
海上起重系统主要由起重船船体、吊物系统、舱室系统以及目标安装平台构成.舱室系统包括船体的动力定位系统、压载系统以及各种控制和监控系统都设置在舱室系统区域.
海上起重作业的目标安装平台(被吊物)多为大型海上采油平台,用于浅海和深海的石油开采工作,质量多达几千吨.目标安装平台由起重船吊起后,安装到预先放置于海面的导管架上.导管架是承载目标安装平台的空间桁架,导管架由钢桩和张力筋腱预先固定在海床上.
1.2 仿真系统总体功能“海洋石油201”深水起重仿真系统主要由船体运动仿真系统、调载系统、起重控制仿真系统、视景系统、教练员系统、辅助系统6个系统组成,系统结构如图 2所示.
Figure 2
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2018/1/PIC/hebgydxxb-50-1-160-2.jpg)
起重控制系统提供仿真系统的软件操作界面,该界面可以进行参数输入输出以及数据监测,吊物系统数学模型的解算在该部分实现.调载系统根据船体和吊机状态,通过压载水仓的调整来抵消船体的倾覆力和倾覆力矩.船体运动仿真系统,主要用于控制船体的位置和姿态.教练员系统拥有仿真系统最高权限,可设置参数发布指令.船体运动仿真系统、调载系统、起重控制仿真系统、视景系统接收到训练要求后,受训人员开始操纵各类控制台,设备操纵信号通过通过数据采集,输入到各控制系统计算模型中.视景系统接收各起重船和吊物系统的位置和姿态数据实时更新图像显示.
2 起重作业数学模型建立 2.1 起重船运动数学模型海上起重过程中受到水动力、锚泊力、风干扰力以及海浪的干扰力等各种因素[12]的影响,起重船和吊物系统的位置和姿态[13]实时改变. 图 3所示为世界坐标系和随船坐标系.
Figure 3
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2018/1/PIC/hebgydxxb-50-1-160-3.jpg)
选在空间固定不动的惯性坐标系为世界坐标系,世界坐标系下船舶位置和姿态表示为:γ=[x, y, z, ξ, η, ζ]T; 世界坐标系下速度和角速度:κ=[u, v, w, p, q, r]T; 随船坐标系下的力和力矩:τ=[X, Y, Z, K, M, N]T.那么船舶运动数学模型可表达为
$\mathit{\boldsymbol{M\dot \kappa }} + \mathit{\boldsymbol{C}}\left( \mathit{\boldsymbol{\kappa }} \right)\mathit{\boldsymbol{\kappa }} = \mathit{\boldsymbol{\tau }},$ (1)
式中:M是刚体质量矩阵,C是刚体科氏向心力矩阵.
将式(1)根据刚体动力学动量和动量矩定理[14]展开,那么船体在随船坐标系中六自由度运动普遍形式为:
$\left\{ \begin{array}{l}m\left( {\dot u + qw - rv} \right) = X + {X_{{\rm{wind}}}} + {X_{{\rm{wave}}}} + {X_{\rm{T}}},\\m\left( {\dot v + ru - pw} \right) = {Y_{\rm{H}}} + {Y_{{\rm{wind}}}} + {Y_{{\rm{wave}}}} + {Y_{\rm{T}}},\\m\left( {\dot w + pv - qu} \right) = {Z_{\rm{H}}} + {Z_{{\rm{wave}}}} + {Z_{\rm{T}}},\\{I_x}\dot p + \left( {{I_z} - {I_y}} \right)qr = {K_{\rm{H}}} + {K_{{\rm{wave}}}},\\{I_y}\dot q + \left( {{I_x} - {I_z}} \right)rp = {M_{\rm{H}}} + {M_{{\rm{wind}}}} + {M_{{\rm{wave}}}},\\{I_z}\dot r + \left( {{I_y} - {I_x}} \right)pq = {N_{\rm{H}}} + {N_{{\rm{wind}}}} + {N_{{\rm{wave}}}} + {N_{\rm{T}}}.\end{array} \right.$ (2)
式中:m、Ix、Iy、Iz分别为船舶的质量和转动惯量,X、Y、Z、K、M、N表示船舶受到的合力和合力矩,式(2)中下标H、T、wind、wave表示船体受到的水动力、锚泊力、风载荷和波浪载荷.
船体水动力包括惯性类水动力和黏性类水动力,不考虑相互之间的影响,可以将水动力分成两大组:一组为水平面水动力,另一组为升沉与横摇、纵摇水动力.
1) 水平面运动的水动力包含纵向水动力XH、横向水动力YH和艏摇水动力NH:
$\left\{ \begin{array}{l}{X_{\rm{H}}} = - {\lambda _{11}}\dot u + {\lambda _{22}}vr + {X_{\rm{N}}},\\{Y_{\rm{H}}} = - {\lambda _{22}}\dot v - {\lambda _{11}}ur + {Y_{\rm{N}}},\\{N_{\rm{H}}} = - {\lambda _{66}}\dot r + {N_{\rm{N}}}.\end{array} \right.$ (3)
式中:-λ11
黏性流体水动力为[15]:
$\left\{ \begin{array}{l}{X_{\rm{N}}} = {X_{uu}}{u^2} + {X_{vv}}{v^2} + {X_{vr}}vr + {X_{rr}}{r^2},\\{Y_{\rm{N}}} = {Y_v}v + {Y_r}r + {Y_{\left. v \right|\left. v \right|}}\left. v \right|\left. v \right| + {Y_{\left. v \right|\left. r \right|}}\left. v \right|\left. r \right| + {Y_{\left. r \right|\left. r \right|}}\left. r \right|\left. r \right|,\\{N_{\rm{N}}} = {N_v}v + {N_r}r + {N_{\left. r \right|\left. r \right|}}\left. r \right|\left. r \right| + {N_{vvr}}{v^2}r + {N_{vrr}}v{r^2}.\end{array} \right.$ (4)
式(4)中黏性水动力系数由经验公式[16]计算:
${X_{uu}} = - \frac{1}{2}\rho S{C_{\rm{t}}},$ (5)
${X_{vv}} = \frac{1}{2}\rho Ld\left[ {0.4\frac{B}{L} - 0.006\frac{L}{d}} \right],$ (6)
${X_{vr}} = \left( {1.11{C_{\rm{b}}} - 0.07} \right){\lambda _{22}} - {\lambda _{22}},$ (7)
${X_{rr}} = \frac{1}{2}\rho {L^3}d\left( {0.0003\frac{L}{d}} \right),$ (8)
$\begin{array}{l}{Y_v} = - \frac{1}{2}\rho LdV\left( {\frac{{\rm{ \mathsf{ π} }}}{2}\left( {2d/L} \right) + 1.4{C_{\rm{b}}}\frac{B}{L}} \right).\\\;\;\;\;\;\;\left( {1 + 0.67\frac{{{d_{\rm{a}}} - {d_{\rm{f}}}}}{d}} \right),\end{array}$ (9)
${Y_r} = - \frac{{\rm{ \mathsf{ π} }}}{8}\rho LdV\left( {\frac{{2d}}{V}} \right)\left( {1 + 0.8\left( {{d_{\rm{z}}} - {d_{\rm{f}}}} \right)} \right),$ (10)
${Y_{\left. v \right|\left. v \right|}} = \frac{1}{2}\rho Ld\left[ {0.048265 - 6.293\left( {1 - {C_{\rm{b}}}} \right)\frac{d}{B}} \right],$ (11)
${Y_{\left. v \right|\left. r \right|}} = \frac{1}{2}\rho {L^2}d\left[ { - 0.3791 + 1.28\left( {1 - {C_{\rm{b}}}} \right)\frac{d}{B}} \right],$ (12)
${Y_{\left. r \right|\left. r \right|}} = \frac{1}{2}\rho {L^3}d\left[ {0.0045 - 0.445\left( {1 - {C_{\rm{b}}}} \right)\frac{d}{B}} \right],$ (13)
$\begin{array}{l}{N_v} = \frac{1}{2}\rho {L^2}dV\left( {2d/L} \right) \cdot \\\;\;\;\;\;\;\;\;\left( {1 - 0.27\left[ {\frac{{\frac{{\left( {{d_{\rm{a}}} - {d_{\rm{f}}}} \right)}}{d}}}{{\left( {2d/L} \right)/\left( {\frac{{\rm{ \mathsf{ π} }}}{2}\left( {2d/L} \right) + 1.4{C_{\rm{b}}}\frac{B}{L}} \right)}}} \right]} \right),\end{array}$ (14)
$\begin{array}{l}{N_r} = \frac{1}{2}\rho {L^3}dV\left( {0.54\left( {2d/L} \right) - {{\left( {2d/L} \right)}^2}} \right) \cdot \\\;\;\;\;\;\;\;\left( {1 + 0.3\left( {{d_{\rm{a}}} - {d_{\rm{f}}}} \right)/d} \right),\end{array}$ (15)
$\begin{array}{l}{N_{\left. r \right|\left. r \right|}} = \frac{1}{2}\rho {L^4}d\left[ { - 0.0805 + 8.6092{{\left( {{C_{\rm{b}}}\frac{B}{L}} \right)}^2} - } \right.\\\;\;\;\;\;\;\;\;\;\left. {36.9816{{\left( {{C_{\rm{b}}}\frac{B}{L}} \right)}^3}} \right],\end{array}$ (16)
$\begin{array}{l}{N_{vvr}} = \frac{1}{{2V}}\rho {L^3}d\left[ { - 0.42361 - 3.5193{C_{\rm{b}}}\frac{B}{L} + } \right.\\\;\;\;\;\;\;\;\;\;\left. {135.4668{{\left( {{C_{\rm{b}}}\frac{B}{L}} \right)}^2} - 686.3107{{\left( {{C_{\rm{b}}}\frac{B}{L}} \right)}^3}} \right],\end{array}$ (17)
${N_{vrr}} = \frac{1}{{2V}}\rho {L^4}d\left[ {0.05877 - 0.43958{C_{\rm{b}}}\frac{d}{B}} \right].$ (18)
式(5)~(18)中:Ct为中横剖面系数,S为中横剖面面积,da、df为船体的首尾吃水深度,ρ为海水密度,V为船速,d、B和L分别为平均吃水深度、船宽和船舶水线间长,Cb为船体方形系数,m为船体质量.
2) 升沉水动力ZH与横摇水动力KH、纵摇水动力MH表达式为
${Z_{\rm{H}}} = - {\lambda _{33}}\dot w - {Z_w}w - {Z_{\dot q}}\dot q - {Z_q}q - {Z_\theta }\theta - {Z_z}z,$
${K_{\rm{H}}} = - {\lambda _{44}}\dot p - 2{L_p}p - {V_\delta } \cdot {G_M} \cdot \sin \varphi - {Y_{\rm{H}}} \cdot {z_{\rm{H}}},$
${M_{\rm{H}}} = - {\lambda _{55}}\dot q - {M_q}q - {M_\theta }\theta - {M_{\dot w}}\dot w - {M_w}w.$
式中:-λ44
2.2 吊物系统数学模型 2.2.1 起重坐标系图 4所示为起重系统坐标系.坐标系均采用垂直轴沿垂线向上的右手坐标系[17].
Figure 4
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2018/1/PIC/hebgydxxb-50-1-160-4.jpg)
空间固定不动的世界坐标系OnXnYnZn; 随船移动的随船坐标系OXYZ; 船体坐标系O0X0Y0Z0; 起重机坐标系O1X1Y1Z1.为便于分析载荷的摆动运动,在吊臂尾部端点建立右手直角坐标系PX2Y2Z2; 为了研究风载对吊物运动姿态的影响,在载荷中心处上建立姿态坐标系QX3Y3Z3,与被吊物固定在一起.
2.2.2 吊物运动方程被吊物系统受力分析见图 5.点P和Q分别代表吊臂顶端和吊物,L代表绳长.
Figure 5
![点击查看原图](http://hit.alljournals.cn/html/hitxb_cn/2018/1/PIC/hebgydxxb-50-1-160-5.jpg)
起重机坐标系原点在世界坐标系系下的坐标为
$\left[ {\begin{array}{*{20}{c}}{{x_1}}\\{{y_1}}\\{{z_1}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0&0&0&{{z_{01}}}&{ - {y_{01}}}\\0&1&0&{ - {z_{01}}}&0&{{x_{01}}}\\0&0&1&{{y_{01}}}&{ - {x_{01}}}&0\end{array}} \right]\left\{ \mathit{\boldsymbol{\gamma }} \right\}.$
式中(x01, y01, z01)是点O1在船体坐标系的坐标; {γ}是船体六自由度运动向量.
在船体坐标系中吊臂端点P的位置为
$\left[ {\begin{array}{*{20}{c}}{{x_P}}\\{{y_P}}\\{{z_P}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{x_1} + \left( {\rho \cos \alpha + a} \right)\cos \beta }\\{{y_1} + \left( {\rho \cos \alpha + a} \right)\sin \beta }\\{{z_1} + \rho \sin \alpha + b}\end{array}} \right].$
式中:ρ是起重机吊臂长度,α为起重臂的俯仰角,β为吊臂旋转角.
在随船坐标系中载荷重心点Q的坐标为
$\left[ {\begin{array}{*{20}{c}}{{x_Q}}\\{{y_Q}}\\{{z_Q}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{x_P} + L\sin \theta \cos \varphi }\\{{y_P} + L\sin \varphi }\\{{z_P} - L\cos \theta \cos \varphi }\end{array}} \right].$
式中:L为吊索长度,φ为吊索在X2PZ2平面内的投影与吊索的夹角,θ为吊索在X2PZ2平面内的投影与Z2轴之间的夹角.
根据受力分析得吊物运动方程为
$\left[ {\begin{array}{*{20}{c}}{m{{\ddot x}_Q}}\\{m{{\ddot y}_Q}}\\{m{{\ddot z}_Q}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - T\sin \theta \cos \varphi + {F_{\rm{w}}}\cos {\alpha _1}\sin \theta \cos \varphi }\\{ - T\sin \varphi - {F_{\rm{w}}}\sin {\alpha _1}\sin \varphi }\\{T\cos \theta \cos \varphi - mg}\end{array}} \right].$ (19)
式中:m为被吊物质量,T为吊绳张力,Fw为被吊物所受风载荷力.
考虑吊物摆动运动过程中的阻尼现象[18],将吊物运动方程组里加入阻尼项2ζωn
$\ddot \theta - \left( {2\dot \varphi \varphi - \frac{{2\dot L}}{L} - 2\zeta {\omega _{\rm{n}}}} \right)\dot \theta + \left( {\frac{{{{\ddot z}_p}}}{L} + \frac{g}{L}} \right)\theta - \frac{{{{\ddot x}_p}}}{L} = 0,$
$\ddot \varphi - \left( {\frac{{2\dot L}}{L} + 2\zeta {\omega _{\rm{n}}}} \right)\dot \varphi + \left( {{{\dot \theta }^2} + \frac{{{{\ddot x}_p}\theta }}{L} + \frac{{{{\ddot z}_p}}}{L} + \frac{g}{L}} \right)\varphi - \frac{{{{\ddot y}_p}}}{L} = 0.$
式中:ζ为无因次阻尼比,ζ=
2.2.3 压载响应数学模型根据吊物系统受力分析(19)得到吊绳张力:
$\begin{array}{l}T = m{{\ddot z}_P}\cos \theta \cos \varphi - m{{\ddot y}_P}\sin \varphi - m{{\ddot x}_P}\sin \theta \cos \varphi - \\\;\;\;\;\;\;m\ddot L + mL{{\dot \theta }^2}{\cos ^2}\varphi + mL{{\dot \varphi }^2} + mg\cos \theta \cos \varphi + \\\;\;\;\;\;\;{F_{\rm{w}}}\left( {\cos {\alpha _1}\sin \theta \cos \varphi - \sin {\alpha _1}\sin \varphi } \right).\end{array}$
根据吊物系统的吊臂尾部端点P的受力分析可推导出吊物系统对船体的作用力和力矩:
$\left\{ \begin{array}{l}{F_x} = - T\sin \theta \cos \varphi + {F_{\rm{w}}}\cos {\alpha _1}\sin \theta \cos \varphi ,\\{F_y} = T\sin \varphi + {F_{\rm{w}}}\sin {\alpha _1}\sin \varphi ,\\{F_z} = - T\cos \theta \cos \varphi ,\\{M_x} = {F_z}{y_P} - {F_y}{z_P},\\{M_y} = {F_x}{z_P} - {F_z}{x_P},\\{M_z} = {F_y}{x_P} - {F_x}{y_P}.\end{array} \right.$ (20)
压载水箱的水移动量根据式(20)和压载舱尺寸得到
$V = {M_y}/\left( {sg{\rho _{\rm{w}}}} \right).$
式中:s为压载舱的中心到船体纵垂面距离,g为重力加速度,ρw为海水密度.
3 视景仿真案例分析 3.1 仿真算法仿真系统在保证算法准确的前提下,计算速度必须满足实时性[21]的要求.吊物系统模型为二阶非线性偏微分方程组,所以利用高阶微分方程的布利斯近似积分法[22]对吊物系统进行迭代求解. 首先给定方程组的近似初始值(x0,y0),取固定步长h>0,可以逐步地求出未知函数yv=y(xv)以及其导数yv′=y′(xv),yv″=y″(xv),首先根据给定初值解算出v=1,…,5时的值.
根据泰勒公式近似得到
${y_v} = {y_{v - 1}} + h{{y'}_{v - 1}} + \frac{{{h^2}}}{2}{{y''}_{v - 1}},$
${{y'}_v} = {{y'}_{v - 1}} + h{{y''}_{v - 1}}.$
当v=5时,将方程二阶导数的值按照泰勒公式来表示, 可得到近似解:
$\begin{array}{l}{y_5} \approx {y_0} + 5h{{y'}_0} + 25\frac{{{h^2}}}{{2!}}{{y''}_0} + 90\frac{{{h^3}}}{{3!}}{{y''}_0} + \\\;\;\;\;\;\;\;420\frac{{{h^4}}}{{4!}}y_0^{\left( 4 \right)} + 1920\frac{{{h^5}}}{{5!}}y_0^{\left( 5 \right)} + 8790\frac{{{h^6}}}{{6!}}y_0^{\left( 6 \right)}.\end{array}$
方程真正的解可由泰勒公式直接给出:
$\begin{array}{l}{\eta _5} = {y_0} + 5h{{y'}_0} + 25\frac{{{h^2}}}{{2!}}{{y''}_0} + 125\frac{{{h^3}}}{{3!}}{{y''}_0} + \\\;\;\;\;\;\;\;625\frac{{{h^4}}}{{4!}}y_0^{\left( 4 \right)} + 3125\frac{{{h^5}}}{{5!}}xy_0^{\left( 5 \right)} + 15625\frac{{{h^6}}}{{6!}}y_0^{\left( 6 \right)}.\end{array}$
为得到真正的值,必须对近似值增加修正:
$\begin{array}{l}{\delta ^ * } = {\eta _5} - {y_5} = 35\frac{{{h^3}}}{{3!}}y_0^{\left( 3 \right)} + 205\frac{{{h^4}}}{{4!}}y_0^{\left( 4 \right)} + \\\;\;\;\;\;\;\; \cdots + 6835\frac{{{h^6}}}{{6!}}y_0^{\left( 6 \right)}.\end{array}$
为避免高阶导数,用δ替换δ*
$\delta = {{\bar y}_5} - {y_5} = \frac{5}{{24}}\frac{{{h^2}}}{{2!}}\left( {9{{y''}_4} + 20{{y''}_1} - 29{{y''}_0}} \right).$
相应的在y′上的修正量为
$\varepsilon = {{\bar y'}_5} - {{y'}_5} = \frac{h}{{24}}\left( {11{{y''}_5} + 5{{y''}_1} - 16{{y''}_0}} \right).$
下一步计算是在近似解y5和y5′上添加修正量δ和ε,然后用x5代替x0,对微分方程继续迭代求解.
3.2 仿真案例 3.2.1 仿真案例的作业工况起重仿真系统是基于“海洋石油201”起重船的实际数据建立的.起重船全长为204.6 m,最高航速6.2 m/s,采用DP3动力定位系统,最大起吊能力为4 000 t.
起重仿真作业过程是对2 400 t的海上平台进行安装,根据“海洋石油201”船实际作业工况与海况资料,制定了两种不同海况级别的仿真案例.作业海况和工况参数如表 1所示.
表 1
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起吊开始 起吊完成 卸载开始 卸载完成
工况1 7.5 50 2 0.31 22.5 8 2 400 0.105 0.010 2.2 150 180 620 650
工况2 15.0 50 4 0.62 22.5 12 2 400 0.105 0.010 2.2 150 180 620 650
表 1 作业工况参数 Table 1 The working condition parameters
3.2.2 起重视景仿真工艺流程为了确保仿真系统的可靠性,起重仿真案例是根据实际海上平台吊装作业的工艺过程制定的.
具体的起重仿真工艺过程如下:
1) 根据导管架位置,定位起重船; 2)驳船载被吊物靠近起重船; 3)提升吊臂并旋转180°至船尾; 4)起重船与驳船缆绳连接; 5)操纵吊机运动和吊钩升降,完成被吊物起吊过程; 6)驳船移走; 7)DP系统控制移船靠近导管架; 8)安装平台完毕,卸载吊钩.安装完毕如图 6所示.
Figure 6
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3.2.3 仿真结果分析图 7为在两种不同作业工况下起重船的纵荡、横荡和垂荡随时间变化曲线.
Figure 7
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在图 7(a)和(b)中,180 s后,平台组块被完全吊起,船舶的垂荡明显增大,在650 s之后减小.这是因为船180 s时组块起吊完成,吊物系统会给船舶产生很大的作用力,这个作用力对船体而言,相当于很大的干扰力.在作业工况1下,船舶垂荡的幅值达到1.2 m; 在作业工况2下,船舶垂荡的幅值达到了3.0 m,是工况1的2.5倍.在由工况1变为工况2的过程中,横荡增大了0.65 m,纵荡基本保持不变.
图 8所示为起重船的艏摇、横摇和纵摇随时间的变化.从图 8可以看出,艏摇和纵摇在180 s组块被吊起后时瞬间变大,尤其是纵摇增大特别明显,之后纵摇又慢慢减小.这是因为被吊物吊起后会产生很大的倾覆力矩,让船舶瞬间开始倾斜,然后DP系统马上对船舶姿态进行调节,使得船舶摇荡渐渐趋于稳定.由工况1变为工况2时,船体纵摇从0.008 rad增大到0.023 rad,船体艏摇从0.028 rad增大到0.05 rad,船体横摇基本无变化.
Figure 8
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图 9所示为吊钩偏角为φ和θ随时间变化曲线.在组块被吊起之前,吊钩只有自身的质量,并且初始吊索绳长为3 m,在船舶运动和吊机运动共同影响下,吊钩在仿真系统运行后就产生了较大摆动.在作业工况1下,随着吊钩的下放,吊索长度增加,吊索的摆动角度慢慢减小,在组块吊起之后,θ角有小幅度增加.在组块吊起之前,工况1下的φ角幅值达到0.21 rad,θ角幅值达到0.19 rad; 在第180 s组块被吊起之后,φ角幅值为0.04 rad,θ角幅值为0.09 rad.当由工况1变为工况2时,在组块被吊起之前,φ角幅值达到0.7 rad,θ角幅值达到0.4 rad; 在第180 s组块被吊起之后,φ角幅值为0.47 rad,θ角幅值达到0.6 rad.在尾吊的状态下,海况的增加对于θ角度的影响比对φ影响更加明显.
Figure 9
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图 10所示为船舶受到的反作用力.垂向力变化幅度最大,在组块被吊起之后,垂向力在工况1下达到-2.6×104 kN,在工况2下达到2.95×104 kN.由工况1变为工况2时,横向力幅值由0.05×104 kN变为0.25×104 kN,纵向力基本保持不变.
Figure 10
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图 11为吊索张力随时间的变化曲线.在预加载和卸载过程中,吊索张力基本呈线性变化,在被吊物起吊后,吊索张力在2.4×104 kN左右波动.由工况1变为工况2时,吊索张力幅值由2.75×104 kN变为3.05×104 kN.
Figure 11
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3.3 海试试验对比验证为了对起重仿真系统进行校核与验证,课题组调研人员于2015年7月16日登上“海洋石油201”起重船,全程跟踪了海上采油平台起吊安装作业,作业地点为南海海域.海试基本参数如表 2所示.
表 2
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WZ12-1 2 372.94 2 90 7.5 0.31
表 2 海试参数 Table 2 Parameters of sea trial
起重船位置、姿态数据可以直接由船舶的动力定位系统提供.被吊物的运动位置和姿态,通过调研人员与现场施工人员的目测记录获得.实际的起重作业过程十分漫长,无法获取整个施工作业过程所有的数据.这里提供采油平台被吊起一个小时内的船舶与被吊物的姿态数据,将其与起重仿真系统图 8(a)和9(a)计算结果对比.海试的数据曲线如图 12所示, 为海试过程中记录的船舶摇荡与被吊物姿态角的数据曲线,与仿真系统详细对比结果如表 3所示.
Figure 12
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表 3
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试验 纵摇角 艏摇角 φ θ
仿真 -0.009~0.008 -0.029~0.006 -0.030~0.040 -0.07~0.09
海试 -0.007~0.010 -0.032~0.028 -0.030~0.037 -0.09~0.10
偏差 0.001 0.003 0.003 0.010
表 3 海试试验与仿真系统结果对比 Table 3 Comparison of sea trial results and simulation system
将海试试验与仿真系统结果对比可知,仿真系统偏差保持在10 %以内,满足仿真系统的精度要求,利用仿真系统进行海上起重作业工程预演与人员培训,都是可靠的.
4 结论基于“海洋石油201号”起重船实测数据,综合利用虚拟现实技术、多通道数据交互技术、数值模拟技术,构建了一套深水起重作业的交互式视景仿真系统.针对起重作业过程分别构建了船体运动和吊物系统的数学模型.将动力学模型通过软件技术嵌入仿真系统当中,与仿真系统中的DP系统,压载系统以及视景系统实时通讯.
对不同作业工况下起重作业进行了仿真模拟,得到了船体和吊物系统的受力与运动状态,在仿真和结果分析的基础上,得到以下结论:
1) 船体位置和姿态主要受到海洋环境参数和吊物系统反作用力影响.在进行尾吊起重作业时,船体垂荡和横荡主要受到吊物系统反作用力的影响,纵荡基本无影响.船体纵摇和艏摇受环境影响变化很大.
2) 起重船进行尾吊作业时,吊物摆动角度受工作环境影响很大,其中θ角受环境影响更明显一些.吊索张力增大会减小吊物系统的摆动角度.
3) 海况的改变对起重船受到的反作用力影响较大,吊物系统对船体的垂向力与吊索张力基本上大小相等,方向相反.
深水起重作业视景仿真系统的建立,可为起重作业人员培训和工程预演提供平台.仿真过程中得到的起重作业的相关数据与运动规律,都可以作为海上起重作业的理论参考依据.
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