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Article(id=1243880214418272945, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243880211004113260, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.10.007, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1713974400000, receivedDateStr=2024-04-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774493753293, onlineDateStr=2026-03-26, pubDate=1729353600000, pubDateStr=2024-10-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774493753293, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774493753293, creator=13701087609, updateTime=1774493753293, updator=13701087609, issue=Issue{id=1243880211004113260, tenantId=1146029695717560320, journalId=1240685776644648972, year='2024', volume='28', issue='10', pageStart='1463', pageEnd='1632', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774493752479, creator=13701087609, updateTime=1774494057708, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243881491290243855, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243880211004113260, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243881491290243856, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243880211004113260, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1526, endPage=1540, ext={EN=ArticleExt(id=1243880215223579329, articleId=1243880214418272945, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Experimental study on a semi-submersible platform DP system based on thruster biasing, columnId=1241023037940748650, journalTitle=Journal of Ship Mechanics, columnName=Hydrodynamics, runingTitle=null, highlight=null, articleAbstract=

For semi-submersible platforms equipped with dynamic positioning (DP) system, which has a small water-plane area and low metacentric height, vertical motion (roll, pitch, heave) will be affected by the normal control force of the thrusters. In light of this, this paper proposes a novel thrust allocation method based on thruster biasing, which aims to suppress the vertical motion and ensure the positioning accuracy of the horizontal motion. Model scale tests are conducted for the dynamic positioning of a semi-submersible platform in the ocean wave basin, to analyze and compare the six-degree-of-freedom motion responses under different environmental loads and thruster biasing configurations. The results show that the thruster biasing strategy can ensure the ability of station-keeping and significantly reduce the response amplitude near the natural frequency of the vertical motion of the platform, the reduction of the power spectrum peak is up to 54.7% under the given test cases, while the vertical motion in the wave-frequency is unaffected. The research results give a novel idea for the control of semi-submersible platform vertical motion.

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半潜式平台在进行动力定位作业时，由于其水线面面积较小而初稳性高较低，其垂向运动（横摇、纵摇、垂荡）易受到推进器法向力作用的影响。基于此，提出一种基于推进器偏置的推力分配模式，旨在合理利用推进器的法向力抑制平台垂向运动，而不影响平台水平面定位功能。在海洋工程水池开展半潜式平台的动力定位模型试验，对比和分析不同载荷工况及推进器偏置模式下平台的六自由度运动响应。结果表明，推进器偏置策略能够基本保证水平面定位精度，并显著减小平台垂向运动在其固有频率附近的响应幅值，在该试验工况下，功率谱密度（PSD）峰值减小高达54.7%，对波频区间的运动影响则较小。该研究结果可为半潜平台垂向运动抑制提供新思路。

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通讯作者，E-mail：
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唐利纲（1996-），男，博士研究生

王一听（1993-），男，博士，通讯作者，E-mail：。

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唐利纲（1996-），男，博士研究生

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唐利纲（1996-），男，博士研究生

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王一听（1993-），男，博士，通讯作者，E-mail：。

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王一听（1993-），男，博士，通讯作者，E-mail：。

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figureFileBig=ddU/J8C5SXfY8htHh/zBuQ==, tableContent=null), ArticleFig(id=1243880227504500958, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Fig.17, caption=Time traces of the vertical motion of the semi-submersible under 135° heading angle in Bias Mode 2, figureFileSmall=/wd1nd2vh6lhgesKguTWUg==, figureFileBig=HziWvcuj+gMwujisNb+e7w==, tableContent=null), ArticleFig(id=1243880227617747169, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=图17, caption=135°艏向角-偏置模式2工况平台运动时历, figureFileSmall=/wd1nd2vh6lhgesKguTWUg==, figureFileBig=HziWvcuj+gMwujisNb+e7w==, tableContent=null), ArticleFig(id=1243880227701633255, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Fig.18, caption=Time traces of the vertical motion of the semi-submersible under 135° heading angle in Biasing Mode 3, figureFileSmall=VjSPBXtgQp/6qZW0gkjerw==, figureFileBig=EezYO8Qvp9GjmXno0fDKcQ==, tableContent=null), ArticleFig(id=1243880227793907948, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=图18, caption=135°艏向角-偏置模式3工况平台运动时历, figureFileSmall=VjSPBXtgQp/6qZW0gkjerw==, figureFileBig=EezYO8Qvp9GjmXno0fDKcQ==, tableContent=null), ArticleFig(id=1243880227852628208, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Fig.19, caption=Power spectrum of roll motion under 135° heading angle, figureFileSmall=UUptXyqIgA4qHmjebZaMMg==, figureFileBig=nkAC7Sp6MJI4QE+e/N2iSw==, tableContent=null), ArticleFig(id=1243880227932319988, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=图19, caption=135°艏向角工况下平台横摇运动功率谱密度, figureFileSmall=UUptXyqIgA4qHmjebZaMMg==, figureFileBig=nkAC7Sp6MJI4QE+e/N2iSw==, tableContent=null), 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journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=图21, caption=135°艏向角工况下平台垂荡运动功率谱密度, figureFileSmall=abPXZ0UsB6x6qZNyunPz3Q==, figureFileBig=qkKKTJcEp2HOkvxC5BfgLw==, tableContent=null), ArticleFig(id=1243880228406276362, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Fig.22, caption=Time traces of the speed of the semi-submersible thruster under 90° heading angle, figureFileSmall=ExOJ3RvE8GV0tcSWk/PmNQ==, figureFileBig=OXUT0/iXkNi+MplSO8O4Jw==, tableContent=null), ArticleFig(id=1243880228515328270, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=图22, caption=90°艏向角工况下平台推进器转速时历曲线（模型值）, figureFileSmall=ExOJ3RvE8GV0tcSWk/PmNQ==, figureFileBig=OXUT0/iXkNi+MplSO8O4Jw==, tableContent=null), ArticleFig(id=1243880228636963088, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.1, caption=

Properties of the semi-submersible platform

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
排水量/t74270.8重心垂向坐标（距基线）/m28.9
吃水/m23横摇惯性半径/m35.6
重心纵向坐标（距中线）/m0纵摇惯性半径/m34.5
重心横向坐标（距中线）/m0艏摇惯性半径/m38.5
), ArticleFig(id=1243880228737626384, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表1, caption=

半潜平台参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
排水量/t74270.8重心垂向坐标（距基线）/m28.9
吃水/m23横摇惯性半径/m35.6
重心纵向坐标（距中线）/m0纵摇惯性半径/m34.5
重心横向坐标（距中线）/m0艏摇惯性半径/m38.5
), ArticleFig(id=1243880228838289687, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.2, caption=

Layout of azimuth thrusters

, figureFileSmall=null, figureFileBig=null, tableContent=
推进器编号 X/m Y/m Z/m（距基线）推进器编号 X/m Y/m Z/m（距基线）
T147.6329.22-2.75T5-47.63-29.22-2.75
T221.02539.375-2.75T6-21.025-39.375-2.75
T3-21.02539.375-2.75T721.025-39.375-2.75
T4-47.6329.22-2.75T847.63-29.22-2.75
), ArticleFig(id=1243880228926370075, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表2, caption=

推进器布置位置

, figureFileSmall=null, figureFileBig=null, tableContent=
推进器编号 X/m Y/m Z/m（距基线）推进器编号 X/m Y/m Z/m（距基线）
T147.6329.22-2.75T5-47.63-29.22-2.75
T221.02539.375-2.75T6-21.025-39.375-2.75
T3-21.02539.375-2.75T721.025-39.375-2.75
T4-47.6329.22-2.75T847.63-29.22-2.75
), ArticleFig(id=1243880229010256157, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.3, caption=

Parameters of the irregular waves

, figureFileSmall=null, figureFileBig=null, tableContent=
类型项目数值方向
不规则波
（Jonswap谱）		有义波高/m3.5
谱峰周期/s9.545°/90°
谱峰因子γ2
), ArticleFig(id=1243880229085753632, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表3, caption=

不规则波参数

, figureFileSmall=null, figureFileBig=null, tableContent=
类型项目数值方向
不规则波
（Jonswap谱）		有义波高/m3.5
谱峰周期/s9.545°/90°
谱峰因子γ2
), ArticleFig(id=1243880229169639715, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.4, caption=

Motion deviation statistics of the semi-submersible under 90° heading angle

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式3
纵荡运动最大值/m5.33305.36326.7740
纵荡运动最小值/m-6.8568-5.6960-8.6403
纵荡运动标准差/m2.01192.12693.6876
横荡运动最大值/m5.50902.31645.5218
横荡运动最小值/m-18.2883-17.8461-19.3114
横荡运动标准差/m5.34775.11776.4159
艏摇运动最大值/°11.099812.83507.7427
艏摇运动最小值/°-11.5324-10.9864-11.3712
艏摇运动标准差/°4.29553.88063.3410
), ArticleFig(id=1243880229249331496, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表4, caption=

90°艏向角下平台水平面运动偏差统计值

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式3
纵荡运动最大值/m5.33305.36326.7740
纵荡运动最小值/m-6.8568-5.6960-8.6403
纵荡运动标准差/m2.01192.12693.6876
横荡运动最大值/m5.50902.31645.5218
横荡运动最小值/m-18.2883-17.8461-19.3114
横荡运动标准差/m5.34775.11776.4159
艏摇运动最大值/°11.099812.83507.7427
艏摇运动最小值/°-11.5324-10.9864-11.3712
艏摇运动标准差/°4.29553.88063.3410
), ArticleFig(id=1243880229358383403, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.5, caption=

Motion deviation statistics of the semi-submersible under 135° heading angle

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式2偏置模式3
纵荡运动最大值/m8.59257.60788.69068.1754
纵荡运动最小值/m-9.3340-9.4361-11.0998-11.7016
纵荡运动标准差/m3.39303.28134.35183.5154
横荡运动最大值/m8.905410.02456.46265.2246
横荡运动最小值/m-9.4080-13.1503-8.0072-8.8279
横荡运动标准差/m4.10235.32092.83102.6993
艏摇运动最大值/°10.02129.20279.35607.7593
艏摇运动最小值/°-11.7824-13.8997-10.0050-7.8291
艏摇运动标准差/°4.69594.97374.24892.7132
), ArticleFig(id=1243880229467435312, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表5, caption=

135°艏向角下平台水平面运动偏差统计值

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式2偏置模式3
纵荡运动最大值/m8.59257.60788.69068.1754
纵荡运动最小值/m-9.3340-9.4361-11.0998-11.7016
纵荡运动标准差/m3.39303.28134.35183.5154
横荡运动最大值/m8.905410.02456.46265.2246
横荡运动最小值/m-9.4080-13.1503-8.0072-8.8279
横荡运动标准差/m4.10235.32092.83102.6993
艏摇运动最大值/°10.02129.20279.35607.7593
艏摇运动最小值/°-11.7824-13.8997-10.0050-7.8291
艏摇运动标准差/°4.69594.97374.24892.7132
), ArticleFig(id=1243880229584875828, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.6, caption=

Statistics of the vertical motions of the semi-submersible in different biasing modes under 90° heading angle

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式3
横摇运动最大值/°2.66712.14591.8572
横摇运动最小值/°-3.3201-3.3105-2.8144
横摇运动标准差/°0.79070.67220.6734
纵摇运动最大值/°1.28741.11001.1450
纵摇运动最小值/°-0.3335-0.0409-0.1123
纵摇运动标准差/°0.19830.15520.1901
垂荡运动最大值/m1.00340.94010.8380
垂荡运动最小值/m-0.9482-0.7765-0.8424
垂荡运动标准差/m0.23710.21220.2273
), ArticleFig(id=1243880229681344825, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表6, caption=

90°艏向角-不同偏置模式下平台垂向运动统计值

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式3
横摇运动最大值/°2.66712.14591.8572
横摇运动最小值/°-3.3201-3.3105-2.8144
横摇运动标准差/°0.79070.67220.6734
纵摇运动最大值/°1.28741.11001.1450
纵摇运动最小值/°-0.3335-0.0409-0.1123
纵摇运动标准差/°0.19830.15520.1901
垂荡运动最大值/m1.00340.94010.8380
垂荡运动最小值/m-0.9482-0.7765-0.8424
垂荡运动标准差/m0.23710.21220.2273
), ArticleFig(id=1243880229752647996, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.7, caption=

Statistics of the vertical motions of the semi-submersible in different bias modes under 135° heading angle

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式2偏置模式3
横摇运动最大值/°2.50342.45082.49152.1862
横摇运动最小值/°-1.7095-1.5688-1.5489-1.2574
横摇运动标准差/°0.59520.51430.57600.4762
纵摇运动最大值/°2.62502.37242.19302.2228
纵摇运动最小值/°-2.3241-2.1286-1.9616-2.7584
纵摇运动标准差/°0.64440.62080.53030.6546
垂荡运动最大值/m0.89860.75640.86090.7973
垂荡运动最小值/m-0.8215-0.8332-0.7337-0.7182
垂荡运动标准差/m0.21750.20200.20580.2000
), ArticleFig(id=1243880229861699902, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表7, caption=

135°艏向角-不同偏置模式下平台垂向运动统计值

, figureFileSmall=null, figureFileBig=null, tableContent=
无偏置模式偏置模式1偏置模式2偏置模式3
横摇运动最大值/°2.50342.45082.49152.1862
横摇运动最小值/°-1.7095-1.5688-1.5489-1.2574
横摇运动标准差/°0.59520.51430.57600.4762
纵摇运动最大值/°2.62502.37242.19302.2228
纵摇运动最小值/°-2.3241-2.1286-1.9616-2.7584
纵摇运动标准差/°0.64440.62080.53030.6546
垂荡运动最大值/m0.89860.75640.86090.7973
垂荡运动最小值/m-0.8215-0.8332-0.7337-0.7182
垂荡运动标准差/m0.21750.20200.20580.2000
), ArticleFig(id=1243880229958168896, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=EN, label=Tab.8, caption=

Statistics of power in different bias modes under 90° heading angle

, figureFileSmall=null, figureFileBig=null, tableContent=
艏向角参数无偏置模式偏置模式1偏置模式3
功率最大值/kW8453.97198731.56089380.2113
90°功率平均值/kW4442.17765201.57746059.7893
功率标准差/kW2127.74472048.95331976.9966
), ArticleFig(id=1243880230016889154, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243880214418272945, language=CN, label=表8, caption=

90°艏向角工况不同偏置模式下消耗功率统计值

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功率最大值/kW8453.97198731.56089380.2113
90°功率平均值/kW4442.17765201.57746059.7893
功率标准差/kW2127.74472048.95331976.9966
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基于推进器偏置的半潜式平台动力定位模型试验研究
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唐利纲 1, 2 , 王磊 1, 2 , 贺华成 1 , 王一听 1
船舶力学 | 流体力学 2024,28(10): 1526-1540
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船舶力学 | 流体力学 2024, 28(10): 1526-1540
基于推进器偏置的半潜式平台动力定位模型试验研究
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唐利纲1, 2, 王磊1, 2, 贺华成1, 王一听1
作者信息
  • 1.上海交通大学　海洋工程国家重点实验室，上海　200240
  • 2.上海交通大学　三亚崖州湾深海科技研究院，海南　三亚　572000

    • 唐利纲（1996-），男，博士研究生

    王一听（1993-），男，博士，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Experimental study on a semi-submersible platform DP system based on thruster biasing
Li-gang TANG1, 2, Lei WANG1, 2, Hua-cheng HE1, Yi-ting WANG1
Affiliations
  • 1.State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2.SJTU-Sanya Yazhou Bay Institute of Deepsea Science and Technology, Sanya 572000, China
出版时间: 2024-10-20 doi: 10.3969/j.issn.1007-7294.2024.10.007
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摘要
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半潜式平台在进行动力定位作业时，由于其水线面面积较小而初稳性高较低，其垂向运动（横摇、纵摇、垂荡）易受到推进器法向力作用的影响。基于此，提出一种基于推进器偏置的推力分配模式，旨在合理利用推进器的法向力抑制平台垂向运动，而不影响平台水平面定位功能。在海洋工程水池开展半潜式平台的动力定位模型试验，对比和分析不同载荷工况及推进器偏置模式下平台的六自由度运动响应。结果表明，推进器偏置策略能够基本保证水平面定位精度，并显著减小平台垂向运动在其固有频率附近的响应幅值，在该试验工况下，功率谱密度（PSD）峰值减小高达54.7%，对波频区间的运动影响则较小。该研究结果可为半潜平台垂向运动抑制提供新思路。

推进器偏置  /  动力定位  /  半潜式平台  /  模型试验  /  垂向运动

For semi-submersible platforms equipped with dynamic positioning (DP) system, which has a small water-plane area and low metacentric height, vertical motion (roll, pitch, heave) will be affected by the normal control force of the thrusters. In light of this, this paper proposes a novel thrust allocation method based on thruster biasing, which aims to suppress the vertical motion and ensure the positioning accuracy of the horizontal motion. Model scale tests are conducted for the dynamic positioning of a semi-submersible platform in the ocean wave basin, to analyze and compare the six-degree-of-freedom motion responses under different environmental loads and thruster biasing configurations. The results show that the thruster biasing strategy can ensure the ability of station-keeping and significantly reduce the response amplitude near the natural frequency of the vertical motion of the platform, the reduction of the power spectrum peak is up to 54.7% under the given test cases, while the vertical motion in the wave-frequency is unaffected. The research results give a novel idea for the control of semi-submersible platform vertical motion.

thruster biasing  /  dynamic positioning  /  semi-submersible platform  /  model test  /  vertical motion
唐利纲, 王磊, 贺华成, 王一听. 基于推进器偏置的半潜式平台动力定位模型试验研究. 船舶力学, 2024 , 28 (10) : 1526 -1540 . DOI: 10.3969/j.issn.1007-7294.2024.10.007
Li-gang TANG, Lei WANG, Hua-cheng HE, Yi-ting WANG. Experimental study on a semi-submersible platform DP system based on thruster biasing[J]. Journal of Ship Mechanics, 2024 , 28 (10) : 1526 -1540 . DOI: 10.3969/j.issn.1007-7294.2024.10.007
正文
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0　引言
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动力定位（DP）系统的成本不随水深增加，并能在限制水域或恶劣海况下实现高精度定位，因而在深海资源的开采领域得到了广泛的应用[1]。在DP系统设计过程中，通常只将水平面内的三自由度运动（纵荡、横荡和艏摇）作为控制目标，而不考虑船舶垂向运动（垂荡、横摇和纵摇）。剧烈的船舶摇荡，会严重影响船舶操纵性，造成甲板上浪、拍底等诸多问题，并对船员的日常工作及船载设备的正常使用带来一定的影响[2]。
对于水线面较小，横稳心高较低的半潜式船舶，其静回复力相对于惯性力较小，因而垂向运动易受DP系统控制作用的影响。Sørensen等[3]最早发现位于平台底部的推进器在动力定位作业时，会显著增大平台的横摇和纵摇运动幅值。这是由于平台的横摇和纵摇固有频率较低，与DP系统水平控制力的固有频率相接近，从而增大了横摇-横荡及纵摇-纵荡的耦合运动响应。Sørensen等[4]随后提出了一种五自由度控制策略，在传统三自由度控制器的基础上，引入低频横摇和纵摇角速度的反馈，通过增大系统的阻尼来抑制响应幅值。Xu[5]和He[6]等则进一步考虑引入了纵摇加速度及幅值的反馈，提出了惯性控制和比例控制，取得了较好的控制效果。上述研究主要利用推进器的轴向力（推力）实现减摇功能，然而在推力系统实际工作过程中，当推进器的进速与轴线成一偏置角度时，除了产生轴向力以外，还会产生垂直于轴线的法向力，其方向始终从桨叶的迎流侧指向背流侧[7]。Stettler[7]和Islam等[8]对全回转推进器在不同进速和不同攻角下的推力系数进行了全方位的试验测量，结果表明在一定的进速下，推进器的法向力随攻角的增大而增大，近似呈线性关系。Rudaa等[9]和Lee等[10]随后基于全回转推进器的这一特性设计了减摇控制器，利用推进器产生的横倾力矩抑制横摇运动。Couce等[11]将推进器的法向力应用于拖轮减速领域，当航速在8节以上时，通常会设置拖轮进入侧向减速模式，效果比直接利用推进器的轴向推力更为有效，其制动力可达最大系柱推力的2.5倍，显现出利用法向力进行垂向运动控制的巨大潜力。在DP系统中，侧向减速模式又称为推进器偏置模式[12-14]，即在一组全回转推进器中，推进器的推力互相抵消一部分，而整组推进器的合力保持不变。据Kongsberg公司[15]对其动力定位系统K-Pos的描述，当推进器无法输出零推力、需要较大的功率消耗或环境力方向频繁变化时，会设置推进器进入偏置模式，推进器偏置能改善船舶的操纵性，提高系统的动态性能和定位精度，同时增加系统的阻尼，但并未对其机理给出过多解释。工程实践中也同样可以观测到偏置模式下船舶垂向运动减小的现象，但其中影响机制尚不清晰，推进器偏置策略对垂向运动的影响也需进一步探讨。
实际上，在推进器进入偏置模式后，由于船舶的摇荡运动，螺旋桨盘面处的进速将不再平行于轴线，而是成一定夹角，由此引起的法向力具有一定的垂向分量，对小水线面船舶垂向运动的影响不可忽略。因此，合理地使用推进器偏置产生的法向力，就能在不影响水平面定位精度的前提下，减小船舶的垂向运动。现阶段针对推进器法向力的研究集中于水平面方向，本文首次将其从水平面推广至垂直面，提出基于推进器偏置的垂向运动抑制方法。以一座半潜式平台为研究对象，根据平台推进器的布置形式和外部载荷的作用方向提出三种偏置模式，旨在合理利用偏置推进器产生的法向力抑制平台的垂向运动，并同时保证DP系统的水平面定位功能。针对推进器偏置模式下的平台运动特性，在海洋工程水池中开展模型试验研究，探究不规则波条件下动力定位平台在不同偏置模式下的六自由度运动响应，揭示推进器偏置对平台垂向运动的影响机制。
1　推进器偏置模型
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1.1　轴向力和法向力
全回转推进器在任意进速下的推力如图1所示。假定推进器固定，而流体自远前方以速度Va流向推进器。进速Va与推进器轴线的夹角δ称为有效攻角，其与推进器的方位角、船舶运动和流体速度有关[7]。
全回转推进器除了产生轴向力（即推力）FT，还会在垂直于轴线的方向上产生法向力FN，无论推进器是正转或反转，法向力的方向始终从桨叶的迎流侧指向背流侧。轴向力和法向力的大小可以通过下式表达：
式中，ρ为流体密度，n为推进器的转速，D为螺旋桨的直径，KT和KN分别为推进器的轴向力系数和法向力系数，δ为有效攻角，J为进速系数。
1.2　推进器偏置模式
偏置的概念最早由Kongsberg公司[15]提出，并在DP系统的推力分配中进行了应用。其基本思路是对全回转推进器进行分组，然后使组间推进器的推力相互抵消一部分或完全抵消，从而能够通过调节推力实现正向或是负方向的合力，而不需要转动螺旋桨，以此提升系统的动态性能和定位精度。以一座配备八个全回转推进器的半潜式平台为例进行说明，如图2所示，T1∼T8为八个全回转推进器，推进器的期望推力为200 kN，沿Y轴负方向。不考虑推进器偏置时，假定合力平均分配至每个推进器，则各推进器的推力为25 kN，沿Y轴负方向。现在设定T2和T7、T3和T6为两个推进器偏置组，偏置量的大小为25 kN，经过推力偏置后，T2和T3的推力将变为75 kN，方向不变。T7和T6的推力仍为25 kN，但方向变为沿Y轴正方向。在该模式下偏置推进器能够提供一定的水平合力，共同抵抗波浪力及力矩。为了能够进一步分析偏置模式下推进器法向力对平台垂向运动的影响，我们对偏置模式进行了简化，使偏置组内推进器轴向力完全抵消，从而排除偏置推进器推力对平台垂向运动的影响。本文根据平台推进器的布置形式和外部载荷的作用方向，提出如图3所示三种偏置模式，其中外侧的四个推进器T1、T4、T5和T8参与推力分配，用于控制平台在水平面内的运动。偏置模式下，T2和T7、T3和T6产生大小相等、方向相反的偏置力，推力方向如箭头所示，且方向固定。当不采取偏置模式时，按照推力最优分配原则，内侧的四个推进器停止工作，本文将其表示为“无偏置模式”。需要说明的是，本文所述的无偏置模式并不是严格意义上的无偏置模式（即8个全回转推进器皆不存在偏置力的情况）。实际上，在进行推力分配时，由于全回转推进器方位角变化速率限制，偏置现象是普遍存在的。因此，本文所定义的无偏置模式仅针对在进行推力分配时是否考虑偏置力而言，在这里我们将其与传统意义上的无偏置模式相区别开来。由于此时偏置推进器的轴向力互相抵消，不改变控制器的合力，对比有无偏置的情况，就能确定推进器偏置的作用。
1.3　偏置推进器法向力
以偏置模式1为例，分析不同垂向运动下偏置推进器法向力产生机理。由于螺旋桨盘面处的流体进速受平台的六自由度运动、波浪和海流等多方面因素的影响，本文假设在DP系统的作用下，平台在水平面内的三自由度运动为小量，且忽略各自由度运动之间的耦合作用，仅单独考虑由垂向运动引起的法向力。
如图4所示，偏置模式1中，当平台产生逆时针横摇运动p时，根据相对运动原理，螺旋桨盘面处的局部流体方向如Va所示，此时有效攻角为δ，产生的法向力FN3竖直向上，FN6竖直向下，顺时针横摇时，两者相反。偏置推进器产生的法向力将抵抗平台的横摇运动。如图5所示，当平台产生逆时针纵摇运动q时，螺旋桨盘面处的局部流体方向如Va所示，此时有效攻角为δ=90°，产生的法向力FN3斜向上，FN2斜向下，顺时针纵摇时，两者相反。偏置推进器产生的法向力与力臂之间形成的减摇力矩将共同抵抗平台的纵摇运动。图6工况下，当平台进行向上垂荡运动w时，推进器盘面处的局部流体方向如Va所示，此时有效攻角δ=90°，偏置推进器产生等大反向的轴向力FT3、FT6，受Va的影响，偏置推进器将在垂直平面内产生竖直向下的法向力FN3和FN6，共同抵抗平台的垂荡运动，偏置模式2、3与之类似。此外，偏置推进器法向力大小与进速系数、有效攻角以及推进器转速密切相关，其中有效攻角取决于偏置推进器的布置情况，以及回转角等诸多因素。与此同时，偏置推进器对平台垂向运动的抑制作用还受法向力间力臂的限制，不同偏置模式间有效攻角、旋转力臂的差异将进一步影响偏置推进器的作用效果。
与以往的减摇控制方式不同，本文所提出的方法仅需根据载荷方向调整推进器偏置模式即可，不需要对DP系统控制算法做过多更改，且不需要船舶垂向位置信息反馈，能够极大地减小控制算法的复杂度。
2　动力定位模型试验
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2.1　平台参数及海况
试验中选用的半潜式平台主要参数如表1所示，平台配备有8个全回转推进器，最大推力为877.7 kN，推进器的布置位置如表2所示。针对上述提出的推进器偏置模式，在不规则波的条件下开展动力定位模型试验。不规则波的参数如表3所示。本文中给出的所有数值均已换算为实型值（特殊标明除外）。
2.2　动力定位模型试验系统
试验在上海交通大学海洋工程国家重点实验室的深水试验池中进行，其中模型缩尺比为1:50，试验场景如图7所示。对试验过程中所有的测量数据进行实时采集，每个工况下测量时间不少于25 min （相当于实际3小时），以获得足够的数据进行统计分析。
动力定位模型试验系统主要包括以下几个部分：
（1）位置参考系统
试验中采用非接触式光学捕捉系统Qualisys测量平台的六自由度运动，在水池岸边布置两个红外摄像机，并在平台甲板上方固定若干反光灯球，依据灯球和平台重心的相对位置即可推算出平台的实时运动。试验中采样频率为50 Hz，测量精度达微米级。
（2）动力定位控制系统
控制系统以1 Hz的频率接收位置参考系统输入的平台运动信息。为了避免高频信号的干扰，使用卡尔曼滤波算法估计平台的低频运动。基于模糊PID控制器计算所需的推力和力矩，经推力分配算法将转速和转角指令发送至各全回转推进器，详细控制算法可以参考课题组之前的工作[16]。通过控制系统的人机交互界面可以对推力分配模式进行设置，本文对推进器（T2、T7、T3、T6）采用偏置模式，通过调节推进器的转速及方位角，即可实现上述三种偏置模式。试验过程中，偏置推进器的推力为虚拟推力，通过控制螺旋桨转速得到，综合能耗考虑，文中采用的偏置转速为450 r/min（推进器模型转速）。
（3）推力系统
控制指令经驱动器-伺服电机-传动机构带动推进器工作，试验中选用Ka-470型螺旋桨搭配No.19A型导管，螺旋桨直径为76 mm，导管直径为93 mm，相关推力系数KT、转矩系数KQ，以及敞水效率η可以参考文献[17]。此外，本模型试验系统的硬件设施和理论基础可以在文献[17]、[18]中找到。
3　试验结果
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3.1　静水衰减试验
波浪试验之前，先在静水中对平台进行了自由横摇、纵摇以及垂荡的衰减试验，获得固有周期和阻尼系数等重要参数。图8所示为半潜式平台垂向运动自由衰减试验的运动时历。经计算得到平台的横摇（roll）运动固有周期TΦn=36.8 s，对应频率ωΦn=0.171 rad/s，无因次阻尼系数μΦ=0.007。纵摇（pitch）运动固有周期Tθn=33.8 s，对应频率ωθn=0.186 rad/s，无因次阻尼系数μθ=0.026。垂荡（heave）运动固有周期Tzn=21.7 s，对应频率ωzn=0.289 rad/s，无因次阻尼系数μz=0.046。
3.2　水平面运动响应
试验过程中，平台的目标位置设在（0，0）处，当目标艏向为90°时，平台主要受到横向载荷的影响，因此采用偏置模式1、3进行平台运动响应分析。为了避免瞬态效应的影响，选取中间8000 s进行展示。图9所示为90°艏向工况下平台水平面运动时历，表4为运动统计值，其中艏向角已换算成期望偏差。无偏置模式下，平台的纵荡（surge）最大偏差不超过6.8568 m，最大艏摇（yaw）运动小于11.5324°，平台横荡（sway）运动比较大，最大偏移接近18 m。当采用偏置模式后，偏置推进器产生的轴向力相互抵消。偏置模式1、3工况下，艏摇运动标准差均有不同程度的减小，偏置模式1中平台的纵荡运动最大偏差为5.6960 m，横荡运动最大偏差为17.8461 m，偏置模式3中平台的纵荡偏置最大值为8.6403 m，横荡偏移值最大为19.3114 m。由此可见，推进器偏置模式下，偏置组内推力相互抵消，合力为零，能够基本保障平台的定位精度。
当平台期望艏向角调整为135°时，此时波浪载荷作用方向为45°，平台同时承受着横向载荷与纵向载荷，因此采用偏置模式1、2、3进行平台运动响应分析。图10给出了135°艏向工况下平台水平面运动时历，表5给出了相应偏差的统计值。无偏置模式下，平台的三自由度运动都比较大，纵荡运动最大偏移达8.5925 m，横荡运动达9.3340 m，艏摇运动最大值达11.7824°，该工况下艏向干扰力矩相对较大，艏摇方向剧烈的运动又会加剧纵荡和横荡方向上环境力的变化，进一步引起平台的位置偏移。偏置模式1工况下，纵荡、横荡、艏摇运动方向最大偏移值分别为9.4361 m、13.1503 m、13.8997°。偏置模式2工况下，纵荡、横荡、艏摇运动方向最大偏移值分别为11.0998 m、8.0072 m、10.0050°。偏置模式3工况下，纵荡、横荡、艏摇运动方向最大偏移值分别为11.7016 m、8.8279 m、7.8291°。由此可见，本文针对不同浪向工况设计的推进器偏置模式基本能够维持平台的定位功能。
3.3　垂直面运动响应
通过对比有无偏置模式下平台运动差异，分析推进器偏置对垂向运动的影响。图11~12为90°艏向工况下采用不同偏置模式时平台的垂向运动时历，该工况下，平台的纵摇运动为小量。其统计值如表6所示，对比分析运动响应的最大值（max）、最小值（min）、标准差（std）可以看出，推进器偏置能够有效减小平台垂向运动的最大值及标准差。其中，偏置模式3工况下横摇运动最大值由2.6671°下降至1.8572°，标准差从0.7907°减小到0.6734°，减小幅度达14.8%。偏置模式1工况下平台的垂荡运动最小值从-0.948 m增加至-0.7765 m，垂荡运动幅值的抑制作用能够大大改善平台作业过程中的安全性。此外，不同偏置模式下推进器偏置作用对平台垂向运动影响存在些许差异。这是因为当螺旋桨回转角不同时，平台垂向运动引起的局部来流与螺旋桨轴向形成的有效攻角有所差异，进而影响偏置推进器法向力的大小。另一方面，不同偏置模式下所引起的桨桨干扰效应也会进一步影响局部迎流，造成偏置作用的不同。
图13~14为90°艏向工况下采用不同偏置模式时平台垂向运动功率谱密度（PSD）。平台垂向运动的能量主要集中在固有频率附近，推进器偏置能够有效降低其在谐振区间的响应幅值。以横摇运动为例，无偏置模式下，其谐振区间幅值高达16.97 deg2 s/rad。采用偏置模式3后下降至7.68 deg2 s/rad，PSD峰值减小达54.7%。该艏向角下，平台的纵摇运动为小量，但可以看出推进器偏置在一定程度上仍能够抑制纵摇运动。此外，通过图15可以发现两种偏置模式对于平台的垂荡运动的影响基本一致，能够有效抑制其谐振区间的响应幅值，但对波频段的影响较小。这是因为偏置推进器的法向力与推进器的转速、有效攻角、进速系数密切相关[7]，当前两者因素一定时，进速系数随着平台摇荡速率而改变。波频区间段，平台摇荡速率低，偏置推进器产生的法向力相对于波浪力矩而言较小，难以体现出有效的抑制作用。谐振区间段，由于共振而引起大规模的摇荡运动，此时偏置推进器在垂直平面内的法向力能够大大抑制平台的垂向运动。
图16~18给出了135°艏向角下采用不同偏置模式时平台垂向运动时历，其统计值如表7所示。可以看出，推进器偏置策略能够有效降低平台垂向运动的最大偏移值及标准差，增加系统阻尼。其中，三种偏置模式对平台垂荡运动标准差的影响基本一致。
图19~21给出了135°艏向角下采用不同偏置模式时平台垂向运动PSD。与90°艏向工况下结果类似，推进器偏置能够有效减小平台横摇、纵摇、垂荡在其固有频率附近的响应幅值，对波频区间的运动影响则较小。但不同偏置模式对平台横摇、纵摇运动抑制作用的差异较为明显，其中，偏置模式1和偏置模式3能有效减小平台横摇运动，对纵摇运动的影响较小，偏置模式2则能有效抑制平台纵摇运动，但对横摇运动影响较小。此外，三种偏置模式均能在一定程度上降低谐振区间垂荡的响应幅值，PSD峰值减小达21.4%左右。
3.4　能耗分析
为进一步实现推进器偏置模式的应用，有必要对推进器所引起的油耗（由偏置引起的推力抵消）进行分析。对于动力定位模型试验而言，需考虑螺旋桨的动力性能。从理论上讲，要实现螺旋桨的动力相似，必须保持桨模和实桨之间的进速系数和雷诺数相等。然而，当实尺度螺旋桨和螺旋桨模型的进速系数和雷诺数相等同时满足时，螺旋桨模型的进速和转速将会过高而难以实现。因此，在动力定位模型试验中，主要保证傅汝德数相等[19]，所以难以从桨模转速推断出实桨转速。在这里，我们仅给出了试验过程中推进器的模型转速，然后由模型试验中推力系统功率消耗得到实际功率。
由于文章篇幅限制，在这里我们仅选取90°艏向角工况做进一步阐述。在偏置模式下，T2、T7、T3和T6偏置转速为450 r/min，无偏置模式时，停止工作，因此我们仅列出剩余四个推进器转速时历曲线，时间为141~1273 s（对应实型值1000~9000 s）。图22为90°艏向工况下推进器T1、T4、T5和T8的转速时历。可以看出，推进器偏置对剩余四个推进器性能影响较小，对于T1、T5而言，偏置模式下的转速最大值略大于无偏置模式，T4和T8推进器转速在无偏置模式下会稍大于偏置模式，由此可以推断出三种模式下用于实现定位功能的推进器性能相差不大。但是，偏置模式下T2、T7、T3和T6推力相抵消所引起的能耗则应纳入考量。综合考虑8个全回转推进器，表8给出了90°艏向工况不同偏置模式下实际DP系统功率统计值。可以看出，偏置模式下由于推力相抵消会造成系统功率的最大值及平均值增大，这些因素在偏置模式设计中需要重点关注。
4　结论
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针对小水线面半潜式动力定位平台，本文提出了一种基于推进器偏置的推力分配策略，旨在合理利用推进器法向力抑制平台的垂向运动，通过模型试验对比分析平台六自由度运动响应，确定推进器偏置的作用，主要结论如下：
（1）推进器偏置策略能够在保证平台水平面定位功能前提下，有效减少其垂向运动的最大偏移值及标准差，增加运动阻尼，但同时会造成推力系统功率增大。
（2）不同偏置模式之间的减摇（横摇、纵摇）效果存在差异，但对垂荡运动的影响基本一致。
（3）推进器偏置策略能够有效抑制平台垂向运动在谐振区间的响应幅值，在文中给出的试验工况下，PSD峰值减小最高达54.7%，对波频区间段影响则较小。
本文针对推进器偏置策略的减摇机理和垂荡抑制机制进行了初步探索，为了分析法向力对垂向运动的影响，采用组间轴向力相互抵消的偏置模式，从而排除轴向力的干扰，确定法向力的作用，这种做法在工程实践中会造成系统功率增加，降低冗余度。在工程实践中更倾向于组间推力不完全抵消的偏置模式，从而能够利用偏置推进器的合力抵抗一部分波浪力矩，实现定位功能，根据文中理论分析与模型试验结果，该模式同样能够抑制垂向运动。在接下来的研究工作中我们将进一步优化偏置策略，综合考虑运动性能及油耗，为实际小水线面船舶的垂向运动控制提供一定的借鉴。
基金
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  • 国家自然科学基金资助项目(51179103; 51979167)
文献
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2024年第28卷第10期
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doi: 10.3969/j.issn.1007-7294.2024.10.007
  • 接收时间：2024-04-25
  • 首发时间：2026-03-26
  • 出版时间：2024-10-20
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  • 收稿日期：2024-04-25
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国家自然科学基金资助项目(51179103; 51979167)
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    1.上海交通大学　海洋工程国家重点实验室，上海　200240
    2.上海交通大学　三亚崖州湾深海科技研究院，海南　三亚　572000

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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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