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Article(id=1243304974617264228, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.02.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1724169600000, receivedDateStr=2024-08-21, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774356605438, onlineDateStr=2026-03-24, pubDate=1739980800000, pubDateStr=2025-02-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774356605438, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774356605438, creator=13701087609, updateTime=1774356605438, updator=13701087609, issue=Issue{id=1243304968753623545, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='2', pageStart='171', pageEnd='335', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1774356604040, creator=13701087609, updateTime=1774356967523, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243306493370544137, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243306493370544138, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=312, endPage=320, ext={EN=ArticleExt(id=1243304974864728173, articleId=1243304974617264228, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Influence of shaft segment hollowness on the whirling vibration characteristics of ship complex propulsion shafting, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

The structural design of the propulsion shafting of modern ships is relatively complex, and the structure size is an important factor affecting the whirling vibration characteristics. Taking a ship complex propulsion shafting as the object, the influence of changes in shaft segment hollowness on the whirling vibration characteristics of the shafting was studied in this paper. Based on the finite element method, a whirling vibration analysis model of the shafting was established, and the whirling vibration characteristics of the shafting were analyzed under the initial hollowness. On this basis, the range of hollowness values was determined through strength check calculation. Taking the hollowness of the stern shaft and propeller shaft as variables, the influence of changes in the hollowness of shaft segments on the critical speed of the whirling vibration was analyzed and the values range of hollowness was specified according to the requirements of shafting alignment. The results can provide a reference for structural design and whirling vibration control in the design process of ship propulsion shafting.

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现代舰船推进轴系的结构设计较为复杂，结构尺寸是影响其回旋振动特性的一项重要因素。本文以某舰船复杂推进轴系为研究对象，研究轴段空心度变化对轴系回旋振动特性的影响。基于有限元法建立轴系回旋振动分析模型，并在初始空心度下分析轴系的回旋振动特性；在此基础上，通过强度校核确定空心度的取值范围，以艉轴和螺旋桨轴空心度为变量，分析了艉部轴段空心度变化对轴系回旋振动临界转速的影响规律，并结合轴系校中的衡准要求进一步细化了空心度的取值范围。研究成果可为舰船推进轴系设计过程中的结构设计和回旋振动控制提供参考。

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通讯作者，E-mail：
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古铮（1997-），男，博士研究生

刘金林（1981-），男，博士，教授，通讯作者，E-mail：。

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古铮（1997-），男，博士研究生

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古铮（1997-），男，博士研究生

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刘金林（1981-），男，博士，教授，通讯作者，E-mail：。

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刘金林（1981-），男，博士，教授，通讯作者，E-mail：。

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CB/Z Calculation method for whirling vibration of ship propulsion shafting[S]. National Technical Committee for Ship Standardization, 1984. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1243304992313033441, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[15], rfOrder=24, authorNames=刘振勇, journalName=null, refType=null, unstructuredReference=刘振勇. 基于参数化的船舶轴系强度及扭振特性研究[D]. 武汉：华中科技大学，2012., articleTitle=基于参数化的船舶轴系强度及扭振特性研究, refAbstract=null), Reference(id=1243304992388530918, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[15], rfOrder=25, authorNames=Liu Z Y, journalName=null, refType=null, unstructuredReference=Liu Z Y. 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(in Chinese), articleTitle=Research on intensity calculation and torsional vibration of marine shafting based on parameterization, refAbstract=null)], funds=[Fund(id=1243304988215198282, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, awardId=2017CFB584, language=CN, fundingSource=湖北省自然科学基金资助项目(2017CFB584), fundOrder=null, country=null), Fund(id=1243304988320055891, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, awardId=20191C080744, language=CN, fundingSource=国防科技基金资助项目(20191C080744), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1243304980233437430, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, xref=null, ext=[AuthorCompanyExt(id=1243304980237631735, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, companyId=1243304980233437430, language=EN, country=null, province=null, city=null, 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articleId=1243304974617264228, language=EN, label=Fig.10, caption=Variation curves of relevant parameters of front stern bearing with different propeller shaft hollownesses, figureFileSmall=FbVdRkHpOspEtcj5dUBViw==, figureFileBig=mr1xaHvCDjt9iuur3ZrEYQ==, tableContent=null), ArticleFig(id=1243304987070153203, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=CN, label=图10, caption=前艉轴承相关参数随螺旋桨轴空心度的变化曲线, figureFileSmall=FbVdRkHpOspEtcj5dUBViw==, figureFileBig=mr1xaHvCDjt9iuur3ZrEYQ==, tableContent=null), ArticleFig(id=1243304987162427904, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=EN, label=Tab.1, caption=

Density and initial hollowness of each shaft segment

, figureFileSmall=null, figureFileBig=null, tableContent=
轴段密度/（kg·m-3）浮力系数计算密度/（kg·m-3）空心度
螺旋桨轴78500.80663280.584
艉轴78500.80663280.584
中间轴7850—78500.684
齿轮轴7850—78500.671
), ArticleFig(id=1243304987250508295, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=CN, label=表1, caption=

轴系各轴段密度及初始空心度

, figureFileSmall=null, figureFileBig=null, tableContent=
轴段密度/（kg·m-3）浮力系数计算密度/（kg·m-3）空心度
螺旋桨轴78500.80663280.584
艉轴78500.80663280.584
中间轴7850—78500.684
齿轮轴7850—78500.671
), ArticleFig(id=1243304987414086162, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=EN, label=Tab.2, caption=

Natural frequency and critical speed of whirling vibration

, figureFileSmall=null, figureFileBig=null, tableContent=
频率比阶次固有频率/Hz临界转速/（r·min-1）
0一阶横向振动7.81—
1一阶正回旋7.84470.56
-1一阶逆回旋7.77466.04
1/5叶片次正回旋7.8193.75
-1/5叶片次逆回旋7.8093.57
), ArticleFig(id=1243304987539915289, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=CN, label=表2, caption=

回旋振动固有频率和临界转速

, figureFileSmall=null, figureFileBig=null, tableContent=
频率比阶次固有频率/Hz临界转速/（r·min-1）
0一阶横向振动7.81—
1一阶正回旋7.84470.56
-1一阶逆回旋7.77466.04
1/5叶片次正回旋7.8193.75
-1/5叶片次逆回旋7.8093.57
), ArticleFig(id=1243304987644772900, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=EN, label=Tab.3, caption=

Strength check results of dangerous sections

, figureFileSmall=null, figureFileBig=null, tableContent=
危险截面弯矩/（N·mm）合成平均应力/（N·mm-2）弯曲应力/（N·mm-2）合成交变应力/（N·mm-2）安全系数许用安全系数
后艉轴承艉端截面变径处4.60×10877.4519.1929.193.942.00
后艉轴承支承处7.60×10877.4531.6847.773.192.00
后艉轴承艏端截面变径处6.38×108110.5826.6240.523.182.00
), ArticleFig(id=1243304987728658986, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=CN, label=表3, caption=

危险截面强度校核结果

, figureFileSmall=null, figureFileBig=null, tableContent=
危险截面弯矩/（N·mm）合成平均应力/（N·mm-2）弯曲应力/（N·mm-2）合成交变应力/（N·mm-2）安全系数许用安全系数
后艉轴承艉端截面变径处4.60×10877.4519.1929.193.942.00
后艉轴承支承处7.60×10877.4531.6847.773.192.00
后艉轴承艏端截面变径处6.38×108110.5826.6240.523.182.00
), ArticleFig(id=1243304987841905201, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304974617264228, language=EN, label=Tab.4, caption=

Critical speed of shafting whirling vibration with different stern shaft hollownesses

, figureFileSmall=null, figureFileBig=null, tableContent=
空心度临界转速/（r·min-1）
一阶正回旋一阶逆回旋叶片次正回旋叶片次逆回旋
0.500471.19466.6493.8893.69
0.550470.85466.3293.8193.63
0.584470.56466.0493.7593.57
0.600470.40465.8893.7293.54
0.650469.78465.3093.6093.42
0.700468.95464.5193.4493.26
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不同艉轴空心度下的回旋振动临界转速

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空心度临界转速/（r·min-1）
一阶正回旋一阶逆回旋叶片次正回旋叶片次逆回旋
0.500471.19466.6493.8893.69
0.550470.85466.3293.8193.63
0.584470.56466.0493.7593.57
0.600470.40465.8893.7293.54
0.650469.78465.3093.6093.42
0.700468.95464.5193.4493.26
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Critical speed of shafting whirling vibration with different propeller shaft hollownesses

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空心度临界转速/（r·min-1）
一阶正回旋一阶逆回旋叶片次正回旋叶片次逆回旋
0.500461.48457.4691.9891.81
0.550466.73462.4493.0092.83
0.584470.56466.0493.7593.57
0.600472.43467.8094.1293.93
0.650478.48473.4295.2995.09
0.700484.67479.0696.4996.26
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不同螺旋桨轴空心度下的回旋振动临界转速

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空心度临界转速/（r·min-1）
一阶正回旋一阶逆回旋叶片次正回旋叶片次逆回旋
0.500461.48457.4691.9891.81
0.550466.73462.4493.0092.83
0.584470.56466.0493.7593.57
0.600472.43467.8094.1293.93
0.650478.48473.4295.2995.09
0.700484.67479.0696.4996.26
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轴段空心度对舰船复杂推进轴系回旋振动特性的影响研究
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古铮 , 刘金林 , 房诗雨
船舶力学 | 流体与结构声学 2025,29(2): 312-320
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船舶力学 | 流体与结构声学 2025, 29(2): 312-320
轴段空心度对舰船复杂推进轴系回旋振动特性的影响研究
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古铮, 刘金林 , 房诗雨
作者信息
  • 海军工程大学　动力工程学院，武汉　430033

    • 古铮（1997-），男，博士研究生

    刘金林（1981-），男，博士，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Influence of shaft segment hollowness on the whirling vibration characteristics of ship complex propulsion shafting
Zheng GU, Jin-lin LIU , Shi-yu FANG
Affiliations
  • College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
出版时间: 2025-02-20 doi: 10.3969/j.issn.1007-7294.2025.02.014
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摘要
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现代舰船推进轴系的结构设计较为复杂，结构尺寸是影响其回旋振动特性的一项重要因素。本文以某舰船复杂推进轴系为研究对象，研究轴段空心度变化对轴系回旋振动特性的影响。基于有限元法建立轴系回旋振动分析模型，并在初始空心度下分析轴系的回旋振动特性；在此基础上，通过强度校核确定空心度的取值范围，以艉轴和螺旋桨轴空心度为变量，分析了艉部轴段空心度变化对轴系回旋振动临界转速的影响规律，并结合轴系校中的衡准要求进一步细化了空心度的取值范围。研究成果可为舰船推进轴系设计过程中的结构设计和回旋振动控制提供参考。

舰船复杂推进轴系  /  回旋振动  /  轴段空心度  /  有限元

The structural design of the propulsion shafting of modern ships is relatively complex, and the structure size is an important factor affecting the whirling vibration characteristics. Taking a ship complex propulsion shafting as the object, the influence of changes in shaft segment hollowness on the whirling vibration characteristics of the shafting was studied in this paper. Based on the finite element method, a whirling vibration analysis model of the shafting was established, and the whirling vibration characteristics of the shafting were analyzed under the initial hollowness. On this basis, the range of hollowness values was determined through strength check calculation. Taking the hollowness of the stern shaft and propeller shaft as variables, the influence of changes in the hollowness of shaft segments on the critical speed of the whirling vibration was analyzed and the values range of hollowness was specified according to the requirements of shafting alignment. The results can provide a reference for structural design and whirling vibration control in the design process of ship propulsion shafting.

ship complex propulsion shafting  /  whirling vibration  /  shaft segment hollowness  /  finite element
古铮, 刘金林, 房诗雨. 轴段空心度对舰船复杂推进轴系回旋振动特性的影响研究. 船舶力学, 2025 , 29 (2) : 312 -320 . DOI: 10.3969/j.issn.1007-7294.2025.02.014
Zheng GU, Jin-lin LIU, Shi-yu FANG. Influence of shaft segment hollowness on the whirling vibration characteristics of ship complex propulsion shafting[J]. Journal of Ship Mechanics, 2025 , 29 (2) : 312 -320 . DOI: 10.3969/j.issn.1007-7294.2025.02.014
正文
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0　引言
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推进轴系是舰船动力装置的重要组成部分，其动力学特性的优劣直接影响到整个动力装置的运行状态，且关系到舰船航行的可靠性、安全性及声隐身性等性能指标。由于包含不平衡的回转部件，加之螺旋桨在非均匀伴流场中旋转会受到交变弯曲力矩作用，导致轴系在运行过程中出现周期性的弯曲现象，即轴系的回旋振动[1]。当回旋振动共振转速落入轴系工作转速的范围内时将引发共振，不但会加剧相关部件的疲劳磨损，还会激起较大的辐射噪声，严重时甚至出现轴系烧损和断裂等事故。因此，研究推进轴系的回旋振动特性对轴系的总体设计来说至关重要。
影响轴系回旋振动特性的因素包括轴系结构尺寸、轴承位置和支承特性、轴系校中状态及螺旋桨陀螺效应等，各种因素对轴系回旋振动的影响分析是当前研究的热点问题。李小军等[2]以某大型集装箱船推进轴系为对象，在计入螺旋桨陀螺效应的基础上，基于有限元法对比分析了后艉轴承刚度各向同性和各向异性时轴系的回旋振动特性；Kim等[3]对比分析了双艉轴承和单艉轴承两种布置方案下推进轴系的回旋振动特性，并基于中间轴承变位提出了采用单艉轴承时轴系的最佳布置方案，该方案既改善了轴系的校中状态，又可避免回旋振动引起的共振；刘金林[4]、赖国军[5]、Lei等[6]分别以不同的轴系试验平台为研究对象，基于轴承变位研究了不同校中状态对轴系回旋振动特性的影响，为轴系设计过程中的校中及回旋振动特性的综合优化提供了理论支撑。
随着舰船逐渐向大型化、高速化发展，轴系的结构组成也越来越复杂，具有分段多、跨距长、艉部支撑刚度小等特点，轴系本身的结构尺寸是影响其回旋振动特性的一个重要因素[7-8]。轴段的空心设计具有减轻重量、便于轴系内部检查等优点，故当前舰船轴系多设计为空心轴，轴系的空心程度常用轴段空心度这一参数来表示，即轴段内径与外径之比[9]，其变化会对轴系回旋振动的临界转速产生一定影响。本文以某舰船复杂推进轴系为研究对象，建立其回旋振动有限元分析模型，分析艉部轴段空心度变化对轴系回旋振动特性的影响，以期为轴系设计过程中轴段的空心设计和回旋振动控制提供参考。
1　复杂推进轴系回旋振动有限元分析模型
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1.1　轴系布置
某舰船复杂推进轴系的布置简图如图1所示，其主要组成部分包括：大侧斜5叶螺旋桨、螺旋桨轴、艉轴、中间轴、前艉轴承、后艉轴承、艉管轴承、4套中间轴承及各法兰和联轴器等。轴系通过齿轮箱与主机相连，其中包含齿轮轴和大齿轮前后轴承。
1.2　有限元分析模型
在建立有限元模型之前，首先定义轴系的材料属性，并确认各轴段的空心程度，轴段空心度m的表达式为
式中，d为轴段内径，D为轴段外径。针对此轴系，各轴段杨氏模量取2×1011 N/m2，泊松比取0.3，计算密度及初始空心度在表1中列出。
结合舰船推进轴系回旋振动的计算方法，以轴系结构参数和材料属性为依据建立模型，建模流程如图2所示。
对于模型整体，有以下几点说明：
（1）以螺旋桨桨毂端面几何中心为坐标原点，基于笛卡尔坐标系建立有限元模型，轴系艉端指向艏端为x轴正向，竖直向上为y轴正向，垂直纸面向外为z轴正向。
（2）各轴段采用BEAM188梁单元模拟，该单元包含六个自由度且支持计入陀螺效应，适用于细长梁结构的转子动力学分析[10]。定义梁截面时，将截面内径参数化，以便后续分析轴段空心度对轴系回旋振动特性的影响。
（3）采用COMBIN14弹簧单元来模拟轴承的支承作用，在各轴承处分别建立一个垂向和横向弹簧，其中后艉轴承的支承点位于艉端且指向艏端的1/3倍轴承轴向长度处，其余轴承支承点为轴承中截面处。经参考相关文献资料[1，11]，后艉轴承支承刚度设置为2×108 N/m，前艉轴承支承刚度为1×109 N/m，其余轴承支承刚度为10×109 N/m。
最终建立的轴系有限元分析模型如图3所示，包括施加的约束和已划分的网格单元。
2　复杂推进轴系回旋振动计算与分析
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基于已建立的有限元模型，首先分析初始空心度条件下轴系的回旋振动特性。螺旋桨的陀螺效应会影响轴系的回旋振动特性，且螺旋桨的转动惯量越大，陀螺效应越不可忽视。本文所研究的复杂推进轴系的螺旋桨质量和转动惯量都较大，故在有限元计算时须考虑陀螺效应的影响，在固定坐标系下，考虑陀螺效应的转子动力学方程为[12]：
式中，[M]、[C]、[K]分别为结构质量、阻尼、刚度矩阵，[Gc]为回转阻尼矩阵，[Kc]为降低结构刚度的旋转软化矩阵（本文不计入），{u}、、分别为节点位移、速度、加速度向量，{F}为外载荷向量。计入陀螺效应后，定义拟提取的模态数目和荷载步数（对应不同转速），以循环的方式进行各转速下的模态分析，以提取轴系回旋振动的计算结果。
2.1　固有频率和临界转速
当轴系转速为零时，回旋振动的涡动频率退化为横向振动的固有频率，从模态分析结果中提取轴系一阶横向振动振型，如图4所示。
由一阶横向振动振型可知，轴系艉部模态位移较大，提取各转速下轴系的涡动频率，绘制如图5所示的坎贝尔图（局部）。
实际工程中的回旋振动计算，只需计算可能引起共振的轴频、叶频和倍叶频的固有频率及临界转速即可。求取坎贝尔图中涡动频率曲线和轴频、叶频辅助线的交点，可得到如表2所列的轴系正逆向的回旋振动固有频率和临界转速。
观察坎贝尔图可知，轴系转速为零时，正逆向回旋涡动频率与一阶横向振动固有频率相等，而由于受到陀螺效应的影响，正回旋涡动频率随转速升高而升高，逆回旋涡动频率随转速降低而降低[10，13]。该复杂推进轴系的额定转速为150 r/min，故由表2中数据可知，在0.6~1.0倍额定转速范围内未出现一阶回旋振动临界转速，0.8~1.0倍额定转速范围内也未出现叶片次回旋振动临界转速，计算结果满足相关轴系设计标准[14]中的指标要求。
2.2　涡动轨迹
通过绘制系统中各节点的涡动轨迹，可更直观地分析轴系各阶次的回旋振动特性。这里以一阶正回旋和叶片次正回旋为例，绘制轴系回旋振动的涡动轨迹，如图6所示。
观察涡动轨迹图可知，由于该复杂推进轴系伸出舷外的轴段较长，采用水润滑的前后艉轴承支承刚度较小，再加之螺旋桨自身较大的质量和转动惯量，相比于中间轴段，轴系艉轴和螺旋桨轴的回旋振动位移幅值较大。因此，应合理设计轴系的结构尺寸和支承特性，使临界转速尽量远离工作转速范围，避免因剧烈共振引起的艉部异常磨损及其所带来的较大结构辐射噪声。
3　轴段空心度对轴系回旋振动特性的影响分析
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在先前的轴系有限元建模过程中，已对轴系各轴段的内径进行了参数化设置。本章将以螺旋桨轴和艉轴的空心度为变量，在满足轴系强度要求的前提下，分析不同轴段空心度取值对轴系回旋振动特性的影响。
3.1　强度校核
轴系的空心设计需满足强度校核的要求，舰船轴系的空心度取值范围一般为0.5~0.78[9]，本文所选取的轴段空心度变化范围为0.5~0.7。在螺旋桨轴和艉轴的空心度同时取最大值0.7时进行强度校核计算，按空心度为0.7调整相应轴段的截面参数，在附加重力场后进行轴系直线校中状态下的静力学计算，得到如图7所示的轴系弯矩分布云图。
由图7可知，后艉轴承附近产生的弯矩较大，由于螺旋桨伸出舷外较长，轴系最大弯曲应力一般发生在后艉轴承附近[15]。轴系强度校核需要计算应力较大的危险截面的安全系数，保证其满足相关标准中的指标要求，这里选取后艉轴承支承处及其艏艉端截面变径处为危险截面，计算其安全系数，安全系数的计算公式为
式中，σHm、σHa分别为合成平均应力与合成交变应力，其计算公式可参考相关文献[9]，此处不再赘述；σs为轴材料的屈服强度，σ-1为循环交变应力下的疲劳极限，无试验数据时可取材料抗拉强度的0.45倍；n和[n]分别为截面安全系数和许用安全系数。取材料屈服强度为500 MPa，抗拉强度为700 MPa，经计算后，得到如表3所列的各危险截面强度校核结果。
由表3数据可知，螺旋桨轴和艉轴空心度均取最大值时，各危险截面的安全系数均大于许用安全系数，因此，选取的轴段空心度取值范围满足轴系强度校核要求。
3.2　艉轴空心度对轴系回旋振动特性的影响
基于已确定的轴段空心度变化范围，以0.05为步长，分别选取不同的轴段空心度来调整参数化有限元模型，计算不同空心度下轴系回旋振动的临界转速，结果如表4所示（其中0.584为轴段的初始空心度）。在此基础上，进一步分析艉轴空心度变化对临界转速的影响规律，得到如图8所示的变化曲线。
由表4中数据和图8可知，在空心度变化范围内，随着艉轴空心度的不断增大，轴系回旋振动临界转速逐渐降低但幅度较小，一阶正回旋临界转速降低了0.48%，叶片次正回旋临界转速降低了0.47%。由此可知，在该复杂推进轴系的设计过程中，艉轴的空心度变化对轴系回旋振动特性的影响较小，可在满足强度要求的前提下适当增大艉轴空心度，不但可以降低轴系总重，还便于从内部检查轴干质量。
3.3　螺旋桨轴空心度对轴系回旋振动特性的影响
采用与上一节相同的方法，分析螺旋桨轴空心度变化对轴系回旋振动特性的影响，不同螺旋桨轴空心度下轴系回旋振动的临界转速计算结果如表5所示，临界转速随螺旋桨轴空心度的变化曲线如图9所示。
由表5中数据和图9可知，在空心度变化范围内，随着螺旋桨轴空心度的不断增大，轴系回旋振动临界转速逐渐升高，一阶正回旋临界转速升高了5.03%，叶片次正回旋临界转速升高了4.90%，且叶片次回旋振动临界转速逐渐接近临界转速禁区（0.8~1.0倍额定转速）。因此，在该轴系设计过程中，螺旋桨轴的空心度取值不宜过大，否则易使叶片次回旋振动临界转速落入轴系工作转速范围内，从而激起共振，影响轴系的安全稳定运行。
以上分析中，在螺旋桨轴和艉轴空心度的变化范围内，轴系回旋振动的临界转速均不在临界转速禁区内，这符合轴系回旋振动的校核要求。但经校中计算发现，当两轴段空心度取最大值0.7时，前艉轴承的负荷过小（为53.67 kN），小于该轴承相邻两跨轴段总重的20%（为60.58 kN），不满足相关轴系设计规范[9]中对校中的衡准要求，故取艉轴空心度为0.7，在此条件下计算螺旋桨轴空心度取不同值时前艉轴承的负荷，以进一步细化空心度的取值范围。
图10中，G表示前艉轴承相邻两跨轴段的总重量。经分析可知，当螺旋桨轴空心度小于0.66时，前艉轴承负荷大于其相邻两跨轴段总重的20%，满足轴系校中的衡准要求。因此，螺旋桨轴和艉轴空心度的取值范围可分别界定为[0.584，0.66]和[0.584，0.7]，在此范围内增大轴段空心度，可在满足相关轴系设计要求的前提下减轻轴系总重，且可使轴系回旋振动临界转速避开临界转速禁区。
4　结论
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本文以某舰船复杂推进轴系为研究对象，分析了轴段空心度变化对轴系回旋振动特性的影响。首先，依据轴系结构参数建立了回旋振动有限元分析模型，并对初始空心度下轴系的回旋振动特性进行了分析；之后，通过轴系强度计算确定了轴段空心度的取值范围；最后，以艉轴和螺旋桨轴的空心度为变量，分析了轴系回旋振动临界转速随轴段空心度的变化规律，并结合轴系校中的衡准要求进一步细化了轴段空心度的取值范围，得到了以下结论：
（1）初始空心度下轴系艉部的回旋振动振幅较大，在轴系设计时应避免临界转速落入工作转速范围内，以防止激起共振，从而减小轴系艉部的异常磨损；
（2）随着艉轴空心度的增大，轴系回旋振动临界转速逐渐降低但幅度较小，故在该轴系的设计阶段，可适当增大艉轴空心度，以降低轴系总重并提高轴系内部的可维修性。
（3）随着螺旋桨轴空心度的增大，轴系回旋振动临界转速明显升高，尤其是叶片次回旋振动的临界转速逐渐接近临界转速禁区。因此，在该轴系的设计过程中，应慎重考虑螺旋桨轴空心度的取值，避免叶片次共振转速落入工作转速范围内，以提高轴系运行的安全性和可靠性。
（4）结合轴系强度和校中计算细化了轴段空心度的取值范围，研究成果对轴系回旋振动控制中轴段的空心设计具有一定的参考价值。
基金
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  • 湖北省自然科学基金资助项目(2017CFB584)
  • 国防科技基金资助项目(20191C080744)
文献
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2025年第29卷第2期
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doi: 10.3969/j.issn.1007-7294.2025.02.014
  • 接收时间：2024-08-21
  • 首发时间：2026-03-24
  • 出版时间：2025-02-20
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  • 收稿日期：2024-08-21
基金
湖北省自然科学基金资助项目(2017CFB584)
国防科技基金资助项目(20191C080744)
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    海军工程大学　动力工程学院，武汉　430033

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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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