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Article(id=1241038858020769794, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241038854333985467, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.01.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1686672000000, receivedDateStr=2023-06-14, revisedDate=1693324800000, revisedDateStr=2023-08-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1773816321138, onlineDateStr=2026-03-18, pubDate=1736870400000, pubDateStr=2025-01-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773816321138, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773816321138, creator=13701087609, updateTime=1773816321138, updator=13701087609, issue=Issue{id=1241038854333985467, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='1', pageStart='1', pageEnd='154', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773816320260, creator=13701087609, updateTime=1773819065926, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241050370550591873, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241038854333985467, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241050370554786178, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241038854333985467, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=42, endPage=49, ext={EN=ArticleExt(id=1241038858775744517, articleId=1241038858020769794, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Research on unbalanced response of ultra-high speed centrifugal impeller rotor system, columnId=1228282191914926752, journalTitle=Journal of Mechanical Strength, columnName=Vibration·Noise·Monitoring·Diagnosis, runingTitle=null, highlight=null, articleAbstract=

In order to avoid large vibration response and transcritical motion instability of ultra-high speed centrifugal impeller rotor system caused by unbalanced excitation, the unbalanced excitation response of ultra-high speed centrifugal impeller rotor system was analyzed by using Ansys rotor dynamics response analysis module and comprehensively considering the stiffness and damping of sliding bearing, the dynamic response of ultra-high speed centrifugal impeller rotor system under different unbalanced excitation was obtained. At the same time, DEWESoft vibration test system was used to track and record the rotating frequency vibration value of ultra-high speed centrifugal impeller rotor system, and compared with the unbalanced response analysis results, it was concluded that the dynamic balance accuracy level of the ultra-high speed centrifugal impeller rotor system should be better than G1 level. The unbalanced excitation response analysis and control method has been well verified by tests, which has important engineering application significance.

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ZHANG Yong, E-mail：
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为避免因不平衡激励引起的超高速离心叶轮转子系统振动响应大及跨临界时运动失稳，采用Ansys转子动力学响应分析模块，综合考虑滑动轴承的刚度与阻尼，对超高速离心叶轮转子系统进行不平衡激励响应分析，得出不同不平衡激励下超高速离心叶轮转子系统的动态响应。同时，采用DEWESoft振动测试系统对超高速离心叶轮转子系统的转频振动值跟踪记录，并与不平衡响应分析结果对比，得出超高速离心叶轮转子系统动平衡精度等级需优于G1级。该不平衡激励响应分析与控制方法得到了较好的试验验证，具有重要的工程应用意义。

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张勇，男，1990年生，山东东平人，硕士，工程师；主要研究方向为转子动力学；E-mail：。

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2.Hunan Finehigh Intelligent Equipment Co., Ltd., Zhuzhou 412002, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1241038866505846941, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, authorId=1241038866262577299, language=CN, stringName=张勇, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, 2, address=1.西安交通大学 机械工程学院，西安　710049
2.湖南泛航智能装备有限公司，株洲　412002, bio={"content":"

张勇，男，1990年生，山东东平人，硕士，工程师；主要研究方向为转子动力学；E-mail：。

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张勇，男，1990年生，山东东平人，硕士，工程师；主要研究方向为转子动力学；E-mail：。

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Rotor dynamics[M]. Beijing：Tsinghua University Press，1987：41-67.（In Chinese）, articleTitle=null, refAbstract=null), Reference(id=1241038881135579714, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, doi=null, pmid=null, pmcid=null, year=2021, volume=41, issue=9, pageStart=102, pageEnd=107, url=null, language=null, rfNumber=[14], rfOrder=23, authorNames=刘汉阳, 李钦奉, journalName=舰船电子工程, refType=null, unstructuredReference=刘汉阳，李钦奉.基于Fluent的多油腔动静压轴承油膜压力仿真[J].舰船电子工程，2021，41（9）：102-107., articleTitle=基于Fluent的多油腔动静压轴承油膜压力仿真, refAbstract=null), Reference(id=1241038881206882886, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, doi=null, pmid=null, pmcid=null, year=2021, volume=41, issue=9, pageStart=102, pageEnd=107, url=null, language=null, rfNumber=[14], rfOrder=24, authorNames=LIU Hanyang, LI Qinfeng, journalName=Ship Electronic Engineering, refType=null, unstructuredReference=LIU Hanyang，LI Qinfeng. 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Nonlinear vibration response characteristics of high-speed flexible rotor system[J]. Journal of Beijing University of Aeronautics and Astronautics，2018，44（4）：653-661.（In Chinese）, articleTitle=Nonlinear vibration response characteristics of high-speed flexible rotor system, refAbstract=null)], funds=[Fund(id=1241038876337295797, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, awardId=2020GK4059, language=EN, fundingSource=Hunan Province Science and Technology Innovation Program(2020GK4059), fundOrder=null, country=null), Fund(id=1241038876547011002, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, awardId=2020GK4059, language=CN, fundingSource=湖南省科技创新计划项目(2020GK4059), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241038866040279172, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, xref=1., ext=[AuthorCompanyExt(id=1241038866048667781, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, companyId=1241038866040279172, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China), AuthorCompanyExt(id=1241038866052862086, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, companyId=1241038866040279172, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.西安交通大学 机械工程学院，西安　710049)]), AuthorCompany(id=1241038866170302602, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, xref=2., ext=[AuthorCompanyExt(id=1241038866178691211, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, companyId=1241038866170302602, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.Hunan Finehigh Intelligent Equipment Co., Ltd., Zhuzhou 412002, China), AuthorCompanyExt(id=1241038866182885516, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, companyId=1241038866170302602, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.湖南泛航智能装备有限公司，株洲　412002)])], figs=[ArticleFig(id=1241038868682690771, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.1, caption=Structure diagram of the rotor system, figureFileSmall=7mScS6Yv+CWcNQ7xDrwoIQ==, figureFileBig=8ct+W7kLKuId0IddSAgXlw==, tableContent=null), ArticleFig(id=1241038868997263578, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图1, caption=转子系统结构简图

1.锁紧螺母Locking nut；2.离心叶轮Centrifugal impeller；3.密封环Sealing ring；4.齿轮轴Gear shaft；5.径向滑动轴承Radial bearing；6.径向推力复核滑动轴承Radial thrust combined sliding bearing；7.调整垫Adjusting pad。

, figureFileSmall=7mScS6Yv+CWcNQ7xDrwoIQ==, figureFileBig=8ct+W7kLKuId0IddSAgXlw==, tableContent=null), ArticleFig(id=1241038869332807910, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.2, caption=Simplified model of the ultra-high speed centrifugal impeller rotor system, figureFileSmall=dZo75stse0bSJ6ZAK1VaAA==, figureFileBig=h4V2szKe+3nALPZkxEoTQA==, tableContent=null), ArticleFig(id=1241038869416693996, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图2, caption=超高速离心叶轮转子系统简化模型, figureFileSmall=dZo75stse0bSJ6ZAK1VaAA==, figureFileBig=h4V2szKe+3nALPZkxEoTQA==, tableContent=null), ArticleFig(id=1241038869676740847, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.3, caption=Schematic diagram of sliding bearing structure, figureFileSmall=vk0dRoIz5uxpSsYADYopyg==, figureFileBig=pDcWC7P70cSAm6K8pwZFTQ==, tableContent=null), ArticleFig(id=1241038869848707316, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图3, caption=滑动轴承结构示意图, figureFileSmall=vk0dRoIz5uxpSsYADYopyg==, figureFileBig=pDcWC7P70cSAm6K8pwZFTQ==, tableContent=null), ArticleFig(id=1241038869957759224, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.4, caption=Oil film pressure distribution of tilting pad sliding bearing pads, figureFileSmall=Rl30Xtpp7ZwBUQmTR+/BYQ==, figureFileBig=6UvF8RQmxWN7EAp2V/cTHA==, tableContent=null), ArticleFig(id=1241038870075199740, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图4, caption=可倾瓦滑动轴承瓦块油膜压力分布, figureFileSmall=Rl30Xtpp7ZwBUQmTR+/BYQ==, figureFileBig=6UvF8RQmxWN7EAp2V/cTHA==, tableContent=null), ArticleFig(id=1241038870238777606, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.5, caption=Calculation flow chart of the sliding bearing, figureFileSmall=8W0psCGmMYGlzIdnVHhGUA==, figureFileBig=m/t0Y1StkUHinIOzdgvpzw==, tableContent=null), ArticleFig(id=1241038870490435852, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图5, caption=滑动轴承计算流程图, figureFileSmall=8W0psCGmMYGlzIdnVHhGUA==, figureFileBig=m/t0Y1StkUHinIOzdgvpzw==, tableContent=null), ArticleFig(id=1241038870633042192, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.6, caption=Campbell diagram of the ultra-high speed centrifugal impeller rotor system, figureFileSmall=8rYMtJJvnUxvwbxSM23lOQ==, figureFileBig=3uEwpP8FNfwKsNuG4I5RLA==, tableContent=null), ArticleFig(id=1241038870825980181, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图6, caption=超高速离心叶轮转子系统坎贝尔图, figureFileSmall=8rYMtJJvnUxvwbxSM23lOQ==, figureFileBig=3uEwpP8FNfwKsNuG4I5RLA==, tableContent=null), ArticleFig(id=1241038870922449180, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.7, caption=First critical speed vibration mode of the ultra-high speed centrifugal impeller rotor system, figureFileSmall=Ks630o0qTjC+gp/KV+lofA==, figureFileBig=2AcCJdTlyMUw2A3HaFopzw==, tableContent=null), ArticleFig(id=1241038871035695395, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图7, caption=超高速离心叶轮转子系统一阶临界转速振型, figureFileSmall=Ks630o0qTjC+gp/KV+lofA==, figureFileBig=2AcCJdTlyMUw2A3HaFopzw==, tableContent=null), ArticleFig(id=1241038871450931498, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.8, caption=Analysis model of the unbalance response, figureFileSmall=MfkGh42gvsTi1kVmBwbdUw==, figureFileBig=gBO8ZCFF6ngQ+Ksp/1SiMA==, tableContent=null), ArticleFig(id=1241038871916499247, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图8, caption=不平衡响应分析模型, figureFileSmall=MfkGh42gvsTi1kVmBwbdUw==, figureFileBig=gBO8ZCFF6ngQ+Ksp/1SiMA==, tableContent=null), ArticleFig(id=1241038872285598004, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.9, caption=Vibration velocity amplitude of G0.4 level unbalance response analysis, figureFileSmall=YWYmKtvLongFq9emveuVEw==, figureFileBig=uBn0Ei/t4NTQkjCFROGpdg==, tableContent=null), ArticleFig(id=1241038872507896119, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图9, caption=G0.4级不平衡响应分析振动速度幅值, figureFileSmall=YWYmKtvLongFq9emveuVEw==, figureFileBig=uBn0Ei/t4NTQkjCFROGpdg==, tableContent=null), ArticleFig(id=1241038872604365117, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.10, caption=Dynamics characteristic test of the ultra-high speed centrifugal impeller rotor system, figureFileSmall=Ncx2FhKhliS6CbmheLR5QA==, figureFileBig=YTTkoa9g94ZpCy9u27zaFA==, tableContent=null), ArticleFig(id=1241038872684056898, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图10, caption=超高速离心叶轮转子系统动力学特性试验

1、2.轴向方向振动加速度传感器Axial direction vibration acceleration sensor；3.水平方向振动加速度传感器Horizontal vibration acceleration sensor。

, figureFileSmall=Ncx2FhKhliS6CbmheLR5QA==, figureFileBig=YTTkoa9g94ZpCy9u27zaFA==, tableContent=null), ArticleFig(id=1241038872956686664, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.11, caption=DEWESoft vibration testing system, figureFileSmall=jDtyRwj+pnMsM+ymryEKWA==, figureFileBig=eQXAns9Wb5AGMdKHLrgsxw==, tableContent=null), ArticleFig(id=1241038873065738573, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图11, caption=DEWESoft振动测试系统, figureFileSmall=jDtyRwj+pnMsM+ymryEKWA==, figureFileBig=eQXAns9Wb5AGMdKHLrgsxw==, tableContent=null), ArticleFig(id=1241038873262870866, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Fig.12, caption=Full speed vibration waveform and frequency spectrum of the ultra-high speed centrifugal impeller rotor system, figureFileSmall=aKs52Fo62IxA2DexFUFXKg==, figureFileBig=SRSZGZT3YMQb0l0H7nf/6Q==, tableContent=null), ArticleFig(id=1241038873401282903, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=图12, caption=超高速离心叶轮转子系统全转速振动波形图及频谱图, figureFileSmall=aKs52Fo62IxA2DexFUFXKg==, figureFileBig=SRSZGZT3YMQb0l0H7nf/6Q==, tableContent=null), ArticleFig(id=1241038873506140509, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.1, caption=

Materials for rotating parts

, figureFileSmall=null, figureFileBig=null, tableContent=
序号
Serial number		名称
Name		材料
Material
1齿轮轴
Gear shaft		18CrNiMo7-620CrMnTi
2密封环
Sealing ring		45#钢 45#steel
3调整垫
Adjustment pad		45#钢 45#steel
4离心叶轮
Centrifugal impeller		7075
5锁紧螺母
Lock nut		40Cr
), ArticleFig(id=1241038873631969635, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表1, caption=

转动部件材料

, figureFileSmall=null, figureFileBig=null, tableContent=
序号
Serial number		名称
Name		材料
Material
1齿轮轴
Gear shaft		18CrNiMo7-620CrMnTi
2密封环
Sealing ring		45#钢 45#steel
3调整垫
Adjustment pad		45#钢 45#steel
4离心叶轮
Centrifugal impeller		7075
5锁紧螺母
Lock nut		40Cr
), ArticleFig(id=1241038873996874091, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.2, caption=

Input parameters of sliding bearings

, figureFileSmall=null, figureFileBig=null, tableContent=
序号
Serial number		参数名称
Parameter name		值
Value
1转子质量
Rotor mass/kg		2.8
2轴颈直径
Journal diameter/mm		20
3最高转速
Maximum speed/(r/min)		51 800
4润滑介质
Lubricating medium		46#润滑油
46# lubricating
5滑油温度
Lubricating oil temperature/℃		40
6滑油黏度
Lubricating oil viscosity/(Pa·s)		0.040 3
7轴承相对间隙
Bearing relative clearance/%		0.15
8轴承宽径比
Bearing width to diameter ratio		0.8
), ArticleFig(id=1241038874093343086, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表2, caption=

滑动轴承输入参数

, figureFileSmall=null, figureFileBig=null, tableContent=
序号
Serial number		参数名称
Parameter name		值
Value
1转子质量
Rotor mass/kg		2.8
2轴颈直径
Journal diameter/mm		20
3最高转速
Maximum speed/(r/min)		51 800
4润滑介质
Lubricating medium		46#润滑油
46# lubricating
5滑油温度
Lubricating oil temperature/℃		40
6滑油黏度
Lubricating oil viscosity/(Pa·s)		0.040 3
7轴承相对间隙
Bearing relative clearance/%		0.15
8轴承宽径比
Bearing width to diameter ratio		0.8
), ArticleFig(id=1241038874177229172, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.3, caption=

Calculation parameters of sliding bearings

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序号
Serial number		参数名称
Parameter name		轴承1
Bearing 1		轴承2
Bearing 2
Kxx34 17060 510
1轴承刚度
Bearing stiffness/（N/mm）		Kxy00
Kyy34 17060 510
Kyx00
2轴承阻尼
Bearing damping/（N·s/m）		Cxx8 32011 650
Cxy00
Cyy8 32011 650
Cyx00
), ArticleFig(id=1241038874416304503, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表3, caption=

滑动轴承计算参数

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序号
Serial number		参数名称
Parameter name		轴承1
Bearing 1		轴承2
Bearing 2
Kxx34 17060 510
1轴承刚度
Bearing stiffness/（N/mm）		Kxy00
Kyy34 17060 510
Kyx00
2轴承阻尼
Bearing damping/（N·s/m）		Cxx8 32011 650
Cxy00
Cyy8 32011 650
Cyx00
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Critical speed of the ultra-high speed centrifugal impeller rotor system

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序号
Serial number		正/反进动
Forward / Reverse precession		临界转速
Critical speed/ (rad/s)
1反 Reverse1 101.6
2反 Reverse1 655.1
3正 Forward1 937.4
4反 Reverse4 956.6
), ArticleFig(id=1241038874915426696, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表4, caption=

超高速离心叶轮转子系统临界转速

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序号
Serial number		正/反进动
Forward / Reverse precession		临界转速
Critical speed/ (rad/s)
1反 Reverse1 101.6
2反 Reverse1 655.1
3正 Forward1 937.4
4反 Reverse4 956.6
), ArticleFig(id=1241038875003507089, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.5, caption=

Unbalance mass

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序号
Serial number		不平衡等级
Unbalance grade		不平衡质量
Unbalance mass/g
1G0.40.004 2
2G10.010 0
3G2.50.026 2
4G6.30.066 1
), ArticleFig(id=1241038875091587476, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表5, caption=

不平衡质量

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序号
Serial number		不平衡等级
Unbalance grade		不平衡质量
Unbalance mass/g
1G0.40.004 2
2G10.010 0
3G2.50.026 2
4G6.30.066 1
), ArticleFig(id=1241038875418743196, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.6, caption=

Summary of response results for different unbalanced incentives

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序号
Serial number		不平衡等级
Unbalance
grade		不平衡质量
Unbalance mass/g		响应主频率
Response main frequency/Hz		幅值
Amplitude/(mm/s)
1G0.40.004 23201.82
2G10.010 03204.34
3G2.50.026 232011.38
4G6.30.066 132028.72
), ArticleFig(id=1241038875817202082, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表6, caption=

不同不平衡激励响应结果汇总

, figureFileSmall=null, figureFileBig=null, tableContent=
序号
Serial number		不平衡等级
Unbalance
grade		不平衡质量
Unbalance mass/g		响应主频率
Response main frequency/Hz		幅值
Amplitude/(mm/s)
1G0.40.004 23201.82
2G10.010 03204.34
3G2.50.026 232011.38
4G6.30.066 132028.72
), ArticleFig(id=1241038876018528678, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=EN, label=Tab.7, caption=

Data statistics of dynamic characteristic test

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剩余不平
衡质量
Remaining unbalance mass/g		0.85*临界转
速振动幅值
0.85*critical speed vibration amplitude/(mm/s)		临界转速
振动幅值
Critical speed vibration amplitude/(mm/s)		1.15*临界转
速振动幅值
1.15*critical speed vibration amplitude/(mm/s)		备注
Note
0.0080.671.861.34垂直Vertical
0.781.230.94轴向Axial
0.831.961.67水平Horizontal
0.0111.634.832.76垂直Vertical
1.573.591.74轴向Axial
1.785.072.83水平Horizontal
), ArticleFig(id=1241038876224049580, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241038858020769794, language=CN, label=表7, caption=

动力学特性试验数据统计

, figureFileSmall=null, figureFileBig=null, tableContent=
剩余不平
衡质量
Remaining unbalance mass/g		0.85*临界转
速振动幅值
0.85*critical speed vibration amplitude/(mm/s)		临界转速
振动幅值
Critical speed vibration amplitude/(mm/s)		1.15*临界转
速振动幅值
1.15*critical speed vibration amplitude/(mm/s)		备注
Note
0.0080.671.861.34垂直Vertical
0.781.230.94轴向Axial
0.831.961.67水平Horizontal
0.0111.634.832.76垂直Vertical
1.573.591.74轴向Axial
1.785.072.83水平Horizontal
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超高速离心叶轮转子系统不平衡响应研究
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张勇 1, 2
机械强度 | 振动·噪声·监测·诊断 2025,47(1): 42-49
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机械强度 | 振动·噪声·监测·诊断 2025, 47(1): 42-49
超高速离心叶轮转子系统不平衡响应研究
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张勇1, 2
作者信息
  • 1.西安交通大学 机械工程学院，西安　710049
  • 2.湖南泛航智能装备有限公司，株洲　412002

    • 张勇，男，1990年生，山东东平人，硕士，工程师；主要研究方向为转子动力学；E-mail：。

Research on unbalanced response of ultra-high speed centrifugal impeller rotor system
Yong ZHANG1, 2
Affiliations
  • 1.School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
  • 2.Hunan Finehigh Intelligent Equipment Co., Ltd., Zhuzhou 412002, China
出版时间: 2025-01-15 doi: 10.16579/j.issn.1001.9669.2025.01.005
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摘要
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为避免因不平衡激励引起的超高速离心叶轮转子系统振动响应大及跨临界时运动失稳，采用Ansys转子动力学响应分析模块，综合考虑滑动轴承的刚度与阻尼，对超高速离心叶轮转子系统进行不平衡激励响应分析，得出不同不平衡激励下超高速离心叶轮转子系统的动态响应。同时，采用DEWESoft振动测试系统对超高速离心叶轮转子系统的转频振动值跟踪记录，并与不平衡响应分析结果对比，得出超高速离心叶轮转子系统动平衡精度等级需优于G1级。该不平衡激励响应分析与控制方法得到了较好的试验验证，具有重要的工程应用意义。

高速离心压缩机  /  超高速转子系统  /  不平衡激励  /  动态响应  /  跨临界

In order to avoid large vibration response and transcritical motion instability of ultra-high speed centrifugal impeller rotor system caused by unbalanced excitation, the unbalanced excitation response of ultra-high speed centrifugal impeller rotor system was analyzed by using Ansys rotor dynamics response analysis module and comprehensively considering the stiffness and damping of sliding bearing, the dynamic response of ultra-high speed centrifugal impeller rotor system under different unbalanced excitation was obtained. At the same time, DEWESoft vibration test system was used to track and record the rotating frequency vibration value of ultra-high speed centrifugal impeller rotor system, and compared with the unbalanced response analysis results, it was concluded that the dynamic balance accuracy level of the ultra-high speed centrifugal impeller rotor system should be better than G1 level. The unbalanced excitation response analysis and control method has been well verified by tests, which has important engineering application significance.

High speed centrifugal compressor  /  Ultra-high speed rotor system  /  Unbalanced excitation  /  Dynamic response  /  Transcritical
张勇. 超高速离心叶轮转子系统不平衡响应研究. 机械强度, 2025 , 47 (1) : 42 -49 . DOI: 10.16579/j.issn.1001.9669.2025.01.005
Yong ZHANG. Research on unbalanced response of ultra-high speed centrifugal impeller rotor system[J]. Journal of Mechanical Strength, 2025 , 47 (1) : 42 -49 . DOI: 10.16579/j.issn.1001.9669.2025.01.005
正文
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0　引言
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单级大压比离心压缩机作为工业领域的核心设备，对其运行稳定性和可靠性要求严苛，技术含量高，目前基本被国外大型风机企业垄断。随着我国高端装备制造业的快速发展以及“双碳目标”产生的市场需求，国产离心压缩机向高功率密度、高效率、高可靠性、高转速方向发展，故超高速离心叶轮转子系统的不平衡激励研究对于国产高端离心压缩机的技术突破意义重大。
单级大压比离心压缩机离心叶轮转速高，叶轮最大轮缘处的线速度可达510 m/s，故超高速离心叶轮转子系统采用跨临界柔性转子设计，其对不平衡激励异常敏感。此外，不平衡激励与转速的平方成正比关系，转子系统转速愈高，动态响应愈剧烈，特别是在跨临界时，若不平衡激励过大，转子系统阻尼不足以致发生转子共振，则超高速离心叶轮转子系统振动剧烈、运动失稳，因转速非常高，易导致离心叶轮剐蹭、轴承失效、转轴弯曲等破坏性的严重后果[1]。因此，对超高速离心叶轮转子系统的不平衡激励研究对单级大压比离心压缩机的高速稳定性与可靠性具有重要的工程意义。
目前，国内外学者对高速转子系统动力学特性、激励与响应分析等进行了大量的研究，并取得了丰硕的成果。董卫红等[2]针对高速涡轮泵转子系统多摩擦学元件耦合的特点，建立了多摩擦学元件耦合时复杂转子系统的集成动力学模型。邓旺群等[3]提出了一种细长柔性转子高速动平衡方法，通过平衡卡箍完成了动力涡轮转子的高速动平衡试验，且平衡卡箍对转子系统的临界转速和振动特性影响甚微。TIWARI等[4]研究了磁悬浮轴承特性参数和不平衡质量对柔性磁轴承转子系统的动力学特性的影响。KUPPA等[5]进行了不平衡质量和磁悬浮轴承不对中对柔性转子系统的故障分析。YADAV等[6]对不平衡质量对高速转子的影响进行了深入研究。郭夏夏[7]在现有动平衡测试系统设计的基础上，设计高速动平衡转子的仿真系统，建立了高速动平衡转子的动力学旋转模型。岳聪[8]利用高速转子加速起动过程中的振幅响应信息，进行瞬态动平衡方法研究，对动力涡轮转子模型分别开展动平衡方法仿真研究及其稳定性和适用性分析。张国渊等[9]对高速涡轮转子进行多部件、多物理场耦合信息的动力学设计方法进行了深入研究，提高了设计效率和设计质量。张舒月等[10]建立了磁悬浮冷压缩机转子系统，并完成了临界转速和不平衡响应的仿真计算，提出了磁悬浮轴承转子系统建模和动力学计算方法。上述成果对高速转子系统的设计与计算分析具有重要指导意义。在此基础上，跨临界柔性转子动力学特性对不平衡激励更加敏感，工程应用中显现的不平衡激励引起的共振问题较多，对超高速离心叶轮转子系统的不平衡激励分析与控制可确保超高速跨临界柔性转子具有良好的动力学特性。
基于超高速跨临界柔性转子不平衡激励响应分析的局限，本文针对单级大压比离心压缩机超高速离心叶轮转子系统提出一种可靠的不平衡激励响应分析计算方法，同时考虑滑动轴承在额定转速、满功率状态、最高温度情况下动压油膜的支撑刚度以及阻尼影响[11][12]33-37，采用集中质量法合理简化转子系统进行振动响应分析，采用DEWESoft振动测试系统对超高速离心叶轮转子系统的转频振动值跟踪记录，并与不平衡响应分析结果对比分析。该不平衡激励响应分析与控制方法得到了较好的试验验证，具有重要的工程应用意义。
1　超高速离心叶轮转子系统
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超高速离心叶轮转子系统由齿轮轴、离心叶轮、锁紧螺母、导流罩、密封组件、可倾瓦滑动轴承等组成，如图1所示。
超高速离心叶轮转子系统的密封组件与齿轮轴过盈配合，离心叶轮与齿轮轴采用过渡配合，通过锁紧螺母将离心叶轮固定在齿轮轴上，导流罩通过锁紧螺母固定在齿轮轴上。
因锁紧螺母与齿轮轴螺纹之间、离心叶轮与转轴之间有间隙，导致转子系统装配完成后会有质量不平衡，综合零部件材质不均造成的质量不平衡，虽有部件动平衡和组件动平衡环节，可将不平衡质量控制在一定范围内，但对于超高速跨临界柔性转子系统而言，常规的双面动平衡无法有效抑制不平衡激励引起的剧烈的振动响应。
为了准确有效地控制超高速离心叶轮转子系统的不平衡激励的振动响应，需综合考虑滑动轴承的变支撑刚度、阻尼、不平衡激励大小等性能参数，以便控制计算分析方法的精确性。
2　超高速离心叶轮转子系统动力学响应分析
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2.1　超高速离心叶轮转子系统计算模型
将超高速离心叶轮转子系统进行简化，并建立Ansys转子动力学响应分析模型[12]33-37，如图2所示。
超高速离心叶轮转子系统各转动部件的材料属性如表1所示。
2.2　滑动轴承支撑刚度与阻尼
超高速离心叶轮转子系统的动力学特性除本身结构参数外，滑动轴承的支撑刚度与阻尼对动力学特性的影响至关重要[13]。
转子与滑动轴承间的受力分析如图3所示，滑动轴承动压油膜向心力Fe和切向的分力Fφ形成支撑转子系统的支撑力，使转子稳定可靠运行。Fe和Fφ分别为
式中，Fe为动压油膜向心力，N；Fφ为动压油膜切向力，N；l为滑动轴承长度，mm；φ为圆柱坐标系圆周方向，rad；φ1为动压油膜起始角度，rad；φ2为动压油膜截止角度，rad；r为滑动轴承半径，mm；z为圆柱坐标系长度方向，mm；p为动压油膜压力，Pa。
根据雷诺边界条件确定的积分边界，基于不可压缩定常流动的二维雷诺方程[14-15]，采用Ansys的热力学分析模块求解二维雷诺方程，借助二次编程，采用二分法求解动压油膜的压力分布p，图4为滑动轴承动压油膜的压力分布图，其求解及迭代计算的流程如图5所示，进而积分求得动压油膜向心力Fe和切向的分力Fφ，有
式中，h为动压油膜厚度，mm；μ为润滑油动力黏度，Pa·s；p为动压油膜压力，Pa；Ω为转轴运动速度，m/s。
根据超高速离心叶轮转子系统的载荷、转速等，利用上述计算分析方法，求解动压油膜的承载力、最小油膜厚度以及支撑刚度与阻尼等关键参数，以便获得良好的动力学特性，滑动轴承输入参数如表2所示。
因超高速离心叶轮转子系统工作时负载稳定，径向载荷以转子自重为主，根据不同转速下得到的轴承刚度与阻尼，其偏差为2%~3%，故将滑动轴承的动刚度与阻尼考虑为满转速时的刚度与阻尼，其计算参数如表3所示。
动压油膜承载力是由其压力分布P积分所得，因此压力对位移和速度扰动的导数直接决定了滑动轴承动压油膜的动力学特性（动压油膜的刚度系数和阻尼系数）。根据Reynolds边界条件可知，在动压油膜破裂处φ2的压力等于零，即Pφ2=0。则得到高速滑动轴承动压油膜的8个动力学特性系数，其刚度和阻尼系数分别为
2.3　超高速离心叶轮转子系统动力学分析
超高速离心叶轮转子系统采用柔性转子设计方案，其一阶临界转速需远离设备的工作区间，且二阶临界转速需远离设备的最高转速，为确保临界转速在适宜的转速范围内，需要在设计阶段准确地核算转子系统的临界转速。
本文采用Ansys中Modal模态分析模块，通过第2.1节建立的超高速离心叶轮转子系统动力学分析模型，设置支撑轴承的刚度矩阵与阻尼矩阵，可达到超高速离心叶轮转子系统的坎贝尔图，如图6所示。
为了得到超高速离心叶轮转子系统的坎贝尔图，设定转子系统转速梯度，进行求解计算。
由图6可知，该超高速离心叶轮转子系统在转速区间内共有4个临界转速点，且在第4临界转速点之后已超出转子系统的转速区间，故该超高速离心叶轮转子系统转速区间内共有4个临界转速点，如表4所示，但由于不平衡质量引起的转子系统涡动以正进动为主，在工程应用中忽略反进动存在的临界转速点，故该转子系统只有1个临界转速，即1 937.4 rad/s（18 510.2 r/min，额定转速的35.7%），该临界转速的振型如图7所示。
由超高速离心叶轮转子系统的一阶临界转速振型可知，该振型为伞形振动，对悬臂质量的变化异常敏感，若要调整超高速离心叶轮转子系统的临界转速，可对离心叶轮进行减重处理。另外，也可修改轴承跨距，匹配滑动轴承的支撑刚度与阻尼等，优化转子系统的临界转速点。
2.4　不平衡响应分析
超高速离心叶轮转子系统因为转速高，不平衡质量对系统的影响大，特别是在过一阶临界转速时，剩余不平衡质量作为激励源，会引起超高速转子系统的剧烈振动[16]，所以对该转子系统不平衡质量的响应分析至关重要。
超高速离心叶轮转子系统为悬臂结构，根据API 617—2002的规定，其不平衡响应分析时不平衡质量添加在叶轮上，根据高精密转子的动平衡精度要求和动平衡机的实际精度，确定超音速离心叶轮转子系统的不平衡质量。
本文采用Ansys中Harmonic Response谐响应分析模块，对超高速离心叶轮转子系统进行剩余不平衡质量的振动响应分析，计算模型如图8所示。
依据ISO 1940：2003不平衡等级分类，测算不同的不平衡质量，如表5所示。选定离心叶轮0.05 m的半径处为剩余不平衡质量的加重点，添加不平衡质量，设置好滑动轴承刚度与阻尼，考虑陀螺效应的影响，进行分析求解。
为减小计算量，在坎贝尔图确定的临界转速不低于±15%的转速区间内，核算该区域的振动响应。图9所示为超高速离心叶轮转子系统的不平衡等级为G0.4级的响应分析结果。由图9可知，在320 Hz时，振动速度值有明显的波峰，跨过该频率后振动速度值随频率增加而减小，可判定为临界转速点。
根据上述计算结果，在不同剩余不平衡质量的激励下，超高速离心叶轮转子系统的响应主频率和幅值汇总如表6所示。
根据上述计算分析结果，临界转速不会因不平衡质量的改变而发生变化，但不平衡质量的增加会导致不平衡响应幅值急剧增大，G6.3级响应幅值相较G0.4级大了15.78倍，故若剩余不平衡质量大，在跨临界转速时会产生破坏性的后果。根据ISO 10816系列标准对高精密齿轮箱的振动速度有限值的限定，超高速离心叶轮转子系统不平衡响应幅值≤4.5 mm/s，故其动平衡等级要优于G1级。
3　超高速离心叶轮转子系统动力学特性试验
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超高速离心叶轮转子系统采用跨临界柔性转子设计，为确保转子系统平稳地跨临界，需严格控制转子系统的剩余不平衡质量。超高速离心叶轮转子系统的不平衡对动力学响应的影响极大，故试验过程中要保证动平衡精度等级高于G2.5级，并据此对转子系统进行动平衡。在G0.4~G2.5，确定1个优于G1级剩余不平衡质量为0.008 g、1个优于G2.5级的剩余不平衡质量为0.011 g，做完常规动平衡的超高速离心叶轮转子系统进行动力学特性试验。
试验过程采用DEWESoft振动测试系统对超高速离心叶轮转子系统的基频振动速度值跟踪记录，并与Ansys不平衡质量的谐响应分析结果进行对比分析，准确评判超高速离心叶轮转子系统的动力学特性及动平衡精度是否满足超高速跨临界柔性转子的剩余不平衡质量的要求。
试验系统采用永磁同步电动机驱动系统，通过柔性膜片联轴器驱动增速齿轮箱，经2级增速后，达到离心叶轮的工作转速。该试验系统采用高速离心风机性能试验平台，叶轮进气口通过进口消声器从进风廊道进气，出气口连接试验管道，通过管道上的阀门调整风机的运行压力，模拟实际运行时的工况压力。通过变频器调节驱动电动机的转速，以改变超高速离心叶轮转子系统的运行转速，获取转子系统不同转速下的振动速度值，试验结构如图10所示。
超高速离心叶轮转子系统为跨临界柔性转子系统，故其临界转速±15%区间内基频的振动幅值至关重要。为确保转子系统能顺利跨越临界转速，特记录80%一阶临界转速时的基频振动幅值，振动测试系统界面如图11所示。
试验过程中，采用PCB振动加速度传感器，布置在高速轴靠近轴承位置处的垂直、轴向和水平3个方向进行监测，由振动波形图和频谱图构成监测界面，如图12所示。由此可定位不同转速的振动波形图和相对应的频谱图，可从频谱图读出不同转速下超高速离心叶轮转子系统基频的振动幅值。
试验时，根据前期计算结果，将全转速范围分为8个转速区间，利用变频器调整永磁电动机的转速，并由DEWESoft振动测试系统实时记录超高速离心叶轮转子系统的基频振动速度值。
根据超高速离心叶轮转子系统的振动测试数据，如表7所示，当动平衡精度优于G1级时，全转速范围内振动速度值均较小，且过临界时振动值变化不大，振动波形图未出现波峰，符合柔性转子跨临界时的振动烈度限制要求。
为对比不同平衡精度的转子振动烈度情况，特更换动平衡精度优于G2.5但不满足G1的超高速离心叶轮转子，在共振点处振动速度值为4.83 mm/s，超出了标准要求值，且在波形图中出现较大冲击峰值，跨过临界转速后振动速度值恢复正常后，满足标准要求。
此外，由振动冲击波峰处频谱图可知，振动能量的主频率为346.4 Hz，该频率值处3个方向的振动值迅速增大，波形图出现波峰值，跨过该转速后转子振动趋于正常，该频率即为超高速离心叶轮转子系统的实际一阶临界转速，其与理论计算值320 Hz相差7.62%，结果偏差较小，对于工程应用有极大的参考意义，证明了计算结果与试验验证结果的相符性。
4　结论
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超高速离心叶轮转子系统对于不平衡激励的动态响应异常敏感，一旦动平衡精度等级不够，在跨临界时振动速度有效值剧烈增大，振动能量会导致高速转子失稳，产生破坏性的后果。
本文应用Ansys转子动力学谐响应分析模块，研究了超音速离心叶轮转子系统不平衡响应，主要结论如下：
1）对于超高速离心叶轮转子系统，其动平衡精度等级需优于G1级，有效控制剩余不平衡质量的振动响应烈度，可确保在跨临界时转子系统能平稳过渡，避免振动剧烈引起的转动部件剐蹭。
2）对于超高速离心叶轮转子系统的不同动平衡精度等级，85%临界转速下的振动幅值已存在明显差异。在实际工程应用中，可通过监测跨临界前转子系统的振动幅值，评估其平衡精度是否满足要求，若剩余不平衡质量较大，可据此进行超高速离心叶轮转子系统的在线动平衡。
3）超高速离心叶轮转子系统的一阶临界转速振型，以离心叶轮绕轴承支撑位置的伞形振动为主，故要确保气动效率的前提下，预留足够的叶间间隙，避免出现叶轮剐蹭。
4）超高速离心叶轮转子系统的动力学特性对悬臂质量异常敏感，为确保跨临界柔性转子的临界转速远离工作区间，可对离心叶轮进行质量优化，配合轴承刚度与阻尼的设计，确保一阶临界转速远离工作转速区。
因超高速离心叶轮转子系统实际运行时，齿轮啮合区会形成高压油膜，形成对转子系统的辅助支撑，使转子系统的实际临界转速略高于计算值，后续可对啮合油膜刚度对高速齿轮轴转子动力学特性的影响做深入研究。本文具有重大的工程应用意义，有助于单级大压比离心压缩机的研发。
基金
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  • 湖南省科技创新计划项目(2020GK4059)
文献
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2025年第47卷第1期
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doi: 10.16579/j.issn.1001.9669.2025.01.005
  • 接收时间：2023-06-14
  • 首发时间：2026-03-18
  • 出版时间：2025-01-15
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  • 收稿日期：2023-06-14
  • 修回日期：2023-08-30
基金
Hunan Province Science and Technology Innovation Program(2020GK4059)
湖南省科技创新计划项目(2020GK4059)
作者信息
    1.西安交通大学 机械工程学院，西安　710049
    2.湖南泛航智能装备有限公司，株洲　412002
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2种不同金属材料的力学参数
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Number of
species		 占总种数比例
Percentage of
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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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