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Article(id=1222513214680720286, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1222513210519970621, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202303035, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1678291200000, receivedDateStr=2023-03-09, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1769399463577, onlineDateStr=2026-01-26, pubDate=1700841600000, pubDateStr=2023-11-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1769399463577, onlineIssueDateStr=2026-01-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1769399463577, creator=13701087609, updateTime=1769399463577, updator=13701087609, issue=Issue{id=1222513210519970621, tenantId=1146029695717560320, journalId=1210938733613449225, year='2023', volume='52', issue='11', pageStart='1', pageEnd='198', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1769399462585, creator=13701087609, updateTime=1769405983425, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1222540560984957089, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1222513210519970621, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1222540560984957090, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1222513210519970621, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=132, endPage=139, ext={EN=ArticleExt(id=1222513215406334920, articleId=1222513214680720286, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Dynamic characteristic analysis of large-size wind turbine rotor based on experimental modal and operational deflection shape, columnId=1213164439017276071, journalTitle=Thermal Power Generation, columnName=Special topic on new energy power generation technology, runingTitle=null, highlight=null, articleAbstract=

Test for large-size wind turbine rotor under static and rotating conditions have been carried out for rotor dynamic characteristis. Based on experimental modal and operational deflection shape, firstly this test obtained modal data using LMS TEST.Lab system by calculating FRFs and curve fitting. Secondly the resonate speed was obtained according to the vibration sweep test. Then modal parameters were analyzed through operational deflection shape test under the resonate speed. The results show that the resonate frequency under rotating condition is different from the resonate frequency under the static condition. And the modal shape of rotor under rotating condition is travelling wave while it is standing wave under static condition. In conclusion, the integral stiffness is decreased when the rotor is rotating which results in the decrease of the resonate frequency, the modal shape turns to be the travelling wave resulting from the rotating magnetic force. This research results can offer a reference and guidance for rotor dynamics evaluation, simulation model modification and parameter input, and optimization design of rotor structure .

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对大型风力发电机转子设备静止和旋转状态下的动力学特性进行了实验分析。研究主要基于实验模态分析和工作变形分析，采用LMS.TESTLAB系统及无线数采系统，首先测试各响应点锤击激励下振动信号，信号经频响函数计算、曲线拟合后得到其各阶模态参数；然后进行全转速振动测量，并根据实验结果选取共振运行工况，进行工作变形测试分析；最终实现转子静态及旋转状态数据收集、模态参数提取和分析。分析结果表明：发电机转子在旋转过程中，发生共振的频率与实验模态频率存在偏差，转子整体刚度减小；且在旋转电磁力作用下，振型由静止状态时的驻波形式变为行波形式。该研究结果对于转子动力学评估、仿真模型修正及参数输入以及转子结构优化设计具有借鉴参考意义。

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马斌（1990），男，硕士，工程师，主要研究方向为设备故障诊断与状态检修，。

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马斌（1990），男，硕士，工程师，主要研究方向为设备故障诊断与状态检修，。

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马斌（1990），男，硕士，工程师，主要研究方向为设备故障诊断与状态检修，。

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articleId=1222513214680720286, language=EN, label=Tab.1, caption=

Statistical table of modal parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数频率/Hz振型描述
119.45一阶左右摆动
229.36轴向前后窜动
333.92二阶弯曲振动
462.12三阶弯曲振动
), ArticleFig(id=1241137068303249867, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1222513214680720286, language=CN, label=表1, caption=

模态参数统计

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数频率/Hz振型描述
119.45一阶左右摆动
229.36轴向前后窜动
333.92二阶弯曲振动
462.12三阶弯曲振动
), ArticleFig(id=1241137068429078996, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1222513214680720286, language=EN, label=Tab.2, caption=

Vibration information statistical of ODS

, figureFileSmall=null, figureFileBig=null, tableContent=
测点位置主振频率/Hz最大幅值/g相对相位/(°)
测点132.680.240
测点232.680.2847.2
测点332.680.3994.4
测点432.680.37118.0
测点532.680.34135.7
测点632.680.29153.4
测点732.680.26177.0
), ArticleFig(id=1241137068525547990, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1222513214680720286, language=CN, label=表2, caption=

工作变形分析各测点振动信息统计

, figureFileSmall=null, figureFileBig=null, tableContent=
测点位置主振频率/Hz最大幅值/g相对相位/(°)
测点132.680.240
测点232.680.2847.2
测点332.680.3994.4
测点432.680.37118.0
测点532.680.34135.7
测点632.680.29153.4
测点732.680.26177.0
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基于实验模态和工作变形的大型风力发电机转子动力学特性分析
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马斌 , 张庆 , 沙德生 , 李芊 , 王玉玉
热力发电 | 新能源发电技术专题 2023,52(11): 132-139
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热力发电 | 新能源发电技术专题 2023, 52(11): 132-139
基于实验模态和工作变形的大型风力发电机转子动力学特性分析
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马斌 , 张庆, 沙德生, 李芊, 王玉玉
作者信息
  • 中国华能集团清洁能源技术研究院有限公司，北京　102209

    • 马斌（1990），男，硕士，工程师，主要研究方向为设备故障诊断与状态检修，。

Dynamic characteristic analysis of large-size wind turbine rotor based on experimental modal and operational deflection shape
Bin MA , Qing ZHANG, Desheng SHA, Qian LI, Yuyu WANG
Affiliations
  • China Huaneng Clean Energy Research Institute, Beijing 102209, China
出版时间: 2023-11-25 doi: 10.19666/j.rlfd.202303035
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摘要
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对大型风力发电机转子设备静止和旋转状态下的动力学特性进行了实验分析。研究主要基于实验模态分析和工作变形分析，采用LMS.TESTLAB系统及无线数采系统，首先测试各响应点锤击激励下振动信号，信号经频响函数计算、曲线拟合后得到其各阶模态参数；然后进行全转速振动测量，并根据实验结果选取共振运行工况，进行工作变形测试分析；最终实现转子静态及旋转状态数据收集、模态参数提取和分析。分析结果表明：发电机转子在旋转过程中，发生共振的频率与实验模态频率存在偏差，转子整体刚度减小；且在旋转电磁力作用下，振型由静止状态时的驻波形式变为行波形式。该研究结果对于转子动力学评估、仿真模型修正及参数输入以及转子结构优化设计具有借鉴参考意义。

风力发电机转子  /  实验模态  /  工作变形分析  /  振型  /  动态特性

Test for large-size wind turbine rotor under static and rotating conditions have been carried out for rotor dynamic characteristis. Based on experimental modal and operational deflection shape, firstly this test obtained modal data using LMS TEST.Lab system by calculating FRFs and curve fitting. Secondly the resonate speed was obtained according to the vibration sweep test. Then modal parameters were analyzed through operational deflection shape test under the resonate speed. The results show that the resonate frequency under rotating condition is different from the resonate frequency under the static condition. And the modal shape of rotor under rotating condition is travelling wave while it is standing wave under static condition. In conclusion, the integral stiffness is decreased when the rotor is rotating which results in the decrease of the resonate frequency, the modal shape turns to be the travelling wave resulting from the rotating magnetic force. This research results can offer a reference and guidance for rotor dynamics evaluation, simulation model modification and parameter input, and optimization design of rotor structure .

wind rurbine rotor  /  experimental modal analysis  /  operational deflection shape  /  modal shape  /  dynamic characteristic
马斌, 张庆, 沙德生, 李芊, 王玉玉. 基于实验模态和工作变形的大型风力发电机转子动力学特性分析. 热力发电, 2023 , 52 (11) : 132 -139 . DOI: 10.19666/j.rlfd.202303035
Bin MA, Qing ZHANG, Desheng SHA, Qian LI, Yuyu WANG. Dynamic characteristic analysis of large-size wind turbine rotor based on experimental modal and operational deflection shape[J]. Thermal Power Generation, 2023 , 52 (11) : 132 -139 . DOI: 10.19666/j.rlfd.202303035
正文
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在风力发电领域，对于大型变转速运行发电机，其转子尺寸大，刚度低，固有频率一般分布在低频范围。由于其变转速运行，且设计转速较低，在整个运行转速范围内，存在电磁激励力同结构固有频率接近或重叠情况，即存在共振转速工况[1-2]。受产品成本及振动特性的影响，一般设计上重点考虑产品额定工况电磁激励力的基频及二倍频避开结构一阶和二阶模态频率的一定范围[3]。然而即便满足以上设计要求，仍然需要关注其他转速下电机的振动情况，对于振动较大的转速工况，需根据实际测试振动幅值，结合振动疲劳仿真等做出可靠性评估[4-5]。因此，开展电机转子固有属性及动力学特性的研究，有助于在产品设计和仿真模拟初期合理评估其振动特性，规避产品动力学设计问题[6-7]。
目前，对于发电机转子的动力学研究多采用有限元仿真分析的方式。文献[8-9]通过建立转子系统有限元模型，获取转子临界转速，分析了不平衡作用力对转子系统动态特性的影响。文献[10]通过建立进气道流体仿真模型，分析了气流激振力作用下旋转冲压转子的动力学响应特点。文献[11]通过求解静压气体轴承动态刚度系数及动态阻尼系数，研究了供气压力、转速、偏心运行参数对转子动力学参数及稳定性的影响。文献[12]通过建立电磁耦合力表达式，分析了开关磁阻电机电磁耦合状态下转子的弯曲振动规律。这些研究重点考虑电机内一种或几种作用力，然而转子在旋转状态下，存在电磁力、离心力、气动力、偏心、不平衡等多个作用力，且各作用力存在一定耦合，其受力模型复杂，仿真分析难以准确模拟其受力状态。工程上一般通过实验模态参数和仿真模态参数对标的方式，对仿真动力学模型进行修正，以获得较为准确的仿真模型[13]。然而实验模态参数是在转子静止状态下测试提取，与实际旋转状态的模态参数存在差异。实验模态参数作为转子动力学评估的模型修正或仿真输入参数，本身存在一定误差。
为准确合理评估转子动力学特性，需获取实际运行状态下转子动力学参数。本文针对发电机转子静止状态和旋转状态，采用实验模态和工作变形分析方法，对转子的模态参数进行提取分析，研究转子静止和旋转状态的动力学参数变化特性。首先，采用LMS.TESTLAB系统，对某外转子永磁同步发电机进行实验模分析，获取转子静态模态参数；然后，采用无线数采设备采集各转速工况转子振动信号，分析转子动力学响应；最后，对转子进行工作变形测试，提取各测点相位和幅值信息，拟合转子旋转状态下的主要振型，分析旋转状态下转子的动力学变化特性。
1　实验原理及方法
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1.1　激励源分析
本文实验发电机类型为3 MW直驱永磁同步风力发电机，永磁磁钢为表贴式，双套绕组，星型连接，双套绕组相移30°。发电机为外转子、内定子结构，外转子为对称结构。发电机轴系由定轴、转轴和双轴承组成，其中定轴连接实验台底座工装及定子支架，转轴连接转子支架，各部件间皆为螺栓刚性连接。转子极数与定子槽数的极槽比为25/78（极数100，槽数312），转速设计范围为6.0~15.4 r/min。
由于大型风力发电机转速较低，机械旋转激励远离结构模态频率，因此不考虑机械方面的激励力。除机械激励外，电磁激励同样为发电机的主要激励源。永磁同步发电机电磁激励力频率主要为电流基波频率及其倍频，以及定子铁心开槽导致的齿槽频率。电磁激励力频率计算方法为[14]：
fp=f×p×n
fz=f×z×n
式中：fр表示电流频率；p表示电机磁极对数；fz表示齿槽频率；z表示槽数；f表示发电机转频；n为正整数，表示激励频率的倍频。
发电机通用的径向电磁激励力计算方法为[15-16]：
P(θ,t)=b2(θ,t)/2μ0
b(θ,t)=f(θ,t)×λ(θ,t)
式中：P(θ,t)表示电磁激励力；b(θ,t)表示磁场密度；μ0表示空气磁导率；θ表示相位参数；t表示时间参数；f(θ,t)表示磁动势；λ(θ,t)表示气隙磁导。可见，电磁激励力主要由磁动势和气隙磁导的特征决定。转子偏心、转子不圆、定子铁心开槽、永磁体结构设计、定子电流谐波含量等都将影响磁动势和气隙磁导的空间和时间分布，从而影响发电机的电磁激励力。
根据上述电机设计参数及电磁激励公式计算可知，实验电机齿槽频率较高，远离结构的低阶模态频率，可不予考虑。电机的电流基波频率及倍频频率较低，需要重点关注。经过初步测试分析，实验发电机由于安装问题，转子外圆存在一定变形，测量的发电机气隙轮廓如图1所示。转子不圆导致气隙磁场发生非正弦性畸变，最终导致谐波电磁激励增大。本文除分析实验模态和工作变形外，还将对该发电机进行振动测量，以确定其全转速范围内的振动特性。
1.2　振动测量实验
为获取工作转速范围内转子结构的振动响应进行振动测量实验。通过振动测量，可计算得到全转速范围内转子的振动色谱图。联合振动色谱图及后续实验模态测试结果，分析转子全转速范围内是否存在结构共振，并最终确定工作变形测试的最佳运行工况。
由于电机转子为对称结构，振动测量时其测点分布如图2所示。选用IEPE式加速度传感器，发电机转子轴向上均布3个测点，周向上每隔60°布置1个测点，共计9个测点。振动测量时，转子处于旋转状态，选用无线振动采集设备收集振动信号，通过变频器控制电机转速，采集设计转速范围内（6.0~15.4 r/min）的振动信号，转速间隔设置为0.1 r/min，每个转速下运行90 s，采集频率设置为2 000 Hz。数据采集后，绘制各转速工况振动信号的频谱图，最终形成全转速范围的色谱图，通过色谱图分析转子振动特性。无线设备通过胶黏方式固定于转子表面，通过WIFI无线方式将振动信号实时回传到采集所用电脑。
1.3　模态参数实验
1.3.1　模态参数实验方案
结构模态参数的实验方法，一般可分为实验模态、工作模态和工作变形分析。实验模态一般在实验室或厂内进行，采用锤击或激振器激励，可获得较好的信号质量，但是结构边界条件和实际现场安装条件会存在差异；工作模态一般在实际安装现场进行，通常采用环境激励或其它可用激励，如桥梁采用车辆激励，大型叶片采用风激励等，其激励源不可控，信号质量较差，但结构边界条件为实际边界条件，数据可直接应用现场分析[17-18]；工作变形分析一般指结构处于工作状态时，测试结构的振动响应，提取响应的幅值相位等信息，分析其实际振型形态和振动特性。由于工作变形测试时，结构同时存在强迫响应和可能的共振响应，其振型实际为各种振动响应的叠加[19-20]。因此在做工作变形分析时，一般还需要结合实验模态参数判断工作状态下具体的动力学特征。
本文基于实验模态和工作变形分析方法进行相关实验分析。实验模态用于确定结构的固有属性参数分布，工作变形用来分析转子实际旋转状态下的振型和频率变化。通过分析模态参数变化，研究转子在不同状态下的结构动力学特性，为结构优化设计和动力学仿真等提供方向及数据支撑。
模态实验测点布置需根据仿真预实验结果进行，依据模态振型信息，振动拾取位置应避开振型节点，避免振动传感器拾取不到振型信号。本次实验中，为全面清晰获取实验模态振型信息，在转子周向均布24个传感器，同时在轴向上布置2层传感器，共计48个测点，采用分批测量方式，使用力锤进行模态激励。具体布点模型如图3所示。
进行工作变形测试时，转子处于旋转状态，需要选用无线采集设备收集振动信号。由于本次实验无线设备通道数量受限，采用在周向90°范围内，均布7个测点，采集运行过程中的振动信号。测点轴向具体位置根据振动测试结果确定，应保证测点位于变形的敏感区域。由于转子为对称型结构，因此在获取工作变形振型后，可通过模态振型的对称性，将90°振型扩展至360°。工作变形测试时，测点及无线设备布置如图4所示。
1.3.2　模态参数分析方法
模态实验采用锤击激励法，数据采集及处理使用LMS.TESTLAB模块，分析带宽设置为200 Hz，采集力锤的激励信号和振动传感器拾取的响应信号。锤击激励信号能量较大，信噪比高，而大型结构导致部分远离锤击位置的测点响应信号能量小，信噪比低。因此，可将此实验假设为响应信号受噪声干扰，而激励信号无噪声干扰的模型。实际响应信号模型公式为：
Y(ω)=X(ω)+N(ω)
式中：Y(ω)表示实际响应信号；X(ω)表示理想响应信号；N(ω)表示噪声干扰。
计算频响函数时，采用H1估算式，通过7次锤击求平均的方式降低噪声干扰。H1估计式的实现方式为[21]：
H1(ω)=GfY(ω)/Gff(ω)=(GfX(ω)+GfN(ω))/Gff(ω)
式中：GfY(ω)表示激励和实际响应的互功率谱；Gff(ω)表示激励的自功率谱；GfX(ω)表示激励和理想响应信号的互功率谱；GfN(ω)表示激励与噪声信号的互功率谱。由于噪声干扰同响应信号和激励信号不相关，因此噪声与激励力的互功率在多次测量平均后可有效降低，当平均次数足够多时，噪声干扰可认为降低为零[21]。
获得频响函数后，采用最小二乘复频域数法进行曲线拟合，通过多阶迭代稳态图的方式，判断结构的模态频率。在进行迭代计算时，频率容差设置为0.2，阻尼比容差设置为0.5。当确定频率和阻尼后，通过计算留数和选定带宽外的上下残余项，确定模态振型。
对于工作变形分析，采用无线数采设备同步采集各测点振动信号，通过变频器调节发电机转速至选定工况。采集时长150 s，设置采样频率5 000 Hz。数据采集结束，选定某一测点为参考点，进行相位偏差计算：
θ=Nij/NT×360
式中：θ表示相位角度；Nij表示测点i的峰值点和测点j的峰值点相差的采样点数；NT表示1个振动周期时间内的采样点数，且为所有测点采样点数的平均值。结合各点相位偏差和幅值大小，将相关信息输入测点模型，可动态显示运行过程中的转子变形振型及频率信息。
2　实验结果分析
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2.1　振动测量分析
对发电机转子全转速范围进行振动测试，绘制测试数据色谱图，结果如图5所示。由图5可知，转子振动在0~100 Hz范围内存在多个激励源，激励力频率与转速存在线性关系，经计算为电流基波频率和基波频率倍频。其中，非驱动端侧测点振动明显较大，电流基波频率的4倍频（33.33 Hz）在10 r/min时振动幅值最高。根据振动响应特点，可初步判断存在共振情况，且主振位置靠近发电机非驱动侧。
2.2　模态参数分析
2.2.1　实验模态分析
根据前述方案进行实验模态测试，锤击过程中选择多个锤击点进行激励，以避免锤击到振型节点位置而造成对应模态丢失。模态参数提取结果见表1。其中，一阶摆阵和二阶弯曲模态的振型图如图6、图7所示。由测试结果可知，50 Hz范围内转子存在三阶模态，模态振型整体较为平滑，振型结果较理想。
对测试结果进行相关性MAC验证，结果如图8所示。由图8可知，不同阶数的模态振型之间MAC值低于10%，各振型不相关，振型提取质量较好。
根据模态参数提取结果，绘制转子系统坎贝尔图，结果如图9所示。由图9可知，基波倍频激励频率和模态频率存在多个交点工况，这些交点对应的转速为潜在的共振工况。由振动测量分析得知10 r/min工况存在振动峰值，可判断该发电机转子存在共振工况，共振转速为10 r/min。
2.2.2　工作变形分析
针对上述数据分析情况，在非驱动侧周向0~90°范围内均匀布置7个传感器，将电机转速调至10 r/min，转速稳定后，采集其运行状态下的振动数据。运行过程中振动信号时域图谱如图10所示，频域图谱如图11所示。由于转子转速较低，在低频范围内结构无显著振动激励，但在转子旋转过程中，振动传感器受本身工作特性影响会输出转频周期的信号，此信号非结构真实振动信号，因此图10中的振动信号进行了2 Hz的高通滤波。从图10和图11可以看出，各测点振动幅值处于同一量级，各测点信号间存在一定的相位偏差。振动主要频率为32.68 Hz，此频率同时也是基波4倍频的边频频率（基波4倍频33.33 Hz，转频0.33 Hz）。
通过式(7)计算获取运行过程中各测点的相对振动相位，对振动相关信息进行统计，结果见表2。
将获取的振动测点幅值和相位信息输入测点模型，动画显示不同时刻转子振型状态。各测点振型显示如图12所示，根据其对称特性，将振型扩展至全结构如图13所示。
由图12、图13可知，在运行过程中，转子的变形形式同二阶弯曲振型一致，各测点振动幅值相当，且存在一定的相位偏差，即旋转状态下，二阶弯曲振型沿转子周向旋转，振型为行波特征。
3　结论
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1）通过实验模态分析和工作变形分析，得出发电机转子在旋转过程中，实际转子边界条件已经发生改变，转子整体刚度降低，静止状态转子二阶弯曲频率为33.92 Hz，实际旋转状态二阶弯曲共振频率为32.68 Hz。
2）发电机磁场为旋转磁场，电磁激励既是空间分布函数，也是时间函数，在电磁力时间-空间激励下，转子振型由静止状态下的驻波特征变为行波特征。以转子实际旋转状态下动力学参数作为仿真模型修正或输入参数，能够更加合理准确评估转子动力学响应特性，为振动问题解决、结构优化设计提供指导和参考。
基金
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  • 中国华能集团清洁能源技术研究院有限公司研究与开发基金项目(QNYJJ22-18)
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2023年第52卷第11期
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doi: 10.19666/j.rlfd.202303035
  • 接收时间：2023-03-09
  • 首发时间：2026-01-26
  • 出版时间：2023-11-25
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  • 收稿日期：2023-03-09
基金
Research and Development Fund Project of China Huaneng Clean Energy Research Institute(QNYJJ22-18)
中国华能集团清洁能源技术研究院有限公司研究与开发基金项目(QNYJJ22-18)
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    中国华能集团清洁能源技术研究院有限公司，北京　102209
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