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Article(id=1227620264297558662, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227620260010979924, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.05.018, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1652112000000, receivedDateStr=2022-05-10, revisedDate=1660147200000, revisedDateStr=2022-08-11, acceptedDate=null, acceptedDateStr=null, onlineDate=1770617079090, onlineDateStr=2026-02-09, pubDate=1716825600000, pubDateStr=2024-05-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770617079090, onlineIssueDateStr=2026-02-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770617079090, creator=13701087609, updateTime=1770617079090, updator=13701087609, issue=Issue{id=1227620260010979924, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='5', pageStart='729', pageEnd='902', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770617078068, creator=13701087609, updateTime=1770795280844, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228367696677499202, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227620260010979924, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228367696677499203, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227620260010979924, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=896, endPage=902, ext={EN=ArticleExt(id=1227620264565994132, articleId=1227620264297558662, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Angle compensation synchronous averaging for fault feature extraction of planet gear in two-stage planetary gearbox, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The windowed synchronous averaging （WSA） is commonly applied to the fault detection of planetary structures since it can overcome the problem of time-varying transfer path. However，it is unsuitable for the fault feature extraction of the planet gear at the first stage in a two-stage planetary gearbox due to the vibration coupling caused by the two-stage planetary structures. To address the issue，an angle compensation synchronous averaging scheme is proposed in this paper. In the proposed scheme，the speed fluctuation of the observed vibration is eliminated by equal-angle resampling. The second-stage interference from the sun gear at the second stage is constructed by applying the synchronous averaging to the resampled vibration based on the angle compensation strategy. The second-stage interference is removed by subtracting it from the resampled vibration. The corresponding envelope signal is extracted by the envelope analysis from the residual vibration. The WSA is utilized to construct the synthetic envelope signal of the planet gear at the first stage. The envelope synchronous averaging is used to suppress the asynchronous interference and extract the fault feature of the planet gear. According to the experimental results of a two-stage planetary gearbox test rig，the effectiveness of the proposed method is verified.

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加窗同步平均克服了行星齿轮传动引起的振动传递路径时变性问题，可有效应用于单级行星齿轮箱齿轮故障特征提取。但二级行星齿轮箱存在两级行星结构共用传动轴引起的振动耦合问题，该方法不易有效提取第一级行星轮的故障特征，为此本文提出一种角度补偿同步平均的二级行星齿轮箱行星轮故障特征的提取方法。通过等角度重采样消除转速波动的影响；采用角度补偿同步平均分离重采样振动中存在的第二级太阳轮的干扰，并通过差运算将其从重采样振动中消除；提取残余振动的包络信号；通过加窗同步平均构建第一级行星轮的合成包络信号，并采用包络同步平均提取第一级行星轮的故障特征。通过二级行星齿轮箱实验台实测信号分析验证，所提方法能够有效地提取第一级行星轮的故障特征。

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郭瑜（1971―），男，博士，教授。E-mail：。
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晏云海（1989—），男，博士研究生。E-mail：。

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晏云海（1989—），男，博士研究生。E-mail：。

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晏云海（1989—），男，博士研究生。E-mail：。

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Cleveland， OH， USA： NASA Glenn Research Center， 2004., articleTitle=Planetary transmission diagnostics： NASA technical report NASA/CR-2004-213068, refAbstract=null), Reference(id=1227675676694737320, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, doi=null, pmid=null, pmcid=null, year=2021, volume=34, issue=6, pageStart=1293, pageEnd=1304, url=null, language=null, rfNumber=［13］, rfOrder=15, authorNames=王朝阁, 李宏坤, 曹顺心, journalName=振动工程学报, refType=null, unstructuredReference=王朝阁， 李宏坤， 曹顺心， 等. 改进VMD和非凸重叠组收缩降噪的行星齿轮箱早期故障特征提取［J］. 振动工程学报， 2021， 34（6）： 1293-1304., articleTitle=改进VMD和非凸重叠组收缩降噪的行星齿轮箱早期故障特征提取, refAbstract=null), Reference(id=1227675676799594926, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, doi=null, pmid=null, pmcid=null, year=2021, volume=34, issue=6, pageStart=1293, pageEnd=1304, url=null, language=null, rfNumber=［13］, rfOrder=16, authorNames=WANG Chaoge, LI Hongkun, CAO Shunxin, journalName=Journal of Vibration Engineering, refType=null, unstructuredReference=WANG Chaoge， LI Hongkun， CAO Shunxin， et al. 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caption=所提方法和原始信号的包络谱分析, figureFileSmall=2i+vjmSvt8T8IJ2zqbm1Eg==, figureFileBig=OH9+Pzb56f2CXL8jZkNmTw==, tableContent=null), ArticleFig(id=1227675672613679381, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, language=EN, label=Fig.15, caption=Envelope spectrum analysis of the proposed method and conventional method, figureFileSmall=qCXQlU58JqVB67Memfzhvg==, figureFileBig=qEmlTmZ0aca2YKKxxOTQ7w==, tableContent=null), ArticleFig(id=1227675672693371161, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, language=CN, label=图15, caption=所提方法和传统方法的包络谱分析, figureFileSmall=qCXQlU58JqVB67Memfzhvg==, figureFileBig=qEmlTmZ0aca2YKKxxOTQ7w==, tableContent=null), ArticleFig(id=1227675672798228767, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, language=EN, label=Tab.1, caption=

Gear parameters

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类型太阳轮齿数行星轮齿数齿圈齿数
第一级齿轮组202673
第二级齿轮组232167
), ArticleFig(id=1227675672890503464, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, language=CN, label=表1, caption=

齿轮参数

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类型太阳轮齿数行星轮齿数齿圈齿数
第一级齿轮组202673
第二级齿轮组232167
), ArticleFig(id=1227675672974389549, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227620264297558662, language=EN, label=Tab.2, caption=

Characteristic orders of the first-stage planet gear

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类型啮合阶次故障阶次
第一级行星轮73.00×2.81×
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第一级行星轮的特征阶次

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类型啮合阶次故障阶次
第一级行星轮73.00×2.81×
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The meshing sequence of the first⁃stage planet gear

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行星架转数行星轮标记齿行星架转数行星轮标记齿
111414
222159
317164
4121725
571820
621915
7232010
818215
9132226
1082321
1132416
12242511
1319266
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第一级行星轮啮合齿序

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行星架转数行星轮标记齿行星架转数行星轮标记齿
111414
222159
317164
4121725
571820
621915
7232010
818215
9132226
1082321
1132416
12242511
1319266
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角度补偿同步平均的二级行星齿轮箱行星轮故障特征提取方法
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晏云海 , 郭瑜
振动工程学报 | 2024,37(5): 896-902
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振动工程学报 | 2024, 37(5): 896-902
角度补偿同步平均的二级行星齿轮箱行星轮故障特征提取方法
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晏云海 , 郭瑜
作者信息
  • 昆明理工大学机电工程学院，云南昆明　650550

    • 晏云海（1989—），男，博士研究生。E-mail：。

通讯作者:

郭瑜（1971―），男，博士，教授。E-mail：。
Angle compensation synchronous averaging for fault feature extraction of planet gear in two-stage planetary gearbox
Yun-hai YAN , Yu GUO
Affiliations
  • Faculty of Mechanical and Electrical Engineering，Kunming University of Science and Technology，Kunming 650550，China
出版时间: 2024-05-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.05.018
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摘要
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加窗同步平均克服了行星齿轮传动引起的振动传递路径时变性问题，可有效应用于单级行星齿轮箱齿轮故障特征提取。但二级行星齿轮箱存在两级行星结构共用传动轴引起的振动耦合问题，该方法不易有效提取第一级行星轮的故障特征，为此本文提出一种角度补偿同步平均的二级行星齿轮箱行星轮故障特征的提取方法。通过等角度重采样消除转速波动的影响；采用角度补偿同步平均分离重采样振动中存在的第二级太阳轮的干扰，并通过差运算将其从重采样振动中消除；提取残余振动的包络信号；通过加窗同步平均构建第一级行星轮的合成包络信号，并采用包络同步平均提取第一级行星轮的故障特征。通过二级行星齿轮箱实验台实测信号分析验证，所提方法能够有效地提取第一级行星轮的故障特征。

故障特征提取  /  二级行星齿轮箱  /  加窗振动分离  /  包络分析  /  角度补偿同步平均

The windowed synchronous averaging （WSA） is commonly applied to the fault detection of planetary structures since it can overcome the problem of time-varying transfer path. However，it is unsuitable for the fault feature extraction of the planet gear at the first stage in a two-stage planetary gearbox due to the vibration coupling caused by the two-stage planetary structures. To address the issue，an angle compensation synchronous averaging scheme is proposed in this paper. In the proposed scheme，the speed fluctuation of the observed vibration is eliminated by equal-angle resampling. The second-stage interference from the sun gear at the second stage is constructed by applying the synchronous averaging to the resampled vibration based on the angle compensation strategy. The second-stage interference is removed by subtracting it from the resampled vibration. The corresponding envelope signal is extracted by the envelope analysis from the residual vibration. The WSA is utilized to construct the synthetic envelope signal of the planet gear at the first stage. The envelope synchronous averaging is used to suppress the asynchronous interference and extract the fault feature of the planet gear. According to the experimental results of a two-stage planetary gearbox test rig，the effectiveness of the proposed method is verified.

fault feature extraction  /  two-stage planetary gearbox  /  windowed vibration separation  /  envelope analysis  /  angle compensation synchronous averaging
晏云海, 郭瑜. 角度补偿同步平均的二级行星齿轮箱行星轮故障特征提取方法. 振动工程学报, 2024 , 37 (5) : 896 -902 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.05.018
Yun-hai YAN, Yu GUO. Angle compensation synchronous averaging for fault feature extraction of planet gear in two-stage planetary gearbox[J]. Journal of Vibration Engineering, 2024 , 37 (5) : 896 -902 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.05.018
正文
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1　概述
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行星齿轮箱结构紧凑、传动比大、承载能力强，常应用于风力发电等领域。但由于工况相对恶劣，其齿轮易出现疲劳裂纹等故障［1］。因此，研究行星齿轮箱的故障特征提取技术具有较高的学术和应用价值。
在行星齿轮箱振动响应的研究中，因振动传递路径存在时变性导致多数传统故障特征提取方法应用效果不佳。为克服上述问题，McFadden等［2］首先提出了加窗同步平均（振动分离），依据齿轮箱运行规律对振动信号进行加窗截断，获取齿轮各轮齿的数据块，消除时变传递路径的影响，再经齿序重排、信号拼接、同步平均等步骤有效实现对单级行星齿轮箱的故障特征提取。在后续的研究中，学者们对加窗同步平均的应用进行了改进［3⁃4］并取得了良好的效果，例如，Lewicki等［5］基于振动分离技术在直升机行星传动系统上开展了加窗同步平均的应用研究；Hood等［6］将加窗同步平均方法成功应用于OH⁃58C型直升机主传动系统的太阳轮故障特征提取。在近期对行星齿轮传动系统故障检测和特征提取的研究中，ZHANG等［7］提出了结合最小熵反卷积优点的连续振动分离方法。赵磊等［8］将包络分析与加窗同步平均方法相结合以进行行星齿轮箱齿轮故障特征的提取。Guo等［9］基于窄带解调和振动分离技术提出了行星齿轮组局部故障检测方法。上述方法在单级行星齿轮箱的故障特征提取中已取得了良好的效果。但需要指出的是，现有基于加窗同步平均的方法仅限于输出轴不存在振动干扰的单级行星齿轮箱。对于二级行星齿轮箱，如图1所示，两级行星结构共用传动轴，致使第一级行星结构采集的振动往往包含来自第二级太阳轮的干扰，本文称之为二级干扰。由于二级干扰与基于上述方法构建的第一级行星轮的合成振动具有同轴性，故难以通过同步平均方法进行抑制，导致传统加窗同步平均不易有效提取故障特征。但值得指出的是，由于第二级行星结构与单级行星齿轮箱类似，因此通过传统加窗同步平均方法可以有效提取第二级行星结构太阳轮或行星轮的故障特征。
本文考虑包络分析［10⁃11］具有对振动响应较为微弱的齿轮进行故障特征提取的能力，在研究中提出一种结合包络分析和角度补偿同步平均的二级行星齿轮箱行星轮故障特征的提取方法，用于实现二级行星齿轮箱第一级行星轮的故障特征提取。值得指出的是，理论上所提方法对二级行星齿轮箱中第一级太阳轮和行星轮均有效，然而受现有实验条件的限制，本文仅研究针对第一级行星轮的故障特征提取。通过对二级行星齿轮箱实验台的实测振动开展分析，验证了所提方法在第一级行星轮齿根裂纹故障特征提取中的有效性。
2　加窗同步平均简介
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同步平均是一种广泛应用的齿轮振动特征增强方法［11］，但受振动传递路径时变性的影响而无法应用于行星齿轮箱。为此，提出了加窗同步平均法以消除行星传动的传递路径时变性问题，其流程如图2所示。
行星齿轮箱的振动和转速脉冲序列分别由安装于其齿圈上方的传感器和相位设备同步采集，随后选定行星结构的输出轴（行星架）为参考轴，并通过等角度重采样消除转速波动的影响。随后，以行星轮故障特征提取过程为例对振动分离技术进行介绍。首先加窗截取齿圈固定位置处对应的齿轮啮合重采样振动，形成振动数据块；再计算行星轮的啮合齿序［12］：定义Sg为行星轮各齿重复啮合时行星架的最小转数，则有：
式中　LCM（x，y）表示计算x和y之间的最小公倍数；Np和Nr分别表示行星轮和齿圈的齿数。
行星轮的啮合齿序Ts可计算如下：
式中　mod（x，y）表示计算x和y之间的余数。依据Ts重排振动数据块的顺序，最终可将其拼接为完整的行星轮合成振动。由于在固定位置处对重采样振动进行截取，所构建的合成振动类似于从定轴齿轮箱采集的振动。因此可采用同步平均抑制非同步干扰分量并增强行星轮的周期性故障特征。
然而，在二级行星齿轮箱中，由于两级行星结构共用传动轴，致使采集第一级行星结构的振动时，往往包含来自第二级行星结构太阳轮的干扰（二级干扰）。如前所述，通过加窗同步平均构建的第一级行星轮合成振动应与二级干扰具有相同的参考轴，故难以通过同步平均进行抑制。因此，通过加窗同步平均对第一级行星轮进行故障特征提取的效果往往不佳，甚至失效。
3　角度补偿同步平均及行星轮特征
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3.1　角度补偿同步平均方法
为消除二级干扰的影响，一种可行的方法是在加窗同步平均前对其进行抑制。为此，本文提出一种角度补偿同步平均方法以构建二级干扰。该方法的流程图如图3所示，主要步骤简述如下：
（1）等角度重采样。首先同步采集原始振动和转速脉冲。随后以二级行星齿轮箱公共轴作为参考轴，结合齿轮箱传动比构建参考轴相位脉冲序列。通过等角度重采样消除转速波动，并获得重采样振动。
（2）计算角度偏移。为通过同步平均方法获得第二级太阳轮的啮合振动数据块，需从重采样振动中提取太阳轮各转的数据块并对齐至参考位置。为解释方便，假设参考位置如图4（a）所示（图中加粗齿轮表示太阳轮，非加粗齿轮表示行星轮），太阳轮特定齿（标记为黑点）正好处于啮合状态，同时也为参考轴转速脉冲序列中第一个脉冲的位置。根据行星齿轮传动啮合规律，太阳轮旋转一转后，对应行星轮和太阳轮特定齿的参考位置间存在φ1的角度偏移，如图4（b）所示。若该太阳轮特定齿再次与行星轮啮合（对齐参考位置），则太阳轮需先旋转φ=φ1+φ2的角度，如图4（c）所示。这是由于太阳轮旋转时行星轮同步公转所致，其中角度φ2为在太阳轮旋转角度φ1后，太阳轮特定齿再次与行星轮啮合所需的额外旋转角度。
第二级太阳轮的转角φ1可以通过第二级行星齿轮传动结构的传动比计算：
式中　 r2为第二级行星齿轮传动结构的传动比；Nr2和Ns2分别为第二级齿圈和太阳轮的齿数。
相应的φ2可以计算如下：
式中数值m可由算法中当φ1r2m不大于一个重采样点所对应的角度来确定，即r2m≤（2π/fr）/φ1，其中，fr为等角度重采样率。随后，通过对不等式两侧同时取对数，并将不等式左侧的lnr2移动至右侧即可推导出m的计算公式。需要注意的是，通过式（3）可以确定r2<1，由此移动lnr2将致使不等号方向改变。说明m的取值不低于不等式右侧的计算结果。由于m表示迭代次数，因此需要对其进行向上取整，相应最终的推导公式如下式所示：
式中　 表示对x向上取整。最终，角度偏移φ可通过对φ1与φ2进行求和得到。
（3）提取第二级太阳轮啮合振动数据块。为通过同步平均方法获得第二级太阳轮的啮合振动数据块，对齐第二级太阳轮各转数据块的相位是关键。通过步骤2）获得的角度偏移φ可以从重采样振动中提取出第二级太阳轮各转对应的数据块，相应的流程如图5所示。为对齐第二级太阳轮各转对应数据块的相位，在太阳轮的特定齿从参考位置旋转s转后，需要额外旋转增量角sφ，才能够使特定齿与对应行星轮再次啮合。因此，要从重采样振动中提取太阳轮第s转对应的数据块时（数据块长度对应太阳轮的一个完整旋转周期），太阳轮需要偏移一个补偿角度sφ，以实现各数据块与太阳轮特定齿参考位置的相位对齐。最后再通过同步平均提取第二级太阳轮一个周期内的同步振动分量，得到第二级太阳轮的啮合振动数据块。
（4）构建二级干扰。如前所述，为提取二级行星齿轮箱中第一级行星轮的故障特征，需要从重采样振动构建并消除二级干扰。需要注意的是，二级干扰由第二级太阳轮各转对应的数据块组成，其数据长度应与重采样振动相同。而第二级太阳轮啮合振动数据块只对应其一个旋转周期的数据长度。但通过对第二级太阳轮啮合振动数据块进行延拓和连接，可构建出长度与重采样振动相同的二级干扰。然而，延拓将使太阳轮第s转的数据块基于角度sφ向前移动若干数据点，因此在连接前需要将第s转的数据块基于角度sφ向后移动若干数据点，如图6所示。随后，将数据块末尾超出第二级太阳轮完整一转的部分移动并拼接至数据块前端，如图6所示。相应移动的数据长度可计算如下：
式中　 Ls为移动的数据块长度。需要注意的是，当时，第二级太阳轮的特定齿需旋转一个（或数个）周期后才能对齐参考位置。在此情况下，由于步骤（3）中通过同步平均获取的太阳轮啮合数据块的周期为2π，因此Ls可以由sφ和2π的余数确定。最后通过连接各移动后的数据块，构建二级干扰，如图6所示。
3.2　行星轮故障特征分析
二级行星齿轮箱中，假设Nr，Ns和Np分别代表第一级行星结构齿圈、太阳轮和行星轮的齿数，那么相应行星架的啮合频率fm为［9］：
式中　 fc，fs和fp分别为第一级行星架、第一级太阳轮和第一级行星轮的转频。
以行星架作为参考轴，则相应的啮合阶次om为［9］：
式中　 nc为行星架的转速。
行星轮相对于齿圈的故障阶次可计算如下［9］：
4　第一级行星轮故障特征提取方法
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为有效从二级行星齿轮箱中消除来自第二级太阳轮的二级干扰，并提取第一级行星轮的故障特征。本文在研究中结合角度补偿同步平均、传统加窗同步平均和包络分析方法，提出角度补偿同步平均的二级行星齿轮箱行星轮故障特征的提取方法，用于实现二级行星齿轮箱第一级行星轮的故障特征提取。该方法的流程图如图7所示，主要步骤如下：
（1）数据采集。通过安装于第一级齿圈上方的传感器以及相应的相位设备同步采集原始振动和转速脉冲。
（2）基于等角度重采样的转速波动消除。选择二级行星齿轮箱公共轴为参考轴，对原始振动进行等角度重采样消除转速波动并获取重采样振动。
（3）基于角度补偿同步平均的二级干扰构建及消除。通过角度补偿同步平均可计算出相应的角度偏移φ。随后可从重采样振动中提取出第二级太阳轮的啮合振动数据块，并构建出二级干扰。相应的详细过程见第3节。最后，通过对重采样振动和二级干扰进行差运算，可获得消除了二级干扰的残余振动。
（4）基于包络分析的包络信号提取。齿轮损伤会产生周期性冲击特征，然而背景干扰较大时将导致齿轮的故障特征被淹没而不易被提取。而包络分析对信噪比较低的信号具有较好的识别能力。通过对残余振动进行希尔伯特变换，能够从中提取出相应的包络信号。
（5）基于加窗同步平均的第一级行星轮合成包络信号获取。二级行星齿轮箱中，固定于第一级行星架上的第一级行星轮随行星架旋转并与第一级齿圈啮合，行星轮各齿与齿圈特定齿间存在周期性的啮合关系。通过加窗同步平均方法，可以从获得的包络信号中截取第一级行星轮各齿的数据块。随后根据第一级行星轮的啮合齿序Ts（详细计算过程见第2节）对数据块进行重新排列及拼接，构建第一级行星轮的合成包络信号。
（6）基于包络同步平均的故障特征提取。因合成的包络信号类似于从定轴齿轮箱上获取的包络信号，故可通过包络同步平均方法提取第一级行星轮的故障特征。
5　实验研究
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5.1　实验介绍
为验证角度补偿同步平均的二级行星齿轮箱行星轮故障特征的提取方法的有效性，采用了二级行星齿轮箱实验台的实测振动信号进行研究。实验台如图8所示，主要由驱动电机（A）、二级行星齿轮箱（B）和磁粉负载制动器（C）组成。其中，二级行星齿轮箱中的第一级行星轮通过线切割预先加工了齿根裂纹（宽度约为0.5 mm，深度约为1.5 mm），如图9所示。
实验中齿轮箱输入轴转速约为1666 r/min，采用NI9234采集卡以51.2 kHz的采样率采集数据。相应的振动和转速脉冲分别由安装在第一级齿圈上方的传感器和靠近磁粉负载制动器的电涡流传感器采集，如图8中位置（1）和（2）所示。
二级行星齿轮箱的齿轮参数如表1所示，在选择齿轮箱公共轴为参考轴后，第一级行星轮的特征阶次通过式（7）~（9）计算并列于表2中。
二级行星齿轮箱中第一级行星轮的啮合齿序Ts通过式（1）和（2）计算并列于表3中。
5.2　实验验证
实验中，二级行星齿轮箱的部分实测时域波形和转速脉冲如图10（a）和（b）所示。
采用传统加窗同步平均方法对图10所示信号进行分析，结果如图11所示。
通常，行星轮齿根裂纹的故障特征可以通过啮合阶次及其谐波周围的相关边带簇来识别。经计算，在本文中特征阶次分别为啮合阶次73×、故障阶次2.81×。然而，由图11（a）及其放大图（图11（b））可以看出，图谱成分分散，相应啮合阶次及其谐波和对应故障特征的边带簇并不凸显，如73×，143.19×，146×，148.53×，213.38×，219×及292×等。说明通过传统加窗同步平均对二级行星齿轮箱第一级行星轮进行故障特征提取时，因无法消除由齿轮箱公共轴引入的二级干扰而导致提取效果不佳。
随后，采用所提方法对二级行星齿轮箱第一级行星轮的故障特征进行提取。首先经等角度重采样消除转速波动；随后构建二级干扰并将之从重采样振动中消除；最后提取残余振动的包络信号，并通过加窗同步平均方法构建二级行星齿轮箱第一级行星轮的合成包络信号。所得的合成包络信号如图12所示。研究中为便于进行实验对比分析，采用传统包络加窗同步平均［8］方法与所提方法的分析结果进行对比，传统方法得到的第一级行星轮的合成包络信号如图13所示。随后，结合峭度指标［13］对分析结果进行评价。
由图12和13所示的第一级行星轮6个旋转周期对应的合成包络信号中可以看出，通过传统方法难以有效地从合成包络信号中观察到与行星轮故障相关的周期性特征。经计算，传统方法得到的第一级行星轮合成包络信号的峭度指标为3.03。而采用所提方法能够清晰地揭示此类特征。通过计算，所提方法的合成包络信号的峭度指标为4.01，相较传统方法有较大提升，说明对应行星轮的故障冲击能量得到增强。
通过对比图12和13所示的分析结果和相应的峭度指标可以看出，所提方法能够有效地在合成包络信号中呈现出二级行星齿轮箱第一级行星轮齿根裂纹对应的故障成分。
随后，为进一步验证所提方法的有效性，分别对原始信号、包络加窗同步平均构建的合成包络信号、以及所提方法构建的合成包络信号进行包络谱对比分析，相应结果如图14和15所示。
由图14所示的对比分析可知，原始信号的包络谱难以清晰地揭示与第一级行星轮齿根裂纹故障特征相关的谱线（2.81×及其谐波）。相比之下，采用所提方法能够有效地观察到相应的故障特征。
由图15所示的对比结果可知，传统加窗同步平均方法因未能消除二级干扰而导致二级行星齿轮箱第一级行星轮的故障特征提取效果不佳。相反，所提方法能够清晰地揭示该行星轮与齿根裂纹故障相对应的特征，即2.81×及其谐波。
图14和15的对比结果表明所提方法能够有效地提取二级行星齿轮箱第一级行星轮的故障特征，较传统方法更具优势。
6　结论
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在二级行星齿轮箱中，两级行星齿轮组由于共用传动轴，将导致相互间产生振动耦合，致使传感器获取的第一级行星齿轮组的振动存在来自第二级太阳轮的二级干扰。由于二级干扰与通过传统加窗同步平均方法构建的第一级行星轮合成振动具有相同的参考轴，因此使其在提取第一级行星轮故障特征时往往效果不佳。通过将等角度重采样、角度补偿同步平均、包络分析以及加窗同步平均方法相结合，能够有效地构建并消除二级干扰，从而实现对二级行星齿轮箱第一级行星轮齿根裂纹的故障特征提取。相较于传统方法，所提方法鲁棒性更好。
基金
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  • 国家自然科学基金资助项目(51675251)
  • 国家重点研发计划资助项目(2018YFB1306103)
  • 云南省科技重大专项资助项目(202002AC080001)
文献
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参考文献 引证文献
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郭远晶， 金晓航， 魏燕定， 等. 改进TSA降噪与平方包络谱分析的故障特征提［J］. 振动工程学报，2021，34（2）： 402-410.
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2024年第37卷第5期
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文章信息
doi: 10.16385/j.cnki.issn.1004-4523.2024.05.018
  • 接收时间：2022-05-10
  • 首发时间：2026-02-09
  • 出版时间：2024-05-28
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  • 收稿日期：2022-05-10
  • 修回日期：2022-08-11
基金
国家自然科学基金资助项目(51675251)
国家重点研发计划资助项目(2018YFB1306103)
云南省科技重大专项资助项目(202002AC080001)
作者信息
    昆明理工大学机电工程学院，云南昆明　650550

通讯作者:

郭瑜（1971―），男，博士，教授。E-mail：。
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