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Article(id=1240594158512042713, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1240594155198534488, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.03.009, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1688054400000, receivedDateStr=2023-06-30, revisedDate=1689782400000, revisedDateStr=2023-07-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1773710296514, onlineDateStr=2026-03-17, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773710296514, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773710296514, creator=13701087609, updateTime=1773710296514, updator=13701087609, issue=Issue{id=1240594155198534488, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='3', pageStart='1', pageEnd='158', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1773710295724, creator=13701087609, updateTime=1773714468205, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240611655898420098, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1240594155198534488, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240611655902614403, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1240594155198534488, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=75, endPage=81, ext={EN=ArticleExt(id=1240594159145382631, articleId=1240594158512042713, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Torsional vibration analysis of RV reducer based on variational mode decomposition, columnId=1240594156813341537, journalTitle=Journal of Mechanical Strength, columnName=·Vibration·Noise·Monitoring·Diagnosis·, runingTitle=null, highlight=null, articleAbstract=

To investigate the vibration performance of RV reducers and analyze the fault identification, the torsional vibration test bench for RV reducers was built.Based on the mechanical structure and transmission principles of RV reducers,the vibration frequencies under different operating conditions were calculated.The vibration signal of RV reducers of superior and inferior products was collected, and the acceleration signal of the torsional vibration under different speeds and swerves was collected.The torsional vibration signals were decomposed using the variational mode decomposition (VMD) to obtain the intrinsic mode function (IMF).The results demonstrate a high correlation between the extracted IMF features obtained through VMD and the vibration frequencies observed during the operation of RV reducers.Furthermore, by comparing the spectrum of IMF, the reasons behind the abnormal vibration in inferior RV reducers were identified.Ultimately, it is determined that the abnormal vibration in inferior RV reducers were caused by the excitation from the interaction between the auto rotation of the planetary gear and the crankshaft or the revolution of the cycloid gear.This study provides valuable insights for enterprises aiming to improve the transmission accuracy and product quality of RV reducers.

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LI Guoping, E-mail：
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为研究RV减速器的振动性能及对其故障识别分析，搭建了无线式RV减速器扭转振动测试台。根据RV减速器的构成和传动原理，对不同工况下的RV减速器的振动频率进行了计算。对优等品和劣等品RV减速器进行振动信号的采集，采集其在不同转速、转向下扭转振动的加速度信号。通过变分模态分解（Variational Mode Decomposition, VMD）对扭转振动信号进行分解，得到该信号的本征模函数（Intrinsic Mode Function, IMF）。结果表明，通过VMD后得到的IMF特征与RV减速器运行时的振动频率高度吻合。进一步地，通过对比IMF的频谱，鉴别出劣等品减速器振动异常的原因。最终确定劣等品RV减速器的异常振动由行星轮与曲柄轴自转或摆线轮公转激发所导致。该研究为企业提高RV减速器传动精度和产品质量提供有益参考。

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李国平，男，1967年生，湖北武穴人，教授；主要研究方向为RV减速器性能分析；E-mail：。
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张捷艇，男，1999年生，浙江宁波人，硕士研究生；主要研究方向为RV减速器性能分析；E-mail：。

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张捷艇，男，1999年生，浙江宁波人，硕士研究生；主要研究方向为RV减速器性能分析；E-mail：。

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张捷艇，男，1999年生，浙江宁波人，硕士研究生；主要研究方向为RV减速器性能分析；E-mail：。

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Main parameters of 190BX reducer

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参数Parameter值Value
传动比 Transmission ratio R121
输入轴齿轮齿数Number of input shaft gear teeth z112
行星齿轮齿数Number of planetary gear teeth z236
摆线轮齿数Number of cycloid gear teeth z339
针齿壳齿数Number of pin shell teeth z440
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190BX减速器主要参数

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参数Parameter值Value
传动比 Transmission ratio R121
输入轴齿轮齿数Number of input shaft gear teeth z112
行星齿轮齿数Number of planetary gear teeth z236
摆线轮齿数Number of cycloid gear teeth z339
针齿壳齿数Number of pin shell teeth z440
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Effective value of vibration signals

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转速
Rotate speed/(r/min)		品质Quality编号Number
123
1 500优等品
Superior product		0.094 30.092 10.090 5
劣等品
Inferior product		0.163 60.162 60.173 4
2 000优等品
Superior product		0.189 90.168 50.158 4
劣等品
Inferior product		0.253 80.262 00.253 7
2 500优等品
Superior product		0.179 20.171 90.188 1
劣等品
Inferior product		0.346 50.359 50.366 1
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振动信号的有效值

, figureFileSmall=null, figureFileBig=null, tableContent=
转速
Rotate speed/(r/min)		品质Quality编号Number
123
1 500优等品
Superior product		0.094 30.092 10.090 5
劣等品
Inferior product		0.163 60.162 60.173 4
2 000优等品
Superior product		0.189 90.168 50.158 4
劣等品
Inferior product		0.253 80.262 00.253 7
2 500优等品
Superior product		0.179 20.171 90.188 1
劣等品
Inferior product		0.346 50.359 50.366 1
), ArticleFig(id=1240594177461907839, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1240594158512042713, language=EN, label=Tab.3, caption=

Theoretical and actual vibration frequencies of 190BX reducer at 2 500 r/min

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频率类型
Frequency type		理论频率
Theoretical
frequency/Hz		实际频率
Actual
frequency/Hz		归一化
频率误差
Normalized
frequency
error/%
输入轴频率
Frequency of the input shaft f1		41.6741.011.58
行星轮与曲柄轴自转频率
Auto rotation frequency of the planetary gear and the crank shaft f2		13.7713.670.72
摆线轮公转频率
Revolution frequency of the cycloid gear f5		13.7713.670.72
行星轮啮合频率
Meshing frequency of the planetary gear f1c		495.87498.050.44
摆线轮啮合频率
Meshing frequency of the cycloid gear f4c		537.19539.060.35
), ArticleFig(id=1240594177591931267, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1240594158512042713, language=CN, label=表3, caption=

2 500 r/min下190BX型减速器的理论振动频率与实际振动频率

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频率类型
Frequency type		理论频率
Theoretical
frequency/Hz		实际频率
Actual
frequency/Hz		归一化
频率误差
Normalized
frequency
error/%
输入轴频率
Frequency of the input shaft f1		41.6741.011.58
行星轮与曲柄轴自转频率
Auto rotation frequency of the planetary gear and the crank shaft f2		13.7713.670.72
摆线轮公转频率
Revolution frequency of the cycloid gear f5		13.7713.670.72
行星轮啮合频率
Meshing frequency of the planetary gear f1c		495.87498.050.44
摆线轮啮合频率
Meshing frequency of the cycloid gear f4c		537.19539.060.35
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基于变分模态分解的RV减速器扭转振动分析
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张捷艇 1 , 余东 2 , 娄军强 1 , 罗利敏 2 , 贡林欢 2 , 李国平 1
机械强度 | ·振动·噪声·监测·诊断· 2025,47(3): 75-81
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机械强度 | ·振动·噪声·监测·诊断· 2025, 47(3): 75-81
基于变分模态分解的RV减速器扭转振动分析
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张捷艇1 , 余东2, 娄军强1, 罗利敏2, 贡林欢2, 李国平1
作者信息
  • 1.宁波大学 浙江省零件轧制与成形技术重点实验室，宁波　315211
  • 2.宁波中大力德智能传动股份有限公司，宁波　315301

    • 张捷艇，男，1999年生，浙江宁波人，硕士研究生；主要研究方向为RV减速器性能分析；E-mail：。

通讯作者:

李国平，男，1967年生，湖北武穴人，教授；主要研究方向为RV减速器性能分析；E-mail：。
Torsional vibration analysis of RV reducer based on variational mode decomposition
Jieting ZHANG1 , Dong YU2, Junqiang LOU1, Limin LUO2, Linhuan GONG2, Guoping LI1
Affiliations
  • 1.Part Rolling Key Laboratory of Zhejiang Province, Ningbo University, Ningbo 315211, China
  • 2.Ningbo Zhongda Leader Intelligent Transmission Co., Ltd., Ningbo 315301, China
出版时间: 2025-03-15 doi: 10.16579/j.issn.1001.9669.2025.03.009
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摘要
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为研究RV减速器的振动性能及对其故障识别分析，搭建了无线式RV减速器扭转振动测试台。根据RV减速器的构成和传动原理，对不同工况下的RV减速器的振动频率进行了计算。对优等品和劣等品RV减速器进行振动信号的采集，采集其在不同转速、转向下扭转振动的加速度信号。通过变分模态分解（Variational Mode Decomposition, VMD）对扭转振动信号进行分解，得到该信号的本征模函数（Intrinsic Mode Function, IMF）。结果表明，通过VMD后得到的IMF特征与RV减速器运行时的振动频率高度吻合。进一步地，通过对比IMF的频谱，鉴别出劣等品减速器振动异常的原因。最终确定劣等品RV减速器的异常振动由行星轮与曲柄轴自转或摆线轮公转激发所导致。该研究为企业提高RV减速器传动精度和产品质量提供有益参考。

变分模态分解  /  RV减速器  /  扭转振动  /  振动频率

To investigate the vibration performance of RV reducers and analyze the fault identification, the torsional vibration test bench for RV reducers was built.Based on the mechanical structure and transmission principles of RV reducers,the vibration frequencies under different operating conditions were calculated.The vibration signal of RV reducers of superior and inferior products was collected, and the acceleration signal of the torsional vibration under different speeds and swerves was collected.The torsional vibration signals were decomposed using the variational mode decomposition (VMD) to obtain the intrinsic mode function (IMF).The results demonstrate a high correlation between the extracted IMF features obtained through VMD and the vibration frequencies observed during the operation of RV reducers.Furthermore, by comparing the spectrum of IMF, the reasons behind the abnormal vibration in inferior RV reducers were identified.Ultimately, it is determined that the abnormal vibration in inferior RV reducers were caused by the excitation from the interaction between the auto rotation of the planetary gear and the crankshaft or the revolution of the cycloid gear.This study provides valuable insights for enterprises aiming to improve the transmission accuracy and product quality of RV reducers.

Variational mode decomposition  /  RV reducer  /  Torsional vibration  /  Vibrational frequency
张捷艇, 余东, 娄军强, 罗利敏, 贡林欢, 李国平. 基于变分模态分解的RV减速器扭转振动分析. 机械强度, 2025 , 47 (3) : 75 -81 . DOI: 10.16579/j.issn.1001.9669.2025.03.009
Jieting ZHANG, Dong YU, Junqiang LOU, Limin LUO, Linhuan GONG, Guoping LI. Torsional vibration analysis of RV reducer based on variational mode decomposition[J]. Journal of Mechanical Strength, 2025 , 47 (3) : 75 -81 . DOI: 10.16579/j.issn.1001.9669.2025.03.009
正文
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0　引言
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由于人力资源成本的上升和全球产业竞争的激烈化，我国的工业制造模式正在经历一系列的变革。在《中国制造2025》中明确提出要大力推动工业机器人的发展。为了推进机器人产业的发展，必须推动机器人的标准化和模块化发展，攻克机器人本体、减速器、伺服电动机、控制器与驱动器等关键技术的难题成为了重中之重[1]。因此，进行工业机器人核心零部件——RV减速器技术研究具有重要的意义和价值。
RV减速器传动效率高、结构紧凑、传动比大，广泛应用于工业机器人中 [2]。RV减速器的振动是一项重要的性能指标，其振动强弱直接影响减速器的运动精度。RV减速器的振动信号蕴含着减速器状态的信息，其信号特征与设备各零部件有着较强的对应关系，可有效地反映出零件加工以及传动时的误差，振动信号的研究对提高RV减速器的传动精度、控制性能等都有很重要的工程意义。国内外学者对其振动也进行了广泛的研究，对RV减速器故障部位的识别却少有研究。谭晶等[3]介绍了转矩激励下的RV减速器扭转振动频响特征试验方法，用RV减速器实际扭转振动试验验证了两种扭振频响测试方法在固有频率、阻尼比估计及响应分布上的差异，确定了所给试验方法的正确性。张跃明等[4]研发了一种RV减速器在载荷惯量试验条件下的振动在线检测研究技术，对RV减速器机壳处的振动进行分析，反馈出RV减速器的加工及装配误差。汪久根等[5]通过仿真对RV减速器整机的模态频率及瞬态动力学进行了分析，并通过试验验证仿真结果，得到了较高的吻合度。GU等[6]通过对RV减速器振动信号的分析，识别出有制造缺陷的机械零部件，对RV减速器的质量保证有很强的参考价值。WANG等[7]通过测量RV减速器的扭转刚度，找出了扭转刚度波动的机制，并利用该机制实现RV减速器缺陷零部件的诊断。万书亭等[8]提出了一种基于变分模态分解（Variational Mode Decomposition, VMD）和马氏距离（Mahalanobis Distance, MD）结合的方法来检测输电铁塔螺栓的松动。谢锋云等[9]提出了一种基于VMD与支持向量机（Support Vector Machine, SVM）融合的方法用于电动机故障诊断。
本文以190BX型号的RV减速器为研究对象，进行了扭转振动试验，采集不同转速下扭转振动加速度信号。计算该型号RV减速器运行时的激振源频率，通过VMD方法分解扭转振动信号后得到本征模函数（Intrinsic Mode Function, IMF）的特征，与RV减速器的振动频率高度吻合，验证了VMD对振动信号分解的有效性。进一步地，对比RV减速器IMF的差异，有效鉴别出造成劣等品减速器振动异常的部位。
1　RV减速器的结构
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RV减速器是一种高精密的摆线针轮行星传动设备，由一个行星齿轮减速机的前级和一个摆线针轮减速机的后级组成。其组成结构如图1所示，主要包括输出法兰、主轴承、针齿壳、行星齿轮、摆线轮、曲柄轴、输入齿轮、支撑法兰等部分。
传动原理如图2所示，针齿壳6固定时，电动机将动力传输给输入齿轮轴1，从而带动行星齿轮2自转，完成一级减速。曲柄轴3与行星齿轮固定，随着行星齿轮一同转动，并带动摆线轮4做偏心运动，同时摆线轮与针齿壳5中的针齿6啮合，带动摆线轮反向自转，使得曲柄轴绕其齿轮轴线公转并带动输出法兰7自转，完成二级减速。
2　RV减速器振动频率分析
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根据RV减速器的一些主要参数，可以计算出各零部件的振动频率[10]。其中，输入轴频率为
输出轴特征频率为
行星轮和曲柄轴自转频率为
行星轮和曲柄轴公转频率为
摆线轮自转频率为
摆线轮公转频率为
行星轮啮合频率为
摆线轮啮合频率为
式中，n0为RV减速器输出转速；R为传动比；z1为输入轴齿轮齿数；z2为行星齿轮齿数；z3为摆线轮齿数；z4为针齿壳齿数。
本次扭转振动测试中所用的RV减速器型号为190BX，其主要参数如表1所示。
3　RV减速器扭转振动测试
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3.1　试验装置
试验中用到的RV减速器型号为190BX，RV减速器扭转振动测试装置如图3所示，伺服电动机外壳上安装有固定法兰，固定法兰与RV减速器针齿壳间通过螺栓连接，减速器输入轴连接伺服电动机，电动机的转动最终通过RV减速器的输出法兰输出。
加速度传感器为无线加速度传感器，型号为RNT301，量程为±2g（g为重力加速度，取9.8 m/s2），可有效测得RV减速器运行时的振动。将加速度传感器胶粘在RV减速器输出法兰边缘，考虑到测量扭转振动的准确性，粘贴时需要保证加速度传感器的测量方向为减速器的切向，且每次安装在减速器的同一位置，试验的采样频率为4 000 Hz。
3.2　扭转振动测试
试验采用工人根据经验判别出的优等品、劣等品两类RV减速器，测量RV减速器裸机运行（无负载）时的振动。分别测量伺服电动机转速为1 500、2 000、2 500 r/min，转动状态为正转、反转时，RV减速器的扭转振动加速度信号，每次试验采集3组数据，确保信号的一致性。对信号进行去均值、滤波预处理，并取其中1组得到的试验数据如图4、图5所示。图4中，G1、G2、G3分别表示3个优等品减速器样品；图5中，NG1、NG2、NG3分别表示3个劣等品减速器样品。
从时域信号中，只能看出优等品与劣等品之间振动大小的差异，因此需要对信号进一步分析处理。
有效值是一项可以直接评判振动强弱的指标，对一组长度为N的加速度信号{xi}，其有效值定义为
将测量数据代入式（9），计算各个RV减速器振动信号不同工况下的有效值，如表2所示。
由表2可以明显看出，劣等品RV减速器的振动值强于优等品RV减速器，且同一工况下各个优等品RV减速器和劣等品RV减速器的有效值均趋于一致。
4　基于VMD的信号分析与处理
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由于RV减速器零件繁多，振动信号中的振动特征频率混叠在一起，传统的频域分析方法已经无法分辨出减速器振动的特征频率。VMD可以选取不同参数对不同信号进行适配，能达到更好的信号分析效果。
VMD是一种自适应的分解方法，能有效地处理非线性的信号。它能够将原始信号分解为多个IMF，每个IMF都包含确定的中心频率ωk和有限带宽。为最小化各IMF带宽估计值的总和，构建的变分问题计算式为
式中，uk为各IMF分量；f为原始信号；j为虚数单位；δ（t）为单位脉冲函数；∂t为对函数求时间的偏导数。
为了求得式（9）的最优解，引入二次惩罚项α以及拉格朗日算子λ。扩展的拉格朗日表达式为
使用交替乘子算法不断循环迭代、和λn+1的值，直到L(uk，ωk，λ)达到最小值。其中每个IMF分量及其中心频率迭代式分别为
根据式（12）、式（13）进行迭代计算，直到与满足
选取2 500 r/min工况下的具有代表性的优等品与劣等品RV减速器的加速度信号各一个进行VMD分解。由于VMD得到的IMF分量的中心频率是按大小顺序依次排列的，为避免VMD出现过分解或欠分解现象，一般根据信号频谱中重要的幅频特征确定模态数量[11-12]，根据第2节振动频率的计算式，计算出在2 500 r/min工况下RV减速器存在0~600 Hz的振动频率，因此取模态数N'=20对加速度信号进行VMD，并对频率由低到高的6个IMF分量进行分析，部分IMF分量的时域图如图6所示。
对上述6个IMF分量进行快速傅里叶变换（Fast Fourier Transform, FFT），得到频谱图，如图7所示。
由图7可以看出，RV减速器的振动频率。根据第2节的振动频率公式，可计算得到190BX型RV减速器在2 500 r/min下的振动频率，将实际获得的频率与理论计算频率整合成表3。
由表3可知，实际测得的振动频率与理论计算频率高度吻合。在优等品IMF17分量和劣等品IMF15分量的频谱中存在539.06 Hz的主要频率成分，与摆线轮啮合频率f4c=537.19 Hz高度重合；在优等品IMF18分量和劣等品IMF16分量的频谱中存在498.05 Hz的主要频率成分，与行星轮啮合频率f1c=495.87 Hz高度重合；在优等品和劣等品IMF20分量的频谱中存在41.01、83.98、125.00 Hz的频率成分，与输入轴转频的二倍频、三倍频高度重合。
综上可知，加速度信号经VMD后可有效去除其中无关的频率成分，且能有效分离出RV减速器的主要振动频率。
进一步地，取IMF20的局部频谱图，如图8所示。由图8可知，转速2 500 r/min工况下，优等品与劣等品在13.67 Hz存在峰值，该频率与理论计算的行星轮与曲柄轴自转频率f2、摆线轮公转频率f5高度吻合，因此该频率分量可以作为行星轮与曲柄轴自转故障或摆线轮公转故障的依据。
由图8可以看出，在频率为13.67 Hz处，优等品的峰值为0.007 3g远小于劣等品的峰值0.046 7g。在转速2 000 r/min和1 500 r/min工况下，也在行星轮与曲柄轴自转频率、摆线轮公转频率处存在峰值，且优等品RV减速器的峰值远小于劣等品RV减速器的峰值。由此判断，行星轮与曲柄轴自转或摆线轮公转激发的振动是造成劣等品RV减速器扭转振动异常的原因。对另两组优等品、劣等品RV减速器进行对比发现，在行星轮与曲柄轴自转频率、摆线轮公转频率处的幅值均能得出以上结论，具有一致性，故判定为行星轮、曲柄轴或摆线轮的加工误差所致。
5　结论
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采用变分模态分解的方法，有效识别了RV减速器的振动特征，实现了RV减速器振动异常原因的判别。该方法为提高RV减速器传动精度提供了依据和参考，得出的主要结论如下：
1）搭建了RV减速器扭转振动测试台，成功采集了运行时的扭转振动信号。采用VMD方法，提取了IMF，并准确识别出RV减速器的振动频率及高阶倍频，且与理论计算值高度吻合。
2）对优等品RV减速器与劣等品RV减速器的IMF频谱进行对比分析，发现劣等品在13.67 Hz处的振动幅值显著高于优等品，且该频率与行星轮、曲柄轴的自转或摆线轮的公转频率吻合。
3）试验结果表明，行星轮与曲柄轴自转或摆线轮公转激发的振动是造成劣等品RV减速器扭转振动异常的原因，最终确定异常是由行星轮、曲柄轴或摆线轮的加工误差所导致的。
基金
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  • 宁波市科技创新2025重大专项(2018B10007; 2019B10078)
文献
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2025年第47卷第3期
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doi: 10.16579/j.issn.1001.9669.2025.03.009
  • 接收时间：2023-06-30
  • 首发时间：2026-03-17
  • 出版时间：2025-03-15
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  • 收稿日期：2023-06-30
  • 修回日期：2023-07-20
基金
Ningbo Science and Technology Innovation 2025(2018B10007; 2019B10078)
宁波市科技创新2025重大专项(2018B10007; 2019B10078)
作者信息
    1.宁波大学 浙江省零件轧制与成形技术重点实验室，宁波　315211
    2.宁波中大力德智能传动股份有限公司，宁波　315301

通讯作者:

李国平，男，1967年生，湖北武穴人，教授；主要研究方向为RV减速器性能分析；E-mail：。
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https://castjournals.cast.org.cn/joweb/jxqd/CN/10.16579/j.issn.1001.9669.2025.03.009
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2种不同金属材料的力学参数
科
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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