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Article(id=1263881629202825404, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, articleNumber=null, orderNo=null, doi=10.16578/j.issn.1004.2539.2026.01.017, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1725811200000, receivedDateStr=2024-09-09, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1779262462186, onlineDateStr=2026-05-20, pubDate=1768406400000, pubDateStr=2026-01-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1779262462186, onlineIssueDateStr=2026-05-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1779262462186, creator=13041195026, updateTime=1779262462186, updator=13041195026, issue=Issue{id=1263881604263437054, tenantId=1146029695717560320, journalId=1263187878914834467, year='2026', volume='50', issue='1', pageStart='1', pageEnd='191', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1779262456241, creator=13041195026, updateTime=1779263107607, updator=13041195026, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1263884336399528882, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1263884336403723187, tenantId=1146029695717560320, journalId=1263187878914834467, issueId=1263881604263437054, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=133, endPage=141, ext={EN=ArticleExt(id=1263881631241257165, articleId=1263881629202825404, tenantId=1146029695717560320, journalId=1263187878914834467, language=EN, title=Degradation and reliability assessment of accuracy life of RV reducers, columnId=1263881612287140612, journalTitle=Journal of Mechanical Transmission, columnName=Test·Analysis, runingTitle=null, highlight=null, articleAbstract=
Objective

The industrial robot industry has put forward higher requirements for RV reducers, and the precision life reflects the ability of the reducer to maintain transmission accuracy, which is one of the most important design criteria and usage indicators. To improve the precision performance of precision reducers, it is crucial to evaluate their reliability. Therefore, the degradation characteristics of precision reducers were analyzed.

Methods

Taking the RV80E reducer as an example, a random degradation model based on Gamma process was proposed. Combined with the performance degradation data of the reducer transmission accuracy, the model parameters were estimated based on the matrix method and the maximum likelihood estimation method. A Gaussian process regression model optimized by genetic algorithm was established using vibration characteristic data to optimize the prediction of transmission accuracy.

Results

The results show that the prediction accuracy based on Gaussian process regression model is significantly better than that of the traditional regression model. The posterior distribution parameters of the random degradation model are updated by using the algorithm to predict the results, which can effectively evaluate the reliability of the accuracy life of RV reducer and lay the foundation for further reliability optimization design of accuracy life.

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目的

工业机器人行业对RV减速器提出更高的要求，精度寿命体现了减速器传动精度的保持能力，是最重要的设计准则和使用指标之一。为提升精密减速器的精度性能，对可靠性进行评估至关重要。为此，分析了精密减速器的退化特性。

方法

以RV80E减速器为例，提出基于Gamma过程的随机退化模型；结合减速器传动精度的性能退化数据，基于矩阵法和最大似然估计法对模型参数进行了估计；采用振动特征数据建立了基于遗传算法优化的高斯过程回归模型，以优化传动精度的预测。

结果

结果表明，基于高斯过程回归模型的预测精度显著优于传统回归模型；采用算法预测后的结果更新随机退化模型的后验分布参数，能够有效实现对RV减速器精度寿命可靠度的评估，为进一步进行精度寿命的可靠性优化设计奠定了基础。

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聂义轩（通信作者），男，1999年生，河北保定人，硕士研究生；主要研究方向为精密传动；。
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徐航，男，1984年生，河南郑州人，博士，副教授；主要研究方向为精密测量、齿轮工程；。

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徐航，男，1984年生，河南郑州人，博士，副教授；主要研究方向为精密测量、齿轮工程；。

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徐航，男，1984年生，河南郑州人，博士，副教授；主要研究方向为精密测量、齿轮工程；。

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Research on reliability modeling and analysis methods based on the performance degradation［D］. Chengdu：University of Electronic Science and Technology of China，2015：23-27., articleTitle=Research on reliability modeling and analysis methods based on the performance degradation, refAbstract=null), Reference(id=1263881716385628957, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, doi=null, pmid=null, pmcid=null, year=2018, volume=177, issue=null, pageStart=35, pageEnd=49, url=null, language=null, rfNumber=7, rfOrder=11, authorNames=TAO T, ZIO E, ZHAO W, journalName=Reliability Engineering & System Safety, refType=null, unstructuredReference=TAO T，ZIO E，ZHAO W. A novel support vector regression method for online reliability prediction under multi-state varying operating conditions［J］. 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Research on online monitoring and rating of transmission accuracy of RV reducers for industrial robots［D］. Xuzhou：China University of Mining and Technology，2021：10-16., articleTitle=Research on online monitoring and rating of transmission accuracy of RV reducers for industrial robots, refAbstract=null), Reference(id=1263881724912649046, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=42, pageEnd=46, url=null, language=null, rfNumber=14, rfOrder=24, authorNames=李旭东, journalName=null, refType=null, unstructuredReference=李旭东. 基于深度学习的旋转部件故障诊断研究［D］. 北京：中国科学院大学（中国科学院国家空间科学中心），2021：42-46., articleTitle=基于深度学习的旋转部件故障诊断研究, refAbstract=null), Reference(id=1263881725583737691, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=42, pageEnd=46, url=null, language=null, rfNumber=14, rfOrder=25, authorNames=LI Xudong, journalName=null, refType=null, unstructuredReference=LI Xudong. 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Real-time reliability evaluation and life prediction of harmonic reducer based on multistage degradation modeling［J］. Journal of Tianjin University （Science and Technology），2022，55（2）：122-132., articleTitle=Real-time reliability evaluation and life prediction of harmonic reducer based on multistage degradation modeling, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1263881649348067680, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, xref=1., ext=[AuthorCompanyExt(id=1263881649595531618, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, companyId=1263881649348067680, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.Key Laboratory of Optical Sensing and Testing Technology for Mechanical Industry, Zhongyuan University of Technology, Zhengzhou451191, China), AuthorCompanyExt(id=1263881649624891749, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, companyId=1263881649348067680, language=CN, 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label=Fig.8, caption=Reliability curve of the accuracy life, figureFileSmall=sE4HyYdy02JMkrbdyOViGQ==, figureFileBig=9wW763ab5MtU1r0Z83XDOA==, tableContent=null), ArticleFig(id=1263881697997800109, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=CN, label=图8, caption=精度寿命可靠度曲线, figureFileSmall=sE4HyYdy02JMkrbdyOViGQ==, figureFileBig=9wW763ab5MtU1r0Z83XDOA==, tableContent=null), ArticleFig(id=1263881698480145069, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=EN, label=Tab. 1, caption=

Accuracy class indexes

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项目精度等级指标
传动误差1级传动误差≤30″
2级30″<传动误差≤1′
3级1′<传动误差≤3′
空程1级空程≤1′
2级1′<空程≤3′
3级3′<空程≤6′
), ArticleFig(id=1263881699168010933, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=CN, label=表1, caption=

精度等级指标

, figureFileSmall=null, figureFileBig=null, tableContent=
项目精度等级指标
传动误差1级传动误差≤30″
2级30″<传动误差≤1′
3级1′<传动误差≤3′
空程1级空程≤1′
2级1′<空程≤3′
3级3′<空程≤6′
), ArticleFig(id=1263881699948151481, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=EN, label=Tab. 2, caption=

Estimation results of Gamma process parameters

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α β
传动误差增量2.720.78
), ArticleFig(id=1263881701814616766, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=CN, label=表2, caption=

Gamma过程参数估算结果

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α β
传动误差增量2.720.78
), ArticleFig(id=1263881702611534534, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=EN, label=Tab. 3, caption=

First set of feature set data

, figureFileSmall=null, figureFileBig=null, tableContent=
时间/h有效值方差峭度因子时频总能量

500

500

500

500

500

1 000

1 000

1 000

1 000

1 000

1 500

1 500

1 500

1 500

1 500

2 000

2 000

2 000

2 000

2 000

2 500

2 500

2 500

2 500

2 500

3 000

3 000

3 000

3 000

3 000

1.500 0

1.333 3

1.319 4

1.293 9

1.194 4

1.180 6

1.138 9

1.133 7

1.013 9

0.930 6

0.916 7

0.806 3

0.763 9

0.638 9

0.611 1

-0.125 0

-0.263 9

-0.367 9

-0.513 9

-0.625 0

-1.930 6

-2.055 6

-2.111 1

-2.138 3

-2.305 6

-2.958 3

-3.000 0

-3.069 4

-3.177 9

-3.263 9

1.844 9

1.791 0

1.712 8

1.621 9

1.536 1

1.369 4

1.326 0

1.275 1

1.230 8

1.179 4

1.076 2

0.942 3

0.707 8

0.493 2

0.128 1

-0.293 2

-0.865 8

-1.427 7

-2.060 9

-2.655 5

-3.275 3

-3.983 3

-4.606 1

-5.152 5

-5.804 6

-6.420 6

-7.028 2

-7.662 2

-8.259 2

-8.996 6

7.272 1

8.575 8

5.104 4

7.014 9

8.404 7

7.642 5

8.860 9

7.733 1

8.776 5

6.955 3

-0.754 3

-2.922 1

1.161 9

-1.703 0

0.037 3

-9.595 2

-12.199 1

-7.422 2

-11.413 4

-8.547 5

-15.054 9

-13.749 4

-16.180 7

-16.265 3

-14.441 1

-18.773 2

-17.643 9

-16.340 5

-17.641 0

-19.377 3

0.897 4

1.114 5

0.976 5

0.848 3

0.947 1

0.869 2

0.731 0

0.790 3

0.948 3

0.849 8

0.554 7

0.318 0

0.634 0

0.308 4

0.486 1

-0.263 7

-0.164 7

-0.381 8

-0.075 8

-0.342 0

-1.052 6

-0.894 5

-1.150 9

-1.762 5

-1.653 8

-0.815 0

-1.061 7

-1.841 2

-1.633 8

-1.791 7

), ArticleFig(id=1263881703005799113, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=CN, label=表3, caption=

第1组特征集数据

, figureFileSmall=null, figureFileBig=null, tableContent=
时间/h有效值方差峭度因子时频总能量

500

500

500

500

500

1 000

1 000

1 000

1 000

1 000

1 500

1 500

1 500

1 500

1 500

2 000

2 000

2 000

2 000

2 000

2 500

2 500

2 500

2 500

2 500

3 000

3 000

3 000

3 000

3 000

1.500 0

1.333 3

1.319 4

1.293 9

1.194 4

1.180 6

1.138 9

1.133 7

1.013 9

0.930 6

0.916 7

0.806 3

0.763 9

0.638 9

0.611 1

-0.125 0

-0.263 9

-0.367 9

-0.513 9

-0.625 0

-1.930 6

-2.055 6

-2.111 1

-2.138 3

-2.305 6

-2.958 3

-3.000 0

-3.069 4

-3.177 9

-3.263 9

1.844 9

1.791 0

1.712 8

1.621 9

1.536 1

1.369 4

1.326 0

1.275 1

1.230 8

1.179 4

1.076 2

0.942 3

0.707 8

0.493 2

0.128 1

-0.293 2

-0.865 8

-1.427 7

-2.060 9

-2.655 5

-3.275 3

-3.983 3

-4.606 1

-5.152 5

-5.804 6

-6.420 6

-7.028 2

-7.662 2

-8.259 2

-8.996 6

7.272 1

8.575 8

5.104 4

7.014 9

8.404 7

7.642 5

8.860 9

7.733 1

8.776 5

6.955 3

-0.754 3

-2.922 1

1.161 9

-1.703 0

0.037 3

-9.595 2

-12.199 1

-7.422 2

-11.413 4

-8.547 5

-15.054 9

-13.749 4

-16.180 7

-16.265 3

-14.441 1

-18.773 2

-17.643 9

-16.340 5

-17.641 0

-19.377 3

0.897 4

1.114 5

0.976 5

0.848 3

0.947 1

0.869 2

0.731 0

0.790 3

0.948 3

0.849 8

0.554 7

0.318 0

0.634 0

0.308 4

0.486 1

-0.263 7

-0.164 7

-0.381 8

-0.075 8

-0.342 0

-1.052 6

-0.894 5

-1.150 9

-1.762 5

-1.653 8

-0.815 0

-1.061 7

-1.841 2

-1.633 8

-1.791 7

), ArticleFig(id=1263881703756579535, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=EN, label=Tab. 4, caption=

Model parameters

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模型类别参数名称参数值
GA-GPR

推理函数

均值函数

协方差函数

似然函数

@infGaussLiK

@meanConst

@covRQiso

@likGauss

PSO-BP

粒子数量

最大迭代次数

学习率

动量因子

80

1 000

0.01

0.5

BP

最大迭代次数

目标误差

学习率

训练迭代次数

1 000

0.001

0.01

60

), ArticleFig(id=1263881704167621331, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=CN, label=表4, caption=

模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
模型类别参数名称参数值
GA-GPR

推理函数

均值函数

协方差函数

似然函数

@infGaussLiK

@meanConst

@covRQiso

@likGauss

PSO-BP

粒子数量

最大迭代次数

学习率

动量因子

80

1 000

0.01

0.5

BP

最大迭代次数

目标误差

学习率

训练迭代次数

1 000

0.001

0.01

60

), ArticleFig(id=1263881706289939163, tenantId=1146029695717560320, journalId=1263187878914834467, articleId=1263881629202825404, language=EN, label=Tab. 5, caption=

Model prediction accuracy discrimination

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模型RMSERE eR2t/s
BP2.252.470.962 44.60
PSO-BP1.131.420.987 67.22
GA-GPR0.360.490.998 11.61
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模型预测精度判别

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模型RMSERE eR2t/s
BP2.252.470.962 44.60
PSO-BP1.131.420.987 67.22
GA-GPR0.360.490.998 11.61
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RV减速器精度寿命的退化与可靠性评估
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徐航 1, 2 , 聂义轩 1, 2 , 温东杰 1, 2 , 任继华 3 , 洪志辉 4
机械传动 | 试验分析 2026,50(1): 133-141
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机械传动 | 试验分析 2026, 50(1): 133-141
RV减速器精度寿命的退化与可靠性评估
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徐航1, 2 , 聂义轩1, 2 , 温东杰1, 2, 任继华3, 洪志辉4
作者信息
  • 1．中原工学院 机械工业光学传感与测试技术重点实验室，郑州451191
  • 2．中原工学院 智能机电工程学院（工业设计学院），郑州 451191］
  • 3．赣南科技学院 智能制造与材料工程学院，赣州341000
  • 4．东莞市环力智能科技有限公司，东莞523878

    • 徐航，男，1984年生，河南郑州人，博士，副教授；主要研究方向为精密测量、齿轮工程；。

通讯作者:

聂义轩（通信作者），男，1999年生，河北保定人，硕士研究生；主要研究方向为精密传动；。
Degradation and reliability assessment of accuracy life of RV reducers
Hang XU1, 2 , Yixuan NIE1, 2 , Dongjie WEN1, 2, Jihua REN3, Zhihui HONG4
Affiliations
  • 1.Key Laboratory of Optical Sensing and Testing Technology for Mechanical Industry, Zhongyuan University of Technology, Zhengzhou451191, China
  • 2.School of Intelligent Mechanical and Electrical Engineering（School of Industrial Design）, Zhongyuan University of Technology, Zhengzhou 451191, China］
  • 3.School of Intelligent Manufacturing and Materials Engineering, Gannan University of Science and Technology, Ganzhou341000, China
  • 4.Dongguan Huanli Intelligent Technology Co., Ltd., Dongguan523878, China
出版时间: 2026-01-15 doi: 10.16578/j.issn.1004.2539.2026.01.017
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摘要
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目的

工业机器人行业对RV减速器提出更高的要求，精度寿命体现了减速器传动精度的保持能力，是最重要的设计准则和使用指标之一。为提升精密减速器的精度性能，对可靠性进行评估至关重要。为此，分析了精密减速器的退化特性。

方法

以RV80E减速器为例，提出基于Gamma过程的随机退化模型；结合减速器传动精度的性能退化数据，基于矩阵法和最大似然估计法对模型参数进行了估计；采用振动特征数据建立了基于遗传算法优化的高斯过程回归模型，以优化传动精度的预测。

结果

结果表明，基于高斯过程回归模型的预测精度显著优于传统回归模型；采用算法预测后的结果更新随机退化模型的后验分布参数，能够有效实现对RV减速器精度寿命可靠度的评估，为进一步进行精度寿命的可靠性优化设计奠定了基础。

RV减速器  /  精度保持性  /  Gamma过程  /  高斯过程回归  /  可靠性评估
Objective

The industrial robot industry has put forward higher requirements for RV reducers, and the precision life reflects the ability of the reducer to maintain transmission accuracy, which is one of the most important design criteria and usage indicators. To improve the precision performance of precision reducers, it is crucial to evaluate their reliability. Therefore, the degradation characteristics of precision reducers were analyzed.

Methods

Taking the RV80E reducer as an example, a random degradation model based on Gamma process was proposed. Combined with the performance degradation data of the reducer transmission accuracy, the model parameters were estimated based on the matrix method and the maximum likelihood estimation method. A Gaussian process regression model optimized by genetic algorithm was established using vibration characteristic data to optimize the prediction of transmission accuracy.

Results

The results show that the prediction accuracy based on Gaussian process regression model is significantly better than that of the traditional regression model. The posterior distribution parameters of the random degradation model are updated by using the algorithm to predict the results, which can effectively evaluate the reliability of the accuracy life of RV reducer and lay the foundation for further reliability optimization design of accuracy life.

RV reducer  /  Accuracy retentivity  /  Gamma process  /  Gaussian process regression  /  Reliability assessment
徐航, 聂义轩, 温东杰, 任继华, 洪志辉. RV减速器精度寿命的退化与可靠性评估. 机械传动, 2026 , 50 (1) : 133 -141 . DOI: 10.16578/j.issn.1004.2539.2026.01.017
Hang XU, Yixuan NIE, Dongjie WEN, Jihua REN, Zhihui HONG. Degradation and reliability assessment of accuracy life of RV reducers[J]. Journal of Mechanical Transmission, 2026 , 50 (1) : 133 -141 . DOI: 10.16578/j.issn.1004.2539.2026.01.017
正文
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0　引言
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RV减速器作为精密的机械传动装置，广泛应用于航空航天、机器人、工程机械等领域，其性能的优良直接影响着设备性能[1]。精密减速器的寿命指标可分为疲劳寿命和精度寿命。精度寿命是指传动精度从初始精度退化到失效阈值所经历的时间，体现了RV减速器传动精度的保持能力，是RV减速器最重要的设计准则和使用指标之一。随着技术的不断发展，对作为重要领域关键部件之一的RV减速器提出更高的精度寿命要求。因此，搭建RV减速器试验台进行精度寿命试验，分析传动精度退化过程的试验数据，提出更为有效准确的精度寿命可靠性研究方法具有重要意义。
目前，对RV减速器寿命特性的研究主要集中在疲劳寿命计算分析、失效机制和加速疲劳寿命试验等方面。程曼等[2]针对精密减速器主要零件失效形式提出疲劳寿命试验方法，搭建测试装置，完成了模拟实际运作方式和加速度疲劳寿命试验。RV减速器精度寿命的重要性越来越引起学术界和工业界的重视，精度寿命的研究主要集中在丝杆副和导轨副的精度寿命上[3]。王永青等[4]分析了精度保持性的基本内涵，针对数控机床建立了基于多体理论的位置精度保持性评价模型，通过9项精度指标的跟踪检测，完成误差敏感度定量评估。弓宇等[5]分析了精密减速器不同传动精度指标，提出便于操作的测量和数据处理方法，通过搭建试验台进行试验对比，验证了试验方法的可行性。
国内外学者对性能退化数据的可靠性和寿命预测建模方法开展了大量研究，主要包括失效形式的物理模型[6]、机器学习[7]和随机退化模型等。基于随机退化过程的可靠性建模方法充分考虑设备退化过程中随机因素的影响，可以更加准确地评估设备可靠度。常见的随机退化过程包括Wiener过程和Gamma过程等。通常，描述单调性退化过程时采用Gamma过程，其增量非负且独立，能更精确地描述设备性能退化过程。陈友东等[8]采用小子样加速退化试验提出两阶段Gamma过程的退化模型，采用Gibbs抽样估计模型参数进行了机器人大臂关节的可靠性评估。李金峰等[9]针对RV减速器传动误差与回差的测量，基于Gamma过程建立了退化模型，通过二元Copula函数建立了多元退化模型，综合评估了减速器的可靠性及预估寿命。王卫国等[10]利用基于Gamma过程的退化模型来描述装备的性能退化，通过经验公式和粒子滤波估计参数，通过振动信号特征预测直升机减速器行星架裂纹情况，评估了系统剩余寿命。董浩生等[11]采用不同工艺参数对螺杆转子砂带磨削进行正交试验，结合单因素和多因素法，通过不同优化算法预测了工件表面质量。
综上可知，目前针对RV减速器寿命特性的研究主要集中在疲劳寿命方面，针对精度寿命方面的研究很少；而且，基于退化数据的可靠性研究主要集中在采用历史退化数据进行参数估计和建模，缺少对RV减速器性能指标的精准预测和精度寿命可靠度的评估。因此，本文针对RV减速器性能退化特点，利用Gamma随机退化过程，建立传动精度退化模型；同时，提取振动信号，建立基于遗传算法优化的高斯过程回归模型，实现基于振动特征集的传动精度预测；通过预测结果更新随机退化模型的后验分布参数，以实现对RV减速器精度寿命可靠度的评估。
1　精度寿命的理论和退化模型建立
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1.1　精度寿命理论概述
广义的精度保持性[12]是指设备在正常工况下，精度项保持在设计范围内的能力。精度相关质量特性（精度项）适用于机械产品中具有误差的几何量。其适用的具体几何量有机床主轴回转精度、机床直线轴定位精度、轴承的回转精度、精密减速器的传动误差和回差等。
精度保持性通常以精度寿命（精度保持时间）（Accuracy Life, AL）为评价指标，通过精度寿命的评估可以提供精度退化的结果。精度寿命体现了精密减速器传动精度的保持能力，是企业生产制造中最重要的设计准则和运行指标之一。RV减速器的传动精度指标（精度项）包括传动误差和回差等。本文中以传动误差为传动精度的退化指标，进行精度寿命的表征。
传动精度由检测的一组传动误差数据的最大和最小的差值获得。传动误差可由RV减速器输出轴的实际转角与理论转角差值获得，计算式为
E=θiniT-θout
式中，θin为输入轴的实际转角；θout为输出轴的实际转角；iT为减速器的传动比。
进而得出传动精度计算式为
θ=Em1-Em2
式中，θ为传动精度；Em1为最大传动误差值；Em2为最小传动误差值。
关于RV减速器的精度等级，我国尚未制定相应国家标准。目前国内企业对RV减速器的精度指标多按照国家标准GB/T 30819—2014中对谐波减速器的要求进行评级[13]，其部分指标如表1所示。
1.2　基于Gamma过程的可靠性评估
Gamma过程是一种连续时间的随机过程，具有严格单调递增的特性，要求该过程的各个退化增量相互独立且均大于0。因此，Gamma随机过程适用于本文的传动精度指标，具有以下特征：
特征1：初始退化增量为0，即满足X(0)=0，且概率为1。
特征2：任意时刻t≥0时，ΔX(t)=X(t+Δt)-X(t)：PGa[α(t+Δt)-α(t)，β]，PGa(·)为Gamma过程。
特征3：对于任意时刻ti，x(ti) =X(ti)-X(ti-1)，不同时刻下的性能指标退化增量x(ti)相互独立。
设X(t)为t时刻的退化量，根据特征2可得出
X(t+Δt)-X(t)~PGa[α(t+Δt)-α(t),β]
X(t)的概率密度函数为
fX(t)(x)=PGa[x|α(t),β]=βα(t)Γ[α(t)]xα(t)-1e-βxI(0,∞)(x)
式中，α(t)为形状参数，α(t)>0；β为尺度参数，β>0；当x∈A时，指示函数I0,∞x=1，当x∉A时，I0,∞(x)=0；A为特定时间段内收集到的有效数据点集；Γ[α(t)]为α(t)>0时的Gamma函数，Γ[α(t)]=∫0∞tα(t)-1e-tdt。
当采用Gamma过程描述产品失效过程时，需设置退化过程的失效阈值Df，则产品的可靠性为
Rt=P[X(t)<D]=Γ[α(t),Dfβ]Γ[α(t)]
式中，D为退化数据的有效增量；Γ[α(t)，Dfβ]为不完全Gamma函数。
可靠性评估实现步骤如下所述：
1）通过性能退化试验获得历史性能退化数据，建立基于Gamma过程的随机退化模型；根据矩阵法和最大似然估计法，估算先验分布参数αi和βi。
2）在性能退化试验的同时，收集振动信号并对其进行滤波处理和特征提取。以振动信号特征集为训练集输入，性能指标数据为训练集标签；为了提高模型的预测精度，对比多种回归模型的预测精度，建立基于遗传算法优化的高斯过程回归模型，从而实现性能指标的预测。
3）将高斯过程回归模型预测的性能指标对Gamma随机过程进行后验参数αi和βi的更新，此时，更新后的模型更适合于当前设备；最终进行精度寿命可靠度的评估。
1.3　基于高斯过程回归的退化精度预测
基于遗传算法优化的高斯过程回归（Genetic Algorithm-Gaussian Process Regression, GA-GPR）模型利用数据特性进行预测建模。当退化数据呈现高斯分布时，模型的预测精度将显著提升。多维高斯分布包含协方差矩阵、均值向量两个重要参数，其概率密度函数为
f(x1,x2,⋯,xn)=1σ1σ2⋯σn2πnexp-12[(x1-μ1)2σ12+(x2-μ2)2σ22+⋯+(xn-μn)2σn2]
式中，μ为多维高斯分布的均值向量，μ=μ1，μ2，⋯，μn；C为协方差矩阵，C=σ12⋯0⋮⋮0⋯σn2。
通过计算退化数据训练集和测试集的均值向量，进一步计算协方差矩阵，评估各个特征的相关性和分布情况，从而完成对测试样本的预测。
训练集S(X，Y)，令f(xi)=yi，则可推出f=[f(x1)，f(x2)，⋯，f(xn)]，高斯回归模型为
y=fx+ε
式中，x为训练集数据；y为训练集标签；f为高斯过程函数；ε~N(0，σn2)。
设待测样本数据为X*，预测值的样本为f*。基于高斯核函数进行退化数据从低维到高维的映射，推出y与f*的联合先验分布，即
yf*~N0,C(X,X)+δn2InC(X,X*)C(X*,X)C(X*,X*)
由此推出预测值f*的后验分布，即
f*X,Y,x*~N[μ（x*）,var（x*）]
通过预测得到性能指标，基于贝叶斯方法更新参数αi和βi。后验概率密度函数为
f（sxtk）=（xt k+β）tk+αΓ（tk+α）（1s）(tk+α)-1∙extk+βs∙I0,∞（x）=PGa（s(tk+α,xtk+β）
后验期望估计为
s^=xt k+βtk+α-1
根据式（4）、式（5）、式（11）可得参数更新后的实时可靠度函数曲线，即
R(t)=P(TDf>t)=P[X(t)<Df]=∫0Df(1/s^)tΓ(t)xt-1e-（1/s^）xdx
同时，为了比较多种模型的预测精度，本文采用均方根误差（Root Mean Square Error, RMSE）、相对误差（Relative Error, RE）、拟合优度、预测时间4种预测精度判别指标。
1）均方根误差
均方根误差表示预测值与实际值的差异程度，取值范围为[0，∞），值越小，预测精度越好，计算式为
eRMSE=∑i=1n(yi'-yi)2/n
式中，n为预测值的数量；yi'为预测值；yi为实际值。
2）相对误差
相对误差表示预测值与实际值的偏离程度，取值范围为[0，1]。绝对误差与实际值的比值越小，预测精度越好。相对误差计算式为
eRE=[∑i=1n（yi'-yi）2]/∑i=1nyi2
3）拟合优度
拟合优度又称决定系数，衡量回归模型变量与响应变量的关系强度，取值范围为[0，1]。其值越接近1，表示预测精度越好，计算式为
eR2=n∑i=1nyi'yi-∑i=1nyi'∑i=1nyin（∑i=1nyi'）2-（∑i=1nyi）2∙[n（∑i=1nyi'）2-（∑i=1nyi）2]2
2　测量试验
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2.1　性能退化试验
基于RV减速器试验台开展精度寿命试验，进行工作状态的监测，并采集历史退化数据（包含同步采集的振动数据和传动误差数据）。本文以RV80E-121型减速器为研究对象，以传动误差数据最大与最小的差值（传动精度）为RV减速器的性能指标，表征RV减速器的精度寿命；通过测量的振动数据构建高斯过程的回归预测模型，实现对传动精度的预测。
RV减速器综合性能测量仪如图1所示，该仪器主要包括精密机械系统、测控系统、测量软件。RV减速器的输入端由伺服电动机驱动，输出端通过负载电动机调整输出轴载荷大小，通过中控操作台控制调节电动机。测控系统通过高精度圆光栅检测系统的旋转角度，采用转矩传感器检测系统的转矩。RV减速器综合性能测量仪可测量精密减速器的多种精度指标，如传动误差、静态回差、动态回差、传动效率等。
为了研究RV减速器精度寿命的演变，采用恒定应力载荷模式进行退化试验。额定载荷为恒定应力载荷的1.5倍，即额定负载784 N·m的1.5倍；在额定转速2 000 r/min下进行试验，在测试期间每隔500 h测量1次传动误差，共持续3 000 h；测量精度为角秒级别，根据标准GB/T 30819—2014中对传动精度等级的定义，取失效阈值Df=60″。初始传动误差为18.06″；采用三向压电式加速度传感器测量振动数据。一般而言，RV减速器内包含滑动轴承时测量主轴振动信号，包含滚动轴承时测量壳体的振动信号。故本文采用的测量方式为减速器壳体测量法，如图2所示[14]。采样频率为2 kHz，采样时间设定为180 s，同一时间对其传动误差与振动信号进行测量。
图3所示为不同时间下的传动误差曲线，图4为传动精度汇总图。
2.2　基于Gamma过程的退化建模
基于该试验数据，利用矩阵法和最大似然估计法估算Gamma过程的形状参数及尺度参数。基于传动误差退化增量的Gamma随机过程参数估计结果如表2所示。
2.3　振动信号分析
每间隔500 h进行1次振动信号提取，单次试验提取的数据总长度为921 600。每截取6 s，计30 720个数据点为1个样本，共提取30个样本；提取6次共计180个样本。
对所有样本进行时域、频域及时频域特征提取。通过对振动信号的特征提取，部分特征趋势呈单调趋势，但有些无规则分布[15]。根据RV减速器的退化曲线，其传动精度呈单调趋势。从特征数据中选取单调性较好的有效值、方差、峭度因子和时频总能量4种特征，共计样本180×4个。
3　试验评估
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3.1　回归模型预测
为确保训练集和测试集的合理性，随机选取每次试验数据的20个特征集作为训练集样本输入，剩余10个作为测试集样本输出，即样本比例按2∶1分配。为数据规整，将总样本划分6组，前4组为训练集输入，后2组为测试集输出，选取有效值、方差、峭度因子、时频总能量4种特征。部分特征数据如表3所示。
采用对应数量的传动精度退化数据，其中，120个样本用于构建训练集，60个样本作为测试集标签。建立基于遗传算法优化的高斯过程回归模型，通过对测试集预测结果进行分析，评估模型的预测精度。图5所示为高斯过程回归模型预测结果，该结果不涉及训练集的建模。
从图5可以看出，基于遗传算法优化的高斯过程回归模型的预测误差很小，显示了良好的预测效果。
本文采用相同的振动信号特征集，通过反向传播（Back Propagation, BP）神经网络和粒子群优化（Particle Swarm Optimization, PSO）算法优化BP神经网络回归模型分别进行回归预测，对比分析其与高斯过程回归模型的预测精度。模型参数如表4所示。
直观比较各个模型的预测精度，通过均方根误差、相对误差、拟合优度、运行时间4种指标评判预测的结果，如表5所示。
采用BP神经网络和粒子群优化算法优化BP神经网络回归模型的预测结果分别如图6、图7所示。
BP神经网络、粒子群优化算法优化BP神经网络和基于遗传算法优化的高斯过程回归模型均能实现传动精度的预测。对比图5~图7可知，高斯过程回归模型的预测精度远高于其他两个回归预测模型。从表5可知，高斯过程回归模型的均方根误差和相对误差远小于其他两个模型，并且拟合优度更接近1，算法运行时间最短，能实现对传动精度的精确预测。
3.2　精度寿命可靠度评估
通过对RV减速器不同时刻下实测振动信号的特征提取，将提取的特征向量作为回归预测模型的输入，预测出当前时刻的传动精度。通过第1.2节中提出的Gamma随机退化模型，对预测后的传动精度结果进行后验分布参数的更新；通过式（12）计算此时RV减速器精度寿命的可靠度曲线，设定RV减速器传动精度的失效阈值Df=60″。由第1.1节和第2.1节可知，此时为2、3级精度临界点且认定为失效。精度寿命可靠度曲线如图8所示。
由图8可知，3 000 h时，RV减速器精度寿命的可靠度为0.439 1；在服役1 500 h后开始出现明显差异；在1 000 h时其精度寿命可靠度为0.996 3。当设定传动精度的失效阈值Df=60″时，该减速器的预期精度寿命约为2 879 h。
4　结论
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针对RV减速器传动精度退化过程的特点，基于RV减速器试验台，以传动误差为传动精度的退化指标，进行精度寿命的表征。基于Gamma随机过程，利用矩阵法和最大似然估计法对退化模型的形状参数及尺度参数进行了估计；通过对振动信号的特征提取，建立高斯过程回归预测模型；通过多种回归模型预测精度的对比，实现对精度寿命的预测，为模型参数的更新提供了精确的保障，实现了精度寿命可靠度的评估。具体结论如下所述：
1）传动误差作为传动精度的退化指标，可表征RV减速器的精度寿命。通过性能退化试验定期测量传动误差，结合在一定加载情况下减速器的性能退化数据和振动数据，建立了基于遗传算法优化的高斯过程回归模型，并建立了BP神经网络、粒子群优化算法优化BP神经网络；采用多种精度判别指标对比验证了该优化算法回归模型的预测精度，实现了对RV减速器传动精度的准确预测，为后验分布参数的更新提供了精确保障。
2）利用RV减速器性能退化数据，通过对传动精度失效阈值的设定，建立Gamma随机过程退化模型，估计模型的先验分布参数；基于遗传算法优化的高斯过程回归模型的预测值对模型进行后验分布参数的更新，实现了对RV减速器当前状态下的精度寿命可靠度评估，可为后续减速器精度寿命可靠性分析方法的改进提供参考。
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2026年第50卷第1期
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doi: 10.16578/j.issn.1004.2539.2026.01.017
  • 接收时间：2024-09-09
  • 首发时间：2026-05-20
  • 出版时间：2026-01-15
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  • 收稿日期：2024-09-09
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作者信息
    1．中原工学院 机械工业光学传感与测试技术重点实验室，郑州451191
    2．中原工学院 智能机电工程学院（工业设计学院），郑州 451191］
    3．赣南科技学院 智能制造与材料工程学院，赣州341000
    4．东莞市环力智能科技有限公司，东莞523878

通讯作者:

聂义轩（通信作者），男，1999年生，河北保定人，硕士研究生；主要研究方向为精密传动；。
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https://castjournals.cast.org.cn/joweb/jxcd/CN/10.16578/j.issn.1004.2539.2026.01.017
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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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