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本书围绕数控磨齿机可靠性技术中的一系列问题，在可靠性建模、可靠性评估、故障分析及可靠性风险评价等方面进行了研究，以达到提高国产数控磨齿机的可靠性水平的目的。本书首先确定了可靠性评价特征量及这些特征量之间的相互关系，为可靠性评估方法的研究奠定基础；其次对小样本可靠性评估方法进行了研究，建立了基于 RBF 神经网络的可靠性评估流程，同时对数控成形磨齿机故障和可靠性风险进行了综合分析，为提升机床装备可靠性奠定基础。本书适合企业技术装备人员阅读，也可作为高等学校机械制造、智能制造相关专业在校本科生、研究生的教学参考用书。

第 1 章 可靠性建模理论 ·····························································.1
1.1 可靠性建模与可靠性评价 ···············································.1
1.1.1 可靠性建模目的和意义 ·········································.1
1.1.2 可靠性评价函数 ··················································.2 
1.1.3 可靠性评价指标 ··················································.4
1.2 可靠性分布模型简介 ·····················································.5
1.2.1 韦布尔分布模型 ··················································.5
1.2.2 指数分布模型 ·····················································.7
1.2.3 正态分布模型 ·····················································.9
1.2.4 对数正态分布模型 ···············································10
1.3 可靠性分布模型检验方法 ···············································12
1.3.1 统计假设检验 ·····················································12
1.3.2 拟合优度检验 ·····················································14
1.4 本章小结····································································16
第 2 章 数控磨齿机磨削原理························································17
2.1 磨削加工理论 ······························································17 
2.1.1 磨削机理 ···························································17 
2.1.2 磨削加工 ···························································17 
2.1.3 磨削力计算 ························································19 
2.2 成形磨齿机磨削原理 ·····················································20 
2.2.1 成形磨齿原理 ·····················································20 
2.2.2 成形数控磨齿机结构 ············································21 
2.3 摆线轮磨削原理 ···························································22 
2.3.1 摆线轮齿面形状 ··················································22 
2.3.2 摆线轮啮合方程 ··················································25 
2.3.3 摆线轮磨齿机结构 ···············································29 
2.3.4 摆线轮磨削机理 ··················································32 
2.4 本章小结····································································33 
第 3 章 数控磨齿机故障综合分析 ··················································34
3.1 振动信号故障特征提取技术 ············································34 
3.1.1 EMD 算法介绍····················································34 
3.1.2 实验数据采集 ·····················································37 
3.1.3 振动数据的处理与分析 ·········································39 
3.2 数控磨齿机故障树分析（FTA） ·······································42 
3.2.1 FTA 基本方法 ·····················································42 
3.2.2 数控磨齿机故障树的建立 ······································43 
3.2.3 数控磨齿机故障树定性分析 ···································45 
3.3 基于 FTA-AHP 的数控磨齿机可靠性分析····························48 
3.3.1 FTA-AHP···························································48 
3.3.2 在数控磨齿机上应用 FTA-AHP ·······························49 
3.3.3 故障因素层次总排序分析 ······································53 
3.4 本章小结····································································55 
第 4 章 基于 RBF 神经网络的数控磨齿机可靠性评估···························56
4.1 RBF 神经网络简介························································56 
4.1.1 RBF 神经网络结构介绍·········································56 
4.1.2 RBF 神经网络学习算法·········································58 
4.2 基于 RBF 神经网络的扩充算法 ········································60 
4.2.1 RBF 神经网络扩充算法的设计 ································60 
4.2.2 RBF 神经网络可靠性评估流程 ································61 
4.3 实例分析····································································63 
4.3.1 原始故障间隔时间分布模型 ···································63 
4.3.2 RBF 神经网络扩充数据及分析 ································67 
4.3.3 数控磨齿机可靠性评估 ·········································71 
4.4 本章小结····································································75 
第 5 章 基于贝叶斯方法的数控磨齿机可靠性建模分析 ·························76
5.1 可靠性数据的收集 ························································76 
5.1.1 可靠性数据分类 ··················································76 
5.1.2 可靠性数据收集方法 ············································77 
5.1.3 可靠性数据的筛选 ···············································78 
5.2 数控磨齿机先验信息 ·····················································79 
5.2.1 先验信息预处理 ··················································79 
5.2.2 先验信息相容性检验 ············································79 
5.3 数控磨齿机先验分布的确定 ············································82 
5.3.1 常用的先验分布介绍 ············································82 
5.3.2 自助法确定先验分布 ············································82 
5.3.3 分布模型的假设检验 ············································85 
5.4 后验分布计算 ······························································87 
5.4.1 Win BUGS 软件计算·············································87 
5.4.2 后验参数区间和 MTBF 计算···································94 
5.5 本章小结····································································95 
第 6 章 基于模糊 FMECA 的数控磨齿机可靠性评估····························97
6.1 传统 FMECA 方法介绍 ··················································97 
6.2 模糊风险评价模型 ························································98 
6.2.1 模糊语言变量 ·····················································99 
6.2.2 模糊综合评判 ··················································.100 
6.3 数控磨齿机子系统 FMEA 分析······································.102 
6.4 数控磨齿机子系统模糊风险评价（CA） ·························.108 
6.4.1 进给伺服子系统 ···············································.108 
6.4.2 机床液压子系统 ···············································.110 
6.4.3 磨削砂轮子系统 ···············································.111 
6.4.4 电气控制子系统 ···············································.113 
6.4.5 冷却润滑子系统 ···············································.114 
6.5 本章小结·································································.116 
第 7 章 总结与展望 ································································.118
7.1 研究工作总结 ···························································.118 
7.2 展望·······································································.119 
参考文献 ··············································································.120

数控磨齿机作为工业体系中的中高端制造装备，为国民经济和国防建设提供了必要的基础支撑。在当前的新型工业化时代，加快实现数控磨齿机朝着高可靠性、高精度、智能化方向发展，对于推动我国工业产业结构优化升级，助力中高端数控机床实现国产化，进而实现由制造大国向制造强国转变的发展战略具有重要的意义。近十几年来，由于现代工程技术的不断创新，
机床的可靠性研究正朝着多元化、系统化方向发展，但我国在机床的可靠性研究上尚存在诸多不足，高端制造装备加工产品的一致性问题仍未得到很好的解决。因此，开展国产数控磨齿机的可靠性研究能够为解决长期困扰机床可靠性提升的共性问题提供借鉴经验，其研究成果对于提高国产数控磨齿机的可靠性水平和全球行业地位具有现实的工程应用价值。
本书著者长期从事齿轮数字化设计和智能制造方面的研究工作，参与数控磨齿机、摆线轮磨齿机、数控车齿机等机床的研制，积累了一定的研究成果。同时，本书第一著者参与完成了国家自然科学基金面上项目“局部共轭内斜齿轮修形机制与成形磨削理论研究（51575160）”，以及河南省重大科技专项“机器人 RV 减速器摆线针轮精密制造技术研究及装备开发（161100211200）”；主持完成了河南省科技攻关项目“RV 减速器传动特性分析及测试平台（172102210038）”以及河南省自然科学基金项目“高性能重载斜齿轮齿面微观形貌成形机理及分区磨削理论研究（182300410229）”。上述研究和项目的成果为本书的出版奠定了坚实基础。本书围绕数控磨齿机可靠性技术中的一系列问题，在可靠性建模、可靠性评估、故障分析及可靠性风险评价等方面进行了研究，以达到提高国产数控磨齿机的可靠性水平的目的。本书首先确定可靠性评价特征量以及这些特征量之间的相互关系，旨在为可靠性评估方法的研究奠定基础；其次对小样本可靠性评估方法进行研究，建立基于 RBF 神经网络的可靠性评估流程，同时对数控磨齿机故障和可靠性风险进行综合分析，为提升机床的可靠性奠定基础。参与本书撰写工作的有：河南科技大学王会良，中信重工机械股份有限公司智能矿山重型装备全国重点实验室瞿铁、信稳，河南科技大学魏冰阳。
全书共分为 7 章，其中第 1 章由魏冰阳编写，第 2 章由瞿铁编写，第 3、4 章由信稳编写，第 5、6、7 章由王会良编写。全书由王会良统稿并定稿。第 1 章介绍可靠性建模的目的与意义，并对可靠性分布模型进行讲解，为后续章节做铺垫；第 2 章介绍数控磨齿机的结构与磨削原理；第 3 章对数控磨齿机的故障进行综合分析，通过实验得出机床的故障信号，再通过 FTA-AHP 方法进行故障分析；第 4 章对小样本可靠性评估方法进行研究，建立基于 RBF
神经网络的可靠性评估流程并分析其优势；第 5 章通过收集先验信息，采用贝叶斯方法对小样本可靠性分布模型进行计算；第 6 章对基于模糊 FMECA的可靠性风险评价模型进行分析和研究；第 7 章进行总结与展望。
在本书完稿之际，诚挚感谢洛阳科大越格数控机床有限公司、洛阳科大格尔传动研究院、机械装备先进制造河南省协同创新中心、齿轮制造及装备河南省工程实验室等提供的科研平台；同时感谢所有支持本书出版的单位和个人；感谢杨英豪、付一林、李洁、习超斐、方凯、浮文华、张智杰、张旭艳、寇云飞等研究生为本书顺利完稿所付出的努力。此外，本书出版也得到了河南省科技研发计划联合基金（科技攻关类）“高速重载内齿轮球形蜗杆砂轮磨削控制策略及软件开发（222103810040）”和河南省高等学校重点科研项目“非正交直齿面齿轮车齿成形机理及主动控制策略研究（23A460017）”等项目的资助，在此表示感谢。
由于著者水平有限，书中难免存在错误与纰漏之处，恳请广大读者和各位专家批评指正。

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数控磨齿机故障诊断与可靠性评估