行星轮系复合故障的振动机理及联合字典分块稀疏诊断方法研究

As a key part of modern large equipment, the planetary gear train is complex and rich of moving components. In severe working conditions, the coupling modulation phenomena of compound fault often occur, which cannot be detected by existing models and diagnosis techniques. In this project, in consideration of the complexity of non-stationary vibration signals’ time-frequency features in the planetary gear train and the ambiguity of the modulation sideband coupling mechanism, the mapping relation between time-varying transfer paths and vibration modal parameters is studied. The vibration mechanism of the system is improved by considering both the time-varying transfer paths and displacement fluctuating excitation of solar gear’s floating mesh when the model is built. The equivalent modes of different fault excitations, the change law of the characteristic frequencies and the mapping relation between signal symptom and fault mode are studied, through which the coupling vibration response model of the compound fault is obtained. Based on the inner correlation of the time domain and angle domain characteristics of non-stationary fault signals of compound fault, the adaptive joint dictionary which has definite physical meaning and low redundancy is constructed. By utilizing the SVD (singular value decomposition) and EDS (energy difference spectrum), the multi-source non-stationary fault signal is de-noised block by block, leading to a low rank sparse signal model. The block sparse objective function is constructed through regularizing the nuclear norm as well. The compound fault signal could be decoupled and the feature of which could be extracted based on the joint dictionary and the convex relaxation optimization method. A novel vibration mechanism model and precise diagnostic method of planetary gear train’s compound fault are finally obtained.

作为现代重大装备的关键部件，行星轮系结构复杂且运动部件多，在恶劣工况下易出现复合故障耦合振动调制现象，现有模型和诊断方法难以精确辨识故障。针对行星轮系非平稳振动信号时频特征复杂、调制边频带耦合机制不明确且解耦难等问题，通过研究时变传递路径与振动模态参数的映射关系，并在建模时考虑浮动太阳轮啮合间隙的位移波动激励完善行星轮系振动机理，研究不同故障激励的等效模式及特征频率的变化规律、信号征兆与故障模式之间的映射关系，获得复合故障的耦合振动响应模型。基于复合故障非平稳信号时域和角域特征向量的内在相关性，建立物理意义明确、冗余度小的自适应联合字典。利用奇异值分解和能量差分谱对行星轮系复合故障的非平稳振动信号进行分块降噪，获得低秩稀疏信号模型；利用核范数规则化建立分块稀疏目标函数，基于联合字典和凸松驰优化算法解耦复合故障信号，实现故障特征提取，形成行星轮系复合故障的振动机理模型和精确诊断技术方法。

利用集中参数法、有限元法以及现象学方法分别建立了定轴轮系和行星轮系振动机理模型，从理论上研究了定轴齿轮在转速波动下正常、平稳型故障和冲击型故障时的振动调制信号产生机理，归纳总结了频谱特征。根据行星轮系的运动特点，考虑时变传递路径函数、时变啮合力方向，研究了轮系在正常状态下振动调制边带的产生机理、不同部件裂纹故障下的调制边带特征以及浮动式太阳轮结构特征下的调制边带规律，揭示了时变激励力与时变传递路径对振动信号特征的影响机制。根据机理和实验研究，分别建立了转速波动下定轴轮系健康状态与故障状态振动信号数学模型、行星轮系振动响应时空模型以及行星轮系故障振动信号数学模型，为故障特征提取和诊断等信号处理方法的正向设计提供了基础理论。针对齿轮系统时变工况，基于信号稀疏分解理论，提出了系列提取齿轮箱复合故障和滚动轴承故障特征的新方法。基于编辑倒频谱方法和信号稀疏分解，提出了一种低信噪比下滚动轴承故障特征提取方法。联合信号稀疏分解和阶次跟踪方法，实现了齿轮箱中平稳型故障和冲击型故障的解耦诊断。基于平方包络幅值解调和第一类贝塞尔函数相位解调，提出了一种齿轮系统振动调幅调频成分准确分离方法，可实现齿轮系统故障损伤程度的定量诊断。研究成果基本形成了一套完善的齿轮系统“故障机理-特征提取-诊断方法”的理论体系和工程应用技术，具有重要的理论研究意义和工程应用价值。. 研究成果共发表SCI文章17篇，EI收录论文3篇；申请授权发明专利3件，受理发明专利8件；培养博士生3人，硕士生5人；在国内外学术会议作分会主题邀请报告4次；发表论文总引用数量中英文191篇次，SCI总引用为108篇次，Google学术被引149篇次；在国内外同行中有较好的学术影响。

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