【作者】 胡茑庆；

【导师】 温熙森；

【作者基本信息】 国防科学技术大学 ， 机械电子工程， 2001， 博士

【摘要】 20世纪下半叶兴起的混沌理论为非线性动力学系统的研究开创了新途径。对复杂机械 系统中可能出现的强非线性行为(如混沌）展开研究并探讨混沌理论在机械故障诊断中的 应用，对于复杂机械系统的设计、使用、诊断与维修具有重要意义。 随着机械运转速度的日益提高以及各种新型材料在高速机械中的广泛应用，机械系 统的非线性将更加突出，可能直接（或间接）导致机械系统的故障。从理论和实验上对 这个问题进行研究意义重大，而对非线性行为特别是混沌行为的预测与运行状态早期检 测，以及利用基于混沌理论的信号／信息处理方法的研究显得尤为突出。本文正是在这样 的背景下，提出对转子系统中存在的复杂非线性行为展开研究，并对非线性行为的辨识方 法以及基于混沌理论的转子故障早期诊断新方法进行了深入研究与探讨。 本论文主要完成两个方面的研究工作：从碰摩转子实验系统中观测混沌现象并进行辨 识与分析；基于非线性科学理论与技术对转子系统的行为进行分析、预测与早期辨识。概 述地说，围绕上述问题所开展的具体研究内容包括： 1．深入系统地研究了碰摩转子的非线性行为与特征规律。 (1）采用并改进了已有的转子尖锐碰摩模型，通过定量和定性的理论分析，获得了尖 锐碰摩转子振动响应形式；设计了尖锐碰摩转子试验台并开展了细致的实验研究，获得了 不同碰摩情况下的振动响应特征规律；通过理论和实验分析，得出在尖锐碰摩情况下，早 期碰摩在一定条件下会出现1／3X、2／3X的分频成分的结果（X表示工频）。 （2） 建立了基于局部碰摩力变化且具有转、定于偏心的Jeffcott非线性转子的动力学 模型，大量的数值仿真表明局部碰摩转子存在分频现象和一定的分叉规律，获得了大不平 衡、小阻尼、高转速条件下，局部碰摩容易产生拟周期或混沌振动的结果；基于数值分析 结果，设计并建立了局部碰摩转子系统试验台，在大范围的转速里进行了细致的实验研究， 观察到了包括周期、拟周期、次谐波与超谐波以及混沌振动在内的丰富的振动现象。观测 与仿真结果定性一致。 （3）采用基于观测时间序列的重构相空间分析方法对转子系统的非线性行为进行辨识 与分析，获得了系统出现强非线性行为的统计意义上的证据。 研究表明早期碰摩时产生的分频现象这一结果对这类故障的早期诊断提供了依据。理 论与实验分析获得的碰摩转子振动响应的特征规律对于碰摩的预测具有一定的参考价值。 2．提出了具有工程化前景的相空间重构技术和统计特征指数算法，以评判碰摩转子 观测数据所隐含的动力学行为。 （1）在短数据集情况下，为了快速、合理地选择嵌入空间参数，提出了延迟时间选择 的交叉位移改进法和嵌入维数选择的伪近邻距离统计增长法，其特点是速度快、重复性好。 （2）对影响关联维数计算的各种因素进行了深入分析，提出了在短数据集约束下估计 关联维数的具体方法。 国防科学技术大学研究生院学位论文一 o）提出了在短数据集条件下，通过最大瞬时Lyapunov指数来估计最大LyaPunov指数的方法，并指出Lyapunov指数之和与系统的能量耗散机制相关联。从理论上分析并提出了Lyapunov指数之和的变化规律可用来监测强非线性系统的阻尼变化，从而可以监测系统状态变化的新策略和新方法。 研究表明关联维数和最大Lyapunov指数对非线性动力学行为的辨识是行之有效的，其有效性在转子碰摩的各种状态的分类与辨识中获得了证实。 3．提出了通过观测数据的不可长期预测性并结合特征指数 分析对信号的混油特性进行综合判别的新方法。 O）改进了局部线性拟合的非线性预测方法。 c）提出了非线性时间序列预测的相轨迹方法。 ＊）提出了利用观测数据的短期、长期可预测性可对动力学行为进行辨识的新方法。 研究表明，上述预测方法结合特征指数分析，可以对非线性行为进行综合分类与辨识，通过多指数、多角度地对观测数据进行分析，使获得的辨识结果更为可信。该预测方法在转子碰摩非线性行为的分类与辨识中的应用表明是行之有效的。 4．以理论和实验分析所获得的碰摩故障特征规律为基础，提出采用Duffing振子微弱信号检测方法对转子系统碰摩故障特征进行早期检测的新方法。 ＊）理论分析了Duffing方程的全局解和全局分叉规律并讨论了分叉值随阻尼、外部激励幅值的变化规律，发现Duffing方程外轨解的最大轨道所对应的分叉阈值特性可用来进行微弱信号检测。 O）提出了利用Duffing振子进行早期故障特征微弱信号检测的实现模型更多还原

【Abstract】 Chaos theory developed in the late half of 20th century gives a new approach for the research on nonlinear dynamical system. The researches on strong nonlinear behavior such as chaos in complex mechanical system and application of chaos theory in machinery fault diagnosis are of significance to design, operation, diagnosis and maintenance of complex mechanical system.With the increase of machinery operating speed and wide application of various new-style material in high-speed machinery, nonlinear problem of mechanical system which may cause abnormal state even fault directly or indirectly becomes more and more obvious. Theoretical and experimental studies focusing on this problem are very important. Particularly, it is more important to study the prediction of nonlinear behavior and chaotic behavior, early detection of operating state and signal/information processing method based on chaos theory. Under this circumstance, this dissertation suggests two research aspects, namely experimental study on complex nonlinear behavior underlying rotor system with stator-rotor rub and deep study on identification method and early diagnosis of rotor fault based on chaos theory.Subsequently, this dissertation mainly includes, observation and identification of chaotic phenomena from rub-impact rotor rig, analysis and prediction for nonlinear behavior of rotor rub-impact based on nonlinear signal processing, early detection and recognition of rub-impact fault based on nonlinear theory and chaos theory. The detailed contents and innovative work include,1. Nonlinear behavior and characteristic rule of rub-impact rotor are deeply and systematically studied.(1) Combined with quantitative and qualitative analysis, solutions of vibration response of sharp rub-impact rotor are obtained by the improved sharp rub-impact model of rotor. Test rig of sharp rub-impact rotor is designed and meticulous experiment has been accomplished. Characteristic Rile of vibration response is obtained in various cases of rub-impact. The result that the 1/3X,2/3X sub-harmonic components (X denotes operating frequency component) occur in inception of rub-impact in the case of sharp rub-impact under certain condition, is obtained via theoretical and experimental analysis.(2) Dynamics model of Jeffcott nonlinear rotor with eccentric between stator and rotor is built based on rub-impact force. Numerical simulation demonstrates that local rub-impact has sub-harmonic phenomena and bifurcation phenomena. The rub-impact rotor response includes quasi-periodic or chaotic vibration when severe unbalance, small damping and high rotating speed. Based on the result of numerical analysis, rotor test rig about local rub-impact is designedand built. Experimental research has been done within broad range of rotating speed. A very rich and complicated vibration phenomenon including not only periodic (synchronous and non-synchronous) components but also quasiperiodic and chaotic motions, is observed. The observed result is qualitatively consistent with that of simulation.(3) Phase space reconstruction analysis method based on observed time series is used to analyze and identify nonlinear dynamics of rotor system. The evidence with statistical meaning representing strong nonlinear behavior is obtained.The results show that sub-harmonic phenomena produced by local rub-impact provide mechanism and evidence for the early diagnosis of this fault. Vibration response characteristics of rub-impact rotor obtained by theoretical and experimental analysis are of significance to prediction of rub-impact.2. Phase space reconstruction technology and characteristic indices algorithms, which show the wide prospects of engineering application, are presented to In order to distinguish dynamical behavior underlying observed time series from rub-impact rotor.(1) In the case of short data set, to select embedding space parameters as fast and exact as possible, the improved across displacement method for selecting time delay and the relative gain ratio of fal更多还原