Spectral analysis is the classical technique to diagnose bearing, gear, and shaft. The spectrum of a damaged component is compared to one from the healthy condition, so some defect could be detected [57, 72-75]. The Fourier Transform is the most fundamental frequency domain technique where the Fast Fourier Transform (FFT) is widely used computational technique for converting time signal to frequency domain due to its efficiency and less calculation time [72-74]. Others use the difference of power spectral density of the signal to identify the damage due to fault of gear and bearing [75].

The Wigner-Ville Distribution (WVD), wavelet transform (WT), and short time Fourier transform (STFT) are the examples of joint time-frequency analysis [76, 77]. The major difference among these transforms is their resolution properties along time and frequency scales. The joint time-frequency analysis provides information about the vibration energy changes in the system where presenting as an interactive relationship between time and frequency during the period of the time data window. Therefore, the damage could be revealed at much earlier stage. The STFT had been considered by Mc Fadden [78] and suggested that it can potentially be a useful tool for fault detection and localization. The property of WVD was investigated by Mc Fadden [79] and he successfully applied a technique to determine the change in vibration pattern when damage occurs. Further improve of WVD by reducing the cross-term effect [80, 81] was found in Mc Fadden’s researches.

The early works on the application of WVD in gear diagnostics demonstrated the relation between the gear fault and the distribution pattern [79, 80, 82]. Recently it was further established the correlation between a WVD pattern and the severity of the gear fault [27, 29, 83]. Another useful joint time-frequency domain method in vibration analysis is the wavelet method [7, 8, 84, 85]. Because of its superior potential time-frequency technique, the use of wavelet analysis for fault analysis and detection in gear box has been gaining researchers’ attention [86-89]. The Wavelet Transform has achieved a high frequency resolution to signify the presence of damage in the gearbox vibration signal. The application of wavelet analysis was recently developed to diagnose a fault in gear [90] and combination between gear and bearing [33].

摘要与轴承，轴和齿轮相关联的振动问题已经引起很多工程工作的重视。目前，在转子齿轮传动系统的预防性维护进步的同时，正在寻求改善机器健康监测系统的故障诊断技术。以前，大型旋转机械的研究人员和设计人员广泛采用分析程序来研究旋转系统的动态特性。目前，已经开发出包括不同类型故障的技术，并与一些在线振动监测方法一起使用。这些在线监测方法不需要关闭机器，可用作于飞行中诊断。然而，在传动系统中的轴承，轴和齿轮的组合效应下，对故障检测工作进行了很少的工作。

在本论文中，进行了数值模拟和实验研究，以确定不同的损伤情况，涉及轴承损伤，残余轴弯曲量和齿轮齿损伤的不同组合。综合数值模型研究了旋转机械系统的瞬态响应，包括单独缺陷部件的影响。为了提高计算效率，减少计算量，采用模态分析方法应用于运动方程，解决了系统的整体动力学。非线性轴承力被认为是使用赫兹接触变形理论的球和滚道之间的接触的结果，并且考虑到局部缺陷对内圈的影响，该模型被扩展。在残余轴弯曲量的情况下，弯曲量形效应被引入作为运动方程式中的强制功能。在齿轮传动系统模型中，齿轮啮合力由非线性周期齿轮啮合刚度产生。由于磨损引起的齿轮表面轮廓的变化被模拟为啮合刚度振幅的变化。本研究中使用的实验结果是从高速球轴承试验台获得的。在这些测试中，由于每个损坏的影响，即获得振动特征：即轴承缺陷，残余轴弯曲量和齿轮损坏/磨损，用于识别和验证。