Study On Weak Fault Characteristics Extraction Of Rolling Element Bearing And Gear Based On Cyclostationarity

With the development of technology, rotating machinery possesses more and more complex structure, which asks for accurate operation situation to ensure long-term safe running. As vital parts of rotating machinery, rolling element bearing and gear play a very important role in the normal running of overall system. Their any deviation from the normal situation that is caused by defects, no matter how light they are, will disturb the running of connected components. Consequently, more components will be involved in and the performance of the system will deteriorate gradually together with a series of faults. Therefore, picking up fault characters of rolling element bearing and gear as early as possible guarantees the normal operation of overall system. But, it is not an easy task. Early faults of them are weak, and fault information always buries under environment noise. Monitoring their occurrence and evolution is an arduous challenge. Parameters of rotating machinery are periodically time-varying, especially for those under failure situation. Periodical time-variance implies cyclostationarity. Therefore, studying the cyclostationary characters of rolling element bearing and gear could clarify the fault essence and has easier access to picking up weak fault information.The theoretical cyclostationary models of vibration signals from rolling element bearing and gear are taken as the research basis. The corresponding theoretical analysis is carried out by second-order cyclic statistics theory. Several cyclostationary analysis methods are brought forward aiming to the identification of different kinds of weak cyclostationary characters. The contents are as follows:From the viewpoint of theoretical analysis and engineering application, the background and significance of the present study are elucidated. A state of the art review is thoroughly completed, which consists of the cyclic statistics theory, the spectral estimation, and the domestic and aboard study status quo, development and tendency in the cyclostationary phenomena of rotating machinery.Cyclostationary phenomena and basic concepts of cyclic statistics are briefly talked about. Second-order cyclic statistics are emphasized, whose mathematic definition, essence and basic qualities are involved in during the discussion. One section is dedicated to cyclic spectral estimation. Taking classical spectral estimation methods as reference, two estimating forms, averaging and smoothing, are used to cyclic periodogram for the final estimation of spectral correlation density. Discrete mathematic equations and concrete actualizing steps of two estimating methods are listed, respectively.Vibration signal from gear is modeled as a typical modulation signal with the combination of amplitude modulation and phase modulation. Vibration signal form rolling element bearing is modeled with considering the inevitable minor slip between the races and the rolling elements. Theoretical derivation of these models is carried out by second-order cyclic statistics in order to clarify their cyclostationary characters.Three cyclostationary analysis methods are employed to the simulation and experimental signals in this thesis. They are the degree of cyclostationarity (DCS) analysis, single slice spectral correlation density (SCD) analysis and combination slice SCD analysis. DCS analysis is an old method, which universally applies to cyclostationary phenomena in rotating machinery. Single slice SCD analysis is specialized for the modulation information, especially it in gear vibration. This method is based on Hilbert transformation, which makes less computation attainable by employing the decimation in time domain. It offers a comprehensive reflection of the amplitude modulation and phase modulation simultaneously. Compared with conventional demodulation methods, it is more sensitive to the occurrence and the development of the early gear fault with comparative evident phase modulation alternation. Besides, environment noise influence can be eliminated to some extent by averaging process.Combination slice SCD analysis, as a specialized method for rolling element bearing, is based on the smoothing cyclic periodogram estimation method. A series of character cyclic frequencies is set forward according to the operating parameters and geometrical dimensions of bearing. Their corresponding slices of SCD are estimated through smoothing algorithm. Slices on fault character cyclic frequencies have different presentation. Its energy is outstanding and mostly centralizes on the resonance frequency of the system, which is the spectral band full of modulation information. The increase of the smoothing length can eliminate the impact of environment noise to the maximum and at the same time keeps the efficiency and the resolution in cyclic frequency domain. Therefore, it adapts to weak character identification buried under background noise. Considering the inevitable error between the predefined character cyclic frequencies and their real value, the slice of SCD that possesses highest energy near each predefined character cyclic frequency replaces the original counterpart to constitute combination slice SCD analysis. This practical processing ensures the reliability of the method and makes it fit to the combination situation of different kinds of local defects in rolling element bearing.The definition of accumulation energy is brought forward as a monitoring tool according to CS characters of rolling element bearing and gear. Accumulation energy reflects the correlation between spectral lines, which will increase with the development of failure and the deterioration of machine's operation situation. Two accumulation energy factors aiming to gear vibration monitoring are concretely discussed, which are modulation monitoring factor and meshing monitoring factor. Each of them can reflect the occurrence and evolution of gear failure, which is accompanied with the increase of modulation phenomena and meshing vibration. As a brand-new monitoring tool, accumulation energy factor picks up information in whole frequency band. Any form of modulation can be observed and reflected by itself, and meshing vibration of every pair of gear in gearbox can be separated.The adaptive filtering of cyclostationary vibration signals is studied based on the adaptive filtering of the stationary process. The study begins with the discussion of the periodically time-varying filter, which consists of the orthogonal principle, cyclic Wiener-Hopf equation, cyclic Wiener filter and its adaptive algorithm. Considering a reference is hard to find in mechanical adaptive problem, the enhancer of cyclostationary signals is put forward on the base of the cyclic Wiener filter. Some rolling element bearings with different kinds of spot defects are fabricated. Vibration signals are gathered from a rolling element bearing test-bed. A large number of rolling element bearing and gear vibration signals are analyzed by corresponding cyclostationary methods. The results verify the capability of these cyclostationary analysis methods in weak fault characteristics extraction.