A Study Of Cyclostationarity And Frequency Demodulation And Their Applications In The Fault Diagnosis

Due to the periodicity of runing mode of rotating machinery, the vibration signals obtained from these machines are cyclostationary. Therefore, using cyclostationary methods can effectively extract fault's features from these vibration signals, but it will be very difficult in the hypothesis of stationarity. The main aim of this paper is to make use of the difference of the cyclostationarity in gearbox's vibration signals when gears and bearings have faults, and establish a gearbox's integrated diagnosis method based on cyclostationarity. To this goal, the study of the cyclic statistic is an important step before using it.Because of the nonstationarity of cyclostationary signals, the estimators of the cyclic statistic depend on the data origination. That means different time-lag pattern of the Cyclic Autocorrelation Function (CAF) will arrive at different results and different frequency-shift mode of the Spectral Correlation Function (SCF). This will lead to some confusion when extracting the cyclostationarity by different estimator expressions for a same signal. Therefore, the relationship of SCF between different expressions is established. Through this method, the exclusive cyclostationarity can be obtained from the results of different expressions.The discretization in time domain will result in periodic extension in the frequency and cyclic frequency domain. Because the time-lag quadric transformation of meansquare bandlimited signals has double bandwidth in the time parameter, under the Nyquist sample rate, its CAF will appear aliasing in the cyclic frequency inevitability. But for its SCF, it distributes in the frequency and cyclic frequency plane independently. Based on this discover, an alias-free CAF based on inverse Fourier transformation of SCF in the diamond shape support area is brought forward.The quality of estimator of SCF is deduced and a conclusion is made that cyclic periodogram is unbiase and inconsistent. Further more the influence of time average and frequency smooth are deduced too. Because of the limitation of data length, for periodic signals with adding stationary noise (cyclostationary at the first order), SCF do not totally suppress the effect of stationary noise to periodic components. Either PSD or SCF, the SNR of periodic components to background noise is subequal. Therefore, SCF seems more suitable for cyclostationary signals at the second order than at the first order.Through study the vibration signals of gearboxs, we find out that the vibration signals induced by a fault gear is cyclostaionary at the first order, and the signals induced by a fault bearing is cylcostationary at the second order. From the knowledge of pure cyclostationarity and cyclostationarity, we know that cyclostationarity at all lower order must be subtracted to define the accurate order of cyclostationarity in the signals. Therefore a new gearbox integrate fault diagnosis method based on cyclostationarity is set up. Using an adaptive line enhancer and a cyclic adaptive filter, the gearbox vibration signal is separated into three parts, i.e., a first-order cyclostationary part and a second-order cyclostationary part and a stationary part. The firs part is used to judge the fault state of gears, and the second one is for bearings. Therefore, the fault whether of gears or bearings in the gearbox can be determined based on them.In order to explain the feature of amplitude and phase of FM signals, Bessel function of the first kind is studied, because it is a determinant factor to sideband of FM signals. Based on this, the sideband distribution of signals with AM and FM mixed together is analyzed, and the condition of symmetric sideband distribution is determined in spite of the mix mode of AM and MF is addition or multiplication. Square transform isn't suitable for FM signals, because of the special feature of Bessel function of the first kind. To overcome this limitation, two kinds of method were established. They are based on asymmetric filtering and time-lag quadratic nonlinearity transformation, respectively. Through these methods, FM signals are transformed to signals which can be demodulated by normal demodulation methods, so FM demodulation is achieve.At last, all methods in this study are tested by the vibration signals obtained from gearbox SG135-2, which was made by HongDa Gearbox Company in ShaoGuan. In these tests, four fault modes are used, including second gear spalling, fifth gear broken, bearings in the output shaft with a outer race fault and a inner race fault.