Methods of periodically non-stationary random processes for vibrations monitoring of rolling bearing with damaged outer race

Abstract

The vibrations of a rolling bearing with a damaged outer race are analyzed using a method based on periodically non-stationary random processes (PNRPs). PNRPs can be considered as a particular case of poly-periodically non-stationary random processes (PPNRs), which describe the interactions of vibration stochastic rhythms with different periods that are determined based on the characteristic bearing frequencies. A PNRP model for these vibrations is verified using methods for discovering the first- and second-order periodicities. By applying the least squares technique, it is shown that the mean function and variance are time periodic functions, and their basic frequencies are determined. This enables us to calculate the amplitude spectra for the deterministic oscillations and the time changes in the power for the stochastic part. It is shown that the dependencies of the Fourier coefficients for the covariance function on lag have the forms of slowly damped groups. Vibration covariance structures are compared for different fault widths; it is found that high-frequency modulations of the PNRP carrier modulations are narrow-band, and Rice representations are used to model them. The PRNP model of vibrations is then represented in the form of a superposition of the stationary high-frequency components that are jointly periodically non-stationary. The mutual periodical non-stationarity of these components results in variance time changes. Band-pass filtering of the vibration signal is conducted, and the influence of the filter bandwidth on the number and values of the amplitude of the variance harmonics is analyzed. It is shown that PNRP methods for time series processing enable fault detection in cases where the squared envelope and other familiar techniques are ineffective.