Application Of Fractional Fourier Transform In Fault Diagnosis Of Rolling Bearing

Rolling bearings are an indispensable part of mechanical equipment.Whether it can work properly is related to the performance and personal safety of equipment,the whole unit and even the entire production line.Therefore,the fault diagnosis research of rolling bearings plays an important role in protecting human-machine safety and improving production efficiency.Rolling bearing fault feature extraction is the first and important step in fault diagnosis.The traditional fault feature extraction methods mainly include time domain method,frequency domain method and time-frequency domain analysis method.Commonly used frequency domain analysis methods include Fourier transform,short time Fourier transform and wavelet transform,but these methods are suitable for analyzing stationary time signals.The rolling bearing fault signal is a linear frequency modulated signal and belongs to the non-stationary time signal.The above frequency domain analysis method will bring a large error.The analysis with Wigner-Ville transform and Hilbert-Huang transform will produce cross-term interference and endpoint effects.Fractional Fourier transform,as a kind of chirp transform,has better time-frequency focusing for non-stationary time signals,and its one-dimensional linear transformation can avoid cross-term interference,so this paper is for fractional Fourier transform and its numerical algorithm.The application in the extraction of rolling bearing fault features is studied.By analyzing the definition of fractional Fourier transform and its time frequency characteristics,the numerical calculation of discrete fractional Fourier transform has the problem of excessive data volume and long calculation time.A two-phase numerical algorithm is proposed.Discrete sampling method for in-depth analysis and comparison.The single-component and multi-component chirp signals are simulated by discrete sampling method and two-phase numerical algorithm respectively.The validity of fractional Fourier transform for chirp signal and the superiority of two-phase numerical algorithm are verified.The fractional Fourier transform two-phase numerical algorithm is applied to the frequency feature extraction of rolling bearing fault signals.According to the existing rolling bearing fault data,the simulation of the fractional Fourier transform can detect the change trend of the bearing fault frequency.