Research On The Shafting Torsional Vibration Based On Fractional Fourier Transform

Due to the changes of torque at a constant speed rotating shaft, the shaft generatesoscillation moves that lead to occurring torsional vibration and the modulated signal issimilar to LFM signal. Hilbert transform demodulation method can only be used to dealwith a narrowband signal in Engineering application, and it is an integral transformationwhich makes demodulated results via low-pass filter, causing both ends of the modulatedsignal and the middle mutation portion produce wing edges and decay fluctuation, whichmake the obtained detection result error very great.Since the shaft torsional vibration can be regarded as torsional vibration signalmodulating the frequency of the uniform rotation shaft, the fractional Fourier transformhas good energy aggregation properties to a given FM signal in a fractional Fourierdomain of the time-frequency plane, while Gaussian white noise and the otherinterference are distributed over the time-frequency plane evenly, the energy spectrumdoes not occur the aggregation phenomenon. Frequency coupling can be releasedsimultaneously in the analysis of multi-component LFM signals, it also can overcomecross term interference and reduce the complexity of the signal processing. Besides, it isa linear transformation that can be achieved by means of fast Fourier so that the processis simple and it reduces the amount of computation greatly. Therefore, using thefractional Fourier transform’s properties can measure the shaft torsional vibration.The article uses the combination of pre-judgment and fractional autocorrelationmethod based on the Riccati transfer matrix method determined by shaft torsionalvibration simulation of the inherent characteristics of the experimental system to detectand estimate parameters of collected vibration signal of the fractional Fourier domain inthe time-frequency plane and adopts Clean method to realize the separation of differentstrength LFM signals and inhibiting the strong component signal sheltering the weakcomponent signal.In addition, to reduce the side band interference and improve the accuracy, it usessmoothed pseudo Wigner-Ville distribution inhibits cross-term. Meanwhile, loading single component and multi-component torsional vibration excitation on the shafttorsional vibration simulation system to do experiments and using the above method todeal with the collected signals of shafting vibration system. The simulation results showthe errors between torsional vibration experimental parameter values and the torsionalvibration excitation signal is very small. Therefore, it can be applied to the shaft torsionalvibration measurement.