Application of Fractional Damping in Fault Diagnosis of Rolling Bearings

Fractional calculus has the advantage of high computational precision and fast speed. Therefore, the theory of fractional calculus is applied to the fault diagnosis of rolling bearings. A dynamic model of rolling bearingswith a fault in the inner ring based on fractional damping is established. And the dynamic response characteristic of rolling bearings at optimal order, which isdetermined by the fourth-order center distance of the fractional Fourier transformation, is analyzed. The simulationresults show that the axis motiontrajectory of the inner ring gradually changes from chaotic to stable periodic motionwith the increase of fractional order. And the simulation frequency spectrogram at optimal order is more in line with that of the experiment. The fractional damping model can better reflect the vibration characteristics of rolling bearingswith a fault than the integer damping model and can achieve better results than the traditional integer damping.