ESTIMATION OF THE FREQUENCY RESPONSE FUNCTION OF A DEFECTIVE BEARING FROM A MEASURED UNI-AXIAL VIBRATION SIGNAL
Ashuthosh Harish - (January 2021)
SUMMARY
The axle bearing transmits the high axle load to the wheelsets while providing a smooth rolling-movement for the wheelsets in a train. Spalling is one of the significant causes of a failure of the axle bearing. The breakaway of material from the surface of the raceway is known as spalling.
Condition monitoring techniques are developed to detect and estimate spall’s size to mitigate the failure of the axle bearing. The bearing’s condition monitoring must be done by studying its response to the rolling-element moving over a spall, as bearings are sealed and integrated into the machinery.
The rolling-element and spall interaction results in an excitation pulse. The dynamic vibration response in the frequency domain to this excitation pulse has notches (local minima). The notches caused by the excitation pulse are dependent on the size of the spall and Hertzian contact length. These notches caused by excitation pulse can be used as a feature to estimate the size of the spall. However, the dynamic response spectrum will also have notches due to the anti-resonances of the bearing. Thus, making it difficult to differentiate between the notches caused by the excitation force pulse (spall size sensitive feature) and the anti-resonance.
To precisely extract the notches caused by the excitation pulse in the bearing’s dynamic response spectrum, it is essential to separate the frequency response function (resonance and anti-resonance frequencies) from the measured dynamic response. Based on the dynamic vibration response properties, three methods are developed to estimate the bearing's frequency response function (FRF). The three methods are Mean Filter, Kalman Filter implementation, and Ensemble Kalman Filter Implementation.
The results of applying the Mean Filter method on the experimental data and synthetic data show that the Mean Filter successfully estimated the shape ( the location of resonance and anti-resonance) of the FRF of a bearing. However, it is unable to estimate the amplitude of the FRF precisely.
The Kalman Filter implementation method on the experimental data and synthetic data shows that this method successfully estimates the shape of the FRF of defective bearings. However, it is unable to estimate the amplitude of the FRF precisely.
The Ensemble Kalman Filter (EnKF) implementation method successfully estimates the shape and the amplitude of the FRF of a bearing with spalls smaller than Hertzian contact length.
The scope for future work should focus on developing a more in-depth insight into the dynamic vibration response of a bearing to precisely formulate the Kalman filter implementation and EnKF implementation.