Removal of transfer function effects from gear vibration signals under constant and variable speed conditions

Abstract

Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.