Removal of transfer function effects from transmission error measurements using cepstrum-based operational modal analysis

Transmission error (TE) is recognised as one of the best measurements for gear condition monitoring and quality control, especially when measured at low speed. Geometric transmission error (GTE) is closely related to geometric tooth-profile anomalies. The difference between GTE and static transmission error (STE) is instead informative of the meshing stiffness of a gear pair. However, GTE and STE can only be obtained by measuring TE at low speed. When measured at moderate or high operating speeds, dynamic transmission error (DTE) is affected by a few resonances related to internal gearbox elements and/or encoders and their couplings, which distort the effects of geometric tooth-profile and meshing stiffness. Utilising a cepstrum-based operational modal analysis (OMA) method, this paper proposed a novel method to reconstruct equivalent STE or GTE from a single DTE measurement, i.e. from a moderate/high speed test. When measurements are obtained with two or more load cases, this method also allows the separation and detailed identification of the TE components related to geometric mismatch and gearmesh stiffness. The proposed method has been validated on a single-stage spur gear rig and can be useful in gear condition monitoring, gear quality control and as an aid to gearbox modelling.