Vibration signal AM-FM models and spectral characteristics for rotate vector reducer fault diagnosis: an insight into multiple modulations and fault feature analysis

Rotate vector (RV) reducers need to undertake cyclic heavy load, and therefore are prone to faults. However, they feature highly intricate kinematics, due to their complex structure, simultaneous multiple point contacts and coupled spin–revolution of cycloidal and planetary gear stages. This leads to high vibration complexity, and poses a great challenge to vibration based fault diagnosis. To address the above issue, we derive the fault characteristic frequency equations for the main components in both cycloidal and planetary gear stages, including the sun, planets, cycloids and pinwheel. Considering the multiple modulation effects on meshing vibration (including the amplitude modulation and frequency modulation effects due to localized fault, and the extra amplitude modulation effects caused by time-varying measurement angle and vibration transfer path), we establish analytical vibration signal models for the localized fault case of each main component. These analytical signal models provide an insight into the multiple modulation nature of vibrations, and justify the presence of gear rotating and fault characteristic frequencies in vibrations from kinetics perspective. In order to extract fault symptoms from multiple modulation signals, we further derive the explicit equations of Fourier and envelope spectra, thus revealing the fault vibration characteristics explicitly. Such explicit spectral signatures provide a guidance for vibration based fault diagnosis. The above theoretical derivations are validated experimentally. The localized fault of both cycloidal and planetary gear stages is successfully diagnosed.