Velocity synchronous bilinear distribution for planetary gearbox fault diagnosis under non-stationary conditions

Abstract

This paper proposes a time-frequency method, named velocity synchronous bilinear distribution (VSBD), for planetary gearbox fault diagnosis under non-stationary conditions. This method is based on the Cohen's class bilinear distribution (CCBD). The current CCBDs are able to provide a time-frequency representation (TFR) with good time-frequency resolution for multi-component signal with constant frequencies. However, their poor time-frequency resolution in dealing with time-varying frequencies has limited their applications. As such, the VSBD is proposed to solve this problem. This method firstly uses the generalized demodulation to demodulate the signal under analysis into several signals based on the shaft rotational speed to meet the constant-frequency requirement of the bilinear distribution. The CCBD is then applied to the demodulated signals to obtain the TFRs of the demodulated signals and finally the TFR of the original signal is restored from the demodulated TFRs. This method is free from smear effect and has improved time-frequency resolution in comparison with other existing time-frequency methods. This method only considers planetary gearbox systems running under time-varying speed and fixed external load conditions. Therefore, the industrial applications of the proposed method may be restricted to such conditions.