Abstract
Planetary gearbox vibration signals have strong modulation features due to the amplitude modulation and frequency modulation (AM-FM) effect of gear faults, as well as the amplitude modulation (AM) effect of time-varying vibration transfer paths, on gear meshing vibrations. This results in an involute sidebands structure in Fourier spectrum, possibly misleading fault diagnosis. The modulating frequency of both amplitude modulation (AM) and frequency modulation (FM) parts is closely related to the gear fault characteristic frequency. This inspires the idea of joint amplitude and frequency demodulation analysis, thus addressing the complex sidebands issue inherent in Fourier spectrum. Demodulation analysis requires mono-component signals for accurate estimation of instantaneous frequency, and proper selection of an AM-FM component sensitive to gear fault. To this end, we firstly decompose the complex signal into intrinsic mode functions (IMFs) via variational mode decomposition (VMD), by exploiting its capability in decomposing complex modulated signal into constituent AM-FM components. For effective application of VMD in complex planetary gearbox signal analysis, we propose a method to determine a key parameter in VMD, i.e. the number of IMFs to be separated. For accurate instantaneous frequency estimation, we decompose IMFs via empirical AM-FM decomposition, to remove the influence of AM on instantaneous frequency estimation. Then, we select the sensitive IMF that contains the main gear fault information for further demodulation analysis. In order to properly select the sensitive IMF, we propose a criterion based on the gear vibration characteristics and the VMD properties. Finally, we obtain the amplitude and frequency demodulated spectra by applying Fourier transform to the amplitude envelope and instantaneous frequency of the selected sensitive IMF. According to the characteristics exhibited in the demodulated spectra, we can detect planetary gearbox fault. The proposed method is illustrated via a numerical simulated planetary gearbox vibration signal, and is further validated using lab experimental vibration signals of a planetary gearbox. Faults on all the three types of gear (sun, planet and ring) are successfully identified.
Highlights
Planetary gearboxes are widely employed in many engineering systems, such as helicopters and wind turbines, for their unique merits of high load bearing capacity and large transmission ratio in a compact structure [1,2,3]
We propose a criterion to select the sensitive intrinsic mode functions (IMFs) for further demodulation analysis, based on the modulation characteristics of gear vibration signals and the wavelet packet like decomposition property of variational mode decomposition (VMD). (3) Accurate instantaneous frequency estimation is necessary for effective frequency demodulation analysis, but conventional Hilbert transform (HT) based approach is subject to the constraint imposed by Bedrosian and Nuttall theorem [37]
We propose a criterion to determine the number according to the amplitude modulation (AM)-frequency modulation (FM) nature and the spectral characteristics of planetary gearbox vibration signals
Summary
Planetary gearboxes are widely employed in many engineering systems, such as helicopters and wind turbines, for their unique merits of high load bearing capacity and large transmission ratio in a compact structure [1,2,3]. Zhu et al [36] proposed an adaptive version of VMD, by optimizing the number of modes and data fidelity constraint with kurtosis as an optimization index via artificial fish swarm algorithm, and they applied the method to rolling bearing fault detection These studies have demonstrated that VMD can effectively decompose complicated multi-component signals into. Considering the complex AM-FM features of planetary gearbox vibration signals, and exploiting the merits of VMD in AM-FM component decomposition of complex modulated signals, we propose a joint amplitude and frequency demodulation analysis idea for planetary gearbox fault diagnosis, thereby to overcome the difficulty with conventional Fourier spectrum analysis due to sideband complexity, and reveal the gear fault feature in a more effective way.
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