Variational nonlinear component decomposition for fault diagnosis of planetary gearboxes under variable speed conditions

Abstract Planetary gearboxes are extensively used in various heavy equipment and their failures may cause equipment breakdown. Since planetary gearboxes under variable speed conditions will induce time-varying complicated characteristics, which are often contaminated by strong noise and other irrelevant vibration components, fault diagnosis of varying-speed planetary gearboxes is still a challenging task. Although variational nonlinear chirp mode decomposition (VNCMD) can deal with nonstationary signals, it requires some prior knowledge, which limits its practical applications. In this paper, a novel scheme called variational nonlinear component decomposition (VNCD) is proposed as an improved version of the VNCMD to overcome the limitations of the VNCMD. Firstly, the VNCD adopts a new algorithmic framework by modifying the optimization function of the VNCMD to eliminate an upper bound determined by noise, which makes the VNCD more adaptive in practical applications. Secondly, in order to automatically determine initial frequencies and the number of signal components, we propose a novel initial frequencies estimation method based on optimizing a spectrum concentration index and a resampling technique. The initial frequencies estimation method is potential and effective under a strong noise environment, which is suitable to deal with very close time-frequency components. In addition, a high-resolution time-frequency distribution is generated to precisely exhibit time-varying fault features of planetary gearboxes and it improves the signal-to-noise ratio of raw vibration signals. Both our simulated and experimental studies have demonstrated the effectiveness of the proposed VNCD method in fault diagnosis and weak fault feature detection of planetary gearboxes under variable speed conditions.