Accurate fault detection of planetary gearboxes is important to reduce unscheduled machine downtime and avoid catastrophic accidents [1
]. As key components, planetary gearboxes have been widely used in automotive, aerospace and heavy industry applications such as helicopters, wind turbines and mining machines because they have the advantages of large transmission ratios, strong load-bearing capacity and high transmission efficiency [2
]. However, planetary gearboxes inevitably generate various faults because of long term running under complex and severe conditions such as heavy load, fatigue, corrosion and elevated temperature. As shown in Figure 1
, an elementary planetary gear set [3
] is composed of a sun gear, an internal or ring gear and several identical planet gears located around the sun gear. The planet gears are held by a common rigid structure, called planet carrier through planet bearings. In Figure 1
, the ring gear is fixed, the sun gear rotates around its own center, the planet gears rotate around their own centers and revolve around the center of the sun gear.
With a special gear transmission structure, planetary gearboxes exhibit complicated dynamic responses which are more difficult to detect than fixed-axis gear trains [4
]. It is because multiple planet gears produce similar vibrations and these similar vibrations with different meshing phases couple with each other [5
]. Researchers have found that compound vibration transmission paths from the gear mesh points to the acceleration sensors may deteriorate or attenuate vibration responses of gear faults through dissipation, interference and resonance effects [7
]. Besides, abundant work indicates that most of the vibration energy occurs at various sidebands of the gear meshing frequency and its harmonics [8
] and nonlinear transmission path effects caused by the torques or loads would weaken the fault features hidden in vibration signals [5
]. These complicated dynamic responses increase the difficulty of planetary gearbox fault detection and reduce the effectiveness of fault diagnosis methods for fixed-axis gearboxes when applied to planetary gearboxes.
Up to now, researchers have proposed a few interesting methods based on advanced signal processing techniques for detecting planetary gearbox faults. Blunt and Keller [5
] developed the planet carrier method and planet separation method to detect a fatigue crack in a planet carrier of an epicyclic transmission, which was a component of the main transmission gears in the US Army's UH-60 A Black Hawk helicopters. Barszcz and Randall [9
] applied the spectral kurtosis (SK) technique to detect a tooth crack in the planetary gear of a wind turbine. Bartelmus and Zimroz [10
] introduced the load susceptibility concept for the condition monitoring of planetary gearboxes under time-variable operating conditions. It was stated that the acceleration signal envelopes showed deeper amplitude modulation for the gearbox in bad condition than that in good condition. Hameed and Hong [12
] profoundly reviewed different techniques, methods and algorithms developed to monitor the performances of wind turbines to keep them away from catastrophic conditions caused by sudden breakdowns. Lei and Kong [4
] proposed two diagnostic parameters specially designed for fault detection and diagnosis of planetary gearboxes. The two parameters are the root mean square of the filtered signal (FRMS) and the normalized summation of positive amplitudes of the difference spectrum between the unknown signal and the healthy signal (NSDS). Lei and Lin [13
] introduced a method based on multisensor information fusion to classify the pitting damages with different levels in a planetary gearbox.
In summary, researches on planetary gearbox fault diagnosis have only focused on the condition monitoring and fault classifications. Studies on weak feature detections of incipient faults are rare and these weak features are always immersed in noises generated by the equipment and the surrounding environment. It is significant to detect weak fault features as early as possible, which is a complicated and challenging task that requests advanced analytical methods with high reliability, high accuracy and high efficiency.
The emerging notion of multiwavelet transform (MWT), which uses vector-valued scaling and wavelet functions, is an important development of the wavelet theory. Multiwavelets possess excellent properties of orthogonality, symmetry, compact support and high vanishing moments simultaneously [14
]. Since 1994, Geronimo-Hardin-Massopust (GHM) multiwavelet [16
], Chui-Lian (CL) multiwavelet [18
] and Hermite multiwavelet [19
] have been proposed successively and received considerable attention from wavelet research communities both in theory and in applications. Khadem and Rezaee [20
] applied GHM multiwavelet to detect the gearing system faults. Yuan and He [21
] proposed multiwavelet sliding window denoising to detect the gearbox fault features of the hot strip finishing mills. Although these methods showed their advantages over scalar wavelets, prior researches always selected mother multiwavelets from a library of previously designed multiwavelets. However, the chosen standard and fixed multiwavelets were usually not the suitable ones for specified applications [22
To overcome the limitations of standard or fixed MWTs, integrating multiwavelets with lifting schemes (LS) is an exciting motivation to construct customized multiwavelets with desired properties. LS, introduced by Sweldens [23
], is a powerful tool to construct biorthogonal wavelets. It provides a great deal of flexibility and freedom to construct adaptive wavelets by the design of prediction operators and update operators. Wang and Zi [25
] proposed the customized multiwavelets originated from Hermite splines via symmetric lifting schemes. Yuan and He [26
] proposed a method incorporating customized multiwavelet with sliding window denoising, which was an effective and promising tool for gear fault detection.
It is a challenging task to detect weak features of incipient faults, which are always immersed in heavy noises generated by the surrounding environment or the equipment. Multiwavelet denoising plays an important role in eliminating noise as much as possible. Its effect mainly depends on the feature separation by using multiwavelets and the threshold denoising. A redundant multiwavelet possesses the time invariant property [27
] and provides abundant information for feature detection of periodical impulses. Symmetry is another important property which avoids the phase error in MWT. To ensure the time invariant and symmetry property of multiwavelets, a method integrating the symmetric lifting scheme and redundant multiwavelet is proposed to construct customized multiwavelets. Then a critical problem is how to evaluate the obtained multiwavelets and to select the optimal ones for specific applications. The quotient of kurtosis and entropy is proposed to select the optimal multiwavelets because kurtosis is sensitive to sharp impulses of incipient faults and entropy is effective for periodic impulses of moderate or severe faults. Furthermore, based on the correlation of neighboring coefficients, the improved neighboring coefficients (INC) [28
] is adopted to eliminate noises from the decomposed signals.
In this paper, a method which incorporates the customized multiwavelets and INC is proposed for fault detections of planetary gearboxes. The experimental results show that the proposed method is effective and promising to detect these weak impulse features. The rest of the paper is organized as follows: The theory of multiwavelets and the symmetric lifting schemes are briefly introduced in Section 2. In Section 3, the redundant symmetric lifting scheme is proposed to construct customized multiwavelets and the improved neighboring coefficients is introduced into multiwavelets denoising. In Section 4 experimental results are performed. The conclusions are summarized in Section 5.