Transient feature identification from internal encoder signal for fault detection of planetary gearboxes under variable speed conditions
Introduction
Planetary gearboxes are important transmission component of mechanical equipment, such as wind turbines, helicopters and mining machines. Planetary gearboxes typically operate at the harsh circumstances including external random load, rapid change of rotating speed and etc., thus they inevitably incur various unexpected failures. If an early fault is not detected in time, it may gradually evolve into a serious fault and further leads to severe disasters [1], [2]. Therefore, fault detection of planetary gearboxes is significant for condition based maintenance of whole mechanical system, which can effectively enhance the operational reliability and reduce the maintenance cost.
To detect potential faults of planetary gearboxes as early as possible, signal-based methods have been extensively adopted in academic societies and industries, whose basic idea is to mine the underlying feature information indicating the health conditions of monitored equipment from the original sensor information [3], [4]. Among the various types of signal-based approaches, traditional vibration signal analysis techniques have been illustrated to be capable of realizing fault detection of planetary gearboxes [5], [6]. However, owing to the complicated kinematics of planetary gearboxes and the resultant time-varying transfer path between the meshing points of sun gear and planet gear and a stationary sensor, vibration signal is inevitably exposed to the amplitude modulation effect, which leads to great complexity of vibration signal analysis for detecting the failure of planetary gearboxes [7]. Additionally, the efficacy of vibration signal analysis is enormously affected by installation location of vibration sensors, and the installation of additional sensors are intrusive to planetary gearboxes being monitored. Hence, it is attractive to further explore fault detection methods adopting new sensor information.
In recent years, several literatures demonstrated internal encoder signal originally used for motion control and speed measurement contains the rich condition-related information. Therefore, encoder signal is increasingly employed to the fault detection of mechanical equipment. Unlike vibration signal that is usually collected by external piezoelectric sensors, encoder signal is collected from built-in rotary encoders, which means that encoder signal-based fault detection method requires no additional sensors and is cost-effective [8]. Moreover, encoder signal has no amplitude modulation phenomenon and possesses a comparatively high signal to noise ratio, thus it has great capacity to detect faint failures [9]. Finally, encoder signal has more excellent capability in low frequency response compared with vibration signal, which makes it adapted to fault detection of low speed gearboxes and greatly extends application scope of encoder signal based diagnostic methods [10]. Benefiting from above merits, encoder signal-based diagnostic methods are promising tools for planetary gearbox fault detection.
Despite the superiorities of encoder signal, limited literatures on encoder signal analysis can be found. For the purpose of machine fault detection, original encoder signal recording angular position of monitored shaft is usually transformed into more informative kinematic variables, such as instantaneous angular speed (IAS), instantaneous angular acceleration (IAA) and jitter [11]. The presence of the fault will change the dynamic behavior of mechanical equipment and consequently incurs the variation of IAS, IAA and jitter. Bourdon et al. [12] analyzed the relationship between the shape of fault-induced IAS fluctuation and various severity degrees of fault, and illustrated that IAS fluctuation identification is an effective way for fault size estimation. Gubran et al. [13] investigated the feasibility of applying IAS for recognizing the condition of wind turbine blades. Lamraoui et al. [14] presented a novel IAS-based machining process chatter detection method, in which IAS is calculated from the encoder signal acquired from a standard encoder installed on spindle motors. Moreover, Lin et al. [15] accurately detected invisible fault of diesel engine by identifying the fault-related transient features, i.e., fault-related IAS fluctuation. Their studies undoubtedly show the significant benefits on the performance of encoder-signal based fault detection methods. Nevertheless, encoder signal is inevitably affected by various interference components, and the resultant kinematic variables including IAS, IAA and jitter are also deteriorated, which may jeopardize the accuracy of diagnostic results. In view of this problem, Zhao et al. [16] illustrated a self-comparison method to highlight the transient components associated with gear failure and inhibit interference components in jitter signal. In addition, Li et al. [17] established a combined algorithm of empirical mode decomposition (EMD) and autocorrelation local cepstrum for separating feature information from noisy IAS. Zhou et al. [18] applied ensemble empirical mode decomposition to IAS and detected the localized damage of feed-axis gearbox. Miao et al. [19] introduced a sparsity-oriented variable mode decomposition to separate hidden fluctuation information from IAA and successfully realized the fault detection of planetary gearboxes. Moreover, Roy et al. [20] introduced time synchronous averaging to IAS to reduce the negative effect of non-periodic inference components and adopted it for the multi-stage gearbox fault detection.
The above studies mainly explore the efficacy of applying encoder signal to the fault detection of machines operating at a constant speed. However, planetary gearboxes usually operate at variable speed conditions, which leads to encoder signal and corresponding IAS, IAA and jitter exhibit strong non-stationary property. Therefore, these methods are insufficient for variable speed encoder signal analysis. To the best of our knowledge, variable speed encoder signal analysis has not been adequately explored and still need to be studied in-depth. To tackle this problem, this paper presents a three-stage variable speed encoder signal analysis approach for detecting the fault of planetary gearboxes. In the proposed method, difference method is firstly adopted for transforming raw encoder signal into more informative IAS in time domain. Then, self-resampling technique is developed to map IAS in time domain into one in angular domain, wherein original encoder signal acts as an instantaneous reference phase. Finally, low-pass filter and sparsity based algorithm (LpfSpaA), which is the core of this paper, is established for identifying IAS fluctuation associated with gear fault from noisy IAS in angular domain. Through analyzing the extracted fault-induced IAS fluctuation, the underlying failure of planetary gearboxes is automatically recognized. Within the proposed LpfSpaA, a unique convex optimization problem is constructed and an iterative algorithm is deduced based on alternating direction method of multipliers (ADMM) and Majorization-Minimization (MM) to solve it. Meanwhile, to approach the oracle performance of proposed LpfSpaA, an adaptive parameter selection approach is also investigated. Simulation analysis and experimental verification are provided for illustrating the efficacy of the proposed method.
The main contributions of this paper are summarized as follows.
- (1)
The distinct morphological properties of each component of IAS in angular domain are revealed and the corresponding customized convex optimization problem of LpfSpaA is constructed for extracting the fault-induced IAS fluctuation. Meanwhile, an iterative algorithm is deduced and an adaptive parameter selection scheme is explored.
- (2)
From the perspective of industrial application, the proposed three-stage variable speed encoder signal analysis approach offers an available and cost-effective tool for variable speed planetary gearbox fault detection.
The remaining of the paper is structured as follows. Section 2 briefly describes the numerical model of variable speed encoder signal. Section 3 illustrates the proposed three-stage variable speed encoder signal analysis approach in detail. The simulation analysis and experimental verification are provided in Section 4 and Section 5, respectively. At last, Section 6 summarizes this paper.
Section snippets
Variable speed encoder signal
Generally, rotary encoders are mounted on the shaft to measure the angular position, thus encoder signal directly acquired from rotary encoder is an angular position series. In [8], the detailed working principle of rotary encoders and acquisition method of encoder signal are described. For planetary gearboxes with gear fault operating at variable speed conditions, encoder signal acquired by incremental rotary encoders is generally a mixture of four separate signal components.
Proposed variable speed encoder signal analysis for fault detection of planetary gearboxes
For identifying the fault of variable speed planetary gearboxes, a three-stage variable speed encoder signal analysis method is established for extracting underlying fault features from original encoder signal. In the proposed method, difference method is first adopted for converting original encoder signal into informative kinematic variable, i.e., IAS in time domain. Then, self-resampling technique is introduced for resampling IAS in time domain at a constant angular interval. Finally, the
Simulation analysis
For assessing the efficacy of proposed method, the synthetic variable speed encoder signal in Section 2 is analyzed. In the proposed method, original encoder signal is firstly transformed into IAS in time domain as presented in Fig. 7. IAS in time domain mainly includes macroscopic fluctuation derived from operating speed conditions and other complex interference components, while transient features of interest, i.e., fault-induced IAS fluctuation, are too weak to be identified. As a result, it
Experimental verification
In this section, variable speed encoder signal collected from a planetary gearbox experimental rig is analyzed. The experimental rig is displayed in Fig. 14 (a) and the configuration of planetary gearbox is given in Fig. 14 (b). In the experimental rig, the motor is used to drive planetary gearbox and the magnetic brake is used to provide the load. Two incremental rotary encoders of type Heidenhain ERN100 [36] with a high resolution of 5000 pulses per revolution are mounted to acquire encoder
Conclusions
This paper proposes a variable speed encoder signal analysis approach for extraction of fault-induced transient features and fault detection of planetary gearboxes. In the proposed method, original encoder signal is firstly converted into more informative IAS in time domain using difference method, and then IAS in time domain is mapped into the new one in angular domain via self-resampling technique. After that, the proposed LpfSpaA that is formulated based on distinct morphological properties
CRediT authorship contribution statement
Baoxiang Wang: Writing - original draft, Visualization. Chuancang Ding: Investigation, Writing - review & editing, Methodology, Software, Validation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 51421004).
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