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Gear fault detection based on Empirical Mode Decomposition (EMD) and Teager Kaiser Energy Operator (TKEO) technique is presented. This novel method is named as Teager-Huang transform (THT). EMD can adaptively decompose the vibration signal into a series of zero mean Intrinsic Mode Functions (IMFs). TKEO can track the instantaneous amplitude and instantaneous frequency of the Intrinsic Mode Functions at any instant. The experimental results provide effective evidence that Teager-Huang transform has better resolution than that of Hilbert-Huang transform. The Teager-Huang transform can effectively diagnose the fault of the gear, thus providing a viable processing tool for gearbox defect detection and diagnosis.

Gears are important element in a variety of industrial applications such as machine tool and gearboxes [

In this paper, we present a new method to detect gear fault using empirical mode decomposition (EMD) and nonlinear Teager Kaiser Energy Operator (TKEO), which is named as Teager-Huang transform (THT) [

To address the issues discussed above, this paper is organized as follows. Section

Hilbert-Huang transformation is an emerging novel technique of signal decomposition having many interesting properties. In order to facilitate the reading of this paper we will introduce in detail the Hilbert-Huang transformation, which is a relatively novel technique.

Huang et al. [

in the whole data set, the number of extrema and the number of zero-crossings must be either equal or differ at most by one.

at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero.

Empirical Mode Decomposition (EMD) has been proposed recently [

Empirical mode decomposition method is developed from the simple assumption that any signal consists of different simple intrinsic mode oscillations. The essence of the method is to identify the intrinsic oscillatory modes (IMFs) by their characteristic times scales in the signal and then decompose the signal accordingly. The characteristics time scale is defined by the time lapse between the successive extremes.

To extract the IMF from a given data set, the sifting process is implemented as follows. First, identify all the local extrema, and then connect all of the local maxima by a cubic spline line as the upper envelope. Then, repeat the procedure for the local minima to produce the lower envelope. The upper and lower envelopes should cover all the data between them. Their mean is designated

Ideally,

The sifting process has to be repeated as many times as it is required to reduce the extracted signal to an IMF. In the subsequent sifting process steps,

This process can be repeated up to

After each processing step, checking must be done on whether the number of zero crossings equals the number of extrema.

The resulting time series is the first IMF, and then it is designated as

This first IMF is subtracted from the original data, and this difference is called a residue

The residue

Thus, one achieves a decomposition of the data into

Having obtained the IMFs using EMD method, one applies the Hilbert transform to each IMF component:

With this definition

With amplitude

Therefore, the instantaneous frequency

Thus the original data can be expressed in the following form:

Equation (

TKEO is a powerful nonlinear operator and has been successful used in many engineering application [

The instantaneous frequency

In general, the demodulation method given by (

In order to estimate the instantaneous frequency

According to (

Equation (

The final presentation of the the IF and the IA results is an energy time frequency representation. The block diagram of Teager-Huang transform technique is illustrated in Figure

The flow chart of Teager-Huang Transform.

The procedure of proposed THT spectrum method is given as follows:

to decompose the vibration signal

to calculate the THT spectrum according to Section

to draw a diagnostic conclusion according to the THT spectrum.

The performance of the proposed method has been assessed by means of tests on two simulative signals. Several monocomponent and multicomponents signals, characterized by known instantaneous frequency trajectories, have been considered. The evolution versus time of the instantaneous frequency and amplitude of each component of the analyzed signal is finally shown.

The main objective of these tests is to establish the measurement accuracy of the proposed method as well as its advantages in IF and IA estimation. As an example, Figure

The monocomponent signal.

The number of acquired samples is equal to 512 and the sampling frequency is 1920 Hz. Figure

THT spectrum of monocomponent signal.

A significant example is shown in Figure

The multicomponent signal.

Signal

Therefore, the frequency-modulated

The variation range of the frequency-modulated

Figure

The three IMFs component.

Figure

THT spectrum of multicomponent signal

Experimental set-up.

These simple simulation examples illustrate the effectiveness of the THT spectrum for analyzing transient (or nonstationary) vibration signal. The results demonstrate that THT is suited for capturing transient events in dynamic system. THT provides a viable signal processing tool for machine fault detection and diagnosis.

A crack, wear, or broken gear tooth failure may cause fatal accidents; so the recognition of gear tooth fault is very important for the safety of a gearbox. The experimental set-up consists of a single-stage gearbox, driven by a 4.5 kW AC governor motor. The driving gear has 28 teeth and the driven gear has 36 teeth. Therefore, the transmission ratio is 36/28, which means that a decrease in rotation speed is achieved. The module of the gear is 2.5 mm. Localized wear defect of the driven gear had a chipped tooth, from zero thickness at pitch point to 25% thichness at the tooth top, to simulate serious wear. The input speed of the spindle was 1473 r/min; that is, the rotating frequency of the output shaft

It is well known that the most important components in gear vibration spectra are the tooth-meshing frequency and its harmonics, together with sidebands due to modulation phenomena. The increment in the number and amplitude of such sidebands may indicate a fault condition. Moreover, the spacing of the sidebands is related to their source. In particular, fault localized on one tooth or a few teeth, such as gear crack or gear wear, produces modulation effects only during the engagement of the faulted teeth, but repeated once each revolution of the gear. As a consequence, the spectrum presents a large number of sidebands of the tooth-meshing frequency and its harmonics, spread over a wide frequency range, spaced by the rotation frequency of the faulted gear, and characterized by low amplitude [

The original vibration signal with gear wear fault is displayed in Figure

Time-domain vibration signal with gear wear.

Figure

Power spectrum of the vibration signal.

To the data of Figure

IMFs of the signal shown in Figure

From Figure

HHT spectrum of vibration signal shown in Figure

THT spectrum of vibration signal shown in Figure

A method for fault diagnosis of gear wear was presented based on a newly developed signal processing technique named as empirical mode decomposition (EMD) and Teager Kaiser Energy Operator (TKEO). Using EMD method, the original vibration signals of gear fault can be decomposed into intrinsic modes. Therefore, we can recognize the vibration modes that coexist in the system, and to have a better understanding of the nature of the fault information contained in the vibration signal. According to Teager-Huang transform spectrum, the characteristic period of the gear fault can be easily recognized. Practical vibration signal monitored from a gearbox with gear fault is analyzed by the presented method. The experimental result has been shown that Teager-Huang transform can be used as an effective diagnostic method for gear fault. Teager-Huang transform has better resolution than Hilbert-Huang transform. Such a technique can be further applied to the health detection of other of dynamic systems, such as electrical drives. Research is being continued to systematically investigate the suitability and constraints of the THT for nonstationary signal analysis, using vibration signals from different fault types of gear.

The authors are grateful to the National Natural Science Foundation of China (no. 50775219 and no. 50975185), and Zhejiang Provincial Natural Science Foundation (no. Y1080040). The authors are also grateful to the editors and anonymous reviewers for their constructive comments.