**Machinery Faults Detection Using Acoustic Emission Signal**

Dong Sik Gu and Byeong Keun Choi *Gyeongsang National University Republic of Korea* 

## **1. Introduction**

170 Acoustic Waves – From Microdevices to Helioseismology

The authors are grateful for the financial support from the national research project (Grant

Gao, D.; Dai, D. & Pan, Q. (2008). Evaluation of deflecting characteristics of anisotropy

Gao, D. & Pan, Q.(2006). Experimental study of rock drill-ability anisotropy by acoustic velocity*. Petroleum Science*, Vol. 3, No.1, ( March 2006), pp.50-55, ISSN 1672-5107 Gao, D. (1995). Predicting and scanning of wellbore trajectory in horizontal well using

*Engineering Held in Beijing*, China, SPE 29982, pp.297-308, 14-17 Nov. 1995 Gao, D.; Liu, X. & Xu B.(Dec. 1994). *Prediction and Control of Well Trajectory*, Petroleum

Gao, D. & Liu, X.(1990). Anisotropic drilling characteristics of the typical formations. *Journal* 

Gao, D. & Liu, X.(1989). A new model of rock-bit interaction. *Oil Drilling and Production* 

Lubinski, A. & Woods,H.(1953). Factors affecting the angle of inclination and dog-legging in

Patrick, J. & Richard L.(1984). An experimental test of P-wave anisotropy in stratified media.

Xu, B.(Jan. 2011). *Concise Elasticity and Plasticity*, Higher Education Press, ISBN 978-7-04-

Yin H.(1989). Study of formation anisotropy-rock drillability. *Oil Drilling and Production* 

University Press, ISBN 7-5636-0584-3/TE⋅95, Dongying, China

*Technology*, Vol.11, No.5, (Oct. 1989), pp.23-28, ISSN 1000-7393

*Technology*, Vol.11, No.1, (Feb. 1989),pp.15-22, ISSN 1000-7393

formation by using well-log information. *ACTA PETROLEI SINICA*, Vol.29, No.6,

advanced model. *Proceedings of the Fifth International Conference on Petroleum* 

*of the University of petroleum, China*, Vol.14, No.5, (Oct. 1990), pp.1-8, ISSN 1000-7393

No. 2010CB226703) and the supply of many core samples by CCSD.

(December 2008), pp. 927-932, ISSN 0253-2697

rotary bore holes. DPP, 1953: 222-242

030725-2, Beijing, China

*Geophysics*, Vol.49,No.4, (1984),pp. 374-378

**7. Acknowledgment** 

**8. References** 

Application of the high-frequency acoustic emission (AE) technique in condition monitoring of rotating machinery has been growing over recent years. This is particularly true for bearing defect diagnosis and seal rubbing (Mba et al., 1999, 2003, 2005; Kim et al., 2007; Siores & Negro, 1997). The main drawback with the application of the AE technique is the attenuation of the signal and as such the AE sensor has to be close to its source. However, it is often practical to place the AE sensor on the non-rotating member of the machine, such as the bearing or gear casing. Therefore, the AE signal originating from the defective component will suffer severe attenuation before reaching the sensor. Typical frequencies associated with AE activity range from 20 kHz to 1 MHz.

While vibration analysis on gear fault diagnosis is well established, the application of AE to this field is still in its infancy. In addition, there are limited publications on application of AE to gear fault diagnosis. Siores explored several AE analysis techniques in an attempt to correlate all possible failure modes of a gearbox during its useful life. Failures such as excessive backlash, shaft misalignment, tooth breakage, scuffing, and a worn tooth were seeded during tests. Siores correlated the various seeded failure modes of the gearbox with the AE amplitude, root mean square, standard deviation and duration. It was concluded that the AE results could be correlated to various defect conditions (Siores et al., 1997). Sentoku correlated tooth surface damage such as pitting to AE activity. An AE sensor was mounted on the gear wheel and the AE signature was transmitted from the sensor to data acquisition card across a mercury slip ring. It was concluded that AE amplitude and energy increased with increased pitting (Sentoku, 1998). In a separated study, Singh studied the feasibility of AE for gear fault diagnosis. In one test, a simulated pit was introduced on the pitch line of a gear tooth using an electrical discharge machining (EDM) process. An AE sensor and an accelerometer for comparative purposes were employed in both test cases. It was important to note that both the accelerometer and AE sensor were placed on the gearbox casing, it was observed that the AE amplitude increased with increased rotational speed and increased AE activity was observed with increased pitting. In a second test, periodically occurring peaks were observed when natural pitting started to appear after half an hour of operation. These AE activities increased as the pitting spread over more teeth. Singh concluded that AE could provide earlier detection over vibration monitoring for pitting of gears, but noted it could not be applicable to extremely high speeds or for

Machinery Faults Detection Using Acoustic Emission Signal 173

excited. It will be costly and unrealistic in practice to find the resonant modes through experiments on rotating machinery that may also alter under the different operational conditions. In addition, it is also difficult to estimate how these resonant modes are affected in the assembly of a complete bearing and mounting in a specific housing, even if the resonant frequencies of individual bearing elements can be tested or calculated theoretically (Misiti et al., 2009). Therefore, most researchers decide on the band-pass range as on option. To recover the disadvantage of this option, wavelet analysis is included in the process of

Wavelet theory (Burrus et al., 1997) is introduced that is a tool for the analysis of transient, non-stationary, or time-varying phenomena. Wavelet analysis is also called wavelet transform. There are two kinds of wavelet transform: continuous wavelet transform (CWT) and discrete wavelet transform (DWT). CWT is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function. To use CWT, one signal can be decomposed into a series of "small" waves belonging to a wavelet family. The wavelet family is composed of scaling functions, *ϕ(t)* deduced by father wavelet and wavelet functions, *ψ(t)* deduced by mother wavelet. The scaling function can be represented by the

( ) /2

, () 2 2 *j j*

where *j* represents the scale coefficient and *k* represents shift coefficient. Scaling a wavelet simply means stretching (or compressing) it. Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically, delaying a function *f(t)* by *k* is represented by *f(t + k)*. Similarly, the associated wavelet function can be generated using the same coefficients as

 φ*k tk* = −

( ) ( ) /2 , 2 2 *j j*

 ψ*t tk* = −

2 2 0 for all

*t k t l dt k l*

 φ *jk j jk* , , *<sup>f</sup>* () () *t t dt* <sup>∞</sup> −∞ = ⋅

−⋅ − = ≠

0

Using an iterative method, the scaling function and associated wavelet function can be

For many signals, the low-frequency content is the most important part. It is what gives the signal its identity. The high-frequency content, on the other hand, imparts flavour or nuance that is often useful for singular signal detection. In wavelet analysis, we often speak of approximations and details. The approximations are the high-scale, low frequency components of the signal. The details are the low-scale, high-frequency components. A signal can be decomposed into approximate coefficients *aj,k*, through the inner product of the

The scaling functions are orthogonal to each other as well as the wavelet functions as shown

*j k* φ

*j k* ψ

() ()

 φ

α

φ

∞ −∞ ∞ −∞

 

computed if the coefficients *j* and *k* are known.

original signal at scale *j* and the scaling function.

ψ

*t t dt*

( )( )

⋅ =

 φ

traditional envelope analysis in this paper.

following mathematical expression:

the scaling function.

in the following equations:

unloaded gear conditions. (Singh et al., 1996) Tan offered that AE RMS (Root Mean Square) levels from the pinion were linearly correlated to pitting rates; AE showed better sensitivity than vibration at higher toque level (220Nm) due to fatigue gear testing using spur gears. He made sure that the linear relationship between AE, gearbox running time and pit progression implied that the AE technique offers good potential in prognostic capabilities for monitoring the health of rotating machines. (Tan et al., 2005, 2007)

On the other hand, the signal processing method for AE signal was studied using bearing and gearbox. In the results of the research (Sheen, 2008, 2010; Yang et al., 2007), the envelope analysis was found to be useful to detect fault in rolling element bearing. The fault detection frequency of bearing can be presented in the power spectrum. Wavelet transform was used for the signal processing method for the gearboxes (Wu et al., 2006, 2009), but wavelet transforms can give the different results with the envelope analysis. It can be shown the defect frequency, but the efficiency is lower than that of envelope analysis. Thus, the signal processing method for AE signal has not been completed until now, and it must be developed in the future.

Therefore, in this paper, a signal processing method for AE signal by envelope analysis with discrete wavelet transforms is proposed. For the detection of faults generated by gear systems and a cracked rotor using the suggested signal processing, these were installed in each test rig system. In gearbox, misalignment was created by a twisted case caused by arcwelding to fix the base and bearing inner race fault was generated by severe misalignment. Through the 15 days test using AE sensor, misalignment was observed and bearing faults were also detected in the early fault stage. To identify the sensing ability of the AE, vibration signal was acquired through an accelerometer and compared with the AE signal. Also, to find the advantage of the proposed signal processing method, it was compared to traditional envelope analysis. The detection results of the test were shown by the power spectrum and comparison of the harmonics level of the rotating speed. Modal test and zooming by a microscope were performed to prove the reason of the other faults. And the crack was seeded by wire cutting with 0.5 mm depth. The shaft was coupled with motor and non-drive-end was left 6.5 mm by lifting tool. During rotating the shaft, AE signals were acquired by AE sensor with 5MHz sampling frequency and 0.5 seconds storing time. The AE signals were transformed by FFT to create the power spectrums, and in the spectrums several peaks were occurred by the crack growth. Along the growth of the crack, the characteristic of the power spectrum was changed and displayed different frequencies.

### **2. Signal processing method**

Envelope analysis typically refers to the following sequence of procedure: (1) band-pass filtering (BPF), (2) wave rectification, (3) Hilbert transform or low-pass filtering (LPF) and (4) power spectrum. The purpose of the band-pass filtering is to reject the low-frequency high-amplitude signals associated with the *i*th mechanical vibration components and to eliminate random noise outside the pass-band. Theoretically, in HFRT (High Frequency Resonance Technique) analysis, the best band-pass range includes the resonance of the bearing components. This frequency can be found through impact tests or theoretical calculations involving the dimensions and material properties of the bearing. However, it is very difficult to predict or specify which resonant modes of neighboring structures will be

unloaded gear conditions. (Singh et al., 1996) Tan offered that AE RMS (Root Mean Square) levels from the pinion were linearly correlated to pitting rates; AE showed better sensitivity than vibration at higher toque level (220Nm) due to fatigue gear testing using spur gears. He made sure that the linear relationship between AE, gearbox running time and pit progression implied that the AE technique offers good potential in prognostic capabilities

On the other hand, the signal processing method for AE signal was studied using bearing and gearbox. In the results of the research (Sheen, 2008, 2010; Yang et al., 2007), the envelope analysis was found to be useful to detect fault in rolling element bearing. The fault detection frequency of bearing can be presented in the power spectrum. Wavelet transform was used for the signal processing method for the gearboxes (Wu et al., 2006, 2009), but wavelet transforms can give the different results with the envelope analysis. It can be shown the defect frequency, but the efficiency is lower than that of envelope analysis. Thus, the signal processing method for AE signal has not been completed until now, and it must be

Therefore, in this paper, a signal processing method for AE signal by envelope analysis with discrete wavelet transforms is proposed. For the detection of faults generated by gear systems and a cracked rotor using the suggested signal processing, these were installed in each test rig system. In gearbox, misalignment was created by a twisted case caused by arcwelding to fix the base and bearing inner race fault was generated by severe misalignment. Through the 15 days test using AE sensor, misalignment was observed and bearing faults were also detected in the early fault stage. To identify the sensing ability of the AE, vibration signal was acquired through an accelerometer and compared with the AE signal. Also, to find the advantage of the proposed signal processing method, it was compared to traditional envelope analysis. The detection results of the test were shown by the power spectrum and comparison of the harmonics level of the rotating speed. Modal test and zooming by a microscope were performed to prove the reason of the other faults. And the crack was seeded by wire cutting with 0.5 mm depth. The shaft was coupled with motor and non-drive-end was left 6.5 mm by lifting tool. During rotating the shaft, AE signals were acquired by AE sensor with 5MHz sampling frequency and 0.5 seconds storing time. The AE signals were transformed by FFT to create the power spectrums, and in the spectrums several peaks were occurred by the crack growth. Along the growth of the crack, the characteristic of the power spectrum was changed and displayed different

Envelope analysis typically refers to the following sequence of procedure: (1) band-pass filtering (BPF), (2) wave rectification, (3) Hilbert transform or low-pass filtering (LPF) and (4) power spectrum. The purpose of the band-pass filtering is to reject the low-frequency high-amplitude signals associated with the *i*th mechanical vibration components and to eliminate random noise outside the pass-band. Theoretically, in HFRT (High Frequency Resonance Technique) analysis, the best band-pass range includes the resonance of the bearing components. This frequency can be found through impact tests or theoretical calculations involving the dimensions and material properties of the bearing. However, it is very difficult to predict or specify which resonant modes of neighboring structures will be

for monitoring the health of rotating machines. (Tan et al., 2005, 2007)

developed in the future.

frequencies.

**2. Signal processing method** 

excited. It will be costly and unrealistic in practice to find the resonant modes through experiments on rotating machinery that may also alter under the different operational conditions. In addition, it is also difficult to estimate how these resonant modes are affected in the assembly of a complete bearing and mounting in a specific housing, even if the resonant frequencies of individual bearing elements can be tested or calculated theoretically (Misiti et al., 2009). Therefore, most researchers decide on the band-pass range as on option. To recover the disadvantage of this option, wavelet analysis is included in the process of traditional envelope analysis in this paper.

Wavelet theory (Burrus et al., 1997) is introduced that is a tool for the analysis of transient, non-stationary, or time-varying phenomena. Wavelet analysis is also called wavelet transform. There are two kinds of wavelet transform: continuous wavelet transform (CWT) and discrete wavelet transform (DWT). CWT is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function. To use CWT, one signal can be decomposed into a series of "small" waves belonging to a wavelet family. The wavelet family is composed of scaling functions, *ϕ(t)* deduced by father wavelet and wavelet functions, *ψ(t)* deduced by mother wavelet. The scaling function can be represented by the following mathematical expression:

$$\phi\_{j,k}(k) = 2^{j/2} \phi(2^j t - k)$$

where *j* represents the scale coefficient and *k* represents shift coefficient. Scaling a wavelet simply means stretching (or compressing) it. Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically, delaying a function *f(t)* by *k* is represented by *f(t + k)*. Similarly, the associated wavelet function can be generated using the same coefficients as the scaling function.

$$
\bar{\nu}\_{\neq k}(t) = \mathcal{Z}^{\neq 2} \bar{\nu}\_{\neq} \left( \mathcal{Z}^{\neq} t - k \right),
$$

The scaling functions are orthogonal to each other as well as the wavelet functions as shown in the following equations:

$$\begin{cases} ^-\int\_{--}^- \phi(2t - k) \cdot \phi(2t - l) \, dt = 0 \text{ for all } k \neq l\\ ^-\int\_{--}^- \psi(t) \cdot \phi(t) \, dt = 0 \end{cases}$$

Using an iterative method, the scaling function and associated wavelet function can be computed if the coefficients *j* and *k* are known.

For many signals, the low-frequency content is the most important part. It is what gives the signal its identity. The high-frequency content, on the other hand, imparts flavour or nuance that is often useful for singular signal detection. In wavelet analysis, we often speak of approximations and details. The approximations are the high-scale, low frequency components of the signal. The details are the low-scale, high-frequency components. A signal can be decomposed into approximate coefficients *aj,k*, through the inner product of the original signal at scale *j* and the scaling function.

$$\alpha\_{\boldsymbol{\beta},k} = \int\_{--}^{-} f\_{\boldsymbol{\beta}}(t) \cdot \phi\_{\boldsymbol{\beta},k}(t) \, dt.$$

Machinery Faults Detection Using Acoustic Emission Signal 175

real signal *x*(*t*) and its Hilbert transform *y*(*t*) = *Ht*{*t*} are used to form a new complex signal *z*(*t*)= *x*(*t*)+*jy*(*t*), the signal *z*(*t*) is the (complex) analytic signal corresponding to the real signal *x*(*t*). In other words, for any real signal *x*(*t*), the corresponding analytic signal *z*(*t*) = *x*(*t*)+*jHt*{*x*} has the property that all 'negative frequencies' of *x*(*t*) have been 'filtered out' (Douglas & Pillay, 2005). Hence, the coefficients of complex term in the corresponding

Fig. 2 shows an analytic signal of the Hilbert transform for envelope analysis. The solid line is a time signal and the dash is its envelope curve. A high frequency signal modified by wavelet transform is modulated to a low frequency signal with no loss of the fault information due to envelope effect. According to that, the fault signals in the low frequency region can be detected using the analytic signal. That is an important fact for the proposed signal processing method. Therefore, the proposed signal processing method in this paper is an envelope analysis with DWT and using the coefficients of the complex term in Hilbert

Furthermore, to reduce the noise level in the power spectrum, the spectrum values were presented as the mean value of each day. Fig. 3 shows the power spectrums of the two different signal processing method. Fig. 3(a) is from envelope analysis, and Fig. 3(b) shows the envelope analysis intercalated DWT using Daubechies mother function between BPF and wave rectification. In Fig. 3, the DWT has an effect the amplifying sidebands peaks, especially about gear mesh frequencies, so the peaks of the harmonics of the rotating speed (*fr*) and gear mesh frequencies (*fm*) are bigger than another, and we can check up them easily. Therefore, in the following result, the power spectrum through envelope analysis with DWT

analytic signal were used for FFT.

Fig. 2. Analytic signal (dash) of the envelope effect

transform.

will be shown.

Similarly the detail coefficients *dj,k* can be obtained through the inner product of the signal and the complex conjugate of the wavelet function.

$$d\_{\ne k} = \int\_{--}^{-} f\_{\ne}(t) \cdot \varphi\_{\ne k}(t) \, dt$$

However, CWT takes a long time due to calculating the wavelet coefficient at all scales and it produces a lot of data. To overcome such a disadvantage, we can choose scales and positions based on powers of two – the so-called dyadic scales and positions – then wavelet analysis will be much more efficient and just as accurate. Such an analysis is obtained from the discrete wavelet transform (DWT). The approximate coefficients and detail coefficients decomposed from a discredited signal can be expressed as

$$\begin{aligned} \alpha\_{(j+1),k} &= \sum\_{k=0}^N \alpha\_{j,k} \int \phi\_{j,k} \left(t\right) \cdot \phi\_{(j+1),k} \left(t\right) dt = \sum\_k \alpha\_{j,k} \cdot g \left[k\right],\\ \alpha\_{(j+1),k} &= \sum\_{k=0}^N \alpha\_{j,k} \int \phi\_{j,k} \left(t\right) \cdot \boldsymbol{\nu}\_{(j+1),k} \left(t\right) dt = \sum\_k \alpha\_{j,k} \cdot h \left[k\right]. \end{aligned}$$

The decomposition coefficients can therefore be determined through convolution and implemented by using a filter. The filter, *g*[*k*], is a low-pass filter and *h*[*k*] is a high-pass filter. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components. This is called the wavelet decomposition tree as shown in Fig. 1.

Fig. 1. Wavelet decomposition tree

DWT has a de-noise function and a filter effect focused on impact signal. To make up the weak point of BPF of the envelope analysis, DWT was intercalated on typical envelope analysis, between BPF and wave rectification exactly. The signal by DWT will be separated to different band widths by decomposition level and adapted to the signal with impact.

For more complicated signals which are expressible as a sum of many sinusoids, a filter can be constructed which shifts each sinusoidal component by a quarter cycle. This is called a Hilbert transform filter. Let *Ht*{*x*} denotes the output at time *t* of the Hilbert-transform filter applied to the signal *x*. Ideally, this filter has magnitude 1 at all frequencies and introduces a phase shift of *-π/*2 at each positive frequency and *+π/*2 at each negative frequency. When a

Similarly the detail coefficients *dj,k* can be obtained through the inner product of the signal

*d f t t dt jk j jk* , , () () ψ <sup>∞</sup> −∞ = ⋅

However, CWT takes a long time due to calculating the wavelet coefficient at all scales and it produces a lot of data. To overcome such a disadvantage, we can choose scales and positions based on powers of two – the so-called dyadic scales and positions – then wavelet analysis will be much more efficient and just as accurate. Such an analysis is obtained from the discrete wavelet transform (DWT). The approximate coefficients and detail coefficients

> ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] 1 , , , 1 , , 0 1 , , , 1 , , 0

= ⋅ =⋅ = ⋅ =⋅ 

 φ

 ψ

The decomposition coefficients can therefore be determined through convolution and implemented by using a filter. The filter, *g*[*k*], is a low-pass filter and *h*[*k*] is a high-pass filter. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution

DWT has a de-noise function and a filter effect focused on impact signal. To make up the weak point of BPF of the envelope analysis, DWT was intercalated on typical envelope analysis, between BPF and wave rectification exactly. The signal by DWT will be separated to different band widths by decomposition level and adapted to the signal with

For more complicated signals which are expressible as a sum of many sinusoids, a filter can be constructed which shifts each sinusoidal component by a quarter cycle. This is called a Hilbert transform filter. Let *Ht*{*x*} denotes the output at time *t* of the Hilbert-transform filter applied to the signal *x*. Ideally, this filter has magnitude 1 at all frequencies and introduces a phase shift of *-π/*2 at each positive frequency and *+π/*2 at each negative frequency. When a

*t t dt g k t t dt h k*

α

α

*j k jk jk j k j k k k*

*j k jk jk j k j k k k*

and the complex conjugate of the wavelet function.

decomposed from a discredited signal can be expressed as

α

α

Fig. 1. Wavelet decomposition tree

impact.

*N*

 αφ

+ + = + + =

components. This is called the wavelet decomposition tree as shown in Fig. 1.

 αφ

*N*

real signal *x*(*t*) and its Hilbert transform *y*(*t*) = *Ht*{*t*} are used to form a new complex signal *z*(*t*)= *x*(*t*)+*jy*(*t*), the signal *z*(*t*) is the (complex) analytic signal corresponding to the real signal *x*(*t*). In other words, for any real signal *x*(*t*), the corresponding analytic signal *z*(*t*) = *x*(*t*)+*jHt*{*x*} has the property that all 'negative frequencies' of *x*(*t*) have been 'filtered out' (Douglas & Pillay, 2005). Hence, the coefficients of complex term in the corresponding analytic signal were used for FFT.

Fig. 2 shows an analytic signal of the Hilbert transform for envelope analysis. The solid line is a time signal and the dash is its envelope curve. A high frequency signal modified by wavelet transform is modulated to a low frequency signal with no loss of the fault information due to envelope effect. According to that, the fault signals in the low frequency region can be detected using the analytic signal. That is an important fact for the proposed signal processing method. Therefore, the proposed signal processing method in this paper is an envelope analysis with DWT and using the coefficients of the complex term in Hilbert transform.

Fig. 2. Analytic signal (dash) of the envelope effect

Furthermore, to reduce the noise level in the power spectrum, the spectrum values were presented as the mean value of each day. Fig. 3 shows the power spectrums of the two different signal processing method. Fig. 3(a) is from envelope analysis, and Fig. 3(b) shows the envelope analysis intercalated DWT using Daubechies mother function between BPF and wave rectification. In Fig. 3, the DWT has an effect the amplifying sidebands peaks, especially about gear mesh frequencies, so the peaks of the harmonics of the rotating speed (*fr*) and gear mesh frequencies (*fm*) are bigger than another, and we can check up them easily. Therefore, in the following result, the power spectrum through envelope analysis with DWT will be shown.

Machinery Faults Detection Using Acoustic Emission Signal 177

A simple mechanism that permitted a break of disk-pad type to be rotated relative to each other was employed to apply torque to the gear. Contact ratio (Pinion/Gear) of the gears was 1.4. The motor used to drive the gearbox was a 3-phase induction motor with a maximum running speed of 1800 rpm respectively and was operated for 15 days with 1500rpm. The torque on the output shaft was 1.2 kN·m while the motor was in operation,

Gear Pinion

No. of teeth 50 70

frequency 1250 Hz 1750 Hz

BPFO BPFI FTF BSF

Bearing (NSK HR 32206J)

AE sensors used in this paper are a broadband type with a relative flat response in the range frequency from 10 kHz to 1 MHz. They are placed on the right side of the gearbox cases near the coupling in the horizontal direction at the same height with the shaft center (Fig. 4). AE signals are pre-amplified by 60 dB and the output from the amplifier is collected by a commercial data acquisition card with 10 MHz sampling rate during the test. Prior to the analog-to-digital converter (ADC), anti-aliasing filter is employed that can be controlled DAQ software. And Table 2 is shown the detail specifications of the data acquisition system. Before the test, attenuation test on the gearbox components was taken in order to understand the characteristics of the test-rig. The gearbox was run for 30 minutes prior to acquiring AE data for the unload condition. Based on the sampling rate of 10 MHz, the

(*fd*)

8.76 Hz 11.24 Hz 3.84 Hz 0.44 Hz

Fault Freq. (*fd* X *fr*)

219.3 Hz 281.38 Hz 96.13 Hz 11.01 Hz

17 Type Defect Freq.

shaft 25.01 rev/s

and other specifications of the gearbox are given as in Table 1.

Speed of

Meshing

No. of rolling element

Diameter of

Diameter of

outer race 62 mm

inner race 30 mm

BSF : ball spin frequency

Table 1. Specification of gearbox and bearing

**3.2 Acquisition system and test procedures** 

available recording acquisition time was 2 sec.

BPFO : ball pass frequency of outer race BPFI : ball pass frequency of inner race FTF : fundamental train frequency

Fig. 3. The comparison of Power spectrums in Envelope analysis with/without DWT
