**3.2 Acquisition system and test procedures**

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 available recording acquisition time was 2 sec.

Machinery Faults Detection Using Acoustic Emission Signal 179

(a) Harmonics of *fr* (b) Harmonics of *fm*

Fig. 6. Power spectrum of the second day

Fig. 7. Peak level trend among days

Fig. 8. Gear tooth weaned by misalignment


Table 2. Specifications of data acquisition system

### **3.3 Experiment result and discussion**

In general, the misaligned gear which almost always excites higher order *fm* harmonics is shown as in Fig. 5. Often, only small amplitudes will be at the fundamental *fm*, but much higher levels will be at 2 *fm* and/or 3 *fm*. The sideband spacing about *fm* might be 2 *fr* or even 3 *fr* when gear misalignment problems are involved. When significant tooth wear occurs, not only will sidebands appear about *fm*, but also about the gear natural frequencies. In the case of those around *fm*, the amplitude of the sidebands themselves is a better indicator for wear than the amplitude of *fm*.

Fig. 5. Spectrum indicating misalignment of gear

As for significant gear eccentricity and/or backlash, these problems display the following characteristics:


In the results of the envelop analysis with DWT, the high harmonics of *fm* occurred by strong wearing phenomena caused by misaligned teeth. In the power spectrum (Fig. 6), 25Hz (*fr*) and its harmonics are generated and 11.32Hz was the ball pass frequency of inner race (BPFI [*fd*]). In Fig. 6(c) and (d), the center dash line is shown for *fm* and 2 *fm*, and their side lines are the sidebands with difference 25Hz (*fr*).

(on one channel, 5M samples/s on 2 AE channels)

In general, the misaligned gear which almost always excites higher order *fm* harmonics is shown as in Fig. 5. Often, only small amplitudes will be at the fundamental *fm*, but much higher levels will be at 2 *fm* and/or 3 *fm*. The sideband spacing about *fm* might be 2 *fr* or even 3 *fr* when gear misalignment problems are involved. When significant tooth wear occurs, not only will sidebands appear about *fm*, but also about the gear natural frequencies. In the case of those around *fm*, the amplitude of the sidebands themselves is a better indicator for wear

As for significant gear eccentricity and/or backlash, these problems display the following



In the results of the envelop analysis with DWT, the high harmonics of *fm* occurred by strong wearing phenomena caused by misaligned teeth. In the power spectrum (Fig. 6), 25Hz (*fr*) and its harmonics are generated and 11.32Hz was the ball pass frequency of inner race (BPFI [*fd*]). In Fig. 6(c) and (d), the center dash line is shown for *fm* and 2 *fm*, and their side lines are

Single power/signal BNC or optional separate power/signal BNC

Operating frequency range : 100-1,000 kHz

18-bit A/D conversion 10M samples/s rate

Directionality : ±1.5 dB

Table 2. Specifications of data acquisition system

Fig. 5. Spectrum indicating misalignment of gear

the meshing gears. (James & Bery, 1994)

the sidebands with difference 25Hz (*fr*).

**3.3 Experiment result and discussion** 

Wide dynamic range < 90 dB

20/40/60 dB selectable gain

Peak sensitivity [V/µbar] : -62 dB

Resonant freq. [V/ µbar] : 650 kHz

2 Channel AE system on PCI-Board

AE Sensor (Wideband type)

Preamplifier Gain

than the amplitude of *fm*.

characteristics:

frequencies.

Fig. 6. Power spectrum of the second day

Fig. 7. Peak level trend among days

Fig. 8. Gear tooth weaned by misalignment

Machinery Faults Detection Using Acoustic Emission Signal 181

the spots. However, this trouble was not seeded and existed from the initial condition. Thus, it is as assumed that the problem happened in assembly and/or was caused by

(a) Power spectrum of the AE signal using envelope analysis with DWT(suggested)

(b) Power spectrum of the AE signal using traditional envelope analysis

(c) Power spectrum of the signal from accelerometer

To identify the sensing ability of the AE, vibration signal was acquired through accelerometer and compared with the AE signal. Also, to find the advantage of the proposed

The power spectrum of the AE signal using traditional envelope analysis is shown in Fig. 10(b), and the power spectrum using the vibration signal by accelerometer is displayed on Fig. 10(c). The vibration signal was treated by the same method with AE signal. The harmonics of *fr* are generated, and 2 *fr* for detecting the misalignment is created and can be found in all spectrums (Fig. 10) but the power spectrum of the AE signal, Fig. 10(a) and (b), can explicitly display the defect frequencies as compared to the accelerometer signal (Fig. 10(c)). For example, in Fig. 10(c), the sidebands of BPFI are not easily found because of the higher level of noise in the low frequency range below *fr* than in the AE signal with or

signal processing method, it was compared to traditional envelope analysis.

Fig. 10. Sidebands BPFI in the first day power spectrum

misalignment.

without DWT.

(b) Frequency response function

In condition monitoring for general rotating machinery, the harmonics (2 *fr*, 3 *fr*, 4 *fr* …) of *fr* are occurred higher than *fr* when the misalignment was happened. According to the phenomena of misalignment as shown in Fig.5, high level harmonics of *fr* were generated such as in Fig. 6(b), and 2 *fr* was always bigger than *fr* as shown in Fig. 7(a). The level of 2 *fm* from second to thirteenth day was higher than or similar to *fr* as shown in Fig. 7(b). Thus, it is easily catching up to the misalignment that occurred in this test rig. However, it might be that faults of this system are not only misalignment but also resonance trouble, looseness, bearing fault, etc.

Wearing effect by misalignment pollutes the lubrication oil. In Fig. 8, it could be found by the worn teeth and the spots near the pieces of gear teeth. The dripped pieces from the unloading surface raised the wearing effect on the loading surface, and then the gap between gear and pinion was increased. In addition, we could know that the impact marks on the unloading surface (Fig. 8(b)) were generated by misalignment; the impacting force was strong in the initial condition. In this way, the gear teeth were seriously damaged as in Fi g. 8. In Fig. 6(c) and (d), the sidebands are created on wide-spread frequency range near *fm* and 2 *fm*. That is similar to a state excited by impact force. To confirm the natural frequencies of the test-rig, modal test was fulfilled. The result of the modal test as in Fig. 9 show that *fm* and 2*fm* exist on the exiting frequency range. On the other hand, partial frequency bands close to *fm* and 2 *fm* were excited by the impact force, but it is not an exact natural frequency because the phase did not shift enough. Therefore, the peaks near *fm* and 2 *fm* were amplified and have many sidebands of *fr* and 11.32Hz (BPFI [*fd*]). Therefore, it is considered that excessive backlash occurred. Moreover, Fig. 10(a) shows the zooming power spectrum of Fig. 6(a) focused on *fr* harmonics. We could clearly know that if the sidebands were caused by BPFI [*fd*], then the inner race had some kind of fault. To find out the fault, the surface of the bearing inner race was carried out and viewed by a microscope with 100X zoom as shown in Fig. 11. Small spots were found on the surface, and small cracks were found out on

(a) Phase

In condition monitoring for general rotating machinery, the harmonics (2 *fr*, 3 *fr*, 4 *fr* …) of *fr* are occurred higher than *fr* when the misalignment was happened. According to the phenomena of misalignment as shown in Fig.5, high level harmonics of *fr* were generated such as in Fig. 6(b), and 2 *fr* was always bigger than *fr* as shown in Fig. 7(a). The level of 2 *fm* from second to thirteenth day was higher than or similar to *fr* as shown in Fig. 7(b). Thus, it is easily catching up to the misalignment that occurred in this test rig. However, it might be that faults of this system are not only misalignment but also resonance trouble, looseness, bearing fault, etc. Wearing effect by misalignment pollutes the lubrication oil. In Fig. 8, it could be found by the worn teeth and the spots near the pieces of gear teeth. The dripped pieces from the unloading surface raised the wearing effect on the loading surface, and then the gap between gear and pinion was increased. In addition, we could know that the impact marks on the unloading surface (Fig. 8(b)) were generated by misalignment; the impacting force was strong in the initial condition. In this way, the gear teeth were seriously damaged as in Fi g. 8. In Fig. 6(c) and (d), the sidebands are created on wide-spread frequency range near *fm* and 2 *fm*. That is similar to a state excited by impact force. To confirm the natural frequencies of the test-rig, modal test was fulfilled. The result of the modal test as in Fig. 9 show that *fm* and 2*fm* exist on the exiting frequency range. On the other hand, partial frequency bands close to *fm* and 2 *fm* were excited by the impact force, but it is not an exact natural frequency because the phase did not shift enough. Therefore, the peaks near *fm* and 2 *fm* were amplified and have many sidebands of *fr* and 11.32Hz (BPFI [*fd*]). Therefore, it is considered that excessive backlash occurred. Moreover, Fig. 10(a) shows the zooming power spectrum of Fig. 6(a) focused on *fr* harmonics. We could clearly know that if the sidebands were caused by BPFI [*fd*], then the inner race had some kind of fault. To find out the fault, the surface of the bearing inner race was carried out and viewed by a microscope with 100X zoom as shown in Fig. 11. Small spots were found on the surface, and small cracks were found out on

(b) Frequency response function

Fig. 9. Modal test result

the spots. However, this trouble was not seeded and existed from the initial condition. Thus, it is as assumed that the problem happened in assembly and/or was caused by misalignment.

(c) Power spectrum of the signal from accelerometer

Fig. 10. Sidebands BPFI in the first day power spectrum

To identify the sensing ability of the AE, vibration signal was acquired through 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 power spectrum of the AE signal using traditional envelope analysis is shown in Fig. 10(b), and the power spectrum using the vibration signal by accelerometer is displayed on Fig. 10(c). The vibration signal was treated by the same method with AE signal. The harmonics of *fr* are generated, and 2 *fr* for detecting the misalignment is created and can be found in all spectrums (Fig. 10) but the power spectrum of the AE signal, Fig. 10(a) and (b), can explicitly display the defect frequencies as compared to the accelerometer signal (Fig. 10(c)). For example, in Fig. 10(c), the sidebands of BPFI are not easily found because of the higher level of noise in the low frequency range below *fr* than in the AE signal with or without DWT.

Machinery Faults Detection Using Acoustic Emission Signal 183

wire-cutting with 0.5 mm depth on the shaft made from SM45C. As shown in Fig. 12, the crack was positioned at 5mm near to the second drive-end bearing, and the non-driven end

AE signal was acquired by an AE sensor and transferred to amplifier, analog-filter, DAQ board and HDD of a desktop. AE sensor is a wideband type with a relative flat response in the range frequency range from 100 kHz to 1 MHz. AE signals were pre-amplified with 60 dB and the output from the amplifier was collected by a commercial data acquisition card with 5 MHz sampling rate during the test. The signals were stored 0.5sec by every 30sec until the shaft was fractured, and the rotating speed of the motor was 600rpm

The operating speed was 600rpm, and the initial radial load for 160N was employed. The radial load was a variable parameter because it was applied by keeping the lifting distance with 6.5mm of the non-drive end of the shaft, and the test terminated on a fracture of the shaft. Fig. 13 shows the observations of continuous feature values as mean value, RMS, peak value and entropy estimation. In information theory, uncertainty can be measured by entropy. The entropy of a distribution is the amount of a randomness of that distribution. Entropy estimation is two stage processes; first a histogram is estimated and thereafter the entropy is calculated. Here, we estimate the entropy of AE signal with using unbiased estimated approach. Fig. 13(a), relatively high level of AE activity was noted from 18 minutes, and it was increased until 60 minutes. But in RMS, Peak and Entropy estimation, the levels were kept to 18minutes beside a peak in around 9 minutes, since that these were continuously decreased to 70 minutes and were increased with hunting with several minute

Interestingly observations of the AE waveform, sampled at 5 MHz showed changing characteristics as a function of time. Fig. 14 shows a contour map of the peaks level of each frequency with time. Rotating speed (9.5Hz) and 3rd harmonic of rotating speed (28.6Hz, 3X) dominated while the test as shown in Fig. 14(b). It is normally known that 3X is caused by misalignment of the bearings created by the loading system for this test (Hatch & Bently,

of the shaft was left 6.5 mm with bearing housing by the lifting tool.

(10Hz).

Fig. 12. Experiment system

intervals until the fracture.

**4.2 Test result and discussion** 

Fig. 11. Zooming of the inner race surface of the fault bearing


Table 3. Ratio of peaks versus the maximum peak in respective spectrum

According to the above results, we can understand that the AE signal can detect the fault more easily than accelerometers and can be used in the condition monitoring system for early detection fault. Moreover, as shown in Table 3 which is the ratio of peaks versus the maximum peak in the respective spectrum, the peak levels of the harmonics of *fr* and sidebands caused by BPFI are highly generated in the proposed signal processing method (Fig. 10(a)) than the traditional method. This can lead good feature values to evaluate the condition of the machinery. Therefore, the power spectrum of the proposed envelope analysis using AE signal can be shown the clean result with harmonics and sidebands and is a better technique for condition monitoring system.

## **4. Cracked rotor**

### **4.1 Experiment system**

Test rig consisted of a motor, a flexible coupling, rolling element bearings (NSK6200), three steel bearing housings, a lifting tool and a cracked shaft. The transverse crack was seeded by

Frequency [Hz] Traditional Method Proposed method

13.709 1X-BPFI 0.2146 0.2459 25.034 1X 0.8727 0.9525 36.360 1X+BPFI 0.1936 0.3196 38.750 2X- BPFI 0.0952 0.1435 50.070 2X 1.0000 1.0000 61.393 2X+ BPFI 0.1277 0.2470 63.181 3X- BPFI 0.0970 0.1560 75.102 3X 0.3044 0.5465 86.427 3X+ BPFI 0.1699 0.2352 99.540 4X 0.4269 0.4616 110.866 4X+ BPFI 0.1062 0.1675 124.574 5X 0.2312 0.3253 135.899 5X+ BPFI 0.0714 0.1443

Table 3. Ratio of peaks versus the maximum peak in respective spectrum

a better technique for condition monitoring system.

**4. Cracked rotor** 

**4.1 Experiment system** 

According to the above results, we can understand that the AE signal can detect the fault more easily than accelerometers and can be used in the condition monitoring system for early detection fault. Moreover, as shown in Table 3 which is the ratio of peaks versus the maximum peak in the respective spectrum, the peak levels of the harmonics of *fr* and sidebands caused by BPFI are highly generated in the proposed signal processing method (Fig. 10(a)) than the traditional method. This can lead good feature values to evaluate the condition of the machinery. Therefore, the power spectrum of the proposed envelope analysis using AE signal can be shown the clean result with harmonics and sidebands and is

Test rig consisted of a motor, a flexible coupling, rolling element bearings (NSK6200), three steel bearing housings, a lifting tool and a cracked shaft. The transverse crack was seeded by

Fig. 11. Zooming of the inner race surface of the fault bearing

wire-cutting with 0.5 mm depth on the shaft made from SM45C. As shown in Fig. 12, the crack was positioned at 5mm near to the second drive-end bearing, and the non-driven end of the shaft was left 6.5 mm with bearing housing by the lifting tool.

AE signal was acquired by an AE sensor and transferred to amplifier, analog-filter, DAQ board and HDD of a desktop. AE sensor is a wideband type with a relative flat response in the range frequency range from 100 kHz to 1 MHz. AE signals were pre-amplified with 60 dB and the output from the amplifier was collected by a commercial data acquisition card with 5 MHz sampling rate during the test. The signals were stored 0.5sec by every 30sec until the shaft was fractured, and the rotating speed of the motor was 600rpm (10Hz).

Fig. 12. Experiment system

### **4.2 Test result and discussion**

The operating speed was 600rpm, and the initial radial load for 160N was employed. The radial load was a variable parameter because it was applied by keeping the lifting distance with 6.5mm of the non-drive end of the shaft, and the test terminated on a fracture of the shaft. Fig. 13 shows the observations of continuous feature values as mean value, RMS, peak value and entropy estimation. In information theory, uncertainty can be measured by entropy. The entropy of a distribution is the amount of a randomness of that distribution. Entropy estimation is two stage processes; first a histogram is estimated and thereafter the entropy is calculated. Here, we estimate the entropy of AE signal with using unbiased estimated approach. Fig. 13(a), relatively high level of AE activity was noted from 18 minutes, and it was increased until 60 minutes. But in RMS, Peak and Entropy estimation, the levels were kept to 18minutes beside a peak in around 9 minutes, since that these were continuously decreased to 70 minutes and were increased with hunting with several minute intervals until the fracture.

Interestingly observations of the AE waveform, sampled at 5 MHz showed changing characteristics as a function of time. Fig. 14 shows a contour map of the peaks level of each frequency with time. Rotating speed (9.5Hz) and 3rd harmonic of rotating speed (28.6Hz, 3X) dominated while the test as shown in Fig. 14(b). It is normally known that 3X is caused by misalignment of the bearings created by the loading system for this test (Hatch & Bently,

Machinery Faults Detection Using Acoustic Emission Signal 185

hence the voltage-time units (*μ*V2∙sec). So, PAC energy value was determined by an integral of the square sum total of the transferred time signal in each wavelet level. Fig. 15 shown the energy level of every wavelet levels along time, and its value was transferred to

Fig. 15 shows the energy trend of wavelet level 1 to 8. Many peaks were created while the test in wavelet level 1(Fig. 15(a)), a high peak was created around 9 minutes existed in wavelet level 1 to 4. Wavelet level 2, 4, 5 and 6 shows a similar trend after 10minutes. The energy level was slowly increased with time until about 30 minutes, and then it was increased fast until 35 minutes (additionally, it was considered that this increasing was related with the growth of the 3X and 31Hz in Fig. 14(a)), after that it was decreased a little for 10 minutes. And it was hunted with every several minutes about 4 minutes until close fracture. In this trend, we had considered of two phenomena, the high peak and the period hunting. We could mind that the high peak was related with initial crack growth. Because it was

The period hunting was clearly occurred and displayed in wavelet level 2, 4 ~ 8. It was considered that it could indicate a state of the final stage of the fracture in the rotating shaft

(a) Wavelet level 4

(b) Wavelet level 6


logarithmic value because of too low resolution in linear scale.




shown as follows,

because of follows,


Fig. 14. Peak level trend by frequency

2002). However, the harmonic component (3X) was kept the level in the wavelet level 6(Fig. 14(b)), but it was increased from 30 minutes in the wavelet level 4(Fig. 14(a)). Additionally, 1X started increasing earlier than 3X as shown in Fig. 14(a).

Fig. 13. Shaft test results; run-to-failure

31Hz and 62Hz that were the harmonics of the fundamental train frequency (FTF or cage noise) of the bearing were continuously occurred. Cage noise can be generated in any type of bearing and the magnitude of it is usually not very high. Characteristics of this noise include: (1) it occurs with pressed steel cages, machined cages and plastic cages. (2) It occurs with grease and oil lubrication. (3) It tends to occur if a moment load is applied to the outer ring of a bearing. (4) It tends to occur more often with greater radial clearance. In Fig. 14, 62Hz was continuously detected; 31Hz was detected with 3X. In a general bearing system, the amplitude of the bearing fault frequency is depended on the load grade and is increased along the growing load grade. However, 31Hz of the case noise of this test was not followed the load scale because loading force for this test was decreased with the crack growth. So, it was shown that 31Hz was related with the crack growth.

According to this result, we could know that the reason of 3X (28.6Hz) was the moment load by the loading system; 31Hz was connected with the crack growth. Therefore, the peak levels around 3X and 31Hz was excited by the two frequencies and was increased with the crack growth.

To clear more the characteristic of the crack growth, in addition, PAC energy value was observed. In acoustic emission technology, PAC-Energy is a 2-byte parameter derived from the integral of the rectified voltage signal over the duration of the AE hit (or waveform),

2002). However, the harmonic component (3X) was kept the level in the wavelet level 6(Fig. 14(b)), but it was increased from 30 minutes in the wavelet level 4(Fig. 14(a)). Additionally,

0


(c) Peak value [*μV*] (d) Entropy estimation value

31Hz and 62Hz that were the harmonics of the fundamental train frequency (FTF or cage noise) of the bearing were continuously occurred. Cage noise can be generated in any type of bearing and the magnitude of it is usually not very high. Characteristics of this noise include: (1) it occurs with pressed steel cages, machined cages and plastic cages. (2) It occurs with grease and oil lubrication. (3) It tends to occur if a moment load is applied to the outer ring of a bearing. (4) It tends to occur more often with greater radial clearance. In Fig. 14, 62Hz was continuously detected; 31Hz was detected with 3X. In a general bearing system, the amplitude of the bearing fault frequency is depended on the load grade and is increased along the growing load grade. However, 31Hz of the case noise of this test was not followed the load scale because loading force for this test was decreased with the crack growth. So, it

According to this result, we could know that the reason of 3X (28.6Hz) was the moment load by the loading system; 31Hz was connected with the crack growth. Therefore, the peak levels around 3X and 31Hz was excited by the two frequencies and was increased with the

To clear more the characteristic of the crack growth, in addition, PAC energy value was observed. In acoustic emission technology, PAC-Energy is a 2-byte parameter derived from the integral of the rectified voltage signal over the duration of the AE hit (or waveform),



Amplitude


0

0.05

0.1

Amplitude

(a) Mean value [*μV*Ⅹ10-4] (b) RMS value [*μV*]

0.15

0.2

0 20 40 60 80

Time [min]

0 20 40 60 80

Time [min]

1X started increasing earlier than 3X as shown in Fig. 14(a).

0 20 40 60 80

Time [min]

0 20 40 60 80

Time [min]

was shown that 31Hz was related with the crack growth.

Fig. 13. Shaft test results; run-to-failure


0

crack growth.

0.1

0.2

Amplitude

0.3

0.4

0.5



Amplitude



hence the voltage-time units (*μ*V2∙sec). So, PAC energy value was determined by an integral of the square sum total of the transferred time signal in each wavelet level. Fig. 15 shown the energy level of every wavelet levels along time, and its value was transferred to logarithmic value because of too low resolution in linear scale.

Fig. 15 shows the energy trend of wavelet level 1 to 8. Many peaks were created while the test in wavelet level 1(Fig. 15(a)), a high peak was created around 9 minutes existed in wavelet level 1 to 4. Wavelet level 2, 4, 5 and 6 shows a similar trend after 10minutes. The energy level was slowly increased with time until about 30 minutes, and then it was increased fast until 35 minutes (additionally, it was considered that this increasing was related with the growth of the 3X and 31Hz in Fig. 14(a)), after that it was decreased a little for 10 minutes. And it was hunted with every several minutes about 4 minutes until close fracture. In this trend, we had considered of two phenomena, the high peak and the period hunting.

We could mind that the high peak was related with initial crack growth. Because it was shown as follows,


The period hunting was clearly occurred and displayed in wavelet level 2, 4 ~ 8. It was considered that it could indicate a state of the final stage of the fracture in the rotating shaft because of follows,


Fig. 14. Peak level trend by frequency

Machinery Faults Detection Using Acoustic Emission Signal 187

To compare absolutely the energy of each wavelet level, all of PAC energy was displayed on a 3D graph with time and wavelet levels as shown in Fig. 16. In wavelet level 5, after approximately 30 minutes, a large transient rise in PAC energy level was observed and this AE activity gradually observed frequently after 60 minutes until the shaft was fractured. In addition, a peak created at 9 minutes was indicated. In here, we could consider that the frequency range of wavelet level 5 could be shown a good relationship between the PAC energy and the crack growth of the middle and final stage. Even so, the trend of the wavelet level 7 and 8 was not clearly connected with the others because the frequency range of wavelet level 7 and 8 was lower than the useful frequency range (100kHz to 1MHz) of AE

Therefore, the AE signal caused by the crack growth was generated on the whole ultrasound frequency range; the initial crack could be detected using the PAC energy on wavelet level 1 to 4. In addition, it could be presented on wavelet level 5 until the fracture of the shaft. In the frequency domain, it was shown that the harmonic components of the rotating speed and bearing cage frequency were excited by the crack growth, especially on the 3X

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 from a gear system

Fig. 16. PAC-Energy level of total wavelet level

sensor for this research.

(28.6Hz) and 31Hz.

**5. Conclusion** 

Fig. 15. PAC energy trend of each wavelet level

Energy [mV2\*sec]

(a) Level 1 (b) Level 2

0 0.5 1 1.5 2 x 10-6

0

0 0.5 1 1.5 2 x 10-3

Energy [mV2\*sec]

(e) Level 5 (f) Level 6

Energy [mV2\*sec]

(g) Level 7 (h) Level 8

0.5

Energy [mV2\*sec]

(c) Level 3 (d) Level 4

1 x 10-4

0 20 40 60 80

Energy Trend Curve, Level = 2

Time [min]

Energy Trend Curve, Level = 4

0 20 40 60 80

Time [min]

Energy Trend Curve, Level = 6

0 20 40 60 80

Time [min]

Energy Trend Curve, Level = 8

0 20 40 60 80

Time [min]

0 20 40 60 80

Energy Trend Curve, Level = 1

Time [min]

Energy Trend Curve, Level = 3

0 20 40 60 80

Time [min]

Energy Trend Curve, Level = 5

0 20 40 60 80

Time [min]

Energy Trend Curve, Level = 7

0 20 40 60 80

Time [min]

Fig. 15. PAC energy trend of each wavelet level

0.8 1 1.2 1.4 x 10-7

0

Energy [mV2\*sec]

Energy [mV2\*sec]

0.5

Energy [mV2\*sec]

1

1.5 x 10-5

Energy [mV2\*sec]

Fig. 16. PAC-Energy level of total wavelet level

To compare absolutely the energy of each wavelet level, all of PAC energy was displayed on a 3D graph with time and wavelet levels as shown in Fig. 16. In wavelet level 5, after approximately 30 minutes, a large transient rise in PAC energy level was observed and this AE activity gradually observed frequently after 60 minutes until the shaft was fractured. In addition, a peak created at 9 minutes was indicated. In here, we could consider that the frequency range of wavelet level 5 could be shown a good relationship between the PAC energy and the crack growth of the middle and final stage. Even so, the trend of the wavelet level 7 and 8 was not clearly connected with the others because the frequency range of wavelet level 7 and 8 was lower than the useful frequency range (100kHz to 1MHz) of AE sensor for this research.

Therefore, the AE signal caused by the crack growth was generated on the whole ultrasound frequency range; the initial crack could be detected using the PAC energy on wavelet level 1 to 4. In addition, it could be presented on wavelet level 5 until the fracture of the shaft. In the frequency domain, it was shown that the harmonic components of the rotating speed and bearing cage frequency were excited by the crack growth, especially on the 3X (28.6Hz) and 31Hz.
