**(c) CWRU vibration data**

The time course of the vibration signals for a normal bearing and bearings with outer race, inner race and rolling element faults at a shaft rotational speed of 1797 rev/min with its corresponding TWPS are shown in Figures 23 to 26, respectively.

The TWPS for the vibration data shows spectral peaks at 106.9 Hz, 161.1 Hz and 141.166 Hz and their harmonics for outer race, inner race and rolling element faults, respectively. The sidebands at shaft speed (30 Hz) as a result of amplitude modulation are shown for inner and rolling element faults.

Wavelet Analysis and Neural Networks for Bearing Fault Diagnosis 341

Fig. 25. The vibration signal (a), and the corresponding TWPS (b) for rolling bearing with

(a) (b)

Power Spectrum

X: 142.1 Y: 0.007018

<sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>900</sup> <sup>1000</sup> <sup>0</sup>

CWRU-ball-1797

Frequency (Hz)

X: 281.3 Y: 0.001089

The interpolation of a CWT can certainly be accomplished by operator visual inspection with some practice and experience. However, computerized inspection is recommended to meet increasing demand for the on-line automated condition monitoring applications.

Fig. 26. The vibration signal (a), and the corresponding TWPS (b) for rolling bearing with

inner-race fault (FBPI= 162.185 Hz).

rolling element fault (2FB= 141.166 Hz).

**4. Automatic rolling bearing fault diagnosis** 

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -0.8

Time (Sec)

cwru-time-ball

Acceleration (m.sec-2)


Fig. 23. The vibration signal (a), and the corresponding TWPS (b) for new rolling bearing (CWRU data).

Fig. 24. The vibration signal (a) and, the corresponding TWPS (b) for rolling bearing with outer-race fault (FBPO= 107.36 Hz).

Fig. 23. The vibration signal (a), and the corresponding TWPS (b) for new rolling bearing

(a) (b)

0.5 1 1.5 2 2.5 3 3.5 4 x 10-3

**Power Spectrum**

X: 106.9 Y: 0.00357 X: 215.3 Y: 0.002646

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>900</sup> <sup>1000</sup> <sup>0</sup>

x130laplace1

**Frequency (Hz)**

X: 322.3 Y: 0.0005621

Fig. 24. The vibration signal (a) and, the corresponding TWPS (b) for rolling bearing with

(CWRU data).

**Acceleration (m.sec**

 **-2)**

outer-race fault (FBPO= 107.36 Hz).

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -4

x130time1

**Time (Sec)**

Fig. 25. The vibration signal (a), and the corresponding TWPS (b) for rolling bearing with inner-race fault (FBPI= 162.185 Hz).

Fig. 26. The vibration signal (a), and the corresponding TWPS (b) for rolling bearing with rolling element fault (2FB= 141.166 Hz).
