# Wind Turbine Gearbox Fault Diagnosis Based on Improved EEMD and Hilbert Square Demodulation
## 4 The Proposed Method for Gearbox Fault Diagnosis of a Wind Turbine
### Gear Experimental Evaluation  
A set of gear fault vibration signals was kindly provided by the Reliability Research Lab in the Department of Mechanical Engineering at the University of Alberta [25]. The diagram of the experimental system is displayed in Figure 8[26; 27]. The system included a gearbox, a 3-hp AC motor for driving the gearbox and a magnetic brake for loading. The motor rotating speed was controlled by a speed controller, which allowed the tested gear to operate under various speeds. The load was provided by the magnetic brake connected to the output shaft, and the torque could be adjusted by a brake controller. As shown in Figure 8b, the gearbox was driven by the motor through a timing belt, and there were three shafts inside the gearbox, which were mounted to the gearbox housing by rolling element bearings. Gear 1 on Shaft 1 has 48 teeth and meshes with Gear 2 with 16 teeth. Gear 3 on Shaft 2 has 24 teeth and meshes with Gear 4, which was on the output shaft (Shaft 3) and has 40 teeth. Gear 3 was the tested gear. Gears with different levels of crack faults were simulated in the experimental system. As shown in Figure 9a, \(\alpha\) was the crack angle, \(a\) one half of the chordal tooth thickness and \(b\) the face width. The crack thickness was 0.4 mm in the experiment based on the measurement of the thinnest knife of the machine tools in the lab. Figure 8: \(Cont\). Figure 7: The decomposition results of vibration with improved EEMD and the spectrum of the demodulated signal. (**a**) The decomposition results of vibration with improved EEMD; (**b**) the spectrum of the demodulated signal. In this study, we employed the gear with 75% crack level as shown in Figure 9b. The vibration was measured at 2200 RPM with the sampling frequency \(f_{s}=12,800\) Hz. We used two acceleration sensors produced by PCB Electronics with Model Number 352C67. The meshing frequencies are summarized in Table 2[26]. From the configuration of the gearbox system, the fault characteristic frequency was equal to the rotating frequency of Shaft 2. \[f_{eq}=f_{2}=26.1\ \mathrm{Hz} \tag{20}\]  
The time domain waveform of the experimental vibration signal and its spectrum are illustrated in Figure 10, from which the fault characteristic frequency cannot be identified. The vibration signal was analyzed with the proposed method. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Motor Speed (RPM)** & \(f_{1}\) **(Hz)** & \(f_{12}\) **(Hz)** & \(f_{2}\) **(Hz)** & \(f_{34}\) **(Hz)** & \(f_{3}\) **(Hz)** \\ \hline
2200 & 8.73 & 418.89 & 26.19 & 628.56 & 15.72 \\ \hline \hline \end{tabular} Note: \(f_{1}\), \(f_{2}\) and \(f_{3}\) are the rotating frequencies of Shaft 1, Shaft 2 and Shaft 3, respectively. \(f_{12}\) and \(f_{34}\) are the meshing frequencies of Gears 1 and 2 and Gears 3 and 4, respectively.  
\end{table} 
Table 2: Motor speed and characteristic frequencies of the gearbox. Figure 8: Gear test rig. (**a**) Experimental system; (**b**) diagram of the system. Figure 9: Gear crack angle, face width and chordal tooth thickness and experiment fault gear. (**a**) Crack angle, face width and chordal tooth thickness of a gear; (**b**) 75% level crack in the gear. According to the resample criterion presented in Section 3.2, subtract 12-times the maximum frequency with the sampling frequency, and the value of the result is less than the maximum frequency. Therefore, the resample algorithm is unable to be carried out. \[f_{e}=f_{s}-f_{r}=12800-12\times 1667=-7204\;\mathrm{Hz}\leq 1667\;\mathrm{Hz} \tag{21}\]  
The results of the decomposition of the vibration signal directly with EEMD are shown in Figure 11a. The IMF2 was selected for further analysis because it had the biggest kurtosis value compared with the other IMFs. HSD was applied on IMF2, and the obtained demodulation spectrum is shown in Figure 11b. It was found that the identified frequency component matched the gear fault characteristic frequency \(f_{eq}=26.1\;\mathrm{Hz}\) accurately.