## 4 Assembly Looseness Fault Identification of Dimountable Disk-Drum Aero-Engine Rotors
### Case 2: Analysis on the Vibration Signals from Engineering Field  
Maintenance is indispensable in making sure that the components continue to perform the functions for which they are designed. The basic objectives of the maintenance activity are to deploy the minimum resources to ensure system reliability and to ensure that components perform their intended functions properly. At present, the scheduled maintenance, known as time based (or planned) maintenance, and involving repair at regular time intervals, is still widely adopted on most of the aero-engine in service in China. Due to vibrations exceeding limits, the aero-engine of military aircraft in this case cannot be used normally after working for 446 h. However, the first scheduled repair time interval is 500 h. Thus, the reason for the overweight vibration, and reasonable maintenance are needed. According to engineering experience, the fault called rupture accident of the labyrinth seal toothed disk in the high pressure compressor rotor of an aero-engine emerges frequently. In order to solve this problem, our group carried out the related study on the assembly looseness and crack fault condition monitoring of this dismountable disk-drum aero-engine rotor. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Signal 1** & **Signal 2** & **Signal 3** & **Signal 4** & **Average** \\ \hline Condition 1 & 0.340 & 0.328 & 0.314 & 0.310 & 0.323 \\ Condition 2 & 0.273 & 0.258 & 0.241 & 0.239 & 0.253 \\ Condition 3 & 0.167 & 0.155 & 0.143 & 0.147 & 0.153 \\ \hline \end{tabular}
\end{table} 
Table 1: The normalized ensemble multiwavelet transform information entropy of three assembled conditions. Figure 16: The distribution of the frequency band energy on the ensemble multiwavelet transform coefficients in the assembled quality condition 3. Figure 15: The distribution of the frequency band energy on the ensemble multiwavelet transform coefficients in the assembled quality condition 2. The dynamic response signal is acquired from the experimental system, as shown in Figure 6. The sample frequency is 6400 Hz. The dynamic response signal of this aero-engine rotor from one accelerometer and the corresponding frequency spectrum are shown in Figure 17. The dynamic response signal is also damped in the time domain. From the frequency spectrum, the largest amplitude value occurs at 2200 Hz and there are three other main spectral peaks at 1000 Hz, 1400 Hz and 2600 Hz. It is shown that we cannot find the evident features to identify the assembled condition directly, in both time and frequency domains. The proposed method in this paper is applied to the condition monitoring of this aero-engine rotor. The ensemble multiwavelet functions constructed from cubic Hermite splines for the vibration signal in Figure17 are shown in Figure 18. Since the ensemble multiwavelet transform is applied to process the signals of an assembled quality condition to the extent of level 3, by research experience, there are eight frequency bands attained. According to Equation (18), the frequency band energy of the ensemble multiwavelet transform coefficients is, respectively, computed and the distribution is illustrated in Figure 19. We can find that the main frequency band energy of the ensemble multiwavelet transform coefficients for this aero-engine rotor also lies in the fifth frequency band and the energy in other frequency bands are much smaller, which is similar to that in the experiment in case 1. The differences are that the energies of the first frequency band and the seventh frequency band increase distinctly. In order to reflect and evaluate the state of this aero-engine rotor, the normalized wavelet information entropy of the acquired signal is computed according to Equation (19), which is shown in Table 2. According to the results, the normalized ensemble multiwavelet transform information entropy of this rotor is a little larger than the value of condition 2 in case 1, which implies that there is an assembly looseness or crack fault in this aero-engine rotor.