# Electrical Monitoring under Transient Conditions:
## 4 Results
### Results in Laboratory Motors  
Several tests were carried out in the laboratory using different 1.1 kW, 4 pole cage induction motors with different levels of rotor failure and misalignment [10]. In the experiments, the tested motor was coupled to a DC that had the function of load. In each test, the motor was started direct on-line, and it operated until the steady-state regime was well reached; the phase current waveform under the starting was captured by means of a current clamp that was connected to the oscilloscope. In addition, a self-built flux sensor (manufactured at Universitat Politecnica de Valencia, Valencia, Spain) based on a coil with 1000 turns was attached to the external part of the motor frame [28]. The waveform of the electromotive force (emf) induced in the sensor by the stray flux was registered by means of the previous oscilloscope. Different tests were performed for the motor operating under various levels of failures and under different loading conditions. Moreover, different locations of the coil sensor were \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Type of t-f Tool** & \multicolumn{2}{c}{**Advantages**} & \multicolumn{2}{c}{**Drawbacks**} & **Examples** \\ \hline \multirow{4}{*}{Discrete} & - & Low computational burden. & \multirow{4}{*}{-} & Less clear representation \\  & - & Simplicity. & & of fault \\ \cline{1-1}  & - & Easy utilization. & & component evolutions. & WP \\ \cline{1-1}  & - & Easy introduction of fault & & \\ \cline{1-1}  & & severity indicators. & & \\ \hline \multirow{4}{*}{Continuous} & - & Easier tracking of fault & - & Higher \\  & & components evolutions. & & computational burden. \\ \cline{1-1}  & - & Ideal for discrimination & - & More complex tools. \\ \cline{1-1}  & & between faults and versus & - & Their optimization is \\ \cline{1-1}  & & other phenomena. & & often required. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main time-frequency tools for the application of transient-based diagnosis approaches [40]. CWD: Choi–Williams Distributions; CWT: Continuous Wavelet Transform; DWT: Discrete Wavelet Transform; HHT: Hilbert–Huang Transform; UDWT: Undecimated Discrete Wavelet Transform; WP: Wavelet Packets. considered (the three considered positions are those shown in Figure 3). Both the starting current and the stray flux signals were registered using a sampling rate of 5 kHz. The registered waveforms were later transferred to a computer where they were analysed by applying a specific time-frequency transform: the Short-Time Fourier Transform (STFT). Figure 4 shows a picture of the test bench (built at Universitat Politecnica de Valencia, Valencia, Spain) and of two of the considered positions of the stray flux sensor. Figure 5 shows the time-frequency maps resulting from the application of the STFT to the starting current signals for three different fault conditions of the motor: healthy motor, motor with one broken bar, and motor with two broken rotor bars. All experiments were carried out at at Universitat Politecnica de Valencia, Valencia, Spain. Note the clear differences between all three maps; the evolutions of the fault harmonics are clearly evident for the faulty cases. In particular, the evolutions of the main sideband harmonics (\(f\)-\((1-2\):\(s)\) and \(f\)-\((1+2\):\(s)\)) are especially clear. In addition, the evolutions of higher-order rotor fault-related harmonics, such as \(f\)-\((5-4\):\(s)\) and \(f\)-\((5-6\):\(s)\), are clearly noticeable. These are clear indicators of the presence of the rotor damage. Finally, note how the intensity of the patterns created by the fault harmonic evolutions are higher when the level of rotor failure increases. On the other hand, Figures 6 and 7 show the time-frequency analyses of the stray flux signals under starting for the healthy motor and for the motor with two broken bars for two considered positions of the coil sensor: position A and position B. In comparison with Figure 5, note the much richer harmonic content of the stray flux maps depicted in Figures 6 and 7.