# Novel Methodology for Condition Monitoring of
## 4 Experimental Setup  
In this paper, an experimental test bench was used to test different levels of uniform wear in the gears as an incipient failure in a gearbox transmission system. Figure 3 shows a kinematic chain with the principal elements that an industrial system can have, where the main element is the gearbox, which is used to validate the proposed methodology. The test bench is based on a kinematic chain that consists of a three-phase induction motor of 1.5 kW (WEG00236 ET3E145T-W22), electrically connected to a frequency inverter (VFD) (WEGCFW08) to feed and control the rotation speed. The AC machine is mechanically coupled by rigid coupling to a 4:1 gearbox (BALDOR GCF4 \(\times\) 01 AA) that drives its input shaft, and this gearbox is used to test the different levels of uniform wear in the gears studied in this paper. Besides, the gearbox, in turn, is mechanically coupled by rigid coupling to a DC generator \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Equation** & **No.** \\ \hline Maximum value & \(T_{max}=\max(l(x,y))\) & (7) \\ Minimum value & \(T_{min}=\min(l(x,y))\) & (8) \\ Average intensity & \(\mu=\frac{1}{f_{s}g_{y}}\sum\limits_{p=0}^{q-1}ph(p)\) & (9) \\ Standard deviation & \(\sigma=\left(\frac{1}{f_{s}g_{y}}\sum\limits_{p=0}^{q-1}(p-\mu)^{2}h(p)\right) ^{\frac{1}{2}}\) & (10) \\ Variance & \(\sigma^{2}=\frac{1}{f_{s}g_{y}}\sum\limits_{p=0}^{q-1}(p-\mu)^{2}h(p)\) & (11) \\ Skewness & \(S_{k}=\frac{1}{\sigma^{2}f_{s}g_{y}}\sum\limits_{p=0}^{q-1}(p-\mu)^{3}h(p)\) & (12) \\ Kurtosis & \(k=\frac{1}{\sigma^{4}f_{s}g_{y}}\sum\limits_{p=0}^{q-1}(p-\mu)^{4}h(p)\) & (13) \\ Entropy & \(Entropy=-\frac{1}{f_{s}g_{y}}\sum\limits_{p=0}^{q-1}n\log(p)\) & (14) \\ Energy & \(Energy=\frac{\sum_{p=0}^{f_{s}g_{y}}\sum_{p=0}^{q-1}(x,y)^{2}}{f_{s}g_{y}}\) & (15) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Extraction of statistical features from the thermography image. motor (BALDOR CDP3604), and the generator is used as a load, producing approximately 20% of the rated load in the induction motor in working conditions. For the monitoring of the thermal behavior of the gearbox, a thermographic infrared camera (model FLIR A310, from FLIR Systems Incorporated) is used as the primary sensor for data acquisition. The FLIR A310 has a resolution of 320 \(\times\) 240 (76,800) pixels, and by means of a vanadium oxide microbolometer, detects infrared radiation with a thermal sensitivity/Notice Equivalent Temperature Difference (NETD) of 50 mK. The measurements carried out with this camera are obtained with an accuracy of \(\pm\)2 \({}^{\circ}\)C, and it is capable of measuring the object's temperature within a range of \(-\)20 to +120 \({}^{\circ}\)C or 0 to +350 \({}^{\circ}\)C. The acquired thermal images represent the digitized intensity values in 16 bits, and the FLIR Tool software is used for acquiring the thermographic images. The infrared camera is adjusted for each test to different environmental factors for a more accurate measurement. These factors are emissivity, atmospheric temperature, relative humidity, reflected temperature, and the distance between the gearbox and the infrared camera. For each test performed, measuring instruments are used, such as Fluke 975 AIMTER and Fluke 61, for the measurement of environmental parameters, while the emissivity value is adjusted to 0.95, as recommended in previous works related to electrical systems [38]. Calibration and validation are performed for the thermographic temperature values of the camera. For the calibration, the temperature values obtained with the thermographic camera are compared with the output of a comparative method. Several Resistance Temperature Detectors (RTDs) were used to obtain the reference measurement. The calibration guarantees that the measurement obtained with the thermographic camera is the same as that of the equipment to be monitored.