# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
## 3 Test Rig, Gearbox States, and Data Processing
### Test Rig, Gearbox States, and Data Acquisition  
The experimental test rig comprises a three-phase AC motor, a variable frequency drive (VFD) as a motor speed regulator, a speed reducer gearbox, and a dry friction brake (Figure 3a). The triaxial B&K piezoelectric accelerometer with integrated electronics has been bonded to the speed reducer casing. The accelerometer \(X\)-axis points downward (perpendicular to the reducer's base), the \(Y\)-axis is parallel to the reducer input shaft (points to the right), and the \(Z\)-axis is perpendicular to the lateral reducer's surface. The acquisition system uses the signal acquisition board NI USB-4431. The triaxial accelerometer and tachometer (one pulse per revolution) feed the four input channels simultaneously sampled at 24-bit resolution. A LabVIEW 2019 application was developed to acquire the signals from the three-axis accelerometer and the tachometer. Three AC motor nominal rotation speeds of 1350.6 rpm, 1375.6 rpm, and 1400.6 rpm, situated at the upper-speed range, are imposed at the speed reducer input. The pinion P1 mounted on the input shaft can be seen in Figure 3b. The tachometer measures the rotation speed of the reducer output, \(i_{out}\), and then uses the speed reducer ratio in Equation (11) to calculate the pinion P1 rotation speed, \(i_{in}\). Three reducer output rotation speeds, 2.16 rps, 2.20 rps, and 2.24 rps, were employed in the experiments. Table 1 shows the pinion and its corresponding AC motor speeds. In Figure 4a, the schematization of the two stages of the speed reducer with two gear pairs, p1 (P1, G1) and p2 (P2, G2), is shown. Based on the teeth numbers of the two gear pairs, the actual speed reducer ratio \(ir=i_{in}/i_{out}\) is 10.421, as is calculated in Equation (11). \[\frac{i_{in}}{i_{out}}=\frac{19}{51}\cdot\frac{17}{66} \tag{11}\]  
The proposed defect detection task aims to identify four gearbox health states (D1, D2, D3, and D4). State D1 (low oil level in the reducer) is characterized by poor lubrication; the wheel G1, positioned under the pinion P1, is immersed in lubricant only with the teeth \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Nominal Speed Values**} & \multicolumn{2}{c}{**P1 (AC Motor) Speed: \(i_{in}\)**} & \multicolumn{2}{c}{**Reducer Velocity: \(i_{out}\)**} \\ \cline{2-4}  & **[rps]** & **[rpm]** & **[rps]** \\ \hline v1 & 22.51 & 1350.56 & 2.16 \\ \hline v2 & 22.93 & 1375.57 & 2.20 \\ \hline v3 & 23.34 & 1400.58 & 2.24 \\ \hline \end{tabular}
\end{table} 
Table 1: AC motor and associated pinion P1 rotation speeds. Figure 4: (**a**) The two gear pairs (p1, p2) of the speed reducer; (**b**) pitting defect on pinion P1 of p1; (**c**) localized wear on P1 of p1. Figure 3: (**a**) The test rig and the triaxial accelerometer. (**b**) The first stage of the speed reducer with the pinion P1 and wheel G1. underneath. The normal state, without defect, is denoted as D2. State D3 corresponds to an incipient and localized pitting on the pinion P1 tooth flank. D4 state presents localized wear on a pinion tooth flank. A helical gear operates smoother and quieter than a spur gear because more pairs of teeth are in contact during meshing, and the sum of the lengths of the contact lines in the active flanks is greater. Early damage to a gear tooth realized through a localized fault causes only a short-duration variation in the vibration signal. This footprint lasts less than one tooth meshing period and normally takes the form of a modulated oscillation. Two flank surface faults, namely localized pitting and localized wear belonging to pinion P1 of the first reducer stage, are observed in the experiments. A localized pitting defect (which is our case) on a helical gear has a diminished effect on the measured vibration signal and is more difficult to detect. Typically, pitting develops in a small area at or just below the pitch line. Pitting starts near the pitch point, where a high frictional force is present (due to the low sliding speed), and can spread to neighboring regions.