# Evaluation of a Novel Condition Indicator with Comparative Application to Hypoid Gear Failures
## 4 Evaluation of Condition Indicators
### Test Results  
On inspection, the damage to Sample \(A_{H}\) was found to include the fracture and removal of one pinion tooth and the visible cracking of a neighboring tooth. The neighboring tooth was assumed to be a secondary failure as a result of the increased load share once the fully cracked tooth had weakened. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(M_{ring}\) & \begin{tabular}{c} **Testing** \\ **Time** \\ \end{tabular} & \begin{tabular}{c} \(t_{pause}\) \\ **in sec** \\ \end{tabular} & \
\begin{tabular}{c} \(t_{learn}\) \\ **in sec** \\ \end{tabular} &
\begin{tabular}{c} **Observed** \\ **Damage** \\ \end{tabular} \\ \hline \multirow{3}{*}{Sample \(A_{H}\)} & \(1.3\times\) rated & Approx. & & & & light spalling and \\  & torque & 4 h & & & & tooth bending fatigue \\  & & & & & & cracks on the pinion \\  & & & & & & light spalling and \\  & & & & & & tooth bending fatigue \\  & & & & & & cracks on the pinion \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of the tests. Metallurgical analysis found that the cause of the fracture on the pinion gear was tooth root bending fatigue, which had the initiation at a Non-Metallic Inclusion (NMI). The crack from the fractured surface demonstrated a \"fish eye\" feature, around the NMI and near the drive flank surface, while ductile failure surfaces, including wide \"tidemarks\", were seen towards the tooth core. No cracks were found on the ring gear through visible inspection or with magnetic particle inspection. In Figure 10, the results from Sample \(A_{H}\) are presented, showing the colorplot and the trend of TE. It can be seen that immediately after the learning period, only the 22.82 nd order shows up clearly, and some activity at the 2.63 rd order and above the 25 th order can be seen. These contribute only to a slight change of the trend. At approx. 23% of the lifetime of the sample, the testing was interrupted for contact pattern measurement and a new position of the samples was set up. This caused a moderate increase in the trend and some orders are also visible in the colorplot from this point. Otherwise, the trend and the colorplot stay stable until around 39% of the testing time, where a restarting of the test occurs and manifests as a peak in the spectrum and trend. From this point in time, some orders are observed in the colorplot that were not visible before, such as the 13.75 th and 26.33 rd orders. After a stop and restart at approx. 48% of the testing time, the trend increases linearly with slightly changing gradients until around 90% of the lifetime. At this point, a rapid increase in the trend starts, caused by the following orders (exemplary selected orders): 7.03 rd, 11.12 nd, 16.97 th, 19.01 st, 23.99 th, and 24.86 th. The orders between the 11.12 nd and the 19.01 st are smeared over, so it is not possible to find single orders contributing to the change in the trend in this area of the plot. After the rapid increase, the sample fails with a fatigue breakage removing one pinion tooth completely. The visual inspection shows that all other pinion teeth are cracked in their roots. Figure 11 depicts the colorplot and the trend of \(M_{Dr}\). The development of the trend is very similar to that of the TE. The colorplot is generally also similar to the results with TE. The stop at 23% of the testing time and adjustment of the contact pattern is visible here as well, just like the restart at around 39%. The exponential increase in the trend also starts at approx. 90% of the testing time. The following list shows some of the orders causing a change in the trend: 7.9 th, 12.29 th, 16.97 th 26.62 nd, 43 rd, and 54.7 th. Figure 10: Colorplot and trend of TE of Sample \(A_{H}\). The results of the accelerometer, named IEPE1 (ring gear side accelerometer, radially oriented), are presented in Figure 12. The bright areas on the colorplot at the beginning of the measurement, before restart from approx. 13% until 23% (restart) and after 38% of the testing time, dominate both diagrams at first sight.