# Evaluation of a Novel Condition Indicator with Comparative Application to Hypoid Gear Failures
## 4 Evaluation of Condition Indicators  
The results of the damage detection were evaluated for two exemplar samples. An overview of the samples, with the applied load and damage, can be found in Table 3. The speed of the test bed was the same for all the samples, \(N_{Dr}\), the speed of the pinion gear was 291 RPM, and the speed of the ring gear, was the same, with a ratio of \(\frac{42}{13},89.76\) RPM. The results shown as colorplots are scaled to the pinion speed, so the 1 st order is equal to the rotation frequency of the pinion gear and the 13 th order with the meshing frequency. The order scale is the ordinate of the colorplots. It was decided to present the \(S_{diff}^{rel}(i)\) on the colorplots (third dimension, colour) in order to see the influence of weaker frequency bands as well. The relative spectral difference is dimensionless and represents the relative difference to the learned value of each bin (e.g., 1.5 = 1.5 \(\times\) more than learned). Figure 8: **Upper diagram**: Raw torque signal in % of rated torque vs. time in seconds. **Lower diagram**: TE signal in degree vs. time in seconds. Figure 9: High-pass filtered transmission error signals in degree vs. time in seconds. **Upper diagram**: filtered with ring gear frequency. **Lower diagram**: filtered with pinion gear frequency. The abscissas of the colorplot and the trend diagram below, shows the total elapsed testing time from the start until breakage in percentage. The trend line is the \(RSD_{abs}\) of the upper colorplot and it shows dimensionless the sum of the relative spectral difference. In other words, the sum of the changes of all bins in the spectrum. The learning period was varied widely and the results showed very low sensitivity. The selected learning length of 870 s corresponds to approx. 100 hunting tooth cycles (the period of one hunting tooth at the given speed is 8.66 s ) or 55,000 meshing cycles. The following representation of the results shows pinion tooth bending fatigue breakage for Sample \(A_{H}\) and Sample \(B_{H}\). In the description of the results the observed orders are defined at the discrete bins of the spectrum; hence, the numbers of the orders are not round numbers. The choice was made to present the results in this way to emphasize the discrete resolution of the analysis and not to give the false impression of orders laying exactly at the characteristic frequencies of components. The only exceptions to this are a few cases where several harmonics of a gear are dominant, here the integer orders are listed to keep the description compact. In order to offer an overview in the assessment of the results, only a list of the most significant orders is given to help the interpretation of the diagrams. The purpose of the list is to show if the same orders can be systematically recognized for a certain failure mode. The time indications are given as a percentage of the testing time. The start and end of the learning phase and the testing stops are indicated with vertical lines in the trends (\(RSD_{abs}\)) with the respective colors: magenta, green and gray. Additionally, indicators were also calculated for the TE spectra. The CIs (sideband ratio (SBR) and sideband index (SBI)) can be calculated for both gears, as the sidebands of the pinion and ring gear are spaced differently from the meshing frequency. This implies the chance of separating the damages on the gears; hence, the indicators have been calculated for the ring gear and pinion gear. A further objective of the approach using the \(S_{diff}^{rel}(i)\) spectra as the input for the CIs, was to see if the CIs preform better with pre-processed and filtered information while also assessing if any advantage can be generated compared to the manual assessment of the dominant orders, also in terms of separating the damaged gear. As many spectral lines show increased activity on the colorplots, a manual assessment of the spectrum can be difficult and an automated approach may have benefits.