Klassifikation von Grübchenschäden an Zahnrädern mittels Vibrationsmessungen

1.1 Power gearbox (PGB) monitoring

Rolls-Royce demonstrated already the technology of a Power Gearbox (PGB), which is designed as a planetary gearbox and integrated into the novel Rolls-Royce engine family called UltraFan®. This UltraFan® engine is capable to provide power up to 75 megawatt [7].

To ensure a reliable functionality of the PGB, suitable sensors are needed to monitor the PGB condition during flight operations. Since vibration measurements offer a sensitive diagnostic indicator with a short response time to gearbox faults, vibration sensors are often used to monitor gearbox condition [11]. But the application of vibration sensors in the PGB will face extraordinary requirements. The sensors must cope with high frequency vibration levels caused by the gear mesh and lower frequency vibration levels caused by the rotating planets, when sensors are located close to the integrated PGB, see figure 1. In addition, the temperature of the oil used to cool and lubricate the gears can exceed 120^◦C, which limits the operating time when using active electronics.

Fig. 1

Planetary gearbox and sensor.

In addition to failure modes such as gear wear or gear tooth cracks, macro-pitting damage can also occur on the tooth flanks of the gears. A macro-pitting damage is characterized by shell-shaped triangular breakouts. Since this failure mode can lead to potentially destructive subsequent damage, great attention is paid to early failure detection of pitting to avoid unplanned engine shutdowns and expensive gear replacements.

1.2 Diagnosis of macropitting

There are already various studies that have investigated and discussed the possibilities of detecting gear pitting damage during operation. Tan [8] investigated various measurement techniques and concluded that the acoustic emission (AE) measurement method is suitable for early detection of pitting because a high correlation between AE amplitude and the pitting fracture zone was observed. Medina [6] performed measurements on a spur gear with artificially induced pitting damage. A deep learning technique based on a long short-term memory network (LSTM) was applied and by means of this method nine degrees of pitting damage could be classified.

In many publications, pitting damage on the tooth flank is artificially induced and the actual pitting progress is rarely captured as an additional pitting size parameter to evaluate diagnostic methods. Therefore, in this contribution natural pitting was provoked on a standardized back-to-back (B2B) test rig and the pitting development was additionally visually captured during the load-capacity tests. Since pitting damage affects the stiffness of the teeth due to changes in the Hertzian contact zone, the vibrations of the gears are altered, which can be measured with accelerometers. On the other hand, cracks at the tooth surface zone lead to excitation of elastic waves in the material, which can be detected with acoustic emission (AE) sensors [8]. Therefore, in this work both sensor technologies are used for pitting detection.

Data fusion & analysis

Before the feature extraction step is applied, the vibration data (accelerometer and AE sensor data) have to be preprocessed using different filtering methods. The data of the incremental encoder are fused with the data of the accelerometer and the AE sensor to enable the calculation of the order spectrum using a fast Fourier transform in the step vibration analysis. Further analyses such as wavelet analysis are performed to prepare the data for feature extraction.

Feature extraction

In the feature extraction step, statistical parameters of all sensors are first calculated from the four central moments of a probability distribution: mean, variance, skewness and kurtosis. Afterwards sensor-dependent features in the time domain, order domain and time-order domain are determined for each sensor.

Since pitting is expected to occur as locally distributed tooth flank damage, this stimulates an additional oscillation in the shaft order. This in turn leads to sidebands in the accelerometer signal of order one around the tooth mesh order and its harmonics, which is calculated from the product of the shaft rotation order and the number of teeth of the gear mounted on the shaft [5]. Therefore the magnitudes of the mentioned sidebands are extracted from the accelerometers order spectrum and normalized to the magnitudes of the gear mesh order and saved as features. In addition, a cepstrum analysis is performed to extract a feature from the quefrency region corresponding to the sidebands excited by pitting. Furthermore the residual signal is calculated by removing the shaft harmonics and gear mesh order and harmonics, and then various indicators such as FM0, FM4 are extracted from the residual signal. For more information see [12].

In addition, the RMS value of a high-pass filtered AE signal with a cut-off frequency at 20 kHz is extracted from the AE sensor. Furthermore, the magnitudes of the shaft orders of the input shaft and the output shaft and their harmonics are extracted from the order spectrum of the incremental encoder signal and used as features.

DOP calculation & labeling

To evaluate the extracted features and the classification results, the tooth flank images from the VRD are processed and the values DOP_k and DOP_G are calculated. By setting a defined threshold value DOP_Th for one of these two values, the extracted sample features are labeled by dividing them into two classes:

1. Class No pitting: data samples with relative pitting surface < DOP_Th

2. Class Pitting: data samples with relative pitting surface ≥ DOP_Th

Linear discriminant analysis

The output of the feature extraction methods is a matrix of over one hundred features, with some of the features being correlated and the multivariate distribution of the classes does not provide optimal separability properties. The aim is to maximize the class separability of the extracted and labeled features, taking into account the interdependencies between the features to increase the classification accuracy of the classifier. The class separability criterion is defined as the ratio of the variance of the class mixture mean (between-class scatter) to the variance of samples around their respective class mean (within-class scatter) [4]. The criterion is maximized by applying a principal component analysis (PCA) to the covariance matrix of the within-class scatter, followed by a whitening of the diagonal entries of the covariance matrix and a PCA to the covariance matrix of the between-class scatter in order to maximize the distance between classes in the feature space.

SVM classification

The labeled and transformed feature space is forwarded to a support-vector machine (SVM). Using a training data set, the SVM constructs a hyperplane in a highdimensional subspace with the largest margin separating the two labeled feature classes. An SVM is used as a classifier because its high generalization capability makes it very effective in real applications. They have a high computational efficiency because their classification decision is based on only a few trained support vectors. Therefore this classifier can be used for real applications in the aviation industry, e.g. in a condition monitoring system of a PGB.

5.1 Load-capacity test results

Two test runs were carried out with two completely new test gearsets (Test Gear I & Test Gear II) with one test pinion and one test gear per set. Since pitting occurred predominantly on one tooth of the test pinions, the DOP_k value was used to label the data samples.

The first test run with Test Gear I had a test duration of 310 hours (55.8·10⁶ L.C.) and contains a total of 1104 data samples. The most significant pitting occurred on the 8^th tooth of test pinion with a DOP₈ = 3.3 %, see upper picture of figure 6. The second test run with Test Gear II had a test duration of 410 hours (73.8·10⁶ L.C.) and contains a total of 1371 data samples. The most significant pitting occurred on the 10^th tooth of test pinion with a DOP₁₀ = 7.5 %, see upper picture of figure 7.

Fig. 6

Test results of Test Gear I used for SVM training.

Fig. 7

Classification results using data samples from Test Gear II.

5.2 SVM training

The bottom picture of figure 6 shows the DOP₈ pitting curve (blue) and an AE feature (red) for the first test run with Test Gear I. The AE feature is derived from the normalized high-frequency energy, for which the AE signal was high-pass filtered and then the RMS value of the filtered signal was calculated. The feature values show a high correlation with the DOP₈ curve. This test run was used for training the SVM classifier and the DOP_Th value was set to 0.7 % for data labeling.

5.3 Classification results

The results from the second test run Test Gear II are plotted in figure 7 in a comparative manner like for the first test run and show that pitting occurred later on the concerned tooth flank than in the first test and lead to a higher slope of the pitting surface during the test.

The DOP_Th = 0.7 % value is marked by a dashed line and acts as a comparable pitting severity value between the two test runs. The decisions of the SVM classifier between both classes (Pitting & No pitting) are shown in the bottom picture of figure 7. The results indicate that in the range before 34·10⁶ L.C. and after 60·10⁶ L.C. the classifier has the best accuracy. Many misclassifications (false positives) occur mainly in the range between 45·10⁶ L.C. and 60·10⁶ L.C.. It appears that the pitting damage in the second test run already at a lower DOP₁₀ value leads to typical patterns in feature space on which the SVM classifier was trained to classify the data as pitting damage. One reason of the incorrect classifications of the SVM classifier in this range could be that the set DOP threshold value DOP_Th cannot easily be compared between the two test runs. However, this only leads to false positive decisions and would in this case even allow earlier detection of pitting damage due to a higher pitting sensitive of the SVM.

Figure 8 shows the confusion matrix, precision and recall and the F₁-score [1], which allows an evaluation of the classifier. The results show that pitting with a pitting surface of more than 0.23 % could be correctly classified and no false negative results occurred. This means that with a pitting surface greater than 0.23 % the classifier has for the given test data a very high accuracy. The total F₁-score has a low value, but this may be a reason for the not optimal DOP_Th value chosen for the labeling of the classified data samples from Test Gear II.

Fig. 8

Confusion matrix and classifier evaluation results.