Kenneth P. Maynard Applied Research Laboratory, Pennsylvania State University, University Park, PA 16804

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1 Maynard, K. P.; Interstitial l Processi ing: The Appl licati ion of Noi ise Processi ing to Gear Faul lt Detection, P rroceedi ings off tthe IIntterrnatti ional l Conferrence on Condi itti ion Moni ittorri ing,, Uni iverrsi itty off W al les Swansea,, UK,, 2th -- 6th Aprri il l 999, pp Interstitial Processing: The Application of Noise Processing to Gear Fault Detection Kenneth P. Maynard Applied Research Laboratory, Pennsylvania State University, University Park, PA 684 Abstract: The availability of high fidelity data associated with fault development in a gear box has been facilitated by the development of the Mechanical Diagnostics Test Bed, in which off-theshelf industrial gearboxes are run to failure. This has created a unique opportunity to develop and tune diagnostic algorithms aimed at the region of transition-to-failure, rather than at the failure itself, as has been done previously for data from gearboxes with seeded faults. Such a focus may provide earlier and better data to fuel prognostic accurate prognostic models. Several promising diagnostic methods have emerged, one of which is the processing of the interstitial noise, e. g., the noise floor data in the region between higher orders of the gear mesh frequency. Three features were identified in this region: interstitial kurtosis, interstitial envelope detection, and interstitial RMS. By careful selection of the analysis band, the kurtosis for a fault - free gearbox will approach 3. (Gaussian noise). Thus, changes in kurtosis can be an excellent indicator of a developing fault. Similarly, envelope detection of the band-pass filtered data yields spectral data which can facilitate early detection of a gear-tooth fault by detecting low level, broad band envelopes associated with tooth defects. Finally, the filtered RMS acceleration data yields a steady and consistent measure of damage progression. The results of the interstitial processing of data for a typical transitional (from good to failed) test are presented, and the diagnostic and prognostic merit of these results are compared to more traditional indicators. Key Words: Condition-Based Maintenance; Health and Usage Monitoring Systems; HUMS; Prognostics. Background: Various high-frequency techniques have been used for gear fault detection for some years. Enveloping has been used extensively for the detection of rolling contact bearing faults in rotating machinery., 2 High-pass filtering prior to enveloping has often been used to enhance the ability of the envelope detection techniques to identify faults in rolling contact bearings. Bandpass filtering has also been used for bearing diagnostics in systems with significant mechanical energy in higher frequency bands, such as geared systems. 3 Analogous filtering is used in some of the kurtosis -based gear figures of merit, such as NA4 4 and FM4 5. Transitional Gear Failure Data : The test platform used to generate the transitional data was the Mechanical Diagnostics Test Bed (MDTB) (see Figure ). 6 This motor-driven platform

2 employs two digital vector drive motor motors: a 3 HP drive motor, and a 75 HP load (absorption) motor. The MDTB has been used to date to run commercial single-reduction gearboxes to failure by loading by a factor of two or three over the manufacturer s rated load. Most of the failures to date involve gear tooth failures on the output gear. Figure : Mechanical Diagnostics Test Bed facility located at the Pennsylvania State University Applied Research Laboratory The overall test plan and operation of the MDTB are detailed in Reference 6. Basically, the MDTB is operated at normal, rated loading conditions for four days as a break- Then, the loading is increased by a factor of two or three, and the gearbox is operated at that level until preset vibration levels have been exceeded. For all the tests, these levels were observed after significant damage to the gearbox had occurred. Most of the damage was associated with gear tooth fracture, but there have been several shaft failures as well. The Signal Processing Techniques : The processing techniques are designed to isolate a region or regions in the gearbox acceleration spectra which are relatively free from the periodic signals associated with ge ar meshing and its sidebands. This allows the identification of enveloping signals and the use of kurtosis for impact detection in a quiet region of the spectrum, where the acceleration distribution approaches Gaussian. The process is shown schematically in Figure 2. Accelerometer Data Bandpass Filter Between Higher GMF 2 3 Kurtosis RMS Rectify Lowpass Filter DFT Analysis Peak Search Figure 2: Schematic of signal processing method The bandpass filter employed was a forward and reverse FIR (finite-duration impulse response) filter using a Blackman window and 5 coefficients. The lowpass filter is a 25 pole Butterworth 2

3 filter. The most obvious area which would have Gaussian distribution is at or near the noise floor of the data. The assumption is that when impact-like events occur which are associated with gear tooth fracture, the broad-band effects will be evident in the bandpass region. After some experimentation with the data, it was found that the region between the third and fourth multiple of the gear mesh frequency produced good results. Figure 3 shows typical spectra of the raw and bandpass filtered data. Figure 3: Typical spectra of raw and filtered data Kurtosis: Kurtosis is the fourth moment of a distribution (variance being the second and skewness the third), and is defined by: k = N n= ( µ ) y n 2 2 ( σ ) 4 (Eq. ) Where, yn = data value at point n, µ = the mean of the data σ 2 = variance of the data N = total number of data points Kurtosis provides a measure of the size of the tails of a distribution, or the peakedness of the data. One significant advantage of using a kurtosis-based figure is the fact that, for a Gaussian (or normal) distribution, Equation may be shown to equal 3. (for a sine wave, k=.5, for a square wave, k=.). Thus, if one could find a region in which the signal is Gaussian when there is no mechanical fault, but non-gaussian when there is a fault, we could have a figure of merit 3

4 which does not require the establishment of a baseline, i. e., one could know whether there is a fault without knowing the details of history of the machine. Figure 4 shows the histograms of normal (break-in) MDTB data and data at the point of highest kurtosis in a run. Note that Figure 4b shows the broad tails of the high kurtosis data Data Set 36 (k=3.7) Data Set 37 (k=22.39) Data Set 36 (k=3.7) Data Set 37 (k=22.39) Count 6 Coun Standard Deviations Standard Deviations Figure 4a: Full distribution Figure 4b: Re -scaled to show tails Figure 4: Sample histograms of gearbox accelerometer data Figure 5 is the more intuitive plot of the product σi 4 Mi, where σi is the standard deviation value of bin n and Mi is the number of samples in i th bin (of I total) of the histogram. Now, kurtosis becomes simply: k = I 4 σ i M i (Eq. 2) i= The figure dramatically demonstrates the effects of the quartic weighting of the distribution tails Kurtosis Contribution, σ 4 M Data Set 36 (k=3.7) Data Set 37 (k=22.39) Standard Deviation σ Figure 5: Kurtosis contribution 4

5 Enveloping: Envelope detection, or asynchronous demodulation 7, of a waveform may be used to identify low-frequency impact events which modulate high frequency data. The envelope of the bandpass filtered wave form is extracted by first rectifying, then lowpass filtering the data. The resulting waveform is then transformed using a digital Fourier transform (DFT). Finally, the resulting spectrum is searched for peaks near gear shaft speed frequencies, and the values at these peaks are recorded. RMS: The root mean square (RMS) of the acceleration after bandpass filtering was also found to be a credible indicator of gear tooth damage. The RMS is calculated by: RMS= N 2 y n n= (Eq. 3) Results: Interstitial kurtosis, envelope spectrum values, and acceleration RMS were found to be good indicators of imminent damage for all runs in which gear tooth fracture occurred. During the early runs, damage assessment was performed only at the end of the run, so that the actual time of tooth fracture could only be surmised from the data. However, in the latest runs, periodic optical inspection via borescope has been introduced, so that we have a much better correlation. In this paper, only the results from one of the runs (Run 4) with borescopic inspection will be reviewed. Kurtosis: Figure 6 and Figure 7 show the kurtosis as a function of time during the run. Figure 6 includes the thirty-six hour break-in period to show the stability of the kurtosis value (very near 3) before and after the increased loading. 2 Kurtosis /5/98 3/5/98 3/6/98 3/6/98 3/7/98 3/7/98 3/8/98 3/8/98 3/2/98 5

6 Figure 6: Interstitial kurtosis as a function of time over the entire test (Run 4) Figure 7 shows the kurtosis values during the period of three times rated load. Periodic borescopic inspection revealed no damage at 2: AM on March 2, 998. However, except for accelerometer 5, kurtosis already indicates a significant change in the distribution before the damage is visible. At 3: AM, the first visible evidence of damage was noted in the borescopic photographs: one tooth was broken and one showed signs of cracking. By 5: AM, the second tooth had broken off, and by 8:5 AM, there were 8-9 broken teeth. Note that kurtosis maximized at about 4: AM, implying that kurtosis, although an excellent indicator of the onset of tooth impact, may not always be a good measure of the extent of the damage. Barkov and Barkova noted that, for rolling contact bearings, peaks may rise more slowly and may even decrease as impact producing discontinuities are worn away. 8 2 Kurtosis : One broken 2: No visible damage 5: Two broken teeth 3 4: 6: 8: 2 22: 2: 8:5 am: 8 teeth missing 4: 6: 8: Figure 7: Interstitial kurtosis as a function of time while loaded at 3X rated load Envelope: Figure 8 and Figure 9 show the normalized amplitude of the envelope spectral peak at the output gear shaft speed. Note that the parameter is best viewed using logarithmic scaling due to the significant increase in its value. Figure 8 shows that there is about an order of magnitude increase in the amplitude when the load is increased to three times rated load. 6

7 Normalized Amplitude /5/98 3/5/98 3/6/98 3/6/98 3/7/98 3/7/98 3/8/98 3/8/98 3/2/98 Figure 8: Interstitial enveloping as a function of time over the entire test (Run 4) Figure 9 shows the normalized values of the spectral peak during the loading at 3X rated load only. As seen in the figure, except for accelerometer 5, there is about an order of magnitude increase in the amplitude just prior to the onset of visible damage, which occurred between 2: AM and 3: AM on March 2, 998. The value of the parameter continued to rise as the damage increased.. 3: AM:One broken Normalized Amplitude.. 2: AM: No visible damage 5: AM: Two broken teeth.. 4: 6: 8: 2 22: 2: 8:5 AM: 8 teeth missing 4: 6: 8: Figure 9: Interstitial enveloping as a function of time while loaded at 3X rated load RMS: Figure and Figure show similar plots of the RMS acceleration after bandpass filtering. Figure shows that there is about a factor of two increase due to the increased loading from rated load to three times rated load. 7

8 Normalized RMS /5/98 3/5/98 3/6/98 3/6/98 3/7/98 3/7/98 3/8/98 3/8/98 3/2/98 Figure : Interstitial RMS as a function of time over the entire test (Run 4) Figure shows the RMS acceleration after increasing load to 3X rated load. As seen in the figure, except for accelerometer 5, there is about factor of two increase in the amplitude just prior to the onset of damage, which occurred between 2: AM and 3: AM on March 2, 998. The value of the parameter continued to rise as the damage increased : AM: Two broken teeth Normalized RMS : AM: One broken 2: AM: No visible damage. 4: 6: 8: 2 22: 2: 8:5 AM: 8 teeth missing 4: 6: 8: Figure : Interstitial RMS as a function of time while loaded at 3X rated load Comparisons: The interstitial results for a single accelerometer () are compared with the more traditional highpass filtering (3 Hz and 5 Hz) results in Figures 2, 3 and 4. For all of the three parameters, the interstitial results showed clear indications before there was any visible damage. The parameters obtained after highpass filtering did show evidence of 8

9 damage after the gear tooth cracking was visible. However, the interstitial parameters are better prognostic indicators and are more robust. 2 Kurtosis Hz Highpass 5 Hz Highpass Bandpass 3: AM: One broken 5: AM: Two broken teeth 8:5 AM: 8 teeth missing 6 2: AM: No visible damage 3 4: 6: 8: 2 22: 2: 4: 6: 8: Figure 2: Comparison of kurtosis using highpass filtering (3 Hz and 5 Hz) and interstitial filtering. 3 Hz Highpass 5 Hz Highpass Bandpass 3: AM:One broken Normalized Amplitude.. 2: AM: No visible damage 5: AM: Two broken teeth. 8:5 AM: 8 teeth missing. 4: 6: 8: 2 22: 2: 4: 6: 8: 9

10 Figure 3: Comparison of enveloping using highpass filtering (3 Hz and 5 Hz) and interstitial filtering Hz Highpass 5 Hz Highpass Bandpass 2: AM: No visible damage Normalized RMS : AM:One broken 5: AM: Two broken teeth.2. 4: 6: 8: 2 22: 2: 8:5 AM: 8 teeth missing 4: 6: 8: Figure 4: Comparison of RMS using highpass filtering (3 Hz and 5 Hz) and interstitial filtering Conclusions: Interstitial preprocessing by bandpass filtering between the third and fourth multiples of gear mesh frequency greatly enhance the ability of kurtosis, envelope spectrum, and RMS indicators for the diagnosis and prognosis of gear tooth faults resulting in gear tooth fracture. Table summarizes the subjective effectiveness of these parameters. Table : Summary of interstitial parameter effectiveness Able to clearly distinguish between load change and imminent tooth damage Able to indicate imminent damage during transition to failure (prior to tooth cracking visible via borescope) Able to provide some indication of the extent of the gear tooth damage Interstitial Kurtosis Interstitial Envelope Spectrum Interstitial RMS Yes No No Yes Yes Yes No Yes Yes Acknowledgment : This work was supported by the Multidisciplinary University Research Initiative for Integrated Predictive Diagnostics (Contract Number N ) sponsored by the Office of Naval Research. Thanks to Derek Lang, Carl Byington, Yat Pui Shiu, and Michael Van Dyke at PSU ARL for their insight and assistance.

11 References:. P.D.McFadden and J.D.Smith, The vibration monitoring of rolling element bearings by the high-frequency resonance technique - a review, 984 Tribology International 7(), A. G. Ray, Monitoring Rolling Contact Bearings Under Adverse Conditi International Conference of Vibrations in rotating Machinery, Institution of Mechanical Engineers, Cambridge, -4 September 98, A. Y. Azovtsev, A. N. Barkov, and D. L. Carter, "Improving The Accuracy of Rolling Element Bearing Condition Assessment", presented at the 2th annual meeting of the Vibration Institute. 4. Stewart, R. M., Some Useful Data Analysis Techniques for Gearbox Diagnostics, Stewart Hughes Ltd., pp , Zakrajsek, J. J., D. P. Tawnsend, and H. J. Decker, An Analysis of Gear Fault Detection Methods as Applied to Pitting Fatigue Failure Data, Proceedings of the 47th Meeting of the Mechanical Failure Prevention Group, Virginia Beach, VA, April 3-5, Byington, C. S., and J. Kozlowski, Mechanical Diagnostic Test Bed, Proceedings of the 5st Meeting of the Society for Machinery Failure Prevention Technologies, April, Oppenheim, A. V., et al, Signals and Systems, Prentice-Hall, 983, p. 455ff. 8. Barkov, a. and N. Barkova, Condition Assessment and Life Prediction of Rolling Element Bearings Part, Sound and Vibration, June 995, pp. -3.