4.1 Baseline Acoustic Signatures
To confirm that the acoustic measurements contain sufficient information about dynamics of the gears, the spectra of the acoustic signals were compared with that of the vibration signals. Figure 4 presents a typical comparison result at the early stage of the operation when the running-in period of around 325 h is completed. As seen in Figure 4, the acoustic spectra display more components, including the mesh frequencies of \({f}_{m1},{f}_{m2},{f}_{m3},{f}_{m4}\) and their harmonics and sidebands with significant amplitudes. This shows consistency with the vibration spectra. Therefore, it is proven that the acoustic signals measured in such a remote way are adequate and suitable for the condition monitoring of the gearboxes. Besides, because of the distinctiveness of these mesh related components it is a more reliable technique for diagnosing and tracking gear mesh conditions.
There also exist various inevitable noises, such as background noises, bearing and motor acoustic interferences, this simple spectrum analysis usually results in unsteady and unreliable results. Typically, spectral amplitudes will exhibit high fluctuations due to the contribution of additive stationary noises and the spectral leakages of other irrelevant significant components at, for example, 100 Hz, 550 Hz and 626 Hz which mostly originate from the AC motors, as highlighted by the red text in Figure 4. Moreover, the spectral amplitudes of interest at mesh and sideband frequencies can be also affected by nonstationary acoustic interruptions including transient operations of nearby machines and other activities in the manufacturing workshop. Therefore, it is necessary to use more advanced signal processing method such as MSB to attenuate such noises and obtain steady and reliable diagnostic features.
4.2 Diagnostic Features
To suppress the noise in acoustic signals, the MSB analysis was applied to the acoustic signal and yielded typical MSB results as shown by 3D mesh graphs of Figure 5. Both MSB magnitude and coherence cover the low frequency range including several mesh and shaft frequencies of interest. They were obtained by applying Eq. (3) to overlapped short signal segments and separating the long acoustic signals and averaging the complex MSBs of different segments. In total, 50 averages were achieved, at which the MSB coherence averaged for the bi-frequency regions (0‒60 Hz, 90‒3000 Hz) of interests becomes stable, indicating that the average is sufficiently good.
It can be seen from Figure 5(a) that MSB magnitude shows a large number of MSB peaks on the \({f}_{m}\) − \({ f}_{r}\) bi-frequency plane. The most significant peaks do not appear at mesh frequencies, but at \({f}_{m}\) = 626 Hz, which is mainly from the AC motor as it is significantly coupled with motor speed of \({f}_{r1}\) = 17.3 Hz and \(2{f}_{r1}\) = 34.5 Hz. This coupling can be more evidently observed by MSB coherence of Figure 5(b), in which the coherence peaks are appearing at \({f}_{r1}\) = 17.3 Hz and \(2{f}_{r1}\) = 34.5 Hz across nearly all \({f}_{m}\) components. Since these components are less related to gear mesh process, they need to be excluded for the focus on gear transmission monitoring. Nevertheless, MSB magnitudes exhibit many distinctive peaks at the mesh and shaft frequencies that are associated with gear transmission dynamics.
To locate the gear components more accurately, a contour plot of Figure 5(b) is presented in Figure 6. It shows that all the acoustic components can be separable as the MSB-coh peaks represented by dots are distinguishable in the \({f}_{m}{-f}_{r}\) bifrequency plane. For all gear transmissions of interest, several MSB peaks can be observable at the low speed mesh frequencies such as \({f}_{m2}\) = 200.01 Hz and its three harmonics at 400.02 Hz, 600.03 Hz and 800.04 Hz. Particularly, the peaks at bifrequencies of (400.02, 3.39) Hz and (400.02, 6.78) Hz indicate a clear coupling between \({f}_{m2}\) and \({f}_{r3}\) as they are all associated with the low-speed stage of GB1. For the gear rotating at \({f}_{r2}\), there is a peak at (400.01, 15.4) Hz. These coupling relations can be easily understood by the gear arrangement shown in Figure 2. Moreover, these observable peaks prove that the acoustic signals contain rich information about gear dynamics. For this baseline operation, it indicates that these gears have inherent imperfection such as pitch error and eccentricity. In the same way it can also identify the coupling peaks at bifrequencies (\({f}_{m1,}, {f}_{r1,}\)) and (\({f}_{m1,}, {2f}_{r1,}\)), (\({f}_{m1,}, {1f}_{r2,}\)) and (\({f}_{m1,}, {2f}_{r2,}\)) which represent the dynamic characteristics of the inherent imperfect gears for the high-speed stage of GB1.
Based on the characteristics of the peaks and the fact that these peaks will change and more peaks relating to gear transmissions will emerge as gear engagements become poor with operation service time, a gear-monitoring indicator is defined by combining the MSB magnitude peaks at gear mesh frequency and its first few harmonics according to:
$$GMSB\left({f}_{m}\right)={\sum }_{n=1}^{3}{\sum }_{k=1}^{3}\left|{B}_{MS}\left({nf}_{m},k{f}_{rp}\right)\right|/\overline{\left|{B}_{MS}\left({nf}_{m},k{f}_{rp}\right)\right|}+{\sum}_{n=1}^{3}{\sum }_{k=1}^{3}\left|{B}_{MS}\left({nf}_{m},k{f}_{rg}\right)\right|/{\overline{{\left|{B}_{MS}\left({nf}_{m},k{f}_{rg}\right)\right|}}},$$
(6)
where \({f}_{rp}\) is the frequency of pinion rotation, \({f}_{rg}\) is the frequency of gear, and \(k\) and \(n\) are the harmonic orders for the shaft and mesh frequencies respectively. This monitoring feature will capture the information with respect to uniform tooth defects, which often leads to increases in the amplitude of tooth meshing harmonics, and the amplitudes of meshing harmonic sidebands [8, 32]. And unlike previous features as demonstrated in Refs. [30, 31] using the motor current and vibration signals respectively, the proposed \(GMSB({f}_{m})\) is the average of a number of noise purified MSB peaks and thus, will be more stable and accurate for tracking the conditions of progressive gear deteriorations. In addition, the normalization factor \(\overline{\left|{B}_{MS} \left({nf}\!_{m},k{f}_{rx}\right)\right|}\) is calculated as the mean of a number of MSB peaks in baseline operation (the first 20 h of the testing). This ensures that MSB peaks with different amplitudes still produce the equal contributions when applying Eq. (6), and thus changes in all peaks can be highlighted.
4.3 Acoustic Trends and Diagnostics
In order to trace the gear health condition with operating time for the two gearboxes respectively, \(GMSB({f}_{m1},t)\) \(GMSB({f}_{m2},t)\), \(GMSB({f}_{m3},t)\), \(GMSB({f}_{m4},t)\) for the four sets of gears were calculated using the acoustic signals at different operating time \(t\) and then further combined according to:
$${GMSB}_{GB1}\left(t\right)=[GMSB\left({f}_{m1},t\right)+GMSB({f}_{m2},t)]/2,$$
(7)
$${GMSB}_{GB2}\left(t\right)=[GMSB\left({f}_{m3},t\right)+GMSB({f}_{m4},t)]/2,$$
(8)
Figure 7 presents two GMSB trends for the test course. It can be seen that both gearboxes endured gradual deteriorations with operating time, which is well consistent with theoretical predictions of inevitable operation deteriorations. Especially, at the late operating time just before 838 h, GB2 shows an approximately threefold increase in GMSB values with higher fluctuations. This indicates the gearbox may have a significant deterioration, thereby, the test course was stopped at 838 h to avoid any damages to the test facilities by further operation.
A further study of the two trends has observed that GB2 exhibits a higher increase in GMSB values, which can be explained by the higher baseline peaks (BL2 = 1.67 (mPa)2 while BL1 = 0.941 (mPa)2). This means that GB2 probably has higher gear errors which results in higher deteriorating rates. This smaller baseline error also explains that GB1 exhibits more nonlinearity, and remains relatively stable for a longer period between 323 h to 626 h, indicating that GB1 is more load resistance and has longer lifetime.
To diagnose the source of the deterioration, GMSB trends for each mesh gear pair are presented in Figure 8. It can be clearly seen that the low speed stages for both gearboxes show significant deterioration as both trends show steady increase with time as shown in Figure 8(b) and (c). In particular, GB2 shows an approximated sixfold increase while GB1 shows an approximated threefold increase, indicating that the gears of GB2 at the low-speed stage is more severely deteriorated.
However, the gears at high-speed stages for both gearboxes show little changes during the operating course, as illustrated in Figure 8(a) and (d). This indicates that the engagement conditions of the high-speed gears are much less affected during the testing. By opening and inspecting both gearboxes after the tests were completed, it was found that the tooth surfaces of the low speed gears have clear wear and incipient pitting marks as illustrated by the images of Figure 9. However, the tooth surfaces of high-speed gears show minimal deterioration. This means that the low speed gears showed greater degradation as they are more prone to surface wear since the elastohydrodynamic (EHD) films are thinner under higher load and lower speed. Moreover, this inspection result fully confirms the monitoring and diagnostics achieved by the acoustic monitoring.
Based on the analysis made above, acoustic signals perform superbly in tracing the gradual wears of gears. In particular, the monitoring features combined by MSB peaks allow the gradual changes in gearbox deterioration to be highlighted.
4.4 Benchmark with Vibration Trends
By utilizing the same technique, GMSB monitoring trends for the vibration measures were obtained and shown in Figure 10. Similarly, the trends for both gearboxes exhibit a gradual increase with operating time. This shows that acoustic monitoring is consistent with vibration one. However, as can be seen from the general trend, they exhibit more nonlinearities with time. This is probably because that vibration signals are from a localized area of the gearbox housing, which are more prone to the influence of nonlinear transmission paths. Moreover, this localized vibration perception is probably less reflective of the global vibration responses from different vibration excitations. Comparatively, the sound superposition radiated from the vibrations of different gearbox parts and perceived by the acoustic microphones can better globally represent the overall dynamics of the gearbox condition.
This difference in sensing the dynamics of gearbox also causes the vibrations to have lower sensitivity to changes in gear deteriorations. As can be seen from Figure 10, there are only about tripling and doubling increase with respect to GB1 and GB2, which is far less sensitive to the change in gradual wear process. Furthermore, GB2 shows a lower increase or less variation even though the baseline vibration is higher, which is inconsistent with the dynamic effects that higher vibrations would cause a faster wear progression to the gears.