The ability to detect the onset of a gear-system failure via accelerometer measurements is of interest in a research environment as well as in gear systems deployed in the field. The goal in either case is to detect a failure as early as possible while simultaneously minimizing the risk of false shutdowns.

The accelerometer-based gear health monitoring system described herein was developed for use in a laboratory setting for monitoring power recirculating gear tests. In this environment, it is desirable to detect the early onset of failures so the primary failure mode as well as the time to failure can be accurately determined. Minimizing false shutdowns is also critical to maximizing rig uptime and testing efficiency.

The signal processing algorithm uses even-angle resampling along with time synchronous averaging to minimize the influence of vibration sources other than the gear mesh. In the case of hunting tooth ratio gearsets it is shown that it is possible to completely separate the damage response of each gear in the pair from a single accelerometer signal using these techniques. The average log ratio (ALR) algorithm is then employed to monitor the time synchronous averaged signals for the onset of damage. A summary of these signal processing concepts is given, along with an overview of system hardware, signal processing workflow, and sample data.

### 1 Introduction

The ability to detect the onset of a gear system failure via accelerometer measurements is of interest in a research environment as well as in gear systems deployed in the field. The goal in either case is to detect a failure as early as possible while simultaneously minimizing the risk of false shutdowns. This article outlines an accelerometer-based gear health monitoring system used in a laboratory setting for monitoring power recirculating gear tests.

This gear health monitoring system described here uses the average log ratio (ALR), which has been shown to be a sensitive metric for the detection of gear damage in prior work [1] [2] [3] [4] [5]. All previous efforts in evaluating the effectiveness of ALR have consisted of post-processing vibration data after testing had been completed. The system developed here enables real-time data processing and has successfully been used to detect the onset of a variety of failure modes while tests are underway. The first goal of this article is to provide an overview of the gear health monitoring system architecture and to illustrate how it has been used to monitor and shut down various types of gear tests when a failure is detected. Secondly, this article aims to provide a concise introduction to all of the signal processing techniques used, some of which have only been presented separately in the second author’s prior work.

### 2 Existing Work and Motivation

A vast amount of data processing techniques has been documented in literature related to detecting gear failures. For example, in Kundu et al.’s recent comprehensive review of the state-of-the-art in this area, more than 25 different condition indicators (CIs) are compared [6]. Some examples of common CIs used for gear health monitoring include RMS, Kurtosis, FM4, NA4, and crest factor. Other literature has focused on the performance of CIs in more specific cases based on failure mode, such as pitting [7] [8] [9] [10] and wear [11]. Other more application specific comparisons of CIs are also available, for example techniques commonly used in aerospace transmission diagnostics are documented in [12] [13] [14], while various metrics for detecting faults in planetary gearboxes are compared in [15]. In all of the works cited, a common theme is CIs tend to have strengths and weaknesses that depend on the application and type of failure to be detected. Bechhoefer et al propose the concept of a health indicator (HI), which is a mapping of several CIs into a common threshold value [16] [17]. This is shown to reduce the probability of false alarm and increase the sensitivity to fault detection. In any case, for a given application, it is desirable to use a CI that is simple, has a low probability of false alarm, and that is sensitive to detecting the onset of any type of failure that may be present.

The authors of this article frequently use gear health monitoring techniques in a laboratory setting in order to monitor various types of gear tests for the onset of failure. This capability allows test rigs to run unattended for long periods of time and provides the capability of automatic shutdown when gear damage is detected. The motivation for this work was to develop a system that could monitor various gear test types with one CI that was simple and robust. The ALR algorithm, which had been developed in prior work, was found here to be extremely useful in monitoring bending fatigue, pitting, scuffing, and loss of lubrication tests.

### 3 Test Rig Overview

The tests under consideration consist of a highly loaded gear pair subject to constant speed, using either constant or varying torque. Tests can take anywhere from several hours to more than a month running 24 hours a day to complete, so maximizing test rig uptime is critical. These tests are carried out on power recirculating test rigs; an example is shown in Figure 1. Torque is applied either statically through a moment arm and torque applicator disc as shown or can be varied on some test rigs dynamically through a servo-hydraulic torque applicator (not shown). In either case, a drive motor supplies power to the four-square loop, and tests are carried out until the desired failure mode is developed. It is advantageous to be able to detect the early onset of failures via accelerometer data so the primary failure mode as well as the time to failure can be accurately determined.

Accelerometers are mounted to the structure of each test box in the locations shown in Figure 1.

A tachometer signal on the motor shaft provides one pulse per shaft revolution, which is used in the signal processing workflow which follows. The signal processing hardware consists of a National Instruments (NI) chassis which is connected to a 2GHz Windows PC via Ethernet. The user interface, signal processing, and data storage are all handled in NI LabVIEW. An analog input card with a 51.2 kHz sampling rate is used to acquire both the accelerometer signals as well as the tachometer signal, while one output on a digital I/O card is utilized to interface with the variable frequency drive (VFD) on the test rig’s drive motor. This interface with the test rig’s VFD allows the gear health monitoring system to shut down the rig when a failure has been detected.

### 4 Frequency Domain Behavior of Meshing Gears

A brief overview of the frequency domain response of a meshing gear pair is outlined here in order to aid discussion of the signal processing techniques which follow. Additional details can be found in the references cited. The following examples, as well as the signal processing techniques employed, assume constant speed and constant loading over the time interval in which data is collected.

Static transmission error (STE) is the primary source of vibration caused by a meshing gear pair. The source of STE is the deviation of the loaded tooth working surfaces from perfect equi-spaced involute (conjugate) surfaces. STE consists of two components, the load dependent elastic deformation of the gear teeth, and the geometric deviations of the working surfaces from perfect equi-spaced involutes [18]. Sources of geometric deviations may include manufacturing errors as well as tooth damage. A generalized example of the frequency domain response of a meshing gear pair is shown in Figure 2. The response is shown in terms of rotational harmonic number (*n*) i.e. oscillations per revolution of the gear, rather than oscillations per unit time. The first rotational harmonic (*n* = 1) coincides with one oscillation per revolution of the gear. The first tooth meshing harmonic (*n* = *N*) corresponds to one oscillation per tooth meshing event, where *N* is the number of teeth on the gear. Several higher order tooth meshing harmonics are typically present at *n* = 2*N*, *n* = 3*N* etc.

If an otherwise perfect gear pair were to have exactly the same transmission error contribution from every meshing tooth pair, and the gear pair were operated at constant speed and constant loading, the only harmonics present would be the tooth meshing harmonics (A in Figure 2). The mean deviation from perfect equi-spaced conjugate contact of the elastically deformed tooth surfaces, averaged over all teeth on each gear is the source of the tooth meshing harmonics [18] (p.112).

Individual tooth-to-tooth variations from the mean elastically deformed tooth surface deviation are the sources of non-tooth-meshing-harmonic rotational harmonics under constant speed and constant loading [18] (p.113). Tooth-to-tooth variations in an otherwise undamaged gearset typically manifest themselves as low order rotational harmonics (B in Figure 2) and sidebands around the tooth meshing harmonics (C in Figure 2).

An example of the frequency domain response of an undamaged gearset is shown in Figure 3.

Any damage, aside from perfectly uniform wear on every tooth, will contribute to changes in the non- tooth-meshing-harmonic rotational harmonics [1] [18] [19]. For this reason, the rotational harmonics between the tooth meshing harmonics and their sidebands are of primary interest in damage detection. An example of the frequency domain response from the same gearset from Figure 3 after undergoing a bending fatigue (root fillet crack) failure is shown in Figure 4. The strong change in rotational harmonics between the tooth meshing harmonics is evident in this example.

### 5 Signal Processing Workflow

An overview of the signal processing workflow is shown in Figure 5. In summary, the raw vibration data is first resampled to be in terms of even angular rotation increments instead of even increments of time. Time synchronous averaging (TSA) is then used to compute an averaged signal over one rotation for each gear in the meshing pair. Depending on the gear ratio, the TSA process may be used to separate the damage response for each gear in the pair from a single accelerometer signal. TSA is also used to minimize the influence of vibration sources other than the gear mesh. A discrete Fourier transform is then used to examine the frequency domain behavior of the respective TSA signals. Finally, the ALR algorithm is used to quantify gear health based on analysis of the frequency domain data. Computed values of ALR are tracked over time and thresholds are used to determine if gear damage is detected.

Figure 5 also shows locations in the workflow where data is saved. First, one revolution of TSA data is saved for each gear after it is computed. Since several hundred revolutions of the gear of interest are averaged into one revolution of the TSA signal, saving data after the TSA process is complete conserves a large amount of disk space compared to saving the unprocessed time domain vibration data. For example, the TSA data from a test that ran for 50 hours and that gathered a sample of 44 kHz vibration data every 30 seconds from two accelerometers used only 250MB of disk space. After ALR is computed from the TSA data, the ALR response is also recorded for later evaluation. ALR post processing tools have been developed to allow more detailed analysis of the TSA data after test completion if desired.

#### 5.1 Even Angle Resampling

The vibration data is first resampled in order to obtain data points at evenly spaced angular intervals based on the available tachometer signal. As shown in Figure 6, the raw accelerometer and tachometer data is recorded at evenly spaced time intervals per the sample rate of the data acquisition system, which is not conducive to the TSA process that is performed next. The goal of the resampling process is to obtain data points that represent the same physical locations on the gear teeth over subsequent shaft revolutions. Figure 6 shows the data recorded on a small-time scale for clarity; however, in practice a 5- to 10-second “snapshot” of data is recorded every 10 to 30 seconds.

The resampling process is performed such that an integer number of samples per tooth are used to determine the resampling rate. In this manner the same resampled accelerometer signal can be used to compute the time synchronous average for either gear in the pair as is shown in the following section.

Using an integer number of samples per tooth ensures the beginning of every revolution of either gear in the pair will always begin on a discrete data point.

Where:

*N*^{(1)} = Number of teeth in Gear 1.

*N*^{(2)} = Number of teeth in Gear 2.

*i** _{s}* = Integer samples per tooth for resampling process.

An upper practical limit on the number of samples per tooth will depend on the available data sample rate and rotational speed; however, as a general guideline, 20-30 samples per tooth were used in this work and was found to be adequate to detect small amounts of damage; 10 samples per tooth have also been suggested in literature as a minimum value [20]. As an example, in a gear pair where Gear 1 has 41 teeth and Gear 2 has 49 teeth, suppose 30 samples per tooth are desired. The time domain signal for Gear 1 would be resampled to have 41*30 = 1,230 samples (evenly spaced in angular rotation) over each revolution of Gear 1. Likewise Gear 2 would have 47*30 = 1,410 evenly spaced samples over each rotation.

The resampling process uses the square wave from the tachometer signal to mark the beginning of each rotation of the gear on the tachometer signal shaft. Linear interpolation is used between each tachometer pulse to resample the time-based signal into increments of even angular rotation as shown in Figure 7.

Speed is assumed to be constant between each tachometer pulse. Although the response of the accelerometer data is unchanged, the resulting signal no longer uses time as the abscissa coordinate, but is now in terms of number of rotations of the gear of interest. Each accelerometer data point now represents a discrete angular position of the gear, and thus represents the location of a specific contact location on specific tooth working surfaces as shown in Figure 8. These contact locations will be consistent over subsequent shaft revolutions, within the bounds of uncertainty from variations in speed, sample rate, and tachometer pulse jitter. The resampled data in Figure 7 is shown over just a few revolutions for clarity; however, in practice, several hundred revolutions of data were recorded at each recording interval.

A useful implication of the resampling process is that subsequent Fourier analysis results will be in terms of cycles per revolution of the gear (rotational harmonics) instead of cycles per unit time. The value for number of gear rotations is computed separately for each gear in the mesh if the ratio is not 1:1; however, due to the previously chosen resampling rate, one rotation of each gear will always align with a discrete data point.

#### 5.2 Time Synchronous Averaging

The technique of time synchronous averaging (TSA) is then used to reduce or eliminate the presence of non-tooth meshing rotational harmonics from the mating gear in a gear pair [21] [20] [22]. The TSA process also reduces the influence of non-synchronous vibration excitations that might arise elsewhere in the system, such as other rotating shafts, pumps, bearings, etc. by a factor of 1/√*r* where *r* is the number of revolutions used in the TSA process [21].

For gear ratios that are not 1:1, the TSA process can be performed for each gear in the pair, such that the non-tooth-meshing-harmonic rotational harmonics can be monitored for damage independently on each gear. In the case of hunting tooth gear ratios, the non-tooth-meshing-harmonic rotational harmonics from the mating gear can be eliminated, and for non-hunting tooth ratios, the non-tooth-meshing-harmonic rotational harmonics from the mating gear can be minimized. [22] As was previously discussed, the non-tooth-meshing-harmonic rotational harmonics are the harmonics of primary interest when monitoring for gear tooth damage.

After the previous step of resampling, each accelerometer data point now represents a discrete angular position of the gear, and thus represents the location of a specific and repeatable roll angle and contact location on specific tooth working surfaces. The same angular positions (and thus the same contact locations) are represented by the interpolated data on each subsequent revolution. The TSA process averages data points representing the same contact location from multiple revolutions of the gear of interest, in order to produce an averaged signal for exactly one rotation of the gear of interest. As is shown in [22], averaging over a specific number of rotations of the gear of interest (Equations 2a and 2b) is required to minimize or eliminate the damage response from the mating gear. The value of *i** _{TSA}* will depend on the length of each recorded vibration data “snapshot”. Larger values of

*i*

*will incorporate more data into the average but will require longer samples of data at constant speed and constant loading.*

_{TSA}Where:

*i** _{TSA}* = Integer multiple for TSA process.

An example of the output of the TSA process for one gear in the mesh is shown in Figure 9. This represents an averaged response of the gear of interest over exactly one revolution, and each oscillation represents the response from a specific individual tooth. The gear used in the computation of the data in Figure 9 had 41 teeth, which corresponds to the 41 oscillations shown.

#### 5.2.1 TSA Behavior when Mating Gear to Gear of Interest is Damaged

A rigorous explanation of why the damage response from each gear in a hunting tooth ratio gear pair can be separated is developed in [22]. An intuitive explanation of this behavior is as follows: In the case of a gear pair with a hunting tooth ratio, after the specified number of rotations from Equations 2a and 2b, each tooth on the gear of interest will have mated with each tooth on the mating gear exactly *i** _{TSA}* times.

In an example where only one tooth on the mating gear is damaged, after the TSA process every undamaged tooth on the gear of interest will have mated with the damaged mating tooth exactly *i** _{TSA}* times. Although the meshing action of an undamaged tooth on the gear of interest with the damaged mating tooth will produce a change in transmission error and accelerometer response, this change will be incorporated into the averaged signal on every undamaged tooth of the gear of interest exactly the same number of times. Since the techniques employed here are based on monitoring differences in transmission error between teeth (by monitoring non-tooth-meshing-harmonic rotational harmonics), the damage response on the non-damaged gear of interest is not affected. The tooth meshing rotational harmonics of the gear of interest will be affected, however these are excluded from the ALR analysis.

Another way to visualize this behavior is that the transmission error and accelerometer response due to damage moves to different locations of angular rotation on each subsequent rotation of the gear of interest since the damage is on the mating gear, and the damaged tooth is “hunting” between all of the undamaged teeth on the gear of interest.

#### 5.2.2 TSA Behavior when Gear of Interest is Damaged

Following on the previous example, if the gear of interest in a hunting tooth ratio gear pair has exactly one damaged tooth, the change in transmission error due to the damage will remain in the same locations of angular rotation on every revolution averaged into the TSA signal. The change in transmission error from the damaged tooth will be incorporated into the TSA signal in the same location of angular rotation.

*N*^{(d)}*i** _{TSA}* times, where

*N*

^{(d)}is the number of teeth on the damaged gear of interest. This will result in a TSA signal in which the accelerometer response on the damaged tooth is significantly different from the other teeth on the gear of interest, since the other undamaged teeth on the gear of interest have only mated with other undamaged teeth on the mating gear.

#### 5.3 Discrete Fourier Transform

The TSA signal for each gear is then processed using a fast Fourier transform (FFT) to examine the content of each TSA signal in the frequency domain. No windowing function is needed, since the TSA signal represents exactly one revolution of the gear of interest and thus exactly one cycle of the fundamental rotational harmonic period. The end of the TSA signal marks the exact point where the signal would theoretically begin to repeat indefinitely (assuming constant speed, loading and tooth condition). The FFT analysis is repeated separately for the TSA signal of each gear in the pair. Figure 3 and Figure 4 show examples of the frequency domain data produced from this step.

#### 5.4 Average Log Ratio Overview

The average log ratio (ALR) algorithm is employed next to monitor for damage via analysis of the amplitudes of the rotational harmonics computed from Fourier analysis of the TSA signals. A detailed description of the ALR algorithm is provided in [1] and examples of its application are shown in [2], [4], [5] and [23]. It is defined as:

Where:

|*α** _{y}*(n)|

*= Amplitude of nth rotational harmonic, after potential damage.*

_{a}|*α** _{y}* (n)|

*= Amplitude of nth rotational harmonic, from baseline data before damage.*

_{b}When accelerometer measurements are used to monitor gear health, there is inevitably a structural path between the location of the meshing action of the gear teeth and the physical measurement location of the output of the accelerometer. Even when an accelerometer is mounted as closely as possible to the mesh, the vibration caused by the tooth meshing action must still travel through the body of the gear, shafts, bearings, mounting structures, etc., before the accelerometer can record it. This structural path introduces a transfer function that can attenuate the frequency domain response of the gear pair. A significant advantage of the ALR algorithm is by taking the ratios of rotational harmonic amplitudes, the effect of the transfer function between the gear mesh and accelerometer output measurement location is cancelled out, thus the resultant ratio is directly related to tooth damage. Furthermore, if rotational harmonics that may already have small amplitudes experience a comparably small change due to damage, the use of amplitude ratios allows these harmonics to contribute significantly to the overall average despite their relatively small amplitudes. [1] [3]

#### 5.5 Computing the Average Log Ratio

The ALR algorithm requires baseline vibration data in which the gear pair is known to be in an undamaged state. The rotational harmonic amplitudes of the TSA signal for each gear in the pair are computed in this undamaged state at a constant speed and constant torque. These rotational harmonic amplitudes are stored for later use as a baseline for comparison. An example of a spectrum of baseline rotational harmonic amplitudes |*α** _{y}* (n)|

*from an undamaged gear up to the fifth tooth meshing harmonic (*

_{b}*n*= 5

*N*) is shown in Figure 10a.

In a similar manner, vibration data is then recorded from the gear in an unknown state of damage, and the rotational harmonic amplitudes are computed from the TSA signals. This computation yields the “after potential damage” rotational harmonic amplitudes |*α** _{y}*(n)|

*. An example of a spectrum of rotational harmonics |*

_{a}*α*

*(n)|*

_{y}*from a gear which has undergone a bending fatigue failure is shown in Figure 10b.*

_{a}The log ratio loge[|*α** _{y}*(n)|

*/|*

_{a}*α*

*(n)|*

_{y}*] is then computed from the amplitude of each rotational harmonic after potential damage to before damage, yielding a log ratio spectrum as shown in Figure 10c. Positive log ratio values indicate that the rotational harmonic amplitude at the time under consideration has increased relative to the baseline, likewise negative values indicate a decrease. The baseline rotational harmonics |*

_{b}*α*

*(n)|*

_{y}*are taken from data where the gear is subject to similar speed as in the after potential damage data. The average log ratio (ALR) is then computed by taking an average of the absolute value of the log ratio spectrum values as shown in Figure 11. Averages are computed from the log ratios in windows that exclude the tooth meshing harmonics as well as applicable sidebands. [1] Figure 11a shows a log-ratio spectrum of an undamaged gear compared to the baseline, while Figure 11b shows the log-ratio spectrum of the same gear (also from Figure 10b), which has undergone a bending fatigue failure as compared to the baseline.*

_{b}Unless damage present on the teeth contributes exactly the same change in transmission error to every tooth, the damage will manifest itself as changes in the rotational harmonics between the tooth meshing harmonics. Increasing values of ALR on non-tooth-meshing harmonics signify changes (either increases or decreases) in these rotational harmonic amplitudes, thereby implying non-uniform changes on the tooth working surface(s). This change in the log-ratio values between tooth meshing harmonics on a damaged gear is evident in Figure 11b.

ALR may be computed as an average over several windows, for example from zero to the fifth tooth meshing harmonic (*n* = 0 to *n* = 5*N*). This type of overall average value will provide a general assessment of whether any type of damage is present. Alternately the ALR value of individual windows, for example *n* = 0 to *n* = *N*, *n* = *N* to *n* = 2*N*, etc., may be tracked separately in order to extract additional information about the type of damage and progression to failure [4] [5] [24]. In either case, the ALR value(s) are recorded for the particular data snapshot and their trends are tracked over time as shown in the following section.

### 6 Sample Data

Four sample data sets are shown here from tests that developed pitting, bending fatigue, scuffing, and catastrophic loss of lubrication failures. In all cases, one value of ALR was computed up to the fifth tooth meshing harmonic (*n* = 5*N*), excluding the tooth meshing harmonics and one sideband.

For comparison, RMS and FM4 were also computed from the same TSA signals used in the calculation of ALR. RMS was computed simply by taking the root-mean-square value of the time domain TSA signal. FM4 was calculated by first removing the tooth meshing harmonics, each closest sideband, and the first five low order harmonics from the frequency domain TSA signal. An inverse FFT was then used to go back to the time domain, and kurtosis was computed on this signal yielding FM4 [7] [23].

In all of the following figures, ALR is plotted on the same scale regardless of the test type. In all cases, an ALR threshold of 1.0 to 1.2 would be appropriate to set as failure criteria. RMS and FM4 both have scales and thresholds that vary much more significantly.

#### 6.1 Pitting (Hertzian Fatigue) Failure

Figure 12 shows an example of pitting damage on a highly loaded spur gear pair with a 1:1 ratio. This test was conducted at a constant torque and speed. The meshing teeth shown were the only teeth with pitting damage present when the test was stopped. Despite the fact that only one tooth on each gear pitted, resulting in a modest pit size relative to the total available tooth working surfaces, the ALR response (Figure 13) shows the clear onset and progression of damage. Since the gear ratio in this test was 1:1, it was not possible to differentiate between damage on each gear in the pair through time synchronous averaging.

Figure 13 also shows that FM4 did successfully detect the growth of the pit, however the behavior of FM4 before damage was present was somewhat less stable than ALR. RMS did not successfully detect the onset of pitting.

#### 6.2 Bending Fatigue Failure

Figure 14 shows an example of the ALR response from a bending fatigue failure on a very highly loaded hunting tooth ratio spur gear test. This test was conducted at a constant torque and speed. In this case, the hunting tooth ratio allows the calculation of the CI values for each gear in the pair. The ALR data for Gear 1 clearly shows the onset and progression of bending fatigue failure near the end of the test.

Although it could have been stopped earlier, the test was allowed to run until a single tooth on Gear 1 had broken off completely, which is represented by the plateau period in the Gear 1 ALR data in the last seven data points. The Gear 2 ALR data, which was computed from the same raw accelerometer data as the Gear 1 ALR data, shows that the damage response from the bending fatigue failure on Gear 1 was able to be completely separated from the ALR data for Gear 2. This was made possible by using time synchronous averaging over the specific number of revolutions described in [22]. It should be noted the progression to failure in this case was rapid due to the highly loaded nature of the test. Bending fatigue failures at more moderate loads have been found to progress more slowly with additional time between damage initiation and complete tooth breakage.

Figure 14 also shows that FM4 did successfully detect the onset of bending fatigue failure on Gear 1. The behavior of FM4 after the tooth was damaged, where ALR reached and remained at a plateau, was not as consistent. It is interesting to note that the FM4 response for Gear 2 was also successfully separated from the Gear 1 response. This is due to the fact that the FM4 values were processed from the same TSA signal as the ALR data. RMS did not successfully detect the bending fatigue failure in this case.

#### 6.3 Scuffing Failure

Figure 15 shows an example of the ALR response from a scuffing test on a pair of spur gears. In this type of test, the gears are run at a constant speed but are subjected to increasing torque levels as indicated in Figure 15. Torque is increased in a stepwise manner until a scuffing failure is achieved. Scuffing failures can progress slowly in some cases, starting as mild non-progressive scuffing on one or several teeth, followed by runaway catastrophic scuffing at higher loads. Figure 15 shows the ALR response can be somewhat torque dependent before failure occurs; however, the authors have found this behavior is very predictable on undamaged gears. At the “onset of mild scuffing” point indicated, the ALR trends at both low and high torques start to trend upward. During preliminary tests, the onset of mild scuffing was confirmed by stopping the test between load steps for visual inspection. The “scuffing failure” point where ALR trends further upward also correlated with increases in out-of-mesh oil temperature and friction loss.

Figure 15 also shows FM4 does detect the onset of mild scuffing; however, as damage progresses to scuffing failure, the FM4 response becomes less consistent. In contrast, ALR remains at an elevated value once significant scuffing damage is present. RMS is shown to be very torque dependent but does not provide significant information in regard to scuffing progression.

#### 6.4 Loss of Lubrication Failure

Figure 16 shows an example of the ALR response from a loss of lubrication test on a pair of spur gears. Similar to the scuffing test outlined in Figure 15, the gears are run at a constant speed with progressively increasing torque as indicated. In this case, the oil to the gear mesh is turned off at each torque for a fixed period of time, as indicated by the intervals in Figure 15. This test protocol was introduced in additional detail in [25]. Oil is then turned back on during the transition to each higher torque step if failure is not detected. The ALR response clearly shows an initial scuffing event during the first instance of oil-off. The presence of this initial scuffing event was confirmed on preliminary tests by visual inspection. This test then progressed to quasi-steady state operation at progressively higher torques, followed by catastrophic failure at the highest torque. The ALR response shows increasing damage during the second to last torque step, followed by catastrophic failure during the last step. As in previous examples, once damage is present, the ALR signal remains elevated. FM4 also clearly detected the onset of catastrophic failure in this case; however, the increasing damage during the next to last step, as well as the initial scuffing damage, were not as apparent. RMS also did successfully detect catastrophic failure in this case, as well as the initial scuffing failure; however, the RMS response varied more than ALR as test conditions changed throughout the test.

### 7 Summary and Future Work

In conclusion, this article outlined the hardware and signal processing techniques used in a gear health monitoring system implemented to evaluate gear health on four square power recirculating test rigs. Even angle resampling and time synchronous averaging (TSA) were used in conjunction with the Average Log Ratio (ALR) to successfully detect pitting, bending fatigue, scuffing and loss of lubrication failures. ALR was shown to be a stable metric for monitoring for all four of these failure modes, and in all cases, the ALR response was shown to increase predictably as increasing amounts of damage were developed.

The performance of ALR was also shown to be more consistent than FM4 and RMS in these applications. Implementation of the gear health monitoring system described herein has significantly reduced false shutdowns, improved test rig uptime, and has provided critical data relative to failure onset in the authors’ work.

It was also shown that, in the case of hunting tooth ratios, it is possible to use the TSA process to compute separate responses for each gear in the pair, and that damage on one gear can be successfully isolated from the ALR or FM4 response of the mating gear.

The techniques outlined here were developed for use in a single gear mesh under constant speed conditions. Future work includes development of techniques to implement the ALR algorithm in applications where speed may vary, and where multiple gear meshes may also be present. The authors also wish to compare ALR to several of the other signal processing techniques in literature using the available data sets.

### 8 Acknowledgements

The authors wish to express their appreciation to Jeremy Wagner, John Deere, and Rolls Royce for the support of the testing outlined in this paper, as well as the Gear Research Institute for the grant that made writing this article possible.

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^{Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association. (AGMA) This paper was presented October 2022 at the AGMA Fall Technical Meeting. 22FTM19}