Acoustic Emission Characteristics of Galling Behavior from Dry Scratch Tests at Slow Sliding Speed

Abstract

Galling wear, a severe form of wear, is a known problem in sheet metal forming. As the wear state is not directly observable in closed tribosystems, such as in industrial sheet metal forming processes, indirect tool wear monitoring techniques for inferring the wear state of the tool from suitable signal characteristics are the subject of intense research. The analysis of acoustic emissions is a promising technique for tool condition monitoring. This research has explored feature selection using t-tests, linear regression models, and cluster analysis of the data. This analysis has been conducted both with and without the inclusion of control variables, friction, and roughness to discriminate between the behavior of the acoustic emissions during different stages of galling wear. Scratch testing at slow sliding speed (1 mm/s) has been used to produce the galling wear between a tool steel indenter and aluminum sheet at 10 N applied load, for which the acoustic emissions were recorded. The bursts of the acoustic emission signal were processed and investigated to observe how the bursts changed with increasing galling damage (increasing material removal and transfer). Novel parameters in the field of galling wear have been identified, and novel models for observing the change in galling wear have been identified, thus furthering the development of acoustic emissions analysis as a non-invasive condition monitoring system, particularly for sheet metal forming processes.

1. Introduction

Sheet metal forming (SMF) is a common manufacturing process where an external force is applied to plastically deform the sheet into the desired component shape without removing material. Galling wear is a known problem in SMF. Galling wear is a severe form of wear during which material is transferred from the sheet to the forming tool during the forming process, damaging both the tool, the sheet, and future components. According to industrial data statistics reported by Cheung et al. [1], in 60–70% of the product quality problems that arise due to systematic machining processes, tool failure causes a 20% downtime in processing, with only 38% of the tool’s lifespan being fully utilized in industrial production. Additionally, improper tool use results in an extra USD 10 billion in annual costs. An effective condition monitoring system can save up to 40% in costs by maximizing the lifespan of cutting tools and minimizing machine downtime [2].

The wear state is not directly observable in closed tribosystems such as industrial SMF processes. Consequently, indirect tool wear monitoring techniques that can determine the tool’s wear state from relevant signal characteristics are a major area of research focus. However, at present, there is no solution in industrial sheet metal stamping processes, highlighting the need for further research into industrially applicable methods [3].

Acoustic emission(s) (AE) is a promising technique for tool condition monitoring (TCM). Acoustic emissions (AE) are transient, low-amplitude, high-frequency stress, or elastic waves produced by the sudden release of strain energy [4]. The sources of AE are well-documented and include microstructural deformation processes such as plastic deformation, crack initiation and propagation, corrosion, and other forms of material failure [5].

It is known that galling wear can be observed with AE. While galling is understood to be a complex phenomenon, it is known that galling wear arises from adhesive transfer of sheet metal to the tool, which later becomes abrasive due to the buildup of transferred material.

Research has shown that galling wear progresses through three stages [6] characterized by an increasing coefficient of friction (COF). In stage 1, the COF is initially low and stable; in stage 2, it increases but remains relatively steady; and in stage 3, it rises sharply with significant fluctuations. According to Gaard et al. [7], the initial surface damage in steels results from plastic deformation and the flattening of the track. As sliding continues, a transition to the second frictional regime occurs due to a shift in wear mechanisms to abrasive scratching of the sheet surface, during which the track width becomes significantly wider. Eventually, further sliding leads to the final stage where scratching evolves into severe adhesive wear across the entire contact area.

Based on the actual wear state, detection of the most appropriate time to change/repair the tool is critically important. Replacing or maintaining the tool too early results in unnecessary machine downtime and maintenance, leading to excess costs and wasted resources. Conversely, replacing or maintaining the tool too late causes unplanned machine downtime and high scrappage rates due to excessive galling wear [8].

Therefore, there is a clear need to identify and characterize the important features of the AE signal so that the change in the wear state and transition between galling regimes can be detected without a direct measurement of the friction. This research has explored AE feature selection using t-tests, linear regression models, and cluster analysis. Importantly, the data have been examined both with and without the inclusion of the control variables, COF and roughness (Ra), to discriminate between the behavior of the AE during different stages of galling wear at the very early signs of galling wear. The AE features that are most sensitive to galling initiation are identified to allow for the development of predictive maintenance technology.

The literature establishes that selecting appropriate AE features for analysis is crucial to minimize the probability of error [9]. It is important to choose some features that depend on peak voltage (which can be affected by the researchers’ choice of AE setup, especially threshold settings) and others that are waveform-dependent and, therefore, independent of the AE setup [10]. As such, a collection of features can be broadly characterized as follows:

• Raw signal features related to the “as-received” signal.
• Frequency-based features as derived from the observed signal and processed with Fourier techniques/transforms, such as bandwidth and mean frequency.
• Statistical features, including basic mean, standard deviation, and root mean square (RMS) metrics, and also higher order statistics such as kurtosis, skewness, and shape factor statistics.
• Impulse features related to the peaks of the signal.

Naturally, as explained by Sun et al. [4], it is important to select features that are relevant and disregard others. It has long been established that an advantage of AE is that the frequency content is much higher than that of the machine noise [11], and so there has been research to quantify the changes in the frequency domain, using various techniques. These techniques include Fourier transforms, short-time Fourier transforms, wavelets, and wavelet packet transforms. However, there is some conflict in the literature over the frequency domain for galling wear, with differing authors stating that galling produces different frequency responses. Additionally, some authors argue that as galling produces a non-stationary signal, where the signal characteristics change over time, some often used time-frequency techniques, which assume that a stationary signal may be inadequate [12]. Therefore, some frequency features and techniques may be inadequate, which is why feature selection beyond/outside of frequency features is needed.

Feature selection in the use of AE to study failure modes in composites is highly advanced [9] due to the distinct failure behaviors exhibited by composites. Commonly used features include frequency, amplitude, duration, rise time, peak amplitude, energy, counts, centroid frequency, weighted peak frequency, partial power, number of hits, and counts per event, as described by Barile et al. [10,13,14,15,16,17,18]. However, only a few of these features have been applied to AE for measuring galling wear, with many studies primarily focusing on the signal’s frequency content. Ichenihi et al. [19] explored feature selection of both well established, directly measured AE features and a number of self-derived features, mostly ratios of other well-established features; they use the Laplacian score algorithm.

Unterberg et al. [8] ranked the frequency bands of AE and some other spectral features from a stamping process (fine blanking), using machine learning techniques, and they confirmed that frequency content is more important than the other spectral features. Nasir et al. [20] also explored feature selection using artificial intelligence (AI) and machine learning techniques; this work uses statistical moments, along with Shannon entropy and some more simple AE features. Guo et al. [21] studied feature selection in grinding, looking at 16 features in both the time domain and frequency domain to predict surface roughness.

To briefly summarize the literature regarding the concept of an AE “feature space”, (where the data are analyzed without the inclusion of a control variable such as measured friction), galling failure is widely reported in terms of the frequency response. For example, Su et al. [22] investigated peak frequency vs. amplitude, counts vs. rise time, count rate (ring down count) vs. rise angle, and average frequency vs. rise angle in their work. Additionally, Chai et al. [5], Karimian and Modarres [23], and Barile et al. [5,23,24] used Shannon (Information) entropy vs. amplitude; amplitude vs. rise time is used by Han [25], duration vs. amplitude is used by Yu [26], whereas energy vs. weighted peak frequency is used by Bohmann [27]. Hits vs. peak amplitude is used by Mukhopadhyay et al. [28], while hits vs. frequency is used by Boominathan et al. [29], as opposed to the hits vs. centroid frequency and duration vs. energy used by Chou et al. [30]. All these authors used different tests (not necessarily studying wear or metals).

Cluster analysis has been explored in this field. Li et al. [31] have used clustering on the skewness normalized time-frequency matrices against the variance of the normalized time-frequency matrices to discriminate between “normal” and high roughness samples of Inconel in milling applications. Rastegaev et al. [32] proposed a method for simplifying the presentation of clusters of results when wear accumulates chronologically; however, as a stochastic phenomenon (and as evidenced by this research), this may not always be applicable. Pomponi and Vinogradov [33] proposed a real-time approach to clustering the data from AE bursts in fatigue testing, with linear data, in the AE feature space (kurtosis vs. median frequency), using an adaptive sequential k-means algorithm. Van Steen and Verstrynge [34] used hierarchical clustering to correlate damage in concrete beams to peak frequency. Ichenihi et al. [19] explored the clustering in terms of both well-established and directly measured AE features as well as other derived features. Shimamoto et al. [35] employed machine learning techniques to select features and classify AE into three clusters using a k-means clustering algorithm, focusing on peak frequency, centroid frequency, and peak amplitude. By analyzing the AE features within these clusters, they attributed the degree of concrete damage to the clusters as the AE feature characteristics varied among them. Having clustered the data, Shimamoto et al. [35] identified the most important features to be rise time and centroid frequency when clarifying the compressive fracture behavior in concretes. In this work, these clusters come from the measured COF as opposed to direct damage measurement. Qiao et al. [36] studied AE to monitor the failure process of thermal barrier coatings. Cluster analysis of the signal characteristics in the frequency–amplitude parameter space revealed three distinct types of AE signals during indentation testing. These were classified into low–low, low–high, and high–high amplitude–frequency space clusters, each associated with different failure modes in the coatings.

It has been established by several authors that galling wear exhibits a linear “running in” phase during which Sindi et al. [37] show a linear increase in AE amplitude and change in duration of the AE burst, and Wang and Wood [38] showed distinct linear relationships between the RMS of the AE signal and material transferred. Early work by Tan [39] explored feature selection by comparing counts to RMS and showed that a change in counts preceded a change in RMS.

AE is not a direct measure of the quantity of damage, and so this research has explored feature selection primarily using linear regression models and cluster analysis of the AE bursts resulting from scratch tests, both with and without the inclusion of the control variables friction (the “feature space”) to discriminate between the behavior of the AE during different stages of galling wear.

This work assesses AE features not typically used in TCM but have been shown to be useful in other applications of the AE technique. The aim is to examine the usefulness of these parameters for novel wear detection and tool condition monitoring in the sheet metal forming field, therefore providing the potential for forming the basis of preventative maintenance strategies.

2. Materials and Methods

This article analyzes the acoustic emissions from scratch tests which have been previously used in our previous work [40].

2.1. Materials Used in Scratch Testing

The indenter used was a commercially available Chrome-Molybdenum high tensile steel ball bearing (AISI 4140), 10 mm in diameter, with a hardness of 207 HV [41]. The plate material was a 3 mm thick aluminum alloy, Al5083 H32, cut to dimensions of 125 mm × 210 mm. This alloy is commonly used in the automotive industry for lightweight car body components.

To simulate real-world conditions, both the plate and the indenter were tested in their “as-received” state without any additional in-house treatments or lubrication. Prior to testing, the plates were cleaned with acetone and allowed to air dry to remove any dust or contaminants. The hardness of the plates was measured at 100 HV (matching the manufacturer’s report of 89 HB) using a DuraScan Vickers tester by Struers (made by EMCO test, Kuchl, Austria) with a Vickers indenter at a 300 g load. Plate roughness measurements, taken with an Infinite Focus G5 optical profilometer by Alicona, Graz, Austria (purchased from MetOptix), are detailed in

Table 1. Sample plate roughness values (experimentally measured) [40].

Plate	Ra (in Sliding Direction) (µm)	Ra (across Sliding Direction) (µm)
1	0.027	0.202
2	0.031	0.275
3	0.024	0.231
4	0.023	0.229
5	0.021	0.286
6	0.031	0.243
Average	0.026	0.244

.

2.2. Scratch Test Setup

Scratch tests were performed using a Bruker TriboLab UMT machine (Billerica, MA, USA), as shown in Figure 1. The Bruker UMT TriboLab accurately measures both the indenter’s position (Z height, in mm) and the stage’s position (X, Y distance, in mm). The load cell in the Bruker UMT TriboLab records the frictional forces (N) and the applied load (N), which are then used to calculate the coefficient of friction (COF). Both positional and load measurements were recorded at a sampling rate of 1 kHz. The sample plates were secured to the TriboLab UMT stage using the four bolts illustrated, and the indenter was mounted in the indenter holder.

2.3. Scratch Test Conditions

The scratch tests were conducted using load control for the normal force. A constant 10 N normal load was applied during all tests, using a load cell with a range of 0.5 N to 50 N and a resolution of ±2.5 mN. This load produced a maximum contact pressure of 650 MPa (with a mean contact pressure of 430 MPa), which is based on Hertzian contact pressure calculations assuming elastic deformation. This contact pressure is comparable to those found in sheet metal forming and aligns with pressures reported in studies on the galling of aluminum [42,43].

During the tests, the three stages of galling were typically observed: low friction in stage 1, increasing friction in stage 2, and high friction in stage 3 (see Section 2.3 for details). The maximum scratch length achievable in a single pass was 50 mm. Consequently, scratches were applied in 50 mm increments, with tests ending at the 50 mm mark if galling stage 3 was observed (e.g., see Tests 1 and 6–10 in

Table 2. Summary of scratch length and galling stages observed for all tests [40].

Ball Sample Number	Galling Stage(s) Observed for Scratch Increment A [0–50 mm]	Galling Stage(s) Observed for Scratch Increment B [50–100 mm]	Galling Stage(s) Observed for Scratch Increment C [100–150 mm]	Total Scratch Length (mm)
1	1, 2, 3	-	-	50
2	1	-	-	24
3	1	-	-	24
4	1	-	-	36
5	1, 2	-	-	50
6	1, 2, 3	-	-	50
7	1, 2, 3	-	-	50
8	1, 2, 3	-	-	50
9	1, 2, 3	-	-	50
10	1, 2, 3	-	-	50
11	1	2	3	150
12	1	2	3	150
13	1, 2	3	-	100
14	1	1, 2	-	100
15	1, 2	-	-	50
16	1, 2	-	-	50
17	1, 2	3	-	100
18	1, 2	3	-	100
19	1, 2	3	-	100
20	1, 2	3	-	100
21	1, 2	3	-	100
22	1, 2	3	-	100

). If galling stage 3 was not observed in the initial 50 mm increment (scratch increment A), the test continued with the same indenter for an additional 50 mm increment (scratch increment B) and then with scratch increment C. For instance, tests involving 150 mm scratch lengths consisted of three consecutive 50 mm scratches. The only exceptions were tests 2–4, which were terminated early to inspect the indenter surface before galling stage 2 began. In total, 34 scratches were successfully conducted on the sample plates. Some of these tests were part of continued use of the same ball sample after the initial or second 50 mm increment, resulting in 22 individual ball samples, as detailed in Table 2.

The sliding speed was kept to 1 mm/s to minimize the effects of frictional heating during the test (it has been reported that sliding speed affects galling wear [44]). Most tests were stopped after severe galling was detected; however, some tests were stopped at the instant the coefficient of friction reached 0.9, so the total scratch length for each sample varied, depending on when galling occurred. Owing to the stochastic nature of galling initiation and progression, the total sliding distance for each test varied from 24 mm up to 150 mm.

2.4. Mechanical/Scratch Data Processing

The coefficient of friction (COF) was recorded continuously throughout the scratch tests. MATLAB 2020a software was used to differentiate the three stages of galling, as shown in Figure 2. The transition between stage 1 and stage 2 was identified using MATLAB’s “ischange” function on the smoothed COF data. This function detected the point of greatest positive gradient change in the COF before it exceeded 0.5, which was considered the midpoint of stage 2 based on observations of all tests. The transition from stage 2 to stage 3 was determined by the first instance where the COF exceeded 0.9, a criterion developed from comprehensive analysis of the test data and galling observations. If the transition to stage 3 occurred very close to the end of the test (i.e., after more than 95% of the test was completed), this phase was excluded from the analysis, and the test was classified as having only stages 1 and 2 (e.g., see test 14 in Table 2). Similarly, if the transition to stage 2 occurred near the end of the scratch, the test was categorized as exhibiting only stage 1.

2.5. Profilometry/Surface Characterisation

Immediately after each scratch increment, the indenters were measured using an Alicona InfiniteFocus optical profilometer (Alicona, Graz, Austria) without any additional cleaning. The profilometer settings included a 5× objective magnification, a vertical resolution of 1.4 µm, a scan area of 23 × 10 mm, and a lateral measurement range of 0.16 mm. The sample plates were later measured after all scratches were completed, also without additional cleaning, using a 10× objective magnification, a vertical resolution of 1.4 µm, and a scan area of 1 × 55 mm.

Optical profilometry was employed to visually inspect the scratch morphology on the sheet material and to assess material buildup and lump growth on the tool. The longitudinal cross-section profile of the scratch was measured within the scratch width (measurement width = 0.1 mm, as shown in Figure 3) and across the lump growth on the indenter. To analyze the lump growth on the indenter, the form removal tool in the Alicona software (IF Measurement Suite v5.3.2) was used. This “flattening” of the scanned surface facilitated easier comparison between indenter surfaces, measurement of the volume of adhered material, and a better understanding of the evolution of galling.

2.6. AE Acquisition and Processing

2.6.1. AE Data Acquisition

AE signals were recorded using a Vallens AE system equipped with LabVIEW data acquisition hardware. The AE sensors were linked to the data acquisition system (National Instruments, model PXIe-1078, Austin, TX, USA) via a high-speed digitizer (National Instruments, model DCPL2) and an amplifier (Vallen Systeme, model AEP3N, Icking, Germany) with a gain of 40 dB. The Vallens AE sensors F15a (Sensor 1) and R15a (Sensor 2) were used, each with a frequency response detailed in their product data sheets. Both sensors are of the dimensions 22.4 mm height with a diameter of 19 mm; they weigh 34 g and were clamped with similar force.

2.6.2. AE from Scratch Tests

Each sensor was attached to either end of the sample plates using screw clamps, Figure 4. To ensure optimal transmission of the AE signal to the sensor, a small amount of ultrasonic couplant was applied to the sample plate, just enough to cover the sensor face, before the sensors were attached to the sample. Excess fluid was not cleaned off to prevent disturbing the sensor setup.

Hsu-Nielsen pencil lead break tests were conducted on the sample plates to verify the proper mounting of the AE sensors and to assess the background noise. This test involves breaking a 0.5 mm diameter 2H pencil lead against the sample plate. The brittle fracture against the plate induces an AE burst, which was recorded by the system. At the start of each scratch test, this pencil lead break was performed three times in different positions across the sample plate (near one sensor, approximately in the center of the sample, and near the other sensor), and so three bursts are seen in Figure 5. Each pencil lead break was evaluated to ensure a sufficiently large amplitude, confirming that the impact of background noise on the AE sensor was minimal. If a sufficiently large amplitude was not observed, the AE sensor was removed and reapplied with fresh couplant, and the pencil lead break was repeated to ensure the sensors were working properly.

Continuous AE data were recorded across the duration of the scratch tests at a sampling frequency of 5 MHz, which is well above the Nyquist frequency; an example is shown below in Figure 6. This figure shows that the recorded AE signal is continuous with frequent bursts throughout the test, and the friction response of this scratch test is given in Figure 7. Due to the large file sizes, AE data acquisition was paused at the end of each test to ensure that the data could be recorded properly. The AE data were processed post-test, as described in the following subsections.

Characteristics of individual AE bursts were analyzed in relation to the COF and Ra at the specific location where the burst was detected to observe how the bursts changed with worsening damage. Numerous authors have previously investigated burst characteristics [45].

By manual inspection of the recorded signals, the background noise was determined to be approximately 7 mV, and there was significant activity greater than 27.5 mV. A script was written in the MATLAB software package to extract each of the bursts that occurred in the recorded signal, as illustrated for an example burst in Figure 8. At each time where a burst was detected, a “hard” window was formed by adding on sometime before and after the burst time. The signal during this hard window was enveloped (using MATLAB’s envelope feature) to find the burst within the hard window by finding when the smoothed signal envelope exceeded 7 mV. The features for that burst were then calculated.

As the onset of galling has been studied in this research, this often produced relatively low amplitude bursts near the noise level; wavelet denoising was employed to enhance the analysis of the AE signal by reducing the noise level. For each burst, 3 control variables were measured and 26 AE signal features were calculated from the raw AE signal, as given in

Table 3. AE features investigated in this study.

Name	Notation	Equation	MATLAB Function/Code
Duration	$x_{dur}$	---	---
Root mean squared (RMS)	$x_{rms}$	$=\sqrt{{\displaystyle \frac{\sum {x\left(n\right)}^2}{N}}}$	RMS(x)
Root sum of squares (RSSQ)	$x_{RSS}$	$=\sqrt{\sum _{n=1}^N{\left|x_n\right|}^2}$	RSS(x)
Shannon Entropy	$x_{SE}$	$=-\sum _j{p}_{ji}\log p_{ij}$	wentropy(x, ’shannon’)
Peak2rms (Crest factor)	$x_{crest}$	$={\displaystyle \frac{x_p}{x_{rms}}}$	Peak2rms(x)
Clearance Factor	$x_{Clear}$	$={\displaystyle \frac{x_p}{{\left(\frac{1}{N}\sum _{i=1}^N\sqrt{\left|x_i\right|}\right)}^2}}$	---
Shape factor	$x_{sha}$	$={\displaystyle \frac{x_{rms}}{x_m}}$	---
Impulse factor	$x_i$	$={\displaystyle \frac{x_p}{x_m}}$	---
margin	$x_{ma}$	$={\displaystyle \frac{x_p}{x_{ra}}}$	---
Mean Frequency	$x_{MF}$	$={\displaystyle \frac{\sum (power\ast freq)}{\sum power}}$	Meanfreq(x)
Bandwidth	$x_b$	$=0.99F_{max}-{0.99F}_{min}$	Obw(x)
Kurtosis	$x_{kurt}$	$={\displaystyle \frac{\sum {\left(x\left(n\right)-x_m\right)}^4}{(N-1)x_{std}^4}}$	Kurtosis(x)
Skewness	$x_{ske}$	$={\displaystyle \frac{\sum {\left(x\left(n\right)-x_m\right)}^3}{\left(N-1\right)x_{std}^3}}$	Skewness(x)
Average signal level	$x_m$	$={\displaystyle \frac{\sum x\left(n\right)}{N}}$	Mean(x)
Maximum (Peak) Amplitude	$x_p$	$=\mathrm{m}\mathrm{a}\mathrm{x}\left(\left|x\left(n\right)\right|\right)$	Max(x)
Rise Time	$x_{rt}$	Time from burst start to peak amplitude	---
Rise Angle	$x_{ra}$	$={\tan }^{-1}{\displaystyle \frac{x_p}{x_{rt}}}$	---
Decay Time	$x_{dt}$	Time from peak amplitude to end of burst	---
Decay Angle	$x_{da}$	${=\tan }^{-1}{\displaystyle \frac{x_p}{x_{dt}}}$	---
Counts	$x_C$	Number of data points above threshold.	Find(length(x) > c_thres)
Count Rate	$x_{cr}$	$={\displaystyle \frac{Counts}{Duration}}$	---
Signal to noise Ratio	$x_{snr}$	$={\displaystyle \frac{rss\left(x\right)}{rss\left(noise\right)}}$	Signal to noise ratio(x)
Energy	$E$	$={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\left|x\left(n\right)\right|}^{2}dn=P\ast N$	---
Power	$P$	$={\displaystyle \frac{1}{N}}{\displaystyle \sum _{n-0}^{N-1}}{x}^2\left[n\right]=x_{rms}^2$	---
Root amplitude	$x_{ra}$	$={\left({\displaystyle \frac{\sum \sqrt{\left|x\left(n\right)\right|}}{N}}\right)}^2$	---
RA value	$x_{RAv}$	$={\displaystyle \frac{R_t}{x_p}}$	---

along with the relevant equations. These were the times the burst occurred during the test (referred to as “burst time”, not to be confused with “duration”, which is the length of time in which the measured AE remained above the noise threshold); the COF at the nearest time to peak time, as measured by the Tribolab UMT; and the Ra over the burst, measured over 0.5 mm with the center of that 0.5 mm corresponding to the point closest the peak time.

Once the data for each burst were found, individual features were processed with t-tests, linear regression models, and clustering score algorithms to find candidate parameter(s) that best correlate with progressing galling wear, as measured by either COF or Ra. Building on the conclusions presented previously [40], the clustering algorithms were programmed to find 3 clusters to reflect the differing stages of wear, corresponding to “not galling” (COF ≤ 0.3), “transitioning galling” (0.3 < COF < 0.9), and “galling occurring” (COF ≥ 0.9).

2.6.3. t-Tests, k-Means Clustering, and Linear Regression Modeling

When analyzing the data, the MATLAB software packages built-in t-test function (ttest2) was used to conduct the t-tests of the data against the control variables, COF and Ra, as well in the AE domain, without the inclusion of these variables. Initially, t-tests were used to check for statistical significance in the data between each stage of galling wear (when classified against the control variables).

For the cluster analysis, the k-means algorithm was applied using MATLAB’s built-in “kmeans” function to find the intra-cluster and inter-cluster distances for each of the three known COF groups to calculate the cluster score (the ratio of the mean of these distances) for each combination of the AE features in two-dimensional (2D) and three-dimensional (3D) space. K-means clustering is a widely used unsupervised machine learning algorithm that partitions a dataset into clusters based on the similarity of data points. The goal is to group similar data points together while separating those that are dissimilar. The algorithm seeks to minimize the sum of squared distances between data points and their assigned centroids, known as the within-cluster sum of squares (WCSS). This process produces clusters where the data points within each cluster are more similar to each other than to those in other clusters.

To have a quantitative measure of how well the data had clustered for a given combination of variables, the clustering score was calculated. The clustering score is the ratio of the mean of intra-cluster distances (the mean Euclidean distances from each point to the respective cluster centroid) to the mean inter-cluster (centroid) distances.

As an alternative to cluster analysis, linear regression models were used to examine trends that may arise in the data; in particular, linear trends are unsuitable for the k-means clustering algorithm, which assumes spherical distribution. For the linear regression models, MATLAB’s built-in “fit linear model (fitlm)” function was used. A suitable model was chosen such that the r² for the overall model was greater than 0.75 and the model’s p-value was less than 0.05. These features ensure that the linear model is a good fit for the data and that there is a significant relationship between the two features. Significant outliers were removed from the burst data, using MATLAB’s built-in function “rmoutliers” to remove data from the top and bottom 5 percentiles (i.e., the 6th to the 95th percentile inclusive were kept) such that the linear regression models were not skewed by significant outliers.

Given some features are non-linear, the natural logarithm of each variable was also calculated to fix this issue, doubling the number of features investigated. The models were checked for a significant relationship between x and x² to confirm if the model was non-linear. If the model was significantly non-linear, it was excluded from the results.

Linear regression models of the data in the AE domain have been used to discriminate between the behavior of the AE during different stages of galling wear without directly measuring the control variables and using just the AE features.

Given the large number of combinations, the r² value for each model was used to discriminate good models from bad models. Only models with an r² value greater than 0.75 but less than 1 (to filter out the “perfect” comparisons of a variable versus itself) were investigated. Moreover, only models with a significantly different gradient to the transition region were investigated. Subsequently, the models fitted to each stage for each pair of features were compared for statistical significance, using the p-value from the f-test on the model.

3. Results

The results are presented with the raw data first to show the relationship between the burst and the corresponding instantaneous COF and Ra values (Section 3.1). Then, the t-tests vs. wear stage (Section 3.2) and cluster analysis of the AE features in 2D and 3D space are presented (Section 3.3). Finally, the results of the linear regression models of the AE features are plotted against the control variables, followed by an analysis of the 2D plots of the AE features plotted against the other AE features (Section 3.4).

3.1. Raw Data, Correlation of Time, COF, and Ra

This work investigates how the AE bursts correlate with these control variables, both directly and indirectly. Therefore, it is important to confirm how these control variables correlate with the timing of the bursts (see Figure 9A,B) and ensure the same relationship between these features is present to establish confidence in the data (see Figure 10).

3.2. t-Tests of AE Features in Relation to the Control Variables

Table 4. t-test outputs. 1 = significant difference (green), 0 = insignificant difference (red).

AE Feature	Sensor 1			Sensor 2
	Stage 1 to stage 2	Stage 2 to stage 3	Stage 1 to stage 3	Stage 1 to stage 2	Stage 2 to stage 3	Stage 1 to stage 3
COF	1	1	1	1	1	1
Ra (µm)	1	0	1	1	0	1
Duration (µs)	1	1	1	0	1	1
RMS (mV)	0	1	0	0	0	0
Shannon Entropy (Sh)	0	1	0	0	1	1
Peak to RMS (Crest factor)	1	0	1	0	0	0
RSSQ (mV)	1	1	0	0	1	1
Mean Frequency (MHz)	0	0	0	0	0	0
Kurtosis	0	1	1	0	0	0
Bandwidth (MHz)	1	1	1	0	0	0
Skewness	1	1	0	0	0	0
Average Signal Level (mV)	0	0	0	1	0	0
Shape Factor	1	1	0	0	1	1
Impulse Factor	1	1	0	0	1	1
Maximum Amplitude (mV)	0	1	0	0	0	0
Clearance Factor	0	1	1	0	0	0
Rise Time (µs)	1	0	1	1	0	1
Rise Angle (deg)	0	0	0	1	0	0
Decay Time (µs)	1	1	1	0	1	1
Decay Angle (deg)	1	0	0	0	0	0
Counts (n)	1	1	1	0	1	1
CountRate (n/s)	1	1	1	0	0	0
Signal to noise ratio	0	0	1	0	0	1
Energy (mJ)	0	1	0	0	1	1
Power (mW)	0	1	0	0	1	0
root Amplitude (mV)	1	1	1	0	0	0
Margin	0	1	1	0	0	0
RA value (µS/mV)	0	0	0	1	0	0
log Duration (µs)	1	0	1	0	0	1
log RMS (mV)	1	1	1	0	0	0
log Shannon Entropy (Sh)	1	1	1	0	0	1
log Peak to RMS (Crest factor)	0	0	1	0	0	0
log RSSQ (mV)	1	1	1	0	0	1
log Mean Frequency (MHz)	0	0	0	0	0	0
log Kurtosis	0	1	1	0	0	0
log Bandwidth (MHz)	1	1	1	0	0	0
log Skewness	0	0	0	0	0	0
log Average Signal Level (mV)	0	0	0	1	0	0
log Shape Factor	1	1	1	0	0	1
log Impulse Factor	1	1	1	0	0	0
log Maximum Amplitude (mV)	1	1	1	0	0	0
log Clearance Factor	1	1	1	0	0	0
log Rise Time (µs)	1	0	1	1	0	1
log Rise Angle (deg)	0	0	0	1	0	0
log Decay Time (µs)	1	0	1	0	0	1
log Decay Angle (deg)	1	0	0	0	0	0
log Counts (n)	1	1	1	0	0	1
log CountRate (n/s)	1	1	1	0	0	0
log Signal to noise ratio	0	0	0	0	0	0
log Energy (mJ)	1	1	1	0	0	1
log Power (mW)	1	1	1	0	0	0
log root Amplitude (mV)	1	1	1	0	0	0
log Margin	1	1	1	0	0	0
log RA value (µS/mV)	1	0	0	1	0	1

shows whether there was a statistical significance in the data between each stage of galling wear (measured by COF) using t-tests on the control variables and the AE features. As expected, the control variables are statistically significant in each stage, confirming that the boundaries between each wear stage are set correctly. Table 4 shows that the t-tests for Sensor 2 (R15a) have a different frequency response to Sensor 1 (F15a). As with Sensor 1, the control variables are significant between each stage.

For Sensor 1, in terms of the AE features, counts and log bandwidth show a difference between each stage and are the only features to do so. The following features all show a significant difference between stage 1 and stage 2, as well as stage 1 and stage 3, but do not discern a difference between stage 2 and stage 3: duration, peak2rms (crest factor) (and log peak2rms (crest factor)), mean frequency (and log mean frequency) and bandwidth, rise time (and log rise time), decay time (and log decay time), decay angle (and log decay angle), signal to noise ratio, log Shannon entropy, log (root sum of squares), log counts, and log energy.

Conversely, with Sensor 1, count rate and log count rate are the only features for Sensor 1 to discern a difference between stages 1 and 3 and stages 2 and 3, but not 1 and 2. Log skewness is the only parameter to indicate a difference between stage 1 and stage 2, but it does not indicate any other significant change. Moreover, skewness itself is the only parameter to find a difference between stage 2 and stage 3, but no other stage. Log rms, log shape factor, log impulse factor, log maximum (peak) amplitude, log clearance factor, log power, log root amplitude, and log margin all show a difference only between stage 1 and stage 3.

Notably, for Sensor 1, widely reported features such as RMS and Shannon entropy do not show a difference between any stage when processing the data in this way.

For Sensor 2, there are numerous features that do not show any statistically significant changes between any stage, and none show a difference between stage 1 and stage 2. Nevertheless, decay time and duration show a significant difference between stages 1 and 3 and stages 2 and 3, respectively, but not stage 1 and stage 2. Rise time finds a difference between stage 2 and stage 3 but no other stage. Log RMS, log Shannon entropy, log (root sum of squares), log maximum (peak) amplitude, log clearance factor, log rise time, log power, log energy and log margin all show a difference between stage 1 (unworn) and stage 3 (worn).

3.3. Cluster Analysis of the AE Features

Cluster analysis of the AE features has been conducted in both 2D and 3D space, using clustering scores to measure the separation between the low, medium, and high friction groups (i.e., stages 1, 2, and 3 of galling).

In the 2D AE space, there are 2704 possible combinations of AE features, whereas in 3D space, there are 140608 possible combinations of features. In this research, we are searching for the combinations with the lowest clustering score and highest separation. A low clustering score represents high cohesion (low intra-cluster distances), which is measured as the mean distance from each point in the cluster to the centroid. On the other hand, high separation (high inter-cluster distances) is measured as distances between the three centroids. Histograms of the clustering score have been employed to summarize the data, and subsequently, combinations of good features have been investigated/reported.

3.3.1. Cluster Analysis with COF

Table A1. AE features clustering vs. friction.

Sensor 1						Sensor 2
Stage 1 to stage 2		Stage 2 to stage 3		Stage 1 to stage 3		Stage 1 to stage 2		Stage 2 to stage 3		Stage 1 to stage 3
Variable	Score	Variable	Score	Variable	Score	Variable	Score	Variable	Score	Variable	Score
Power	0.09628	No		Rise time	0.01302	Rise time	0.18143	No		Rise time	0.00879
Rise time	0.09628	Good		Average signal level	0.01302	Power	0.18143	Good		Average signal level	0.00880
Average signal level	0.09628	Scores		Power	0.01303	Average signal level	0.18144	Scores		Power	0.00880
Decay time	0.09631			Decay time	0.01304	Decay time	0.18146			Decay time	0.00881
Duration	0.09632			Log rise angle	0.01304	Duration	0.18146			Duration	0.00882
Log rise angle	0.09641			Duration	0.01305	Log rise angle	0.18155			Log rise angle	0.00882
RMS	0.09642			RA value	0.01308	RA value	0.18171			RA value	0.00886
RA value	0.09659			Log decay angle	0.01382	RMS	0.18202			Log decay angle	0.00969
Root amplitude	0.09769			RMS	0.01467	Log decay angle	0.18299			Mean frequency	0.00987
Log decay angle	0.09827			Mean frequency	0.01708	Root amplitude	0.18411			RMS	0.00995
Mean frequency	0.10191			Root amplitude	0.01734	Mean frequency	0.18517			Root amplitude	0.01164
Maximum amplitude	0.10604			Skewness	0.03901	Maximum amplitude	0.22622			Log mean frequency	0.03760
Skewness	0.12057			Bandwidth	0.08890	Log mean frequency	0.28831			Skewness	0.04942
Log Mean frequency	0.22085			Log mean frequency	0.10015	Skewness	0.29443			Maximum amplitude	0.07512
Bandwidth	0.30447			Maximum amplitude	0.10949	Bandwidth	0.48106			Bandwidth	0.13697
Log root amplitude	0.40979			Log bandwidth	0.16527					Rise angle	0.22546
Log bandwidth	0.42576			Rise angle	0.20066					Log root amplitude	0.29489
				Log root amplitude	0.31620					Log bandwidth	0.36628
				Log peak to rms ratio	0.34169					Log count rate	0.42610
				Log kurtosis	0.37730					Log peak to rms ratio	0.43917
				Log rise time	0.45406

(located in Appendix A) gives the clustering scores for each of the features investigated when calculated with friction. This is a ranking of how good each parameter is for discriminating the AE features from bursts arising from different wear states. It is evident that there are no good scores for either sensor when discriminating stage 2 wear from stage 3 wear. However, for both sensors, rise time, power, and average signal level are among the features with the lowest clustering score, along with decay time and duration.

3.3.2. Cluster Analysis of AE in 2D

As with the linear modeling, the separation of the different groups was investigated using only pairs of AE features. Figure 11 shows that clustering in 2D does not find any difference between stage 1 and stage 2, or stage 2 and stage 3, for either sensor. However, it is evident that stage 1 and stage 3 are separable using Sensor 1 but not with Sensor 2. An example of the data is shown in Figure 12, where there is a clear visible difference between stage 1 and stage 3; however, stage 2 overlaps both other stages.

Table A2. Two-dimensional and three-dimensional clustering results for the AE from scratch tests. Only Sensor 1, 1–3 showed any good scores.

Sensor 1
2 Dimensions			3 Dimensions
Variable 1	Variable 2	Clustering Score	Variable 1	Variable 2	Variable 3	Clustering Score
Bandwidth	Rise time	0.28608	Bandwidth	Average signal level	Rise time	0.28608
Bandwidth	Average signal level	0.28608	Duration	Bandwidth	Rise time	0.2861
Duration	Bandwidth	0.2861	Duration	Bandwidth	Average signal level	0.28611
Bandwidth	Decay time	0.28611	Bandwidth	Rise time	Decay time	0.28611
Bandwidth	Power	0.28611	Bandwidth	Rise time	Power	0.28611
Bandwidth	Log rise angle	0.28613	Bandwidth	Average signal level	Decay time	0.28611
Bandwidth	RA value	0.28622	Bandwidth	Average signal level	Power	0.28611
Bandwidth	Log decay angle	0.28795	Duration	Duration	Bandwidth	0.28613
RMS	Bandwidth	0.28981	Duration	Bandwidth	Decay time	0.28613
Bandwidth	Root amplitude	0.29492	Bandwidth	Rise time	Log rise angle	0.28613
Mean frequency	Bandwidth	0.29606	Duration	Bandwidth	Power	0.28614
Rise time	Log bandwidth	0.34677	Bandwidth	Average signal level	Log rise angle	0.28614
Average signal level	Log bandwidth	0.34677	Bandwidth	Decay time	Power	0.28614
Duration	Log bandwidth	0.34678	Duration	Bandwidth	Log rise angle	0.28616
Decay time	Log bandwidth	0.34678	Bandwidth	Decay time	Log rise angle	0.28616
Power	Log bandwidth	0.34678	Bandwidth	Power	Log rise angle	0.28617
Log bandwidth	Log rise angle	0.34679	Bandwidth	Rise time	RA value	0.28622
RA value	Log bandwidth	0.34683	Bandwidth	Average signal level	RA value	0.28622
Log bandwidth	Log decay angle	0.3476	Duration	Bandwidth	RA value	0.28625
RMS	Log bandwidth	0.34843	Bandwidth	Decay time	RA value	0.28625
Root amplitude	Log bandwidth	0.35061	Bandwidth	Power	RA value	0.28625
Bandwidth	Skewness	0.35117	Bandwidth	RA value	Log rise angle	0.28628
Mean frequency	Log bandwidth	0.3513	Bandwidth	Rise time	Log decay angle	0.28795
Skewness	Log bandwidth	0.37654	Bandwidth	Average signal level	Log decay angle	0.28795
Maximum amplitude	Log bandwidth	0.44207	Duration	Bandwidth	Log decay angle	0.28798
Log mean frequency	Log bandwidth	0.44416	Bandwidth	Decay time	Log decay angle	0.28798
Duration	Rise time	0.4777	Bandwidth	Power	Log decay angle	0.28798
Bandwidth	Maximum amplitude	0.48788	Bandwidth	Log rise angle	Log decay angle	0.28801
Duration	Average signal level	0.48953	Bandwidth	RA value	Log decay angle	0.28809
Log bandwidth	Log rise time	0.49001	RMS	Bandwidth	Rise time	0.28981
Bandwidth	Log rise time	0.49448	RMS	Bandwidth	Average signal level	0.28982
Bandwidth	Log mean frequency	0.4962	Duration	RMS	Bandwidth	0.28984
---	---	---	RMS	Bandwidth	Decay time	0.28984
---	---	---	RMS	Bandwidth	Power	0.28985
---	---	---	RMS	Bandwidth	Log rise angle	0.28987
---	---	---	RMS	Bandwidth	RA value	0.28996
---	---	---	RMS	Bandwidth	Log decay angle	0.29168
---	---	---	Bandwidth	Rise time	Root amplitude	0.29492
---	---	---	Bandwidth	Average signal level	Root amplitude	0.29492
---	---	---	Duration	Bandwidth	Root amplitude	0.29495
---	---	---	Bandwidth	Decay time	Root amplitude	0.29495
---	---	---	Bandwidth	Power	Root amplitude	0.29495
---	---	---	Bandwidth	Root amplitude	Log rise angle	0.29498
---	---	---	Bandwidth	Root amplitude	RA value	0.29506
---	---	---	Mean frequency	Bandwidth	Rise time	0.29606
---	---	---	Mean frequency	Bandwidth	Average signal level	0.29606
---	---	---	Duration	Mean frequency	Bandwidth	0.29609
---	---	---	Mean frequency	Bandwidth	Decay time	0.29609
---	---	---	Mean frequency	Bandwidth	Power	0.29609
---	---	---	Mean frequency	Bandwidth	Log rise angle	0.29612
---	---	---	Mean frequency	Bandwidth	RA value	0.2962
---	---	---	Bandwidth	Root amplitude	Log decay angle	0.29677
---	---	---	Mean frequency	Bandwidth	Log decay angle	0.29792
---	---	---	RMS	Bandwidth	Root amplitude	0.29861
---	---	---	RMS	Mean frequency	Bandwidth	0.29977

left (Appendix A) gives the non-trivial combinations of features that have a clustering score of less than 0.5 for separating the low and high COF groups.

3.3.3. Cluster Analysis of AE in 3D

Separation of the different groups was looked for using triplets (x, y, z) of AE features. An example of 3D clustering is given in Figure 13. Figure 14 shows that only Sensor 1 had any clusters with good separation, less than 0.3, between low friction and high friction, while Sensor 2 did not exhibit suitable clustering.

Focusing on the combination of features that have a clustering score of less than 0.3 (Table A2 right, in Appendix A) for separating the low and high COF groups. There are various combinations of duration, bandwidth, mean frequency, average signal level, rise time, decay time, power, log rise angle, log decay angle, RMS, and root amplitude, which show a clustering score of less than 0.3.

3.4. Linear Regression Analysis of the AE Features

Linear regression analysis of the AE features has been conducted to predict both the COF and Ra. In 2D AE feature space, observations of the change in gradients of the models have been used to measure the separation between the low, medium, and high friction groups.

In the 2D AE feature space, there are 2704 possible combinations of AE features. Therefore, in this research, we search for the combinations with the greatest angle change (i.e., difference) between the gradients of each model while still being a valid model. As such, any model with an r² value less than 0.75 was dismissed as a poor fit, along with any model that did not exhibit a statistically significant (p-value > 0.05) change between galling stages.

3.4.1. Linear Regression Models of AE for Predicting COF and Ra

The individual features were inputted into linear models to predict the COF and Ra. As the COF has been normalized with a center 0 and standard deviation 1 as well as the AE Variable, hence it runs outside of the range 0 to 1. The features which showed the greatest angle changes between each stage are given in

Table 5. Most sensitive features to changing stage 1 to stage 2 galling wear.

Sensor 1			Sensor 2
AE Variable	Angle (deg)	Model r2	AE Variable	Angle (deg)	Model r2
Mean frequency	21.704	0.871	Log bandwidth	13.646	0.882
Log mean frequency	21.607	0.872	Bandwidth	13.032	0.881

,

Table 6. Most sensitive features to changing stage 2 to stage 3 galling wear.

Sensor 1			Sensor 2
AE Variable	Angle (deg)	Model r2	AE Variable	Angle (deg)	Model r2
Log mean frequency	18.962	0.872	Log bandwidth	6.598	0.882
Mean frequency	18.420	0.871	Bandwidth	5.447	0.881

and

Table 7. Most sensitive features to changing stage 1 to stage 3 galling wear.

Sensor 1			Sensor 2
AE Variable	Angle (deg)	Model r2	AE Variable	Angle (deg)	Model r2
Mean frequency	3.285	0.871	Bandwidth	7.585	0.881
Log mean frequency	2.645	0.872	Log bandwidth	7.048	0.882

, respectively. An example model is given in Figure 15, and the other models are given in Appendix B.

Only the mean frequency and the logarithm mean frequency (Sensor 1), bandwidth, and log bandwidth (Sensor 2) show a clear and significant change between any galling stage. Interestingly, the data for Sensor 1 are only significant for a change from stage 2 to stage 3, while Sensor 2 is only significant for a change from stage 1 to stage 2, as seen by the rest of the models in Appendix B.

The sensors were positioned symmetrically about the center axis of the sample plate, with a comparable load on the sensor (to ensure good contact with the sensor surface) and a comparable amount of transmission fluid, and the scratch direction was perpendicular to the axis between them, so it is interesting that the analysis highlights different features are more suitable for different sensors. This is assumed to be due to the different frequency responses of the two sensors.

There were no models with a good r² when compared to the roughness for either sensor, so these results are not provided.

3.4.2. Linear Regression Models of AE Features in AE Space

Having identified that individual features may not be sufficiently sensitive to detect the onset of galling wear, linear models of the AE features were applied to find separation without controls (as it may be difficult to measure controls in a closed tribosystem). Given the large number of possible combinations, the r² value for each model was used to discriminate good models from bad models. Only models with an r² value greater than 0.75 but less than 1 (to filter out the “perfect” comparisons of a variable versus itself), where each parameter in the model was determined to be statistically significant, were investigated. All the models that passed this filtering had an r² value of approximately 0.85.

Once again, by looking at the angle change between the linear models for each stage, we see that it is possible to determine which features are most sensitive to galling wear. For both sensors,

Table 8. Greatest angle change between stage 1 to stage 2 for Sensor 1. Those shown in blue text indicate if the model is provided later in the document in Appendix B.

Sensor 1				Sensor 2
AE Variable 1	AE Variable 2	Angle (deg)	Model r2	AE Variable 1	AE Variable 2	Angle (deg)	Model r2
log count rate	Counts	40.284	0.884	Counts	Impulse factor	18.176	0.795
log RMS	Decay time	40.087	0.821	log Shannon entropy	log decay time	11.165	0.767
Count rate	log kurtosis	38.721	0.755	Energy	Power	10.389	0.947
log count rate	log clearance factor	37.266	0.906	Energy	RMS	9.532	0.814
log count rate	Clearance factor	36.204	0.913	RSSQ	Maximum amplitude	6.128	0.942
log RMS	Kurtosis	36.176	0.849	---	---	---	---
Count rate	Counts	35.952	0.901	---	---	---	---
Maximum amplitude	log count rate	35.214	0.867	---	---	---	---
log count rate	log maximum amplitude	34.446	0.941	---	---	---	---
Counts	log RSSQ	32.683	0.903	---	---	---	---

,

Table 9. Greatest angle change between stage 2 to stage 3 for Sensor 1. Those shown in blue text indicate if the model is provided later in the document in Appendix B.

Sensor 1				Sensor 2
AE Variable 1	AE Variable 2	Angle (deg)	Model r2	AE Variable 1	AE Variable 2	Angle (deg)	Model r2
Power	log count rate	64.264	0.860	Energy	RMS	24.824	0.814
Shannon entropy	log energy	56.500	0.773	log Shannon entropy	log decay time	19.853	0.767
RSSQ	log duration	55.266	0.756	Counts	Impulse factor	19.273	0.795
RSSQ	log counts	50.981	0.796	RSSQ	Maximum amplitude	9.542	0.942
Maximum amplitude	log counts	48.942	0.795	Energy	Power	8.419	0.947
log count rate	RSSQ	44.190	0.848	---	---	---	---
log count rate	Maximum amplitude	42.750	0.860	---	---	---	---
Impulse factor	log RSSQ	40.964	0.751	---	---	---	---
RMS	log count rate	39.554	0.920	---	---	---	---
Clearance factor	log duration	36.679	0.766	---	---	---	---

and

Table 10. Greatest angle change between stage 1 to stage 3 for Sensor 1. Those shown in blue text indicate if the model is provided later in the document in Appendix B.

Sensor 1				Sensor 2
AE Variable1	AE Variable2	Angle (deg)	Model r2	AE Variable1	AE Variable2	Angle (deg)	Model r2
Power	log count rate	77.667	0.860	Energy	RMS	34.356	0.814
RSSQ	log duration	74.159	0.756	Energy	Power	18.807	0.947
RSSQ	log counts	72.795	0.796	RSSQ	Maximum amplitude	15.669	0.942
Maximum amplitude	log counts	71.368	0.795	log Shannon entropy	log decay time	8.688	0.767
Maximum amplitude	log count rate	70.504	0.867	Counts	Impulse factor	1.097	0.795
RMS	log count rate	70.259	0.920	---	---	---	---
log count rate	RSSQ	68.661	0.848	---	---	---	---
Shannon entropy	log RSSQ	67.921	0.773	---	---	---	---
log count rate	Maximum amplitude	67.601	0.860	---	---	---	---
log count rate	Counts	65.860	0.884	---	---	---	---

give the angles and r² values for each combination of features, which exhibit a statistically significant change in behavior between stage 1 and stage 2, stage 2 to stage 3, and stage 1 to stage 3 (for completeness), respectively. Note that these tables show all the linear models that produced a good fit for the data with significant changes in the data.

Figure 16 shows an example of log count rate vs counts, with a statistically significant change in models for each stage of galling wear.

4. Discussion

During sliding friction, the AE signal is continuous. This makes it challenging to detect damage early. So, this research focused on the trends of the AE bursts and how these trends differ as the wear/damage progresses and the damage mechanism changes. Previous work has shown that wear can be characterized by the changes in peaks and troughs in the surface profile of the wear scar [40]. It is known that AE is released at the instant of fracture. The question, therefore, is whether the properties of the burst change predictably with increasing wear.

It is understood that various AE sources produce distinct AE signals, each indicative of different material failure modes. Thus, analyzing the fundamental features of the AE signal allows for the identification of the characteristics of the AE sources and an understanding of how those sources are changing.

To investigate how the characteristics of the AE burst changed with progressing galling wear, this research explored linear modeling and cluster analysis to characterize a change in the behavior of the AE signal in scratch testing. AE features not typically used in wear detection but used in other applications of AE were investigated to search for superior features for identifying the change in galling wear regime.

Figure 9A shows the relationship between COF and the time the burst occurred, while Figure 9B shows the relationship between Ra and the time the burst occurred. The stochastic nature is evident as there are several times in which a range of COF and Ra measurements were observed. For example, a burst detected at 20 s could either be low or high friction and exhibit a range of Ra values.

Figure 10 shows the relationship between COF and Ra, measured instantaneously by the load cell during the test and wear scar roughness observed post-test. There is a generally increasing trend as expected; however, there is a clear region of AE bursts that correspond to high COF but low Ra. This is attributed to the material transferred to the indenter causing the friction to increase, which was then not present when the roughness of the wear scar was observed post-test. Nevertheless, the scratch test segments have been split into three categories, and the AE from each of these were examined to search for the most sensitive features to changing galling wear. The stages identified were as follows: “Stage 1”, where the COF remains below a threshold of 0.32; “Stage 3”, where the COF exceeds 0.9; and “Stage 2”, where the COF increases from 0.32 to 0.9. These data were utilized to differentiate the three stages in the observed scratch morphology.

The AE has been characterized and investigated via the evolution of numerous features. Twenty-six features and the natural logarithms (which were included to assure linear relationships for the linear regression modeling) of these features were investigated (52 total), including raw signal features, frequency-based features, statistical features, and impulse features. t-tests and linear regression models were used to evaluate the performance of the AE features versus the control variables for an inherent discrimination between control variables. Subsequently, cluster analysis and linear regression models were used to investigate the AE features for visually significant trends, such as those shown by Pomponi and Vinogradov [33], and changes in behavior in the AE domain without a direct measurement of the control variables.

The ability to detect the transition between each stage is important as these transitions reflect key moments in the progression of wear on the tool—notably the onset of galling and transition to severe galling wear—for developing predictive/preventative maintenance strategies. It is expected from the literature that some features change with time. However, for stochastic phenomena, a simple comparison of how the features change with time is often insufficient to predict when a change in regime is imminent.

4.1. t-Tests

The data analysis highlights that Sensor 1 (F15a) detected fewer bursts in the low COF range compared to Sensor 2 (R15a). This discrepancy is attributed to their differing frequency responses, with Sensor 2 being designed for factory and process monitoring, while Sensor 1 is typically used for structural health monitoring of large structures.

t-tests on AE features revealed that only counts and log bandwidth show differences across all stages, with counts commonly reported in wear detection literature for sheet metal forming and log bandwidth being a novel application. Counts indicate changes in signal activity, whereas bandwidth indicates changes in frequency content. Other features, such as duration, peak to RMS ratio, mean frequency, rise time, and decay time, show significant differences between stages 1 and 2 and between stages 1 and 3, but not between stages 2 and 3.

Conversely, the count rate and log count rate for Sensor 1 only showed differences between stages 1 and 3 and stages 2 and 3, but not between stages 1 and 2. This suggests an increase in AE activity indicating wear but does not predict the onset of wear. Log skewness and skewness showed stage-specific differences, indicating changes in burst shape. Features such as log RMS, log shape factor, and log impulse factor showed differences only between stages 1 and 3, indicating a change from no wear to wear, but they do not serve as predictors for wear initiation.

For Sensor 2, many features did not show significant changes between stages, with decay time and duration showing differences between stages 1 and 3 and stages 2 and 3, respectively, and rise time showing a difference between stages 2 and 3. This implies that the burst time and shape of the AE signal change with progressing galling wear. The t-tests serve as a one-dimensional clustering algorithm to test for significant differences between data arrays, suggesting that incorporating additional variables and cluster analysis would be a logical next step.

4.2. Cluster Analysis

An investigation of how the data clusters with the control variables revealed that there are no good scores for either sensor when discriminating stage 2 wear from stage 3 wear. This means the AE responses from stage 2 (nearly worn) to stage 3 (worn) are very similar and cannot be separated with this technique. Confirming this similarity between stage 2 and stage 3, the clustering often gave similar scores for discerning stage 1 to stage 2, as compared to stage 1 to stage 3.

However, for both sensors, rise time, power, and average signal level are among the features with the lowest clustering score, along with decay time and duration. The implication is that as the wear progresses, there is a greater buildup of strain energy within the material. When suddenly released at fracture, the additional strain energy affects the shape of the AE burst. This confirms our previous result [40], which investigated the series of peaks and troughs of the wear scar and showed the magnitude of these peaks and troughs increased as wear increased.

Following the works of Qiao et al. [36], k-means clustering in the AE parameter space was employed to search for inherent segregation in the data due to the evolution of galling wear. However, there were no good correlations between any stage other than stages 1 to 3 in either two or three dimensions (features). While this shows there is a change in the AE once wear has started, as shown by other authors, it does not serve as a useful prediction method for when galling is imminent with this application.

By observation of the data, it is evident that the issue is due to two factors:

• Firstly, the data distribution is not necessarily circular/spherical, and so the k-means algorithm is sub-optimal for the analysis of these data.
• Secondly, the transition zone is quite wide, and so there is a significant overlap between stages 1 and 2 and stages 2 and 3.

With this knowledge, it may be constructive to conduct the analysis with more complex clustering algorithms, such as density-based scan (DB scan), as used by [46], or hierarchical clustering algorithms as used by [34].

However, the clustering analysis does highlight the following features, which should be investigated in wear detection in sheet metal forming:

• From 2D clustering: duration, RMS, mean frequency (log mean frequency), bandwidth (log bandwidth), skewness, average signal level, maximum amplitude, rise time (log rise time), decay time, power, root amplitude, RA value, log rise angle, log decay angle.
• From 3D clustering: duration, RMS, mean frequency, bandwidth, average signal level, rise time, decay time, power, root amplitude, RA value, log rise angle, log decay angle.

This shows that the clustering is not improved by higher dimensions. Additionally, the same features, indicative of changes in the shape of the burst and the frequency content, are the features most useful for predicting changes in the galling wear regime.

Given that some of the poor clustering scores can be explained by the non-spherical (linear) nature of the distribution of the data, it seems natural to investigate the behavior of the data and the galling wear using linear regression models. As mentioned previously, there are a limited number of papers that have investigated the use of linear modeling for predicting galling wear. However, this is becoming a topic of increasing interest due to advances in machine learning and the desire for predictive maintenance strategies.

4.3. Linear Modeling

Linear modeling showed that only mean frequency and bandwidth (both frequency-based features; hence, after normalization, the models are very similar) were good for detecting a change in the galling regime when the model is predicting the COF. These models are all similar, with a p-value that is both significant and approaching significance for the changes between each stage. For sheet metal stamping, Shanbhag et al. [16,17] showed that mean frequency can be used to observe galling wear. However, bandwidth is novel in this application of AE. Interestingly, mean frequency is shown as an insignificant AE parameter between wear stages by the t-test analysis.

The linear modeling did not find any good models for any AE parameter against Ra, with the r² value remaining relatively low (approximately 0.5, which is below acceptable standards of 0.7). This is indicative of the experimental difficulties of synchronizing the roughness measurements to the AE burst to the level of precision required. The roughness measurements are determined post-test (by observation of the start and end of the wear scar of the scratch), whereas the COF can be synchronized to the accuracy of the two systems. Therefore, it is clear in the COF data and AE data when the tests started, but not as clear when inspecting the scratch in the profilometer post-test. The r² value is sub-optimal (approximately 0.5) as there is a general increase in roughness with increasing wear, so there is still some correlation.

Linear modeling has not been used in this manner in the literature, except for a small number of research articles. However, authors such as Sindi et al. [37] report a linear increase in the amplitude of the raw AE signal with the progression of galling wear. Sindi at al. [37] also showed that the amplitude and duration of an AE burst change with increasing wear. In this work, we sought to further develop this understanding by exploring more features to describe the shape of the AE bursts (such as rise angle and rise time) and how these bursts change with increasing wear.

It has been established that an increase in COF and roughness is a clear sign of galling wear, as it is indicative of transferred material. However, as directly measuring the friction and roughness is inherently difficult in real-world industrial applications (such as sheet metal forming processed), it is important to develop methods to infer these control variables from the observed AE without this direct measurement.

Using the friction and roughness data from the previous subsection to classify the data into low, medium, and high friction responses, linear regression models only found 10 models (pairs of features) that made a suitable model for Sensor 1. For Sensor 2, only five models were identified as suitable—see Table 8, Table 9 and Table 10.

It is noticeable that the angle differences between each stage are much smaller for Sensor 2 than for Sensor 1. Additionally, it is interesting to note that different features showed good behavior for the linear modeling and clustering analysis for the different sensors. The sensors were positioned symmetrically about the center axis of the sample plate in the same way (i.e., comparable clamping load and couplant used on each sensor), and the scratch direction was perpendicular to the axis between them. Therefore, this analysis highlights that different features are more suitable for different sensors, likely due to the different frequency responses of the two sensors.

It is known that AE is a release of strain energy at the instant of fracture. The features identified are perhaps indicative of a change in the release mechanisms of the built-up strain energy, reflecting a change in the damage mechanism taking place. For example, for an increase in rise angle and decay angle between two bursts, more energy must be released in a similar duration period as compared to the previous, which would not be revealed by amplitude or duration as individual features. As established in our previous work [40], the morphology of the scratch changed as the wear progressed, with an increase in size and frequency of peaks and troughs forming in the wear scar as well as an increase in material transferred to the tool. Therefore, this change in the behavior of the bursts is attributed to a change in the damage occurring in the wear scar. While the change in damage is related to this material pairing, it is expected that this damage would be seen for other aluminum alloy/steel tool tribopairs.

5. Conclusions

This research has explored the feature selection of AE characteristics of galling behavior from dry sliding scratch tests at slow sliding speeds. The research used linear regression modeling and cluster analysis of the AE bursts to search for the characteristic traits of the AE bursts during different stages of galling wear.

• t-tests vs. the control variables identified that counts and log bandwidth show a statistically significant difference between each stage. Log bandwidth is novel in this application.
• t-tests suggest other novel features are suitable for galling wear detection. These are peak to rms ratio, (crest factor), rise time, decay time, decay angle, signal to noise ratio, and log Shannon entropy.
• Cluster analysis of the AE features using the k-means algorithm was not suitable to detect the “stage 2” galling regime, particularly where the data are non-spherical/ highly linear, which is why linear modeling was also used. However, cluster analysis identifies features that identify that the shape of the burst changes as the wear progresses from stage 1 to stage 3, which is indicative of a transition between ductile and brittle fracture in the contact. These are duration, RMS, mean frequency (log mean frequency), average signal level, maximum amplitude, and power. Additional novel features are bandwidth (log bandwidth), skewness, rise time (log rise time), decay time, root amplitude, RA value, log rise angle, and log decay angle.
• Linear regression modeling of the AE features identified only mean frequency and bandwidth as individual features that may show a change in the galling wear stage. In this case, mean frequency and bandwidth can be used to predict COF.
• While the previous analysis in this article showed the features that reflect a change in the shape of the burst, linear regression modeling did not rely on such features; rather, they relied on raw signals and impulse features.

This work adds to the knowledge in the field by identifying AE features not currently used in the field of wear detection in sheet metal forming and confirms their viability. Further work could aim to develop a more detailed predictive model, drawing on a combination of the recommended features.