Revisiting an Indentation Method for Measuring Low Wear Rates Using 3D Interferometry

Abstract

Predicting the wear of disc cutters in Tunnel Boring Machines (TBMs) is a complex challenge due to the large scale of the machinery and the numerous operational variables involved. Laboratory-scale tests offer a controlled approach to isolating and analyzing specific wear mechanisms. However, the extremely low wear rates observed in such simulations pose challenges for conventional characterization methods, as gravimetric and profilometric techniques often lack the precision and accuracy needed to measure low wear patterns with an uneven morphology. To address this, this study revisited a methodology for quantifying low wear rates in a reciprocating wear test using AISI H13 tool steel disc cutters. This approach integrates spherical indentation marks as reference points with 3D white-light interferometry, enabling high-precision material loss measurements. Eighteen disc samples were subjected to wear testing, with 3 indentations analyzed per sample, for a total of 54 indentations. The statistical validation confirmed the method’s reproducibility and reliability. The proposed approach provides a robust alternative to existing techniques, addressing a critical gap regarding the accurate quantification of low wear rates in controlled laboratory settings.

1. Introduction

The increasing demands of projects in urban environments have driven the widespread adoption of mechanized excavation using Tunnel Boring Machines (TBMs). The efficiency and cost-effectiveness of these operations rely heavily on the performance and durability of their cutting tools [1], which can represent up to 30% of the cost per excavated meter. Despite advancements in TBM technology, the unpredictable consumption of Tunnel Boring Machine (TBM) disc cutters remains a significant challenge, leading to cost overruns and delays in tunnel construction projects. Accurately predicting cutter wear is, therefore, crucial for optimizing excavation performance, minimizing maintenance downtime, and ensuring cost-effective operations.

Traditionally, disc cutter wear is evaluated through field-based measurements [2], full-scale testing [3,4], and laboratory-scale simulations [5,6]. Each of these approaches has inherent limitations. Although they can capture actual operational conditions, field-based methods often lack precision due to uncontrolled variables and operational constraints. Full-scale testing, although highly representative, is prohibitively expensive and time-consuming, making it impractical for widespread use. Consequently, laboratory-scale testing has emerged as a viable alternative, enabling researchers to isolate and control specific factors that influence wear mechanisms.

Despite its advantages, laboratory-scale testing for disc cutter wear determination presents certain challenges. TBM thrust forces typically reach the mega-Newton range, whereas laboratory equipment operates at a much lower force magnitude, often in the Newton range (i.e., six orders of magnitude lower). Additionally, the critical wear height observed under uniform wear conditions in the field translates to extremely low wear rates in laboratory setups.

Conventional methods, such as mass loss measurements [7,8] and profilometry [9], struggle to capture the minimal amounts of material removed in these tests [10]. Mass loss techniques are generally ineffective in low-wear conditions due to their limited sensitivity. Meanwhile, optical interferometry for “almost zero wear” (AZW) [11,12] determinations suffers from positioning errors that restrict its reliability. These limitations highlight the need for alternative measurement techniques to detect and quantify low wear rates with high accuracy and reproducibility.

This study addressed the challenge of quantifying low wear rates in laboratory simulations of TBM disc cutter wear. Our research framework combines two methodologies: the use of spherical indentation marks as reference points and 3D white-light interferometry for high-precision measurements. This approach aims to overcome the limitations of traditional wear determination techniques, which often rely on operator-dependent measurements and lack the sensitivity required for low-wear applications [13,14,15]. Through the integration of interferometry, we can reduce inaccuracies [16] and enhance the precision of the obtained measurements, offering a simplified and more reliable wear assessment process compared to conventional AZW techniques.

To validate the proposed methodology, we conducted a reciprocating wear test on AISI H13 tool steel disc cutter samples to create indentation marks, and the height before and after the wear experiment was measured. Statistical analyses, including ANOVA and paired t-tests, were performed to confirm the method’s reproducibility and reliability. The key findings demonstrate that this integrated approach provides a robust and statistically validated alternative to existing techniques, effectively addressing the critical gap in quantifying low wear rates in controlled laboratory settings.

2. Materials and Methods

2.1. Steel Characterization

The chemical composition of the disc cutter sample was determined through spark atomic emission spectrometry; the result is presented in

Table 1. Chemical composition of disc cutter sample * (equivalent to AISI H13 steel), in % wt.

C	Si	Mn	Cr	Mo	V	W
0.451	0.988	0.355	5.482	1.145	0.871	0.149

* Fe: balance; P and S < 0.015.

. The disc cutter sample was prepared using standard metallographic procedures, which consisted of grinding and polishing, followed by etching with 3% nitric acid. The observed microstructure was a tempered martensite resulting from quenching and tempering (Figure 1).

Ten Vickers hardness measurements were conducted in an EMCO-TEST M4C G3 Universal Hardness Testing Machine (EMCO-TEST Prüfmaschinen GmbH, Kuchl, Österreich) with a 1 Kg load, resulting in an average value of 615 ± 4 HV.

2.2. Test Rig and Specimen Preparation

To develop a novel laboratory-scale wear test for Tunnel Boring Machine (TBM) disc cutters (AISI H13), we made several simplifications and methodological choices to replicate the real-scale problem while optimizing the practicality of the test. We acknowledge that the actual TBM working environment involves complex conditions, including high contact pressures, heterogeneous rock, and variable cutter velocities—factors that differ significantly from a controlled lab setting. To bridge this gap, we focused on replicating key aspects of the TBM process, such as the variable velocity profile. In real operations, the disc cutter starts with zero velocity, reaches a maximum speed during rock contact, and then decelerates back to zero [17]. To simulate this, we adopted a reciprocating test module, similar to that of Milan et al. [18], in order to replicate the variable velocity profiles in our lab-scale tests.

The test rig used was the UMT Universal tribometer in the reciprocating module. The setup included a fixing bracket for the disc sample, a test block with sandpaper, and a gutter (Figure 2). The upper part was fixed, and the lower part had a 10 mm track with reciprocating movements. The test was performed at a frequency of 3 Hz for 90 s. Water at an inflow rate of 3 mL/test was used as the lubricant.

The disc samples were taken from a 15″ TBM disc cutter and reduced by electro-discharge machining to a length of 20 mm, a width of 15 mm, and a height of 27 mm (Figure 3). The wear test setup was utilized to prepare eighteen samples. First, the contact area of the disc samples was prepared by coarse sanding until a flat surface was obtained. Then, using the same test setup, all the samples were finely sanded with decreasing grit sizes, ranging from 220 to 600 mesh. The flatness of the contact area was verified to ensure complete contact between the disc and the sandpaper.

The final contact areas were measured using a light optical microscope, and five determinations were made using the ImageJ software 1.46r [19]. The applied force for the test was adjusted based on the mean area of contact to achieve 1.5 MPa of contact stress, resulting in an applied force variation between 75 and 96 N.

A key aspect of this study was the use of alumina sandpaper as the counterbody instead of a rock sample. In TBM operations, disc cutters experience complex interactions with heterogeneous rock formations. This heterogeneity introduces uncontrolled variability that complicates laboratory testing. A sandpaper counterbody allows for a controlled abrasive surface, ensuring consistent and repeatable wear measurements. Although this simplification reduces some of the complexity of real interactions between disc and rock samples, the use of alumina sandpaper [20] as the counterbody avoids the complexities associated with preparing rock samples, reduces the test time, and minimizes the variability introduced by the heterogeneity of rock materials, enabling the isolation of specific wear mechanisms and improving the methodological reliability. Future studies will extend this methodology to rock-based counterbodies in order to enhance its applicability in practical tunneling scenarios.

Abrasive grains, with diameters ranging from 15 to 30 μm, provided a consistent and uniform wear surface (Figure 4), enabling us to measure variations in indentation height. This setup allowed for the investigation of regular disc cutter wear while maintaining a controlled tribosystem.

Given the controlled nature of the setup, abrasive wear resulting from the direct interaction between the tool steel disc cutter and the alumina sandpaper was considered to be the primary mechanism at play. The observed changes in surface roughness likely stemmed from the formation of micro-grooves caused by the abrasive particles. Consequently, the reduction in indentation height reflects the overall material loss due to this abrasive action. It is important to note that the experimental design accelerated the wear to facilitate quantifiable measurements. As a result, it may not perfectly replicate the complex interplay of wear mechanisms observed in real-world TBM operations.

2.3. Wear Measurement Procedure

The wear measurement procedure involved creating indentation marks on the contact area of the sample and comparing the height before and after the wear experiment.

Several criteria guided the selection of the reference mark. It needed to be easily identifiable, minimize potential errors, and account for the limitations of interferometry measurements, especially regarding the geometry of the mark, such as closed-angle marks (e.g., a Vickers pyramid). The interferometry measurement required sufficient precision without necessitating nanoscale measurements, as the worn height range was outside the measurement error range.

Considering these criteria, including the necessity of creating a worn height that exceeded the measurement limit and the high time cost for fine preparation, a spherical indentation (Brinell) shape was selected.

Indentations were created using an EMCO-TEST M4C G3 (EMCO-TEST Prüfmaschinen GmbH, Kuchl, Österreich) hardness tester with 5 mm tungsten carbide balls, applying a load of 60 kg for 15 s. The indentations were spaced at least 3 mm apart to avoid the hardening effect, as recommended by ASTM E10-18 [21]. Three indentations were made on each disc sample: central, left, and right indentations (Figure 5).

The applied load used for indenting was determined in preliminary tests with loads of 30 N, 60 N, and 100 N. Figure 6 displays a comparison between the indentations and the mean horizontal profile of each load. The 30 N load resulted in very shallow indentations, with the depth being lost during the wear test. The 100 N load caused a pronounced pile-up, potentially creating a preferential contact surface that would alter the wear conditions compared to flat surface contact. Based on this preliminary assessment, a 60 N load was selected.

The indentation marks and the roughness of the contact area outside the indentations (contact area post-preparation) were measured before and after each wear test using a white-light interferometer (Taylor Hobson Talysurf CCI Lite) integrated with the TalyMap Platinum 6.1 (DigitalSurf) software. The interferometer has a resolution of 1024 × 1024 pixels, with a sampling area of 0.83 × 0.83 mm and a vertical resolution of 0.01 nm. Measurements were conducted as follows using consistent filtering operations: (i) leveling using the least squares (LS) plane method, (ii) form removal using a third-order polynomial, (iii) filling of non-measured points, and (iv) applying a threshold from 0.001 to 99.9%.

The contact area roughness of each sample before the wear test was Sq (root mean square) = 1.1 ± 0.7 μm and Str (texture aspect ratio) = 0.07 ± 0.02, indicating that the sanding resulted in strongly anisotropic surfaces. The variability in the roughness of the contact areas before the wear test was analyzed through the height distribution and quantified using the roughness parameters Ssk and Sku.

The height of each indentation was determined by averaging 100 horizontal profiles extracted from a consistent area within the deepest central region of the indentation (Figure 7). Vertical profiles were not used due to the high roughness resulting from their perpendicular orientation relative to the sanding direction.

The height of the mean horizontal profile was defined using the Surface of a Hole/Peak (Profile) tool available in the TalyMap Platinum 6.1 software, which allows the user to quantify specific measurements in a hole or peak. Among the available methods to limit the extension of the hole, the chosen method (“Hole under the Water Line”) simulates filling the hole with water up to an imaginary level, which identifies the lowest and highest points between the two delimiters of the profile, and then fills the hole up to the lower of the two summits (Figure 8). This method is particularly effective in minimizing errors related to roughness outside the profile and reducing operator influence in defining the indentation extension, making it the optimal choice for this study.

2.4. Statistical Analysis

Statistical analyses were performed using the R programming language [22,23,24]. The two variables analyzed were the indentation height before and after the wear test. A level of 5% (p < 0.05) was considered to be statistically significant in all the analyses.

According to the Central Limit Theorem (CLT), if a population is normally distributed, the distribution of the sample means will also follow a normal distribution, regardless of the sample size. For populations with unknown or non-normal distributions (e.g., asymmetric or uniform), the CLT states that the sampling distribution of the means approaches normality as the sample size becomes sufficiently large (typically n ≥ 30). This principle enables confidence intervals and hypothesis testing to be applied reliably, even when the underlying population distribution is unknown or non-normal.

The statistical treatment of the experimental data was structured into five stages.

• Descriptive Statistics: Median, mean, mode, standard deviation (SD), coefficient of variation (CV), confidence interval (CI), kurtosis, skewness, and p-values were calculated for all measured parameters. These descriptive metrics provided an initial understanding of the data distribution.
• Sample Size Validation: Based on the Central Limit Theorem, sample size adequacy was confirmed by calculating the confidence intervals for the mean. The maximum error, “e”, of the confidence interval was computed according to Equation (1):

  $$\mathrm{n}={\left(\frac{{\mathrm{Z}}_{\frac{\mathsf{\gamma }}{2}}.\mathsf{\sigma }}{\mathrm{e}}\right)}^2$$

  (1)

  where e = CImax − CImin; n = sample size; Z_(γ/2) = normal value associated with confidence coefficient; and σ = standard deviation of X.
• Verification of Statistical Differences Between Groups: Analysis of variance (ANOVA) was applied to assess the statistical significance of the differences between the three groups of indentations: central, right, and left. The null hypothesis assumed similar means across the groups, while the alternative hypothesis suggested that at least one mean was different.
• T-Test for Paired Samples: To evaluate the differences in indentation height before and after the wear test, a paired Student’s t-test was conducted. The null hypothesis posited that the means were similar, while the alternative hypothesis suggested a difference.
• Data Visualization: The results were visualized using boxplots to illustrate the distribution and variability of the indentation heights. Additionally, p-values were reported to indicate the statistical significance of the observed differences.

3. Results and Discussion

3.1. Surface Roughness Variation

The roughness of the contact area outside the indentations, as measured by the Sq parameter, decreased to 0.6 ± 0.3 µm after sanding in the wear test. This reduction indicates the influence of overlap during the sanding process, which contributed to the wear of the sandpaper itself. As illustrated in Figure 9, the worn sandpaper exhibited significant clogging, characterized by metal debris embedded within the abrasive surface. This clogging is a critical factor in the expected decrease in the sandpaper’s efficiency [25], as the accumulation of metal debris obstructs the cutting action of the alumina grains, reducing their ability to effectively remove material from the disc cutter.

While some loss of anisotropy was expected, the measurements of the Str parameter showed consistent average values before and after sanding. However, further insights into the wear process can be gained by analyzing the height distribution of the asperities using a morphological map, as proposed by Mehl et al. [26] (Figure 10). This approach aligns with the findings of Duo et al. [27], who emphasized the critical role of skewness (Ssk) in characterizing wear performance. Data from all 18 sample contact areas outside the indentations were used for this analysis to ensure statistical relevance.

The surface topography analysis before and after the wear test revealed distinct characteristics in terms of asymmetry (Ssk) and kurtosis (Sku). Before the test, Ssk exhibited a mean of −0.322 ± 0.481, indicating a general tendency toward surfaces with more valleys than peaks and considerable variability across the different samples. After the test, the mean Ssk shifted slightly to −0.204 ± 0.449. In contrast, Sku exhibited a mean of 3.405 before and 3.408 after the test, with standard deviations of 0.909 and 0.688, respectively, suggesting a consistent level of “peakedness” and less variability. The Ssk parameter values for unworn surfaces were generally more negative, indicating a predominance of valleys. However, after the wear process, the skewness values decreased, shifting toward a balance between peaks and valleys, with positive Ssk values appearing, suggesting active cutting across the surfaces.

Despite the apparent homogeneity of the sandpaper, considerable variation in the surface topographic parameters was observed, challenging the application of “almost zero wear” methods. The percentage changes in Ssk exhibited a wide range, from 18% to 1245% (Figure 11), while the percentage changes in Sku ranged from 1% to 77%. This, combined with the shift in mean Ssk, suggests that the surface roughness was not uniform and predictable, potentially introducing errors in the “almost zero wear” measurements based on surface roughness. This issue is exacerbated when considering rock heterogeneity, further complicating accurate reference repositioning.

3.2. Wear Measurements

A total of 18 disc samples were tested, and 54 indentations were measured before and after the wear test.

Table 2. Indentation data, including test parameters and height measurements, were recorded before and after the wear test.

Indentation (ID)	Position 1	Mean Area (mm2)	Applied Force (N)	Height Before (nm)	Height After (nm)
1	L	57.06	85.60	7498	4668
2	R	57.06	85.60	8263	5847
3	C	57.06	85.60	7110	4996
4	L	61.26	91.89	8134	4585
5	R	61.26	91.89	9792	7921
6	C	61.26	91.89	7297	4701
7	L	50.60	75.90	7739	6530
8	R	50.60	75.90	6954	4709
9	C	50.60	75.90	8493	4760
10	L	63.04	94.56	8118	7886
11	R	63.04	94.56	8827	8726
12	C	63.04	94.56	10,069	8663
13	L	56.53	84.80	4293	4138
14	R	56.53	84.80	10,160	4130
15	C	56.53	84.80	6727	5507
16	L	54.31	81.46	10,046	7539
17	R	54.31	81.46	8642	5177
18	C	54.31	81.46	9091	6562
19	L	57.90	86.86	7744	4648
20	R	57.90	86.86	8104	5982
21	C	57.90	86.86	8643	6342
22	L	64.25	96.37	10,025	5340
23	R	64.25	96.37	7778	6716
24	C	64.25	96.37	9041	5881
25	L	51.63	77.44	4760	3497
26	R	51.63	77.44	6567	6365
27	C	51.63	77.44	7360	4556
28	L	60.93	91.40	9915	8014
29	R	60.93	91.40	9185	5122
30	C	60.93	91.40	7223	4108
31	L	57.48	86.22	4524	4317
32	R	57.48	86.22	6736	4376
33	C	57.48	86.22	10,016	7397
34	L	54.83	82.24	11,037	6156
35	R	54.83	82.24	11,021	7243
36	C	54.83	82.24	10,080	2856
37	L	58.90	88.35	7903	3727
38	R	58.90	88.35	7222	7360
39	C	58.90	88.35	8258	6503
40	L	65.25	97.88	8315	7469
41	R	65.25	97.88	8237	5428
42	C	65.25	97.88	7677	5503
43	L	52.63	78.95	6277	3968
44	R	52.63	78.95	7697	7127
45	C	52.63	78.95	8016	5629
46	L	62.93	94.40	8643	5451
47	R	62.93	94.40	9778	7689
48	C	62.93	94.40	7312	4282
49	L	58.48	87.72	8323	5613
50	R	58.48	87.72	8776	4118
51	C	58.48	87.72	7966	5613
52	L	55.83	83.75	7059	3591
53	R	55.83	83.75	7521	5033
54	C	55.83	83.75	6816	4569
1	L	57.06	85.60	7498	4668
2	R	57.06	85.60	8263	5847
3	C	57.06	85.60	7110	4996
4	L	61.26	91.89	8134	4585
5	R	61.26	91.89	9792	7921
6	C	61.26	91.89	7297	4701
7	L	50.60	75.90	7739	6530
8	R	50.60	75.90	6954	4709
9	C	50.60	75.90	8493	4760
10	L	63.04	94.56	8118	7886
11	R	63.04	94.56	8827	8726
12	C	63.04	94.56	10,069	8663

¹ L: left indentation; R: right indentation; C: center indentation.

presents the test parameters (mean contact area and applied force) and the height measurements before and after the wear test for each indentation.

3.3. Reliability of Results

Table 3. Statistical summary of height measurements before and after the wear test.

Variable	Median (nm)	Average (nm)	Mode (nm)	SD 1 (nm)	CV 2	CI 3 Min 95%	CI Max 95%	E 4 (nm)
Before test	8110	8643	8126	1455.2	17.9	7737.9	8514.2	776.3
After test	5477	5613	5641	1429.6	25.3	5260.0	6022.7	762.6

¹ Standard deviation; ² coefficient of variation; ³ confidence interval; ⁴ error.

presents the descriptive statistics calculated for the two variables: height before and after the wear test. The sample size calculated for both variables was approximately 14 units, confirming that the sample size of 18 units per group (54 in total) was statistically sufficient for the study.

Table 4. Shape analysis of data distribution and distribution classification for height measurements before and after the wear test.

Variable	Kurtosis	Skewness	Sig (p)	Distribution
Before test	0.6117	−0.3502	0.0913	Normal
After test	−0.6878	0.3741	0.1424	Normal

shows the shape parameters, including kurtosis and skewness, and the p-values for normality testing. Based on parametricity criteria, both variables demonstrated a normal distribution.

The ANOVA for the variable “height before the wear test” (Figure 12) for the three groups (central, left, and right indentations) yielded a significance value of p = 0.46. As p > 0.05, the null hypothesis was accepted, indicating no statistically significant difference between the groups. Therefore, all indentations can be considered a single group.

Figure 13 shows a 3D comparison of the indentation heights before the wear test in the same disc sample for the center, left, and right indentations.

Considering the same three groups, the ANOVA for the variable “height after the wear test” (Figure 14) resulted in a significance level of p = 0.32. As p > 0.05, the null hypothesis was again accepted, confirming no statistically significant difference between the groups after the wear test.

Figure 15 presents a 3D comparison of the center, left, and right indentation heights in the same disc sample after the wear test.

A paired Student’s t-test was conducted to compare the indentation heights before and after the wear test (Figure 16), yielding a significance level of p = 0. As p < 0.05, the null hypothesis was rejected, indicating a statistically significant difference between the indentation heights before and after the wear test.

Figure 17 illustrates a 3D comparison of the same indentation before and after the wear test.

4. Conclusions

This study revisited a methodology for the evaluation of low wear rates in laboratory-scale wear tests. This approach integrates spherical indentation marks as reference points with 3D interferometry to quantify material loss with high precision in order to address the limitations of conventional techniques such as mass loss measurements and AZW methods. Unlike mass loss measurements, which lack sensitivity under low-wear conditions, and AZW, which can suffer from positioning errors, this method offers an accurate and reproducible means of quantifying low amounts of material removal based on widely available and consolidated methods and equipment commonly found in tribology labs.

The limitation of AZW based on surface roughness changes was supported by our findings regarding significant variability in surface topography parameters before and after a wear test, with changes in Ssk ranging from 18% to 1245%. Such variability suggests that the surface roughness is not uniform and predictable, potentially introducing substantial errors in AZW via interferometry measurements only.

The statistical validation confirmed the reproducibility and reliability of the proposed method. The descriptive analysis demonstrated that the sample size was statistically sufficient (>14) and that the indentation height measurements were normally distributed. The hypothesis testing indicated no significant variation between indentation positions (left, center, and right) before or after testing, which confirmed the uniformity of the indentation process and consistency in sample preparation. A paired t-test revealed a statistically significant reduction in indentation height, with an average decrease of approximately 35%, demonstrating the methodology’s effectiveness in detecting subtle wear patterns. Using alumina sandpaper as a counterbody allowed for a controlled environment and simplified the wear conditions for the initial validation of the method. This simplification reduces some of the complexity of real-world TBM operations and helps to achieve the objective of accelerating wear while maintaining an isolated abrasion wear mechanism.

These findings highlight the potential of this lab-scale setup as a robust and precise alternative for quantifying low wear. This method contributes to advancing tribological research and wear analysis by providing a more sensitive and reproducible technique for assessing low wear rates, offering a pathway to improving TBM cutter disc performance, and achieving potential cost savings in industrial applications.