Optimization of Measurement Area Selection for Accurate 3D Surface Topography Characterization in High-Feed Tangential Turning of 42CrMo4 Alloy Steel

Abstract

Accurate characterization of 3D surface topography is essential for assessing the quality of machined components. This study investigates the influence of measurement area selection on the evaluation of roughness parameters in high-feed tangential turning of 42CrMo4 alloy steel. Cylindrical surfaces were machined using different process parameters, and their surface topography was analyzed by varying the size of the areal measurement region. Key roughness parameters were examined to determine the impact on the reliability and consistency of surface characterization. The results highlight how different measurement areas influence roughness values and their variations. The findings contribute to improved metrological practices in tangential turning, and they are particularly relevant for precision machining applications where surface integrity plays a critical role. The area width of the measurement area was shown to play a critical role in data reliability. The results showed that S_a and S_k stabilized after 5.5–6.0 mm, while S_sk and S_ku stabilized earlier, at approximately 5.0 mm. S_pk and S_vk required the longest evaluation area widths, up to 6.0 mm, to achieve consistent values.

1. Introduction

With rapid industrial advancements and increased global competition, manufacturing quality has become central to modern production strategies [1]. Quality assurance is no longer a supplementary component of manufacturing, but a vital element integrated throughout the design, process planning, and production phases [2]. As industries adopt smarter manufacturing systems and digital twins, precision and consistency in the final product are essential. Among the many aspects of quality control, surface quality—particularly surface roughness—plays a decisive role in determining the functional performance, aesthetics, wear resistance, fatigue life, and lubrication behavior of machined components [3]. In sectors such as automotive, aerospace, biomedical, and precision engineering, where surface integrity directly affects the reliability of the component [4], the demand for detailed and accurate surface roughness evaluation has significantly increased.

Surface roughness, often quantified through various statistical and functional parameters, serves as an indicator of the machining process capability and tool condition [5]. It is influenced by a complex interaction of cutting parameters, tool geometry, material properties, machine dynamics, and environmental conditions. Traditionally, surface roughness has been assessed using 2D profile measurements along a defined line, which provides a simplified representation of the surface characteristics [6,7]. However, with the appearance of advanced machining methods and the increasing demands for functional surface designs, profile measurements alone are insufficient [8]. They are unsuccessful in capturing the spatial variations, texture orientations, and localized anomalies that may exist across a machined surface. To overcome this limitation, areal surface topography measurements (commonly known as 3D surface roughness measurements) have gained prominence. Areal surface roughness assessment provides a more comprehensive representation of the surface texture by capturing the full spatial structure of the machined surface over a defined area [9]. The different parameters offer deeper insights into the topographical features that influence mechanical contact [10], fluid retention [11], coating adhesion [12], and wear behavior [13]. With the evolution of measurement standards such as ISO 25178 [14], areal surface characterization has become standardized and methodologically developed, allowing for more precise quality control and process optimization. However, this transition also introduces new challenges [8,15], particularly relating to the selection of the measurement area, filtering techniques, sampling density, and parameter suitability for specific applications. Choosing the correct measurement parameters is of primary importance in surface topography analysis [16,17]. Measurement area size, orientation, and resolution can significantly influence the values of roughness parameters [8,18], especially in high-feed machining scenarios where the surface topography shows definite directional features and periodically spaced patterns [19]. Incorrect area selection or insufficient resolution can lead to misleading results, lowering the effectiveness of process optimization and quality assessment. Consequently, establishing best practices for areal measurement strategies is essential [18], particularly when dealing with complex machining processes like varied feed burnishing [20,21] and tangential turning [22].

Tangential turning [22] is a specialized machining technique characterized using cutting tools with significantly inclined rake angles and a predominantly tangential cutting direction. Its kinematic and geometric relations are shown in Figure 1. The abbreviations are the following: radius of the workpiece to be machined (R_w), machined workpiece radius (r_w), workpiece length (L_w), tool length (L_t), inclinational angle of the tool (λ_s), revolutions of the workpiece (n_w), tangential feed rate of the tool (v_t,t) depth of cut (a_p) from the workpiece. Cylindrical workpieces with shorter length than the tool can be machined in high-feed conditions in the axial directions.

This method allows for higher material removal rates while maintaining acceptable tool life and surface quality [23], making it especially suitable for high-volume and high-efficiency manufacturing environments. The tangential approach results in unique surface patterns and texture formations that deviate from those generated in conventional turning [24]. Due to its kinematic structure and the inclination of the cutting edge relative to the feed direction, tangential turning tends to generate periodic surface features with significant anisotropy and feed marks that influence both the form and the function of the resulting surface [25]. The analysis of surface roughness in tangential turning presents specific challenges, many of which come from the high feed rates and the distinct texture patterns created during the machining process. At increased feed rates, the distance between adjacent cutting edge passes increases, often leading to the formation of periodic waviness-like structures [26,27]. Accurate assessment of such surfaces requires careful alignment of the areal measurement area with the dominant surface features, as well as careful filtering to isolate roughness from form and waviness. One of the most critical considerations in areal measurement of tangential turning surfaces is the selection of the measurement area [18]. The area must be large enough to include multiple periods of the surface structure to produce statistically representative roughness values, but small enough to avoid overlapping with adjacent machining features or geometrical transitions. Furthermore, the scanning resolution must be fine enough to capture the surface micro-features [28]. Modern optical profilometers and confocal microscopes offer the capability to capture high-resolution topographies, but their performance can be constrained by factors such as surface reflectivity, or steep slopes.

In addition to instrumentation challenges, standardization in roughness evaluation for tangential turning is still evolving. Although ISO 25178 [14] provides a framework for areal measurement, it does not yet offer strict guidance modified to high-feed machining processes. This creates variability in experimental methodologies and limits comparability between studies [5,29]. For example, the use of different cutoff lengths, filtering strategies, and parameter subsets can lead to significantly different interpretations of the same surface. As manufacturing industries continue to push the boundaries of productivity and precision [30,31], clear and representative surface roughness evaluation will remain a critical component of quality assurance. Areal surface metrology, when properly implemented, offers the potential to bridge the gap between surface characterization and functional performance [32]. However, this potential can only be realized through careful attention to measurement practices, especially in emerging machining processes such as tangential turning. According to ISO 25178-3, the long-wavelength filter is typically chosen as five times the largest spatial scale of interest, yet this guidance may be insufficient for machining processes that produce strongly periodic textures, such as tangential turning. This standard also acknowledges that the defaults may not be appropriate for highly directional or textured surfaces, and recommends adaptation based on functional needs.

Given these complexities, the present study focuses on the analysis of areal surface roughness parameters in tangential turning operations. While areal roughness measurement principles are standardized in ISO 25178 [14], these guidelines are not specifically given to tangential turning, which differs significantly from traditional longitudinal turning in its kinematics and feed-induced topography. The current study contributes by experimentally quantifying the parameter stabilization length under high-feed tangential turning, highlighting how process-specific anisotropies affect reliable measurement area selection. The objective is to investigate the influence of the evaluation area width on the resulting surface texture, while highlighting the sensitivity of different roughness parameters to measurement area selection and process conditions. The study aims to establish clearer correlations between measurement setups and functional surface characteristics. Additionally, the precision with which ISO 25178 S-parameters are evaluated from 3D topography maps in tangential turning is analyzed, which helps accurate 3D surface topography characterization after the machining process. These maps were acquired using a chromatic confocal system, and the study focuses on how measurement area width influences the reliability of these extracted roughness metrics. The topic is thus the metrological interpretation of 3D data, not the 3D reconstruction or modeling of the surface. Furthermore, the study highlights the need for measurement strategies that are designed to the specific kinematics of tangential turning. The research contributes to a deeper understanding of how surface roughness evolves in tangential turning and how it can be reliably quantified using areal metrology techniques.

2. Materials and Methods

To achieve the goal of the study, a series of machining experiments were designed and carried out, which are followed by the measurement of the generated surfaces. The cutting conditions were chosen to produce a range of roughness levels, while the metrology study focuses on their measurement stability.

2.1. Machining Conditions and Surface Preparation

The cutting tests were conducted using an EMAG VSC 400 DS hard machining center (EMAG GmbH & Co. KG, Salach, Germany), a high-precision machine tool specifically designed for the efficient machining of hardened materials. The arrangement and fixation of the tool and the workpiece are illustrated in Figure 2.

The test specimens were made from 42CrMo4 alloy steel, heat-treated to a hardness of 410 HV10 (or 390 HB), providing a suitable material condition for the detailed analysis. Each cylindrical workpiece had a diameter of 65 mm, offering sufficient surface area for comprehensive evaluation. Although the experiments were limited to 42CrMo4 alloy steel, the results gained regarding the relationship between evaluation area width and parameter stability are relevant for similar steel alloys. Future research will extend these findings to other materials, including aluminum and titanium, to assess how material properties affect surface measurement convergence behavior. Tangential turning was performed with a tool supplied by Hartmetall-Werkzeugfabrik Paul Horn GmbH (Tübingen, Germany). The tool holder used in the experiments had a 45° holder inclination angle and was identified by the code H117.2530.4132. It was equipped with an uncoated carbide insert (MG12 grade) with flat rake face, designated as S117.0032.00. The tangential turning tool used in this study had a total inclination angle of 45°, with a main cutting edge angle of 0°, a flank angle of 10°, a rake angle of 0°, and a cutting edge radius of 0.06 mm. These tool specifications were selected to ensure stability of the cutting process across all trials.

Five experimental setups were designed. Base values were chosen in Setup C for the cutting speed (v_c), the feed (f), and the depth of cut (a_p), which were 300 m/min, 1.0 mm/rev and 0.1 mm, respectively (based on previous experiments). Two additional setups were designed, to study the effect of the changing feed with 0.6 mm/rev (Setup A) and 0.8 mm/rev (Setup B) values, since this parameter has the most effect on the surface roughness among the three. Furthermore, one additional variation (0.2 mm) of the depth of cut was analyzed as Setup D, and 200 m/min cutting speed was also tested in Setup E. These values were determined according to the recommendations of the tool manufacturer and industrial partners, and the results of previous experiments. The selected parameters represent a typical high-feed tangential turning scenario, suitable for investigating surface topography in a widely applicable industrial context. While this study focuses on establishing a foundational understanding of areal roughness parameter stability under these conditions, future investigations are planned to extend the analysis toward high-speed cutting regimes and lower feed rates, including micro-feed applications. These forthcoming studies will build on the current findings and further explore the influence of expanded process parameter ranges on 3D surface characterization. Various types of tangentially turned surfaces could be analyzed by the designed experimental setup plan, which is shown in

Table 1. Values of the setup parameters in each experimental setup.

Setup Parameter	Setup
	A	B	C	D	E
vc [m/min]	300	300	300	300	200
f [mm/rev]	0.6	0.8	1.0	1.0	1.0
ap [mm]	0.1	0.1	0.1	0.2	0.1
Color code 1

¹ Blue indicates varying feed rates (darker shades for higher values), orange indicates increased depth of cut, and green indicates reduced cutting speed, with this color scheme used consistently throughout the manuscript.

.

2.2. Surface Topography Measurement and Analysis Steps

After machining, the surface roughness of the workpiece was evaluated using an AltiSurf 520 three-dimensional topography measuring instrument (Altimet, Thonon-les-Bains, France). The device has a measuring capacity of 200 mm × 200 mm × 200 mm, and 0.5 μm axis resolution. In this study, a modular chromatic confocal sensor system is used, which offers a vertical resolution of 12 nm and a vertical accuracy of 60 nm. Furthermore, it has a lateral resolution of 1.55 µm and spot size diameter of 3.1 µm. This system provides detailed surface texture measurement, enabling a comprehensive evaluation of the relationship between surface roughness parameters and evaluation area width. The measurements were processed and analyzed using AltiMap Premium 6.2.7487 software (Altimet, Thonon-les-Bains, France), which can calculate various surface parameters and characteristics. The combination of high-resolution optical scanning and advanced software analysis allowed for an in-depth assessment of surface quality. The AltiSurf 520 was selected due to its suitability for high-resolution areal measurements on hard, reflective surfaces, such as those produced by tangential turning on 42CrMo4 steel. Its chromatic confocal technology enables precise height acquisition without contact, which is essential for capturing subtle topographical features of fine-finished, hard materials. Nevertheless, it is acknowledged that the exclusive use of a single profilometer introduces a potential limitation regarding data consistency and metrological comparability. Cross-verification of results using alternative surface measurement systems—such as white-light interferometers or stylus profilometers—was not within the scope of this study but is identified as a valuable direction for future work. Such comparative analysis could help assess instrument-specific influences on areal roughness parameter values and further improve the robustness of evaluation area width recommendations

The three-dimensional topography measuring instrument was set to register an area with 10 mm width in the direction parallel to the symmetry axle of the workpiece and 8 mm height perpendicular to the latter on the periphery of the machined cylinders. The direction of the symmetry axle of the workpiece (which is the resultant axial feed direction) was set to be the main measurement axis with a 1 μm resolution, while the secondary axis perpendicular to the latter was set to have 10 μm resolution. The topography of a machined surface has a significantly greater alteration in the feed direction, which caused the one magnitude difference in the resolution of the two axes. The aim of the study was to analyze the roughness-filtered surfaces of the machined shaft. Therefore, the following operators are used in the surface evaluation software (in order of their application) to prepare the data for assessment:

• Zoom (Area extraction). This operator makes the extraction of a part of the studied surface possible. It is used to create the defined surfaces from the measurements.
• Leveling. This operator removes the general slope of a surface, which may result from a non-horizontal measurement. It uses the Least Squares Plane Method, which determines a plane that minimizes the sum of squared distances between the surface points and the plane. The horizontal positioning error of the workpieces is corrected in this study by this.
• Form Removal (F-operation). This operator mathematically removes the general shape of a surface (the form), allowing separate analysis of the waviness and roughness. It approximates the surface form using a slowly varying function, such as a low-degree polynomial or a circular/spherical fit, which is then subtracted. The polynomial degree is user-defined, but higher degrees increase computation time and may also remove waviness. In this study, a degree of 2 is applied to remove the cylindrical curvature of the measured surface.
• Thresholding. This operator cuts a surface at defined top and/or bottom altitudes, helping to remove excessive peaks and valleys that suppress details or to simulate wear. Thresholds can be adjusted as a ratio or depth. The removed areas can either be set to the minimum height value or marked as non-measured points, depending on the selected option. This operator is used to remove the outlier peaks and valleys from the analysis. The removed ratio of the measured points is 0.5% from the top and bottom.
• Fill In Non-Measured Points. This operator reconstructs missing surface data when non-measured points are present, either from measurement gaps or user-defined exclusions. It replaces these points based on neighboring valid data, ensuring a seamless and efficient fill. It is used to make the surfaces better for analysis.
• Roughness Filtering. This operator separates surface roughness and waviness based on a wavelength threshold (cut-off), which is set to 2.5 mm due to the applied feeds [14]. Small wavelengths are assigned to roughness.

To determine the minimal evaluation area width required for reliable surface roughness characterization, a systematic analysis was performed on areal surface topography data collected from machined samples. This study examined central surface zones, avoiding edges and groove transitions. Future research may analyze multiple circumferential areas to assess possible positional variation or chatter periodicity. The measurement setup allowed for flexible adjustment of the evaluation area along the feed direction. The shortest possible evaluation area width was defined by the selected cutoff value of 2.5 mm, as recommended by the standard [14] for high-feed turned surfaces. The selected cutoff of 2.5 mm aligns with ISO 25178 guidance for high-feed machined surfaces. Given the feed rates (0.6–1.0 mm/rev) and periodic texture features produced by tangential turning, a shorter cutoff would suppress relevant roughness wavelengths, while a longer one would risk combining roughness and waviness. Based on this constraint, the smallest analyzable evaluation area width was set to 2.5 mm. From this baseline, the width gradually increased in uniform increments of 0.2 mm, generating a series of analyzed sections at 2.6 mm, 2.8 mm, 3.0 mm, and so forth. This stepwise progression continued until reaching the maximum available area width of the measured surface, which was 8.0 mm. Each increment allowed for a consistent comparison of roughness parameters over increasingly longer sampling area widths. The intention behind this approach was to identify the point at which further extension of the evaluation area width no longer caused significant variation in the calculated surface parameters, indicating statistical convergence. Due to the highly periodic nature of the tangentially turned surface, the evaluation area height was set to 2.5 mm, since the increase in the measurement area in this distance results in no significant change in the roughness values. This statement is also supported by the pre-experiments carried out before this study.

The following three-dimensional roughness parameters of the surface (S-parameters) are analyzed in this study [14]:

• S_a [µm]—Arithmetical Mean Height,
• S_k [µm]—Core Roughness Depth,
• S_vk [µm]—Reduced Valley Depth,
• S_pk [µm]—Reduced Peak Height,
• S_sk [-]—Surface Skewness,
• S_ku [-]—Surface Kurtosis.

To ensure a comprehensive assessment of the surface topography, six S-parameters were selected for the analysis. One general parameter was chosen to represent the overall surface texture. In addition, three parameters derived from the Abbott–Firestone curve were included to characterize the material ratio curve and provide insights into the load-bearing properties of the surface. Furthermore, two functional parameters were considered to describe the surface, which are critical for evaluating surface functionality in machining applications. This combination of parameters was selected to capture both the general and application-specific aspects of the machined surface. By applying this method, the study aimed to define a practical and efficient evaluation area that ensures both reliable S-parameter values and minimal measurement time.

3. Results

Surface topography measurements were performed on each machined workpiece using the selected areal measurement system. Figure 3 shows the evaluated surface topographies for each result after Zoom, Leveling, and Form Removal operators were applied. The form (F) was removed using a second-order polynomial fit. The highly periodic characteristics of the tangentially turned surface can be observed from the surface diagrams, where the grooves generated by the tangential motion of the cutting tool during the concentrical rotation of the workpiece are reported. The measured points in the direction of the evaluation height (smaller side) show significantly lower variance than the points recorded in the direction of the evaluation width (longer side), which corresponds with the initial assumption about the evaluation area size selection.

The measured surfaces were divided into shorter evaluation areas. Starting from the width defined by the cutoff setting (2.5 mm), additional widths were analyzed in 0.2 mm increments to 8.0 mm. The results are summarized in

Table 2. Arithmetical mean height measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Sa [µm]	A	0.55	0.54	0.57	0.57	0.56	0.55	0.55	0.56	0.56	0.55	0.55	0.55	0.55	0.54
	B	0.70	0.68	0.75	0.73	0.72	0.70	0.71	0.71	0.71	0.71	0.72	0.73	0.72	0.71
	C	0.91	0.92	1.04	1.01	0.99	0.97	0.96	0.98	0.97	0.99	0.96	0.99	1.01	0.99
	D	0.91	0.92	0.96	0.95	0.91	0.98	0.99	0.99	1.02	0.98	0.98	1.04	1.04	1.04
	E	0.92	0.97	0.98	0.97	0.96	0.92	0.97	0.95	0.96	0.95	0.93	0.97	0.95	0.95
S Param.	Setup	Evaluation Area Width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Sa [µm]	A	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5
	B	0.55	0.55	0.56	0.56	0.56	0.57	0.56	0.57	0.56	0.56	0.56	0.56	0.56	0.56	0.57
	C	0.72	0.72	0.72	0.71	0.71	0.71	0.70	0.69	0.70	0.70	0.69	0.69	0.70	0.71	0.71
	D	0.99	0.98	0.97	0.98	0.97	0.99	0.99	0.98	1.02	1.02	1.02	1.02	1.01	1.01	1.03
	E	1.06	1.05	1.03	1.06	1.07	1.07	1.08	1.05	1.05	1.09	1.08	1.08	1.06	1.05	1.06

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Table 3. Core roughness depth measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Sk [µm]	A	1.38	1.46	1.45	1.44	1.45	1.44	1.42	1.44	1.40	1.38	1.39	1.38	1.37	1.38
	B	1.35	1.35	1.34	1.32	1.39	1.37	1.36	1.32	1.37	1.32	1.31	1.33	1.37	1.36
	C	1.91	1.91	1.90	1.86	1.96	1.97	1.91	1.90	1.88	1.96	1.88	1.85	1.80	1.80
	D	1.02	1.05	1.20	1.19	1.14	1.11	1.11	1.14	1.19	1.23	1.23	1.20	1.18	1.21
	E	0.96	0.93	0.91	0.96	1.03	0.96	0.88	0.86	0.93	0.94	0.90	0.89	0.88	0.92
S Param.	Setup	Evaluation Area Width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Sk [µm]	A	0.94	0.92	0.96	0.95	0.95	0.94	0.93	0.96	0.95	0.96	0.95	0.94	0.97	0.96	0.97
	B	1.37	1.37	1.38	1.40	1.40	1.41	1.42	1.43	1.44	1.46	1.45	1.44	1.44	1.47	1.47
	C	1.38	1.37	1.42	1.40	1.39	1.39	1.40	1.40	1.39	1.37	1.38	1.38	1.39	1.42	1.43
	D	1.86	1.85	1.86	1.85	1.84	1.88	1.89	1.88	1.90	1.87	1.88	1.91	1.91	1.92	1.90
	E	1.27	1.24	1.22	1.22	1.23	1.26	1.30	1.26	1.27	1.23	1.23	1.25	1.26	1.26	1.24

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Table 4. Reduced valley depth measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Svk [µm]	A	0.45	0.46	0.46	0.44	0.45	0.46	0.44	0.45	0.46	0.43	0.44	0.43	0.45	0.45
	B	0.41	0.41	0.39	0.37	0.37	0.38	0.37	0.39	0.39	0.39	0.37	0.36	0.36	0.38
	C	0.49	0.49	0.46	0.47	0.48	0.49	0.48	0.49	0.54	0.54	0.55	0.53	0.52	0.53
	D	0.35	0.36	0.37	0.37	0.37	0.35	0.36	0.35	0.35	0.37	0.35	0.35	0.36	0.36
	E	0.23	0.24	0.24	0.24	0.24	0.23	0.23	0.23	0.22	0.22	0.22	0.22	0.22	0.21
S Param.	Setup	Evaluation Area Width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Svk [µm]	A	0.95	0.93	0.91	0.89	0.92	0.93	0.92	0.90	0.88	0.92	0.92	0.91	0.90	0.91	0.93
	B	0.47	0.47	0.46	0.47	0.46	0.46	0.46	0.46	0.47	0.46	0.47	0.47	0.48	0.51	0.51
	C	0.39	0.40	0.40	0.40	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.39	0.42
	D	0.54	0.54	0.54	0.54	0.54	0.54	0.55	0.56	0.53	0.53	0.53	0.54	0.54	0.53	0.54
	E	0.36	0.37	0.37	0.37	0.36	0.36	0.36	0.36	0.34	0.35	0.35	0.35	0.35	0.35	0.35

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Table 5. Reduced peak height measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Spk [µm]	A	0.68	0.65	0.65	0.66	0.62	0.60	0.62	0.59	0.61	0.62	0.63	0.63	0.64	0.62
	B	0.73	0.74	0.75	0.76	0.79	0.77	0.78	0.78	0.74	0.77	0.78	0.75	0.73	0.74
	C	0.80	0.80	0.82	0.82	0.81	0.79	0.80	0.81	0.80	0.71	0.73	0.74	0.76	0.76
	D	0.83	0.79	0.86	0.83	0.85	0.88	0.87	0.87	0.85	0.82	0.83	0.84	0.85	0.80
	E	1.07	1.09	1.11	1.04	1.01	1.06	1.10	1.11	1.10	1.06	1.08	1.09	1.09	1.10
S Param.	Setup	Evaluation Area Width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Spk [µm]	A	0.22	0.22	0.21	0.22	0.22	0.22	0.23	0.23	0.23	0.23	0.23	0.22	0.23	0.24	0.24
	B	0.63	0.63	0.65	0.64	0.65	0.66	0.67	0.67	0.65	0.63	0.64	0.63	0.64	0.63	0.62
	C	0.74	0.73	0.70	0.71	0.72	0.71	0.70	0.69	0.69	0.69	0.69	0.68	0.68	0.68	0.68
	D	0.73	0.72	0.72	0.73	0.72	0.75	0.74	0.74	0.73	0.74	0.73	0.73	0.73	0.74	0.74
	E	0.75	0.77	0.78	0.78	0.78	0.73	0.75	0.77	0.77	0.79	0.78	0.80	0.78	0.79	0.80

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Table 6. Surface skewness measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Ssk [-]	A	0.28	0.28	0.26	0.18	0.21	0.18	0.20	0.24	0.23	0.24	0.24	0.21	0.20	0.22
	B	0.41	0.41	0.36	0.28	0.35	0.33	0.29	0.32	0.36	0.34	0.29	0.31	0.36	0.35
	C	0.60	0.55	0.47	0.40	0.46	0.48	0.46	0.39	0.41	0.43	0.47	0.41	0.33	0.34
	D	0.50	0.53	0.55	0.66	0.69	0.57	0.46	0.46	0.53	0.61	0.57	0.52	0.41	0.45
	E	0.76	0.70	0.58	0.65	0.73	0.74	0.65	0.65	0.65	0.71	0.72	0.63	0.63	0.67
S Param.	Setup	Evaluation AREA width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Ssk [-]	A	1.06	1.06	1.08	1.08	1.06	1.03	1.05	1.06	1.06	1.09	1.06	1.08	1.08	1.08	1.13
	B	0.24	0.23	0.25	0.26	0.25	0.26	0.25	0.22	0.23	0.22	0.22	0.20	0.18	0.16	0.16
	C	0.31	0.33	0.35	0.36	0.33	0.32	0.33	0.33	0.34	0.33	0.34	0.35	0.34	0.30	0.33
	D	0.35	0.37	0.37	0.35	0.35	0.32	0.35	0.35	0.31	0.24	0.28	0.31	0.33	0.30	0.29
	E	0.46	0.53	0.55	0.48	0.42	0.46	0.48	0.52	0.50	0.48	0.45	0.49	0.51	0.50	0.50

and

Table 7. Surface kurtosis measurement results.

S Param.	Setup	Evaluation Area Width [mm]
		2.5	2.6	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0
Sku [-]	A	2.74	2.76	2.66	2.62	2.67	2.65	2.65	2.64	2.61	2.64	2.69	2.67	2.70	2.71
	B	2.56	2.62	2.43	2.42	2.50	2.54	2.44	2.46	2.49	2.43	2.36	2.37	2.41	2.44
	C	2.80	2.68	2.40	2.38	2.47	2.55	2.53	2.40	2.42	2.39	2.47	2.36	2.29	2.33
	D	2.33	2.35	2.36	2.47	2.59	2.37	2.27	2.30	2.28	2.40	2.38	2.22	2.13	2.13
	E	2.54	2.37	2.25	2.33	2.43	2.54	2.29	2.34	2.31	2.38	2.45	2.26	2.29	2.33
S Param.	Setup	Evaluation Area Width [mm]
		5.2	5.4	5.6	5.8	6.0	6.2	6.4	6.6	6.8	7.0	7.2	7.4	7.6	7.8	8.0
Sku [-]	A	0.71	0.70	0.66	0.63	0.65	0.69	0.67	0.63	0.64	0.66	0.70	0.70	0.66	0.66	0.68
	B	2.73	2.69	2.72	2.72	2.69	2.72	2.70	2.69	2.70	2.72	2.73	2.73	2.74	2.75	2.66
	C	2.38	2.41	2.39	2.43	2.41	2.43	2.45	2.49	2.47	2.45	2.48	2.49	2.46	2.44	2.46
	D	2.33	2.36	2.39	2.34	2.37	2.40	2.37	2.38	2.39	2.34	2.35	2.38	2.42	2.40	2.34
	E	2.12	2.18	2.23	2.11	2.08	2.11	2.12	2.19	2.17	2.11	2.09	2.11	2.17	2.20	2.16

. These tables present the values of the selected S-parameters measured at each evaluation area width.

4. Discussion

Six key S-parameters (S_a, S_k, S_vk, S_pk, S_sk, and S_ku) were analyzed and the evaluation of the results is divided into seven subsections, where each parameter is analyzed separately, which is concluded by a comprehensive analysis of the outcomes. Two types of diagrams were created to support the analysis. The first set of graphs illustrates the variation in the S-parameter values as a function of the evaluation area width, allowing a direct observation of how each roughness parameter changes with increasing measurement area. The second type of graph presents the incremental deviation along the evaluation area width, highlighting the relative change between consecutive area widths. This visualization focuses on the transition point beyond which further area extension yields reducing gains, enabling the definition of a practical minimum length for stable characterization.

4.1. Analysis of the Arithmetical Mean Height S-Parameter

The S_a parameter, representing the average height of surface irregularities over a defined area, is a widely used metric for assessing surface roughness. In this study, S_a was evaluated across five tangential turning setups, with varying feed rates, depths of cut, and cutting speeds. Figure 4 and Figure 5 present the results to be analyzed.

As the evaluated surface area width increased from 2.5 mm to 8.0 mm, S_a values showed a tendency to converge and stabilize. This stabilization suggests that shorter measurement area widths, especially below 4 mm, may not sufficiently represent the full surface profile, particularly in rougher conditions. For instance, Setup A (low feed and depth) showed stable S_a values (around 0.54–0.57 µm) as early as 3.5 mm, indicating a smooth and uniform surface. In contrast, Setup D (high feed and depth) exhibited a steady rise in S_a, peaking at around 1.08 µm, with stabilization occurring only after 6 mm, reflecting a coarser surface that requires longer evaluation area widths for reliable characterization. Setup B (moderate feed) began around 0.70 µm, with steady convergence near 0.69–0.71 µm by 6.0 mm. Setup C, with a high feed rate, rose from around 0.90 µm to over 1.02 µm, stabilizing after 5.5 mm. Setup E, operated at a lower cutting speed, displayed more persistent fluctuations in S_a (0.93–0.97 µm), lacking a clearly defined stabilization point. This suggests greater surface variability, likely influenced by reduced thermal softening during cutting. The analysis revealed a consistent trend: increased feed or depth of cut generally led to higher S_a values, demonstrating the reliability of the parameter in capturing process-induced surface texture changes.

Despite some minor fluctuations at shorter area widths (especially 2.5–3.2 mm), overall deviations remained low, indicating reasonably consistent measurements even at smaller scales. However, longer area widths—particularly those exceeding 5.5 mm—were more reliable in capturing representative roughness values, especially for rougher surfaces. In conclusion, the S_a parameter effectively reflects the influence of cutting parameters on surface texture in tangential turning. A minimum evaluation area width of 6.0 mm is generally recommended to ensure stable and representative roughness values across various machining conditions.

4.2. Analysis of the Core Roughness Depth S-Parameter

The S_k parameter quantifies the height range of the core roughness profile. This makes it particularly valuable for assessing functional surface properties, such as wear resistance, lubrication behavior, and load-carrying capacity. Unlike peak-sensitive metrics, S_k focuses on the central portion of the surface, offering a measure for tribological performance. However, S_k may exhibit notable fluctuations when the measurement area is too limited, especially on surfaces with heterogeneous features. Figure 6 and Figure 7 provide the basis for the forthcoming analysis.

In general, S_k values across the five tangential turning setups show low to moderate variability. A common pattern occurs in which values stabilize after approximately 5.0 to 5.5 mm of evaluation area width, with earlier values often underestimating the actual roughness depth. For Setup A (v_c = 300 m/min, f = 0.6 mm/rev, a = 0.1 mm), S_k starts at 1.378 µm and shows slight fluctuations between 1.35 and 1.47 µm. Stabilization is observed beyond 5.0 mm, where values remain consistently around 1.45–1.47 µm. This suggests that short evaluation area widths may slightly underestimate the core roughness of the surface. Setup B, using a higher feed (0.8 mm/rev), shows a small initial reduction from 1.354 µm to 1.317 µm, followed by a stabilization around 1.39–1.42 µm after 5.0 mm. This reflects localized variability at shorter area widths, likely due to increased surface texture irregularities. Setup C (highest feed at constant depth) begins at 1.914 µm, decreases slightly, then increases again, stabilizing around 1.88–1.92 µm beyond 5.0 mm. It demonstrates a clear need for longer evaluation to minimize the effect of feed-induced surface heterogeneity. Setup D, with increased depth (a = 0.2 mm), starts lower at 1.019 µm and steadily increases to about 1.26 µm by 8 mm. Stabilization occurs after 5.5 mm, highlighting that short measurements can significantly underestimate S_k under these more intensive cutting conditions. Finally, Setup E (reduced cutting speed) displays the lowest S_k values (around 0.88–1.03 µm), stabilizing gently after 5.0 mm, although variability remains modest throughout.

For the S_k parameter, a measurement area width of at least 5.5–6.0 mm is recommended to achieve stable and representative results across various tangential turning setups.

4.3. Analysis of the Reduced Valley Depth S-Parameter

The S_vk parameter quantifies the depth of the valleys that lie below the core roughness level, representing the capacity of the surface to retain lubricant or trap particles. This makes S_vk particularly relevant for functional surfaces in tribological applications. However, due to its sensitivity to extreme values in the lower portion of the surface profile, S_vk can fluctuate significantly if the measurement area is too short and fails to capture representative valley features. Figure 8 and Figure 9 contain the data selected for assessment.

Across all tangential turning setups, S_vk demonstrates higher variability at shorter evaluation area widths (2.5–4.0 mm), where isolated valleys may be over- or under-represented. As the measurement length increases, S_vk tends to rise slightly and then stabilize, reflecting the greater probability of capturing deep valley features over longer areas. Unlike peak-related parameters, S_vk commonly increases with area width, as more substantial valleys are included in the sampled area.

4.4. Analysis of the Reduced Peak Height S-Parameter

The S_pk parameter captures the height of the peaks located above the core material portion of the surface. It plays a crucial role in characterizing the initial contact behavior of the surface, particularly in tribological contexts involving wear or sliding. Figure 10 and Figure 11 illustrate the outcomes to be examined.

In general, all setups display noticeable fluctuations in S_pk for area widths below 4.0 mm. These variations stem from the uneven spatial distribution of peak features across the surface. However, with increasing area width, particularly beyond 5.5 mm, the S_pk values stabilize significantly, reflecting a more statistically representative inclusion of peak heights. Setup A (v_c = 300 m/min, f = 0.6 mm/rev, a = 0.1 mm) begins at 0.682 µm and shows a slight downward shift, settling into a narrow band between 0.62 and 0.66 µm after 5.0 mm. The total variation is modest, around 0.065 µm, indicating a relatively uniform peak distribution. Setup B initially spikes to 0.792 µm before tapering down and stabilizing between 0.67 and 0.71 µm after 5.0 mm. The early peak suggests an overrepresentation of local features in short profiles. Setup C begins at a higher range (around 0.80–0.82 µm) and gradually decreases to approximately 0.73–0.75 µm, achieving consistent values after 5.5 mm. This gradual shift illustrates the smoothing effect of longer sampling areas. Setup D shows the most distinct peak height decrease. Initial values near 0.83–0.88 µm decrease to approximately 0.75–0.78 µm beyond 5.5 mm. The pronounced drop confirms that short measurements greatly overestimate S_pk under these cutting conditions. Setup E presents the highest S_pk values (approximately 1.07–1.10 µm), stabilizing after 4.0 mm around 1.06–1.08 µm. The high peaks correlate with the lower cutting speed and higher feed rate, which tend to generate rougher, more irregular topographies. In conclusion, short profile area widths (2.5–4.0 mm) are expected to overestimate S_pk due to localized peaks. A minimum evaluation area width of 6.0 mm is recommended for reliable and stable S_pk values, particularly in high-feed or rough surface scenarios.

4.5. Analysis of the Surface Skewness S-Parameter

The S_sk parameter evaluates the asymmetry of the height distribution of a surface, classifying whether peaks or valleys dominate the topography. Positive S_sk values indicate a surface skewed towards higher features (peaks), while negative values suggest valley-dominant structures. Figure 12 and Figure 13 present the data subject to analysis.

In this study, all machining setups produced positive S_sk values, confirming a consistent peak-dominant nature across the tested surfaces. A strong relationship emerges between the machining parameters and S_sk. Lower feed conditions, such as in Setup A (f = 0.6 mm/rev), result in more balanced surfaces, with S_sk stabilizing in the range of 0.16–0.28. This indicates a surface profile with only a slight peak feature. In contrast, higher feed setups such as Setup C and D (f = 1.0 mm/rev) exhibit significantly higher skewness. Setup C ranges from 0.243 up to 0.604, while Setup D reaches values near 0.688, suggesting more prominent peak features determined by more intensive material removal. Setup E, which incorporates a lower cutting speed, presents the highest skewness values in the dataset. Shorter segments show values as high as 0.759, likely due to altered chip formation or tool-workpiece interactions at reduced speeds. Although these values decrease over longer measurement lengths, they remain consistently higher than in other setups, indicating a persistent peak-dominant morphology. Across all setups, S_sk tends to decrease with increasing measurement area width. For example, in Setup C, the S_sk value drops from 0.604 at 2.5 mm to approximately 0.288 at 8.0 mm. This trend demonstrates that short evaluation area widths may overestimate skewness by capturing isolated or extreme features, particularly in high-feed or low-speed conditions. Stabilization of S_sk values is generally achieved between 5.0 and 6.0 mm, where further increases in area width result in minimal change (typically less than 0.02). This suggests that measurement area widths beyond 6 mm offer reduced advantages in precision. The S_sk parameter is highly responsive to both cutting conditions and measurement area width. For accurate and consistent skewness evaluation, a minimum area width of 5.0 mm is recommended, while 5.0–6.0 mm represents the optimal range for balancing measurement time and data stability.

These findings carry functional implications. Surfaces with positive S_sk values, especially in high-feed and low-speed conditions, are characterized by peak-dominated topographies. Such features are known to influence tribological behavior, particularly during initial contact or running-in. Elevated skewness can lead to higher initial friction and wear, but once these peaks wear down, the surface may exhibit enhanced load-bearing capacity due to a more stable core profile. Therefore, skewness is not only a geometric descriptor but also a functional indicator in wear-critical applications.

4.6. Analysis of the Surface Kurtosis S-Parameter

The S_ku parameter describes the sharpness or flatness of the surface height distribution curve. A perfectly Gaussian height distribution yields an S_ku of 3. Values greater than 3 suggest the presence of sharp peaks or deep valleys, while values below 3 indicate a flatter, more uniform surface profile. In this study, S_ku values consistently remain below 3, implying relatively smooth, well-distributed topographies without extreme outliers. Figure 14 and Figure 15 show the results to be analyzed.

Across all setups, S_ku values generally range from 2.1 to 2.8, indicating a slight platykurtic tendency. This suggests surfaces produced by tangential turning tend to avoid sharp extremes, which is advantageous in applications where uniformity and consistency are desired. A subtle downward trend is observed in most cases with increasing area width, reflecting the averaging effect over larger surface areas. In Setup A (f = 0.6 mm/rev), S_ku begins at 2.741 and fluctuates slightly around this value as area width increases. This stability implies that the surface is relatively homogeneous, and shorter area widths may still offer a representative measure of kurtosis. Setup B (f = 0.8 mm/rev) starts at 2.56, decreases to around 2.36, and then slightly increases again. This slight variability suggests a 5–6 mm evaluation area width is more appropriate to achieve a consistent result. Setup C (f = 1.0 mm/rev) shows a steady decline in S_ku from 2.801 down to 2.343, indicating that small measurement areas may overstate kurtosis due to isolated features. The same trend is more pronounced in Setup D (with deeper cutting), where S_ku decreases from 2.333 to 2.157, highlighting the importance of longer profiles for reliable characterization. Setup E (low cutting speed) begins at 2.537 and changes between 2.25 and 2.45, showing no strong directional trend. Minor increases beyond 5.0 mm indicate that further area width contributes little to result refinement. In all setups, S_ku stabilizes beyond 5.0–6.0 mm, with changes typically less than ±0.05. Below 4.0 mm, fluctuations are more noticeable, especially at higher feeds. For consistent kurtosis evaluation in tangential turning, a minimum measurement area width of 5.0 mm is recommended. The optimal range lies between 5.0 and 6.0 mm, as longer area widths offer little additional accuracy while significantly increasing measurement time.

From a functional perspective, the consistently platykurtic S_ku values (<3) observed across all setups suggest a lack of extreme peaks or deep valleys. This implies more uniform and predictable surface contact behavior, which is beneficial for applications requiring stable frictional or sealing properties. Such surfaces are less likely to experience inconsistent localized stress concentrations, enhancing both wear predictability and operational stability in precision components.

4.7. Comprehensive Discussion of the Results

This subsection provides observations of two interrelated aspects of surface roughness evaluation in tangential turning: the influence of machining parameters on surface formation, and the metrological implications of selecting the appropriate evaluation area width for S-parameter estimation.

The tangential turning process, especially under high-feed conditions, results in complex topographical features characterized by distinct peaks and valleys. The experimental findings show that increasing feed rate and depth of cut directly affects the surface roughness. Setups C and D, which used the highest feed (1.0 mm/rev), consistently produced the roughest surfaces, reflected in increased S_a, S_k, and S_pk values. These surfaces showed prominent peaks, as confirmed by higher S_sk values in short evaluation areas. Conversely, Setup A (f = 0.6 mm/rev) resulted in a more regular surface with significantly lower S_a and S_pk, indicating a smoother texture with reduced peak dominance. Cutting speed played a secondary role. Setup E (v_c = 200 m/min) showed higher instability in roughness parameters such as S_a, S_pk, and S_sk, particularly across shorter segments. This suggests that reduced thermal softening and chip deformation at lower speeds may contribute to irregularities and delayed parameter stabilization. The results highlight that, while feed and depth of cut primarily define topographical scale and symmetry, cutting speed can intensify the influence of localized irregularities.

From a metrological perspective, the study underlines the critical role of evaluation area width in reliably capturing areal S-parameters. Parameters sensitive to local extremes—such as S_pk and S_vk—were found to be significantly influenced by short evaluation widths (under 4.0 mm), often leading to over- or underestimation. In contrast, amplitude parameters like S_a and core roughness parameters such as S_k displayed more gradual convergence, stabilizing typically between 5.5 and 6.0 mm. The evaluation also shows that S_sk values, indicative of height distribution asymmetry, tended to be overestimated in shorter areas due to the influence of isolated peaks. These values declined consistently as the evaluation area increased, confirming the importance of adequate sizes for skewness estimation. On the other hand, S_ku values remain below 3 in all setups, denoting a consistent platykurtic nature across machining conditions (surfaces with relatively flat distributions free of sharp outliers). This may indicate tribologically favorable topographies across the setups studied. The observed convergence behavior supports the adoption of a minimum evaluation length of 5.5–6.0 mm, especially in high-feed tangential turning scenarios. Evaluation areas shorter than 4.0 mm failed to provide consistent or representative values across multiple parameters, particularly in rougher surfaces. This reinforces ISO 25178 recommendations regarding the proportionality of L-filter length to surface feature wavelength and justifies surface-specific calibration in industrial settings.

Functional implications of the skewness and kurtosis values were also considered. The positive S_sk values in high-feed setups indicate surfaces dominated by sharp peaks, which may lead to accelerated initial wear but can provide better load distribution after running-in. The consistently platykurtic S_ku values (<3) suggest the surfaces are free from extreme outliers, contributing to improved tribological stability and predictable wear.

By separating the influences of process parameters and metrological setup, the findings highlight the need for a dual approach in roughness evaluation. Machining conditions govern the generation of topographic features, while the metrological choices determine how well these features are captured and quantified. An integrated, parameter-specific understanding—using a full suite of S-parameters across a sufficiently long area—is essential for accurate surface assessment in high-feed tangential turning.

4.8. Comparison with Other Scientific Works

Several studies have addressed the relationship between measurement scale and surface roughness parameters; however, their focus, materials, and surface formation mechanisms differ significantly from the present work. Yong et al. investigated the influence of evaluation area width on various 3D roughness parameters of polyurethane coatings, where roughness developed from buckling and wrinkling in a cross-linked polymer matrix [33]. Although they also examined S-parameters like S_a, S_sk, and S_ku, their surfaces were not machined but chemically generated. Moreover, their motivation centered on the correlation between roughness and gloss, not metrological stability or mechanical surface function. Thus, their findings cannot be directly applied to metal cutting operations, where surface topography is governed by tool kinematics and chip formation. One notable similarity between their work and the current study is the consistent observation that shorter evaluation area widths tend to overestimate peak- or valley-sensitive S-parameters due to localized features. Both studies confirm that Surface Skewness (S_sk) and kurtosis (S_ku) become more stable and representative only beyond a critical evaluation area width (about 5 mm in this study and approximately 4–5 mm in theirs). From a metrological standpoint, both studies demonstrate that surface topography evaluation should consider the scale of measurement relative to the dominant spatial features of the surface. However, the practical implications diverge: the findings of Yong et al. are relevant for visual quality control in coatings, while this study contributes to quality assurance in precision-machined components where surface texture affects wear, friction, and load-bearing behavior.

In contrast, Molnár and Szabó focused on reducing 3D surface measurement time for hard-turned and ground surfaces by identifying minimum area sizes for S-parameter stability [18]. Their work applied a statistical approach using full-factorial DOE and assessed different S-parameters across area sizes ranging from 2.45 mm to 0.55 mm. While similar in goal, this study differs in two key respects. First, our experiments were dedicated exclusively to tangential turning—a non-standard high-feed machining technique producing different surface textures than conventional turning or grinding. Second, this analysis emphasized the convergence behavior of six ISO 25178 S-parameters across increasing area widths within the same surface rather than shrinking areas, which offers insights relevant to anisotropic surfaces produced by directional feed marks. A key similarity lies in the experimental approach: both studies analyze how increasing the evaluation area affects the reliability of ISO 25178 S-parameters such as S_a, S_k, and S_ku. However, while their work focused on surfaces generated by longitudinal turning, the present study applies the areal filtering to surfaces produced by tangential turning—a high-feed machining technique characterized by more complex and directionally varying textures. Their results showed S-parameter stabilization around 5 mm, which closely supports the present finding that a minimum area width of 5.5–6.0 mm ensures representative measurement. Thus, while both confirm the importance of appropriate evaluation area, the present study extends the conclusions to tangential turning and applies full areal analysis techniques for more generalized guidance.

In summary, while these papers provide foundational insights into the effect of evaluation scale on roughness characterization, the present work is the first to systematically quantify the minimum evaluation area width for key S-parameters in the context of high-feed tangential turning, under controlled machining and measurement conditions.

5. Conclusions

This study presents a detailed experimental investigation into the surface topography of outer cylindrical surfaces produced by tangential turning of metallic components. The research focuses specifically on the effect of key machining parameters on selected areal surface roughness parameters. The work aims to enhance the understanding of surface integrity characteristics in tangential turning, which is a less conventional turning strategy involving an altered cutting geometry that influences force distribution and surface formation mechanisms. Experiments were carried out under varied conditions of cutting speed (200 m/min and 300 m/min), feed rates (0.6 mm/rev, 0.8 mm/rev, and 1 mm/rev), and depths of cut (0.1 mm and 0.2 mm), all applied to high precision turning of alloyed steel. A 3D areal surface characterization was performed using high-resolution profilometry, and the S-parameters were extracted and analyzed along a range of measurement area widths, from 2.5 mm to 8 mm in 0.2 mm increments. The primary goal was to determine the effect of the evaluation area width on the values of the roughness parameters.

Results reveal that all roughness parameters exhibit sensitivity to both the feed rate and depth of cut. An additional key observation was the influence of measurement area width. While trends in the S-parameters were consistent across different area widths, slight fluctuations were noted, highlighting the importance of choosing appropriate areal widths for reliable topography characterization. The Arithmetical Mean Height and Core Roughness Depth S-parameters stabilize at an evaluation area width of 5.5 to 6.0 mm, corresponding to approximately 2.2 to 2.4 times the applied cut-off. Reduced Valley Depth and Reduced Peak Height reach consistent values at 6.0 mm, which equals 2.4 times the cut-off length. Surface Skewness and Surface Kurtosis require a minimum evaluation area width of 5.0 mm, or twice the cut-off, to ensure reliable results.

The study concluded that the use of tangential turning introduces unique challenges in areal measurement due to the influence of oblique cutting angles and asymmetric tool engagement, making consistent S-parameter interpretation critical. Overall, detailed surface topography analysis improves the metrological understanding of how this technique compares to conventional turning methods, especially in high-feed and high-precision applications. Tangential turning can improve the productivity of the machining of outer cylindrical surfaces due to its unique geometric and kinematic relations. While this procedure may offer efficiency advantages due to its ability to handle high feeds and stable chip formation, its potential for improving component service life through enhanced surface quality remains an open question. The current study provides a foundation for evaluating surface features that could influence functional behavior, but further research is needed to quantify their effects under real-world operational conditions.

Future work should explore optimal strategies for selecting evaluation locations, especially in the context of surface homogeneity, periodic variations caused by tool rotation, or chatter. Statistical sampling across multiple radial positions or circumferential locations may result in more precise measurements, particularly for industrial quality control. While the current study focused on stability of areal parameters across increasing evaluation areas, upcoming research may consider decomposing areal datasets into directional profiles to analyze anisotropy or periodicity along toolpath-generated textures. Additionally, quantifying the uncertainty and repeatability of parameter values across different locations could lead to interesting findings. Further work may also explore predictive models for parameter convergence, potentially based on texture period multiples.