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Surface roughness

Surface roughness refers to the finer spaced irregularities in a surface's texture that typically result from the inherent action of a production process or by material condition.^[1] It constitutes one component of overall surface texture, alongside waviness (broader deviations), lay (the direction of the surface pattern), and form (the general shape), and is quantified at a microscopic scale through deviations from an ideal flat surface.^[2]^[3] In engineering and manufacturing, surface roughness is a critical quality parameter that directly impacts component performance, including friction, wear, adhesion, heat transfer, corrosion resistance, and lubrication efficiency.^[1]^[3] For instance, smoother surfaces reduce drag in aerodynamic applications and enhance biocompatibility in medical devices, while controlled roughness can improve grip or oil retention in mechanical assemblies.^[1] Excessive roughness may lead to premature failure in high-precision parts, such as those in aerospace or automotive industries, underscoring its role in design, quality control, and functionality.^[4]^[1] Common parameters for characterizing surface roughness include the arithmetic average roughness (Ra), which calculates the average absolute deviation of profile heights from the mean line over a sampling length; the root mean square roughness (Rq), which provides a statistical measure of deviations; the total profile height (Rt), the maximum peak-to-valley distance; and the ten-point height (Rz), the average of the five highest peaks and five deepest valleys, both indicating the extent of surface irregularities.^[2]^[3] These are defined in standards like ASME B46.1, which guides measurement and specification for ensuring consistency across manufacturing processes.^[1] Measurement of surface roughness employs techniques such as stylus profilometry for contact-based profiling, optical interferometry for non-contact analysis, and scanning probe microscopy for nanoscale resolution, each suited to different scales and applications.^[3] Factors influencing roughness include machining parameters like cutting speed, feed rate, tool geometry, and material properties, with tighter control achieved through processes like polishing or grinding.^[2] Overall, optimizing surface roughness enhances product durability, efficiency, and reliability in diverse fields from optics to structural engineering.^[4]

Fundamentals

Definition and Scales

Surface roughness refers to the deviations of a real surface from its ideal geometric form, measured in the direction of the surface normal, and is characterized by the height, wavelength, and directional pattern of these surface irregularities.^[5] These deviations arise primarily from manufacturing processes such as machining, grinding, or polishing, where tool geometry, material properties, and process parameters influence the resulting texture.^[6] Surface roughness is categorized into scales based on the wavelength of the irregularities, which reflects the spatial frequency of surface features. Macro-roughness encompasses broader features often visible to the naked eye and resulting from large-scale forming processes like casting or forging that introduce undulations. Micro-roughness involves finer features typically generated by intermediate manufacturing steps such as milling or turning, where tool marks and feed rates create periodic patterns. Nano-roughness includes the smallest features, emerging from advanced finishing techniques like chemical etching or atomic layer deposition, which produce variations at atomic- or molecular-scale. In standards such as ASME B46.1 and ISO 4287, the separation between roughness and waviness scales is defined by cutoff wavelengths (λs) selectable in the range of 0.08 mm to 8 mm, depending on the application.^[7]^[8] Key concepts in describing surface roughness include lay, wavelength, and amplitude. Lay denotes the predominant direction of the surface pattern, usually aligned with the manufacturing tool path—for instance, parallel to the cutting direction in lathe operations or perpendicular in grinding.^[1] Wavelength, denoted as λ, represents the horizontal spacing between repeating surface features, such as the distance between consecutive tool marks. Amplitude refers to the vertical height deviations of the surface peaks and valleys from a reference level. To visualize, consider a two-dimensional surface profile resembling a wavy line with irregular peaks and troughs; the lay would indicate the overall orientation of these waves, wavelength the repeat distance along the horizontal axis, and amplitude the peak-to-trough height.^[9] A foundational aspect of roughness analysis is the mean line, a reference line that divides the surface profile such that the area above it equals the area below, providing a baseline for measuring deviations. Profile deviation then describes the vertical distances from this mean line to the actual surface points, capturing both positive (peaks) and negative (valleys) excursions without quantifying them statistically here.^[4] These elements establish the terminology for assessing how roughness influences functional performance in engineering contexts.^[6]

Historical Context

The understanding of surface roughness originated in the early 20th century amid advancements in precision manufacturing, particularly with the development of stylus-based profilometers in the 1930s. In 1933, E. J. Abbott and F. A. Firestone at the University of Michigan introduced the first profilometer, a mechanical device using a diamond-tipped stylus to trace surface profiles and quantify deviations from flatness, enabling more objective assessment beyond visual or manual inspection.^[10] By 1936, Abbott commercialized an improved version through the Profilometer Company, which measured roughness via electrical amplification of stylus movements, marking a shift from qualitative to quantitative evaluation in industries like automotive parts production.^[11] These early instruments laid the groundwork for metrology but were limited to basic profiles, often requiring manual operation.^[12] Post-World War II, the rapid expansion of automotive and aerospace sectors drove standardization efforts to ensure component reliability and interchangeability, as inconsistent surface finishes contributed to failures in high-stress applications like aircraft engines. In the late 1940s, the American Society of Mechanical Engineers (ASME) formalized the arithmetic average roughness parameter, Ra, in its B46.1 standard of 1940 (updated in 1947), defining it as the average absolute deviation of profile heights from the mean line over a sampling length, which became a cornerstone for specifying tolerances in manufacturing drawings.^[13] This parameter simplified communication of surface quality requirements, influencing global practices in post-war reconstruction and military-to-civilian technology transfers.^[8] By the 1950s, comparator blocks with etched roughness samples emerged as visual aids for calibration, further standardizing inspections in these industries.^[14] The 1970s saw a transition from manual to automated measurement systems, spurred by electronic advancements, with stylus profilometers incorporating digital data acquisition for faster, repeatable profiling of machined surfaces. From the late 1970s, analog systems evolved into digital ones, allowing computational analysis of profiles and reducing operator error in quality control.^[15] In the 1980s, the advent of computing introduced fractal analysis to characterize multiscale roughness, as proposed by Mandelbrot in 1984, where the fractal dimension quantifies self-similar irregularities across length scales, providing a scale-invariant descriptor beyond traditional parameters like Ra.^[16] This approach revealed limitations in linear metrics for complex surfaces, influencing tribology research.^[17] The 1990s marked the shift toward three-dimensional areal characterization, extending 2D profile methods to volumetric data as optical and stylus technologies advanced, with initial concepts for areal parameters emerging to capture isotropic roughness in modern machining. The ISO 25178 series, developed from late-1990s deliberations by ISO TC 213, was officially numbered in 2005 and published starting in 2010, redefining texture terms for areal metrology and incorporating invariants like segmentation for functional analysis.^[18] Recent post-2020 developments integrate artificial intelligence for predictive modeling, particularly in additive manufacturing, where machine learning algorithms forecast surface roughness from process parameters like layer thickness and scan speed, enabling real-time optimization and reducing post-processing needs.^[19] These AI-driven methods address gaps in pre-2000 standards, which emphasized 2D parameters and overlooked predictive capabilities for emerging fabrication techniques.^[20]

Importance and Applications

Engineering and Manufacturing Impacts

Surface roughness plays a pivotal role in manufacturing processes, directly affecting machinability, coating adhesion, and fatigue life of components. In turning operations, excessive surface roughness generated by high feed rates or improper tool geometry can reduce tool life and increase cutting forces, leading to diminished overall process efficiency.^[21] Similarly, in milling, uneven roughness profiles from vibration or spindle speed variations compromise surface integrity, often requiring secondary operations to achieve functional tolerances.^[22] Grinding processes, while capable of producing finer finishes, are sensitive to wheel wear, where increased roughness accelerates abrasive degradation and elevates energy consumption during production.^[23] Optimal surface roughness enhances coating adhesion by promoting mechanical interlocking and increasing contact area between substrate and coating layers, thereby improving durability in applications like protective films on machined parts.^[24] However, overly rough surfaces can trap contaminants or create stress risers, weakening adhesion strength and leading to delamination under load.^[25] Regarding fatigue life, machined surfaces with lower roughness exhibit higher endurance limits by minimizing crack initiation sites from peaks and valleys; for instance, in high-cycle fatigue tests of additive manufactured components, reducing roughness through post-processing can improve fatigue strength by up to 50% under cyclic loading.^[26] In product performance, surface roughness critically influences assembly fit, sealing effectiveness, and aesthetic quality across industries. Controlled roughness ensures precise tolerances in press fits and interference assemblies, preventing misalignment or excessive wear during mating of components.^[27] For sealing applications, smoother surfaces reduce leakage paths in gaskets and O-rings, enhancing pressure retention in hydraulic systems.^[28] Aesthetically, polished low-roughness finishes improve visual appeal in consumer goods, correlating with perceived quality in automotive exteriors and electronic casings. In the automotive sector, piston-cylinder interfaces demand specific roughness levels—typically 0.2–0.8 μm—to balance lubrication retention for reduced friction while maintaining sealing against blow-by gases, thereby optimizing engine efficiency and emissions.^[29] In electronics manufacturing, PCB pad roughness affects solder joint formation; moderate roughness improves wetting and intermetallic bond strength in lead-free soldering, reducing void formation and enhancing thermal cycling reliability.^[30] Economically, achieving low surface roughness incurs higher production costs due to extended machining times, specialized tooling, and post-processing steps like polishing or chemical treatment, which can double part expenses in high-precision components.^[31] These investments yield benefits in longevity, such as extended service life in fatigue-prone parts, often justifying the premium through reduced warranty claims and maintenance. In additive manufacturing, post-2020 research highlights roughness challenges in 3D-printed lightweight structures, where as-printed surfaces with Ra values exceeding 10 μm compromise compressive strength and fatigue resistance in lattice designs; hybrid approaches combining printing with CNC finishing have demonstrated up to 70% roughness reduction, enabling viable lightweight components without excessive material use.^[32]^[33] As of 2025, advancements in AI-optimized hybrid manufacturing have achieved up to 80% roughness reductions in polymer AM processes, improving sustainability.^[34]

Effects in Tribology and Surface Interactions

Surface roughness significantly influences tribological performance by promoting asperity-asperity interactions in contacting surfaces, which increases the real area of contact and elevates the coefficient of friction compared to smooth interfaces. In the Greenwood-Williamson model, rough surfaces are characterized by multiple spherical asperities with varying summit heights following a Gaussian distribution; under load, only the tallest asperities deform elastically, leading to discrete contact spots that contribute to higher frictional resistance through shear at these junctions. This effect is pronounced in dry or boundary lubrication regimes, where friction coefficients can rise significantly for roughness values exceeding 0.1 μm Ra, as asperity interlocking amplifies tangential forces. Surface texture also modifies the Stribeck curve, which plots friction coefficient against the lubrication parameter (viscosity × speed / load), by shifting the transition from boundary to mixed and hydrodynamic regimes. Increased roughness raises the minimum friction point and broadens the mixed regime, as asperities penetrate the lubricant film, delaying full hydrodynamic separation; for instance, in textured surfaces with dimples or grooves, optimal patterns can reduce friction by up to 30% in the mixed regime by trapping lubricant and minimizing direct asperity contact.^[35]^[36] Roughness exacerbates wear mechanisms, including abrasive, adhesive, and fatigue types, by concentrating stresses at peaks and valleys that accelerate material removal. In abrasive wear, sharp asperities act as cutting tools, increasing wear rates proportionally with roughness amplitude; adhesive wear intensifies as valleys trap debris, promoting material transfer between surfaces under high loads. Fatigue wear arises from cyclic loading on asperity junctions, leading to subsurface crack initiation and spalling, particularly in rolling contacts. In bearings, excessive roughness (e.g., >0.2 μm Ra) can double fatigue life reduction due to pitting from asperity-induced stress concentrations, while in gears, it heightens scuffing risks by disrupting lubricant films and promoting adhesive seizure under high-speed meshing.^[37]^[38] In lubrication interactions, surface roughness alters oil film thickness and elastohydrodynamic lubrication (EHL) efficacy, often reducing film stability in high-pressure contacts like gears and cams. Roughness protrusions disrupt the pressure buildup in the inlet zone, thinning the central film by 10-20% for composite roughness >0.3 μm, and increasing the lambda ratio (film thickness / roughness) sensitivity; in full EHL, smooth surfaces maintain thicker films (>1 μm), but roughness transitions contacts to mixed regimes where asperities intermittently touch, elevating wear.^[39] The real contact area fraction η, influenced by roughness, relates to load F and hardness H via the approximation A = \eta \frac{F}{H}, where A is the real contact area. This derives from plastic deformation theory: under full yielding, the load is supported at the hardness pressure H (≈3Y, with Y the yield strength), so for complete contact, A_r = \frac{F}{H}; however, on rough surfaces, only a fraction η of the nominal area deforms into contact (η ≈ 0.01-0.1 for typical engineering roughness, decreasing with finer texture), yielding the scaled form. To arrive at this, start with Hertzian elastic contact for a single asperity (load w \propto \delta^{3/2}, area a \propto \delta), sum over asperity distribution for rough surfaces (real area A_r \propto F), then for plastic dominance in boundary conditions, cap pressure at H, resulting in linear proportionality modulated by η from roughness statistics.^[40] Beyond tribology, surface roughness affects biological interactions, enhancing implant biocompatibility by promoting cell adhesion and osseointegration; moderate roughness (1-2 μm Ra) on titanium implants increases osteoblast proliferation by 50-100% via improved protein adsorption, though excessive roughness (>5 μm) can induce inflammation. In optics, roughness induces scattering losses proportional to the square of the roughness amplitude over wavelength, with rms roughness > λ/10 (e.g., 50 nm at 500 nm light) causing >1% total integrated scatter, degrading performance in mirrors and lenses. Recent studies on nano-roughness (10-100 nm scales) highlight its role in self-cleaning surfaces, where hierarchical textures mimic lotus leaves to achieve water contact angles >150°, repelling contaminants; post-2020 advancements include laser-textured polymers with nano-protrusions enduring 1000 abrasion cycles while maintaining superhydrophobicity for applications in solar panels and textiles.^[41]^[42]^[43]

Measurement Methods

Contact-Based Techniques

Contact-based techniques for measuring surface roughness involve physical interaction between a probe and the surface, allowing direct tracing of the topography to generate a profile. These methods, primarily used in engineering and manufacturing, provide high-resolution data for assessing surface texture but require careful handling to avoid altering the sample. Stylus profilometry, the most established approach, employs a diamond-tipped stylus that traverses the surface along a straight line, capturing vertical displacements as it follows the contours. In stylus profilometry, the stylus tip—typically with a radius of 2–5 μm—moves at a constant speed over a sampling length, which is divided into evaluation and traverse segments to isolate the surface profile from form errors. Cutoff filters are applied to separate waviness (longer wavelengths, λs) from roughness (shorter wavelengths, λc), with λc often set between 0.08 mm and 8 mm according to standards like ISO 4287. These instruments achieve lateral resolutions down to 0.1 μm and vertical resolutions of about 1 nm, making them suitable for precise profile measurements on metals and polymers. Beyond mechanical stylus tracing, other contact methods utilize inductive and capacitive sensors to detect surface variations without direct scraping. Inductive sensors measure changes in electromagnetic inductance caused by surface proximity, while capacitive sensors detect alterations in electrical capacitance between the probe and surface. These are often integrated into portable or automated systems for industrial applications. Datum establishment in these setups can be skidded, where a shoe or skid rides on the surface to provide a reference plane, or skidless, which uses optical or mechanical means for more accurate alignment on curved or irregular surfaces, reducing errors from skid averaging. Contact-based techniques offer advantages in accuracy for one-dimensional profiles, particularly on conductive or rigid materials, and are calibrated using step height artifacts traceable to national standards, ensuring traceability to sub-nanometer levels. However, limitations include potential surface damage from the probe's contact pressure (typically 0.1–1 mN), which can scratch soft materials, and challenges in measuring steep slopes beyond the stylus tip angle (around 90°). To address these, hybrid contact-optical methods have emerged since 2020, combining stylus probing with real-time optical feedback for in-situ monitoring in manufacturing processes like additive fabrication. While non-contact techniques avoid these risks for delicate surfaces, contact methods remain essential for validating roughness parameters in controlled environments.

Non-Contact Techniques

Non-contact techniques for measuring surface roughness offer advantages over contact-based methods by avoiding surface deformation and enabling rapid assessment of delicate or complex geometries, such as those in additive manufacturing components.^[44] These methods primarily utilize optical principles to capture 3D topography without physical probing, achieving high-speed data acquisition suitable for in-line industrial applications.^[45] Optical interferometry stands as a cornerstone of non-contact measurement, leveraging interference patterns from light waves to reconstruct surface profiles. White light interferometry (WLI), also known as coherence scanning interferometry (CSI), employs broadband light sources to scan vertically and detect coherence peaks, providing vertical resolutions below 1 nm for smooth surfaces up to several micrometers in height range. Phase-shifting interferometry (PSI), a variant using monochromatic light, achieves sub-nanometer vertical precision (e.g., λ/1000 ≈ 0.6 nm for λ = 600 nm) by analyzing phase shifts in interference fringes, though it is limited to step heights under λ/4 (≈150 nm) without additional scanning. However, both techniques face field-of-view limitations, typically restricted to small areas (e.g., 0.5–2 mm laterally), necessitating stitching for larger samples.^[47] Confocal microscopy and laser scanning methods extend non-contact capabilities to structured 3D topography mapping, particularly for optically rough surfaces. Confocal laser scanning microscopy uses a pinhole to eliminate out-of-focus light, enabling vertical resolutions around 1–10 nm and lateral resolutions of 0.2–0.5 μm, ideal for areal measurements over fields up to several millimeters.^[44] Laser scanning often incorporates structured light projection, such as fringe patterns, to triangulate surface points and generate full 3D datasets, with vertical resolutions of 10–50 nm suitable for complex geometries in additively manufactured parts.^[45] Coherence scanning interferometry (CSI), bridging interferometry and confocal approaches, combines vertical scanning with coherence detection to achieve nanoscale height resolution (down to 1 nm) while handling slopes up to 45°, making it robust for varied topographies.^[48] Advanced non-contact methods push resolutions to the nanoscale, with atomic force microscopy (AFM) operating in non-contact or tapping (semi-contact) modes to measure roughness without direct tip-surface abrasion. In non-contact mode, the AFM tip oscillates near the sample in the attractive van der Waals regime, yielding sub-nanometer lateral and vertical resolutions (e.g., <1 nm) over scan areas from nanometers to micrometers, though it is slower for large fields.^[49] Emerging post-2020 developments integrate AI-enhanced image analysis for real-time roughness evaluation in additive manufacturing, where machine learning models process optical or laser-scan images to predict parameters like Ra with accuracies exceeding 90%, enabling in-process monitoring and reducing post-fabrication inspection needs.^[20] Key comparison metrics among these techniques highlight trade-offs in resolution and data type. Interferometric methods excel in vertical resolution (<1 nm) but offer moderate lateral resolution (0.5–1 μm due to diffraction limits), favoring profile data for smooth surfaces, whereas confocal and laser scanning provide balanced resolutions (lateral 0.2–1 μm, vertical 1–10 nm) and are better suited for areal 3D datasets on rough or curved geometries.^[44] AFM achieves the highest resolutions (sub-nm laterally and vertically) for nano-scale features but is limited to small areas, contrasting the broader fields of optical techniques.^[50] Overall, selection depends on surface scale and geometry, with optical methods prioritizing speed for industrial use.^[45]

Roughness Parameters

Profile Roughness Parameters

Profile roughness parameters quantify the texture of a surface along a single linear trace, known as the profile, separating it into amplitude (height-related), spacing (lateral), slope, counting, and functional aspects. These parameters are standardized in ISO 21920-2:2021, which specifies terms and calculation methods for surface texture evaluation by profile methods, replacing earlier standards like ISO 4287 to incorporate updated functional parameters such as those related to material ratio for better correlation with performance.^[51] Calculations are performed over an evaluation length, typically comprising multiple sampling lengths to average out local variations, ensuring statistical reliability.^[51] Amplitude parameters focus on the vertical deviations z(x) of the profile from its mean line. The arithmetic mean deviation, denoted Ra, measures the average absolute height deviation and is calculated as

Ra = \frac{1}{l} \int_{0}^{l} |z(x)| \, dx

where l is the evaluation length.^[51] Graphically, Ra illustrates the typical "average" roughness height, smoothing over outliers like deep scratches, making it widely used for general quality control due to its simplicity and low sensitivity to extreme features.^[51] The root mean square (RMS) deviation, Rq, weights larger deviations more heavily and is given by

Rq = \sqrt{ \frac{1}{l} \int_{0}^{l} z^{2}(x) \, dx }.

This parameter, analogous to standard deviation in statistics, provides a quadratic measure of roughness amplitude, often slightly higher than Ra for non-sinusoidal profiles.^[51] For peak-to-valley extents, Rz represents the average maximum height across the profile, computed as the mean of (maximum peak height minus maximum valley depth) over five equal sampling sections within the evaluation length; graphically, it captures the "ten-point" average roughness depth, emphasizing repetitive high-low excursions rather than a single outlier.^[51] In contrast, Rt denotes the total profile height, simply the difference between the absolute highest peak and lowest valley over the entire evaluation length, offering a direct visual measure of the full vertical span but sensitive to isolated defects.^[51] Spacing and slope parameters address the horizontal and angular characteristics of the profile. The mean spacing between profile elements, RSm, quantifies the average distance between consecutive local maxima (peaks) or the mean width of repeating motifs, calculated by summing peak-to-peak distances and dividing by the number of intervals; graphically, it reflects the dominant wavelength of surface undulations, useful for identifying periodic machining marks.^[51] The RMS slope, Δq (often denoted Rdq in legacy contexts), measures the average steepness as the root mean square of the profile's derivative:

\Delta q = \sqrt{ \frac{1}{l} \int_{0}^{l} \left( \frac{dz}{dx} \right)^{2} \, dx },

with the mean slope angle derived as \arctan(\Delta q); this parameter highlights abrupt changes, such as in honed or ground surfaces, where high slopes indicate sharp edges.^[51] Counting parameters, such as peak count Pc, enumerate discrete features by counting the number of profile crossings above a specified threshold (typically 10% of Rz) per unit length, providing a density metric for protrusions; graphically, it visualizes the frequency of resolvable peaks, aiding in assessing contact points for wear prediction.^[51] The bearing ratio curve, or Abbott-Firestone curve, derives functional parameters from the cumulative distribution of profile heights, plotting the material ratio (bearing length percentage) against normalized height levels from the highest peak downward.^[51] The relative material ratio Rmr(dc) (or Rmr(p,dc)) is the material ratio at the section level cp + dc, where cp corresponds to material ratio p (default 0%) and dc is the relative profile depth (usually <0%), originating from integrating the probability density function of heights, offering insight into load-bearing behavior at specific depths below a reference level.^[51] Peak material volume Vmp, a related functional metric, quantifies the volume of material above the core region in the peaks (typically from the highest peak down to a material ratio threshold, e.g., 5%), crucial for assessing initial wear in tribological applications.^[51] These parameters, updated in ISO 21920-2 from ISO 4287, emphasize functional relevance over purely geometric description.^[51] For multi-scale characterization, the fractal dimension Df of a profile offers a scale-invariant measure of roughness complexity, estimated via the box-counting method: cover the profile with squares of side length ε, count N(ε) as the minimum number of squares intersecting the curve, and compute

D_f = \lim_{\epsilon \to 0} \frac{\log N(\epsilon)}{\log (1/\epsilon)}.

This yields Df between 1 (smooth line) and 2 (space-filling curve), with higher values indicating rougher, self-similar irregularity; the method, validated for profiles, assumes self-affinity over a range of scales but defers detailed multi-scale theory to advanced analysis.^[52]

Areal Roughness Parameters

Areal roughness parameters, as defined in the ISO 25178-2:2021 standard, extend traditional profile-based metrics to three-dimensional surface topographies, enabling the characterization of complete areal fields rather than linear traverses. These parameters account for the full spatial variation in height, accommodating both isotropic and anisotropic textures prevalent in modern manufacturing processes. The ISO 25178-2:2021 standard specifies over 30 such parameters, categorized into amplitude, spacing, hybrid, functional, and feature-based types, with computations performed on digitized surface data after form and waviness removal. Unlike profile parameters, areal metrics capture interactions across the entire evaluation area, providing more representative assessments for functional performance in applications like sealing and friction.^[53]^[54]^[55] Amplitude parameters quantify vertical deviations from a reference plane. The arithmetical mean height Sa represents the average absolute height deviation, calculated as

Sa = \frac{1}{A} \iint_A |z(x,y)| \, dx \, dy

where A is the sampling area and z(x,y) is the ordinate at point (x,y). As the areal analog to the profile Ra, Sa offers a scale-dependent but robust measure of overall roughness, insensitive to isolated peaks or valleys, and is widely used for quality control in machined surfaces. The root mean square height Sq, defined as

Sq = \sqrt{ \frac{1}{A} \iint_A z^2(x,y) \, dx \, dy },

extends the RMS profile parameter and emphasizes larger deviations due to its quadratic nature. The maximum height Sz is the sum of the absolute highest peak Sp and deepest pit Sv within the area, providing a sensitive indicator of extreme features, though it lacks scale invariance and can be influenced by measurement artifacts. These parameters maintain scale dependence similar to their profile counterparts but benefit from areal averaging for reduced variability.^[53]^[54]^[55] Spacing and hybrid parameters address lateral and gradient aspects of the texture. The mean spacing of local peaks Ssm is the average distance between consecutive maxima identified via watershed segmentation, offering insight into texture periodicity without scale invariance. The root mean square gradient Sdq, given by

Sdq = \sqrt{ \frac{1}{A} \iint_A \left[ \left( \frac{\partial z}{\partial x} \right)^2 + \left( \frac{\partial z}{\partial y} \right)^2 \right] dx \, dy },

quantifies average surface slope, which is scale-dependent and correlates with contact stiffness in tribological contexts. Functional parameters link texture to performance; the developed interfacial area ratio Sdr measures the fractional increase in true surface area over the nominal projection:

Sdr = \frac{A_\text{real} - A_\text{nominal}}{A_\text{nominal}},

where A_\text{real} integrates the surface element ds = \sqrt{1 + (\partial z / \partial x)^2 + (\partial z / \partial y)^2} \, dx \, dy. This hybrid metric, scale-dependent like Sdq, is essential for evaluating wettability and adhesion, with values often exceeding 100% on rough surfaces.^[56]^[54]^[57] Parameters derived from the areal bearing area curve, analogous to the Abbott-Firestone curve, assess load-bearing and fluid retention. The material ratio Smr(c) at height level c (normalized from 0 to 100%) indicates the percentage of the surface above that level supporting load, derived by intersecting the cumulative height distribution with horizontal planes. Volume parameters include the closed void volume Svc (voids above the core zone), reduced peak height volume Spk (lubricant film thickness), and reduced valley volume Svk (oil reservoir capacity), computed as

Svk = \frac{1}{A} \int_0^{h_v} (1 - Smr(h)) \, dh \cdot V_0,

where h_v is the valley threshold and V_0 a scaling factor; similar integrals apply to Svc and Spk. These scale the profile volumes Vmc, Vvc, Rk, and are critical for lubrication modeling, with Svk values in the range of 0.1-10 μm³/μm² typical for lubricated bearings.^[58]^[54] Post-2020 research has applied areal parameters to additive manufacturing, where defects like stair-stepping from layer deposition create anisotropic textures in laser powder bed fusion parts, with Sa typically ranging 5-30 μm, influencing fatigue strength and guiding process optimization for defect mitigation.^[59]

Standards and Advanced Characterization

International Standards

The primary international standards for surface roughness specification, measurement, and reporting are developed under the International Organization for Standardization (ISO) Geometrical Product Specifications (GPS) framework, which ensures consistent terminology, parameters, and procedures across industries. ISO 4287:1997 defined key profile roughness parameters, such as the arithmetical mean deviation R_a, and established sampling lengths equal to the cut-off wavelength \lambda_c of the profile filter to separate short-wavelength roughness from longer-wavelength waviness components.^[60]^[61] These standards specified Gaussian filters as the default for profile separation, with phase-correct variants to minimize distortion in the roughness profile during filtering.^[61]^[62] ISO 4288:1996 complemented this by providing rules and procedures for assessing surface texture conformity, including guidelines for stylus instrument measurements, tolerance comparisons, and the application of the 16% rule for parameter evaluation across multiple sampling lengths.^[63]^[64] Although these standards were withdrawn following the publication of updated equivalents, they remain foundational for legacy applications and continue to influence global practices.^[65]^[63] The ISO 21920 series (Parts 1–3, published 2021) modernizes the profile method, replacing ISO 4287 and 4288 with refined terms, parameters, and graphical symbols for technical drawings, including default cut-off values and enhanced rules for specification to improve interoperability.^[66]^[67] For areal (3D) surface texture metrology, the ISO 25178 series—particularly Part 2 (updated 2021)—defines over 40 parameters for characterizing functional surfaces, incorporating segmentation of the surface into peak, core, and valley zones based on the areal material ratio curve to assess material removal or addition effects.^[68] These parameters are organized into invariance classes, such as those robust to scale changes (e.g., fractal-based) or rotation, enabling consistent evaluation across measurement scales.^[69]^[70] In the United States, ASME B46.1-2019 adapts ISO GPS principles for practical implementation, defining surface texture constituents (roughness, waviness, lay) and parameters while providing US-specific guidance on measurement and control.^[1] It includes rules for symbolization on engineering drawings, where the standard roughness symbol—a check mark with a horizontal line—can be annotated with the R_a value and tolerance to indicate required surface finish.^[71]^[72] Post-2020 developments address advanced applications, with ISO 21920 incorporating provisions for nano-scale textures through finer resolution parameters and cut-offs suitable for micro- and nano-manufacturing.^[73]^[74] Emerging efforts also integrate surface roughness into digital twin frameworks under ISO 23247 (2021), enabling virtual simulation and prediction of texture evolution in manufacturing processes like additive methods.^[75]

Fractal and Multi-Scale Analysis

The application of fractal theory to surface roughness was pioneered by Benoit Mandelbrot in 1982, who demonstrated that many natural and engineered surfaces exhibit self-similar properties across scales, allowing characterization through a fractal dimension D_f that quantifies geometric complexity.^[76] For one-dimensional roughness profiles, $1 < D_f < 2, while for two-dimensional areal surfaces, $2 < D_f < 3, with higher values indicating increased irregularity.^[77] This dimension can be estimated from the power spectral density (PSD) of the surface topography, where for areal measurements, the PSD scales as \mathrm{PSD}(f) \propto 1/f^{8-2D_f}, reflecting the self-affine nature of typical rough surfaces.^[78] Multi-scale analysis extends fractal approaches by addressing the limitations of assuming scale-invariance, particularly for non-stationary surfaces where roughness varies with measurement scale. Wavelet decomposition techniques enable hierarchical separation of macro- and micro-scale features, decomposing the surface profile into approximation and detail coefficients at multiple resolution levels to isolate contributions from different frequency bands.^[79] This method is motivated by real-world surfaces, such as those in manufacturing or biology, where long-wavelength undulations (form) coexist with short-wavelength asperities (roughness), requiring scale-specific analysis for accurate functional assessment. In applications, fractal models facilitate wear prediction by relating D_f and scaling parameters to contact mechanics and material removal rates, often using Weierstrass-Mandelbrot functions to simulate evolving topographies under load.^[80] Similarly, these models support topography simulation for design optimization, generating synthetic surfaces that mimic measured fractal signatures. Recent advancements integrate machine learning for estimating fractal parameters, such as in biomimetic superhydrophobic surfaces inspired by natural textures like lotus leaves, where convolutional neural networks analyze topographic data to predict D_f and enhance wetting property simulations.^[81] Despite these benefits, fractal and multi-scale analyses remain non-standardized and serve as complements to ISO-defined roughness parameters like R_a or S_a, lacking formal metrology protocols for routine industrial use.^[76]

References

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Surface Characteristics Measurement Using Computer Vision
In 1933, Abbott and Firestone developed the first profilometer technology [18]. ... High precision calculation accuracy down to 0.2 μm Ra, checked by a stylus ...
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Bottom-up approach for traceable calibration of tip geometry of ...
Feb 8, 2022 · By 1938 Abbott et al [2] had set up a company to manufacture and sell the profilometer.
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Paradigm shifts in surface metrology. Part I. Historical philosophy
Jul 5, 2007 · So, around 1933, simple tactile methods began to be used, namely a stylus on a beam connected to a transducer, amplifier and meter. It is ...
[12]
Roughness standards evolution. I. (a) ASME B46.1. 1940. Surface...
The topographical images analyze and the computation of four height parameters (average roughness Ra, root mean square roughness RRMS, surface skewness SS and ...
[13]
What is ASME B46.1? - Michigan Metrology
The ASME B46.1 standard was first developed in the 1940s to govern “the geometric irregularities of surfaces.” B46.1 defines surface roughness, waviness, and ...Missing: introduction | Show results with:introduction
[14]
50 Years of Quality: A Superficial History of Surface Finish
Mar 30, 2011 · The earliest surface measurement devices were reference surfaces machined to various degrees of roughness. Machinists would literally scratch ...Missing: post WWII
[15]
The History and Current State of 3D Surface Characterisation
The measurement process was achieved by drawing a stylus across a surface and recording vertical deviations of the surface. From the late 1970s analogue ...
[16]
Fractal dimension as working tool for surface-roughness problems
Surface analysis in terms of fractal (noninteger) dimension is designed to describe, by a single parameter, surface roughness over many orders of magnitude.
[17]
A note on the description of surface roughness using fractal dimension
Two methods for estimating the fractal dimension of a profile of a rough surface are compared, the divider method and the spectral method. It is shown that the ...
[18]
Surface texture parameters: why so complex? - Digital Surf
Nov 13, 2018 · Areal surface texture started in the 1990s by simply extrapolating profile parameters to the third dimension. ... ISO 25178 was developed with the ...
[19]
Machine learning based approach for surface roughness prediction ...
Sep 1, 2025 · This paper introduces a data fusion approach for predicting SR in 3D printing process, addressing the lack of studies in real-time monitoring ...
[20]
Application of Artificial Intelligence for Surface Roughness ...
The paper discusses the limitations, challenges, and future directions for applying AI in surface roughness prediction for additively manufactured components.
[21]
A Review of the Factors Influencing Surface Roughness in ... - MDPI
This work presents a review of the factors that affect surface roughness generation in machining (turning/milling) processes.
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Comparison of Surface Roughness When Turning and Milling
Aug 7, 2025 · The effects of milling process parameters on cutting forces and surface roughness were studied during peripheral up milling of bamboo scrimber.
[23]
Surface Roughness Chart Guide: Symbols, Values & Measurement
Nov 11, 2021 · Machining processes such as turning, milling, and grinding will depend on multiple factors. Hence, the factors affecting surface finish ...
[24]
Influence of Surface Roughness - Science of Adhesion - 3M
Rough surfaces can lead to stronger bonds by increasing contact area and mechanical interlocking, but excessive roughness can cause issues if adhesives can't ...
[25]
Surface roughness profile and its effect on coating adhesion and ...
Surface roughness affects coating adhesion and corrosion creep, though a direct link between adhesion and corrosion protection is difficult to quantify. ...
[26]
[PDF] evaluation of the effect of surface finish on high-cycle fatigue of slm ...
surface roughness can affect the fatigue life of a part. Generally speaking, a rougher part will have a shorter fatigue life for the same loading conditions.<|control11|><|separator|>
[27]
Surface Finish: Standards, Techniques, Applications, and More - Jiga
Sep 1, 2025 · Surface finish directly impacts fine part tolerances and fit during assembly. In transition fits, the surface roughness must be insignificant ...
[28]
Surface Roughness & Finish for Bearings and Seals - Hallite
If the surface is too coarse, premature seal failure may occur due to the roughness of the surface, hence causing small cuts or scores in the sealing lip.<|separator|>
[29]
Simulation on the effect of cylinder liner and piston ring surface ...
When the surface roughness of the cylinder liner increases, the friction of the asperity decreases slightly, the friction of the fluid increases, and the total ...
[30]
A systematic literature review: The effects of surface roughness on ...
The studies were found to emphasize the effects of surface roughness on the wettability and IMC layer formation of lead-free solder materials. Moreover, the ...
[31]
What are the Hidden Costs Associated with Surface Finish ...
Apr 27, 2021 · Hidden costs include extensive finishing, grinding, polishing, and manual processes for smooth surfaces, which can double the cost of a part.
[32]
Analyzing Surface Roughness Variations in Material Extrusion ... - NIH
Sep 1, 2023 · The study found that increasing infill density reduces surface roughness, while increasing layer thickness, printing speed, and extrusion ...
[33]
Improving Surface Roughness of FDM-Printed Parts Through CNC ...
This paper presents a comprehensive review of recent studies on CNC post-processing of FDM-printed parts, analyzing its impact on surface roughness, ...
[34]
The Influence of Surface Texturing on the Frictional Behaviour of ...
This study investigates numerically the effect of surface texturing on the Stribeck curve, i.e., friction in lubricated contacts; in particular, the ...
[35]
Effect of surface roughness on friction and lubrication regimes
Majority of the work pertaining to the surface roughness and friction is found in dry sliding contacts, however very little work related to stribeck curve ...
[36]
The Impact of Surface Roughness on the Friction and Wear ... - MDPI
Surface roughness plays a critical role in the performance of bearings, directly influencing factors such as the friction coefficient and wear rate. A reduction ...3. Results And Discussion · 3.3. Friction And Wear... · 3.4. Wear MechanismMissing: gears | Show results with:gears
[37]
Tribology technologies for gears in loss of lubrication conditions
Feb 22, 2025 · This paper reviews the main progress in surface technologies, such as coatings, surface texturing, and thermochemical treatments, with a focus on gear surface ...Nitriding Steels · Self-Lubricating And... · Other Coatings Tested For...
[38]
Surface roughness effects in point contact elastohydrodynamic ...
The effect of surface roughness in elastohydrodynamic lubrication (EHL) is predicted using a perturbation approach.
[39]
Real Contact Area - an overview | ScienceDirect Topics
The real contact area is the sum of all the miniscule areas of contact between abrasive grains and a workpiece.
[40]
Role of surface quality on biocompatibility of implants - A review
The key aspects of surface quality that affect biocompatibility are surface roughness, surface feature, surface chemistry, crystallinity and porosity.
[41]
Surface roughness characterization of smooth optical films ...
To minimize scattering losses of high precision optics, optical elements with very low surface roughness are required. Nowadays, superpolished substrates ...
[42]
A comprehensive review on realization of self-cleaning surfaces by ...
Aug 3, 2024 · This review article focuses on the fundamentals of wettability, material parameters controlling surface wettability and three different paths to realization of ...
[43]
[PDF] Optical Methods of Surface Measurement
Jul 10, 2012 · • Three optical methods for measuring surface topography: – Confocal microscopy. – Focus variation microscopy. – Coherence scanning ...
[44]
Roughness measurements across topographically varied additively ...
May 5, 2023 · In this work we aim to define best practices for precise, comparable surface roughness measurements of representative metal AM parts.Roughness Measurements... · 3. Results And Discussion · 3.4. Morphology
[45]
[PDF] Improved vertical-scanning interferometry
We describe a method that combines phase-shifting and coherence-peak-sensing techniques to permit measurements with the height resolution of phase-shifting ...
[46]
How White Light Interferometry Can Measure Surface Roughness
May 14, 2020 · This article outlines the utilization of mean roughness measurements with white light interferometry (WLI) optical profilers.
[47]
3D modeling of coherence scanning interferometry on 2D surfaces ...
Coherence scanning interferometry (CSI) is a three-dimensional (3D) optical measuring technique enabling a height resolution down to the nanoscale. Generally, ...
[48]
Nano-scale Topography Measurements by AFM - Park Systems
Mar 22, 2024 · This whitepaper reviews AFM methodologies that are typically used to investigate the topography and roughness of a samples.
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How to Use AFM to Analyze Surface Metrology - AZoOptics
Jul 14, 2023 · This method provides the operator with high lateral and vertical resolution, but one disadvantage of AFM is its speed at acquiring topographical ...Surface Metrology Techniques · What Is Afm? · Afm's Suitability For...
[50]
ISO 21920-2:2021 - Geometrical product specifications (GPS)
In stock 2–5 day deliveryThis document specifies terms, definitions and parameters for the determination of surface texture by profile methods.
[51]
Evaluating the fractal dimension of profiles | Phys. Rev. A
In this paper, we present the variation method for one-dimensional (1D) profiles and show that, in the limit, it is equivalent to the classical box-counting ...
[52]
Sa (Arithmetical Mean Height) | Area Roughness Parameters
Sa is the extension of Ra (arithmetical mean height of a line) to a surface. It expresses, as an absolute value, the difference in height of each point.
[53]
Areal field parameters - Surface Metrology Guide - Digital Surf
In the ISO 25178 standard, all areal parameters start with the upper case letter S or the upper case letter V. In contrast with naming rules used with profile ...Missing: formulas | Show results with:formulas
[54]
Sal (Auto-correlation length) | Area Roughness Parameters - keyence
surface texture parameters in ISO 25178 ; Sa (arithmetical mean height) · Sz (Maximum height) · Sq (Root mean square height) ; Ssk (Skewness) · Sku (Kurtosis) ...Missing: formulas | Show results with:formulas
[55]
Areal surface texture parameters - Sensofar
ISO 25178 introduces a standardized nomenclature for surface texture parameters, differentiating them from traditional profile parameters.Missing: definitions formulas
[56]
Surface Roughness Measurement—Parameters - Evident Scientific
Maximum height (Rz) represents the sum of the maximum peak height Zp and the maximum valley depth Zv of a profile within the reference length.Missing: 21920-2 | Show results with:21920-2
[57]
Surface Texture Parameters by Family - Michigan Metrology
The definitions and more detailed discussions of the various surface texture parameters may be found in the following references: ISO 25178-2:2009 “Geometrical ...<|separator|>
[58]
Application of Areal Topography Parameters in Surface ... - MDPI
To address this issue, five areal surface texture parameters defined in ISO 25178-2, Sa, Sz, Sq, Sdq, and Sdr were selected for detailed analysis.
[59]
Profile parameters from ISO 4287 - Surface Metrology Guide
The most common surface texture parameters, also called roughness parameters, are calculated on profiles and are defined in ISO 4287.
[60]
[PDF] QUICK GUIDE TO SURFACE ROUGHNESS MEASUREMENT
Roughness parameters. (EN ISO 4287). Ra – arithmetical mean roughness value: The arithmetical mean of the absolute values of the profile deviations (Z i) from ...
[61]
[PDF] Explanation of Surface Characteristics・Standards 〉〉〉
Roughness profile will have bigger profile distortion & smaller amplitude when cutoff λc is short. Primary profile P. Roughness profile R phase correct λc 0.8mm.
[62]
ISO 4288:1996 - Surface texture: Profile method
ISO 4288:1996 specifies rules for assessing surface texture using the profile method, comparing measured values with tolerance limits and measuring roughness ...
[63]
[PDF] ISO-4288-1996.pdf - iTeh Standards
Aug 1, 1996 · ISO 4288:1996 is an international standard for measurement of surface roughness and waviness, prepared by ISO technical committees.
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ISO 4287:1997 - Surface texture: Profile method
Surface texture: Profile method — Terms, definitions and surface texture parameters.
[65]
ISO 21920-1:2021 - Surface texture: Profile
In stock 2–5 day deliveryThis document specifies the rules for indication of surface texture by profile methods in technical product documentation by means of graphical symbols.Missing: roughness | Show results with:roughness
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Improved standards for surface texture - Mahr | Metrology
Apr 6, 2022 · The International Standards Organization (ISO) in Geneva has published the new profile standards ISO 21920-1, -2 and -3 for surface textures with edition 2021- ...
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Structure of ISO 25178 - Surface Metrology Guide
Structure of ISO 25178 ; Part 6: Classification of methods for measuring surface texture. This part defines each instrument technique and classifies them.Missing: invariance | Show results with:invariance
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Feature parameters - ScienceDirect
The International Standards Organisation (ISO) will shortly be publishing the areal surface texture documents under the ISO number ISO/TS 25178.Missing: metrology | Show results with:metrology
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Functional Importance of Surface Texture Parameters - PMC
Negative skewness of smooth surfaces can improve the contact and lubrication conditions [75]. It was also found that negatively skewed surfaces of smooth [76] ...
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[PDF] B46.1 - 2019 : Surface Roughness, Waviness, and Lay Basic Terms
May 21, 2022 · Roughness: The finer spaced irregularities of the surface texture that usually result from the inherent action of the production process or ...
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The Basics of Surface Finish
Jan 6, 2021 · Surface roughness, frequently shortened to roughness, refers to small irregularities in surface geometry. Roughness is the most commonly ...
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Understanding ISO 21920 Surface Roughness Standards
Aug 18, 2025 · Explore ISO 21920 and how it reshapes surface roughness standards. Learn how to implement new profiles and improve measurement clarity and ...Missing: post- 2020 nano- digital twins
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ISO 21920: Standard for Roughness Measurement - ZEISS
The DIN EN ISO 21920 defines basic symbols and parameters for indicating surface roughness on technical drawings and in technical documents.Missing: 2021 | Show results with:2021
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Surface roughness digital twin based on stereolithography physics ...
May 10, 2025 · This paper proposes a digital model to generate the profile of additively manufactured (AM) surfaces, specifically for vat polymerization ...Missing: nano- | Show results with:nano-
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Harmonised standards - Public Health - European Commission
Harmonised European standards under the medical devices Regulations are developed by CEN and Cenelec as European standardisation organisations,Missing: roughness | Show results with:roughness
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Harmonized Standards List - Medical Device Regulation
EN ISO 5366-1:2009 Anaesthetic and respiratory equipment – Tracheostomy tubes – Part 1: Tubes and connectors for use in adults (ISO 5366-1:2000)Missing: roughness | Show results with:roughness
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Probabilistic, Fractal, and Related Techniques for Analysis of ...
In section 4 we discuss briefly the fractal approaches to surface roughness, in particular using a kind of parametric-homogeneous functions having fractal ...
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[PDF] Measuring the Fractal Dimensions of Surfaces - DTIC
Jun 2, 2025 · An intriguing concept proposed by Mandelbrot (1967, 1977,. 1982) Is to use fractals to fill the void caused by the absence of suitable geometric.
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On How to Determine Surface Roughness Power Spectra
Dec 27, 2024 · A self-affine fractal surface has a power spectrum C_{\text{2D}}(q)\sim q^{-2(1+H)}, (where H is the Hurst exponent related to the fractal ...
[80]
Multiscale characterization and contact performance analysis of ...
Jun 15, 2023 · The multi-scale separation method of machining surfaces is proposed to determine the optimal wavelet basis function and decomposition level in ...
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Fractal geometry model for wear prediction - ScienceDirect.com
We develop a fractal geometry model, which predicts the wear rate in terms of these two fractal parameters for wear prediction. Using this model we show that ...
[82]
Application of Machine Learning in the Quantitative Analysis ... - MDPI
Surface roughness, which can be quantitatively characterized by the fractal dimension (FD), was calculated to identify the surface structural irregularity ...Missing: post- | Show results with:post-