surface-texture-measurement

name	surface-texture-measurement
description	Surface texture measurement — 2D profile parameters (Ra, Rz, Rq, Rsk, Rku, Rsm, Rc), 3D areal parameters (Sa, Sz, Sq, Ssk, Sku, Sal, Str), Abbott-Firestone curve (material ratio Smr, void volume Vvc), measurement methods (contact stylus, coherence scanning interferometry, focus variation, confocal), filter selection (Gaussian λc, ls, λf cutoffs), sampling length and evaluation length, traceability, and ISO 21920/25178 standards.
metadata	{"priority":7,"promptSignals":{"phrases":["surface texture measurement","surface roughness measurement","Ra Rz Rq","ISO 4287","profilometer","surface topography"],"minScore":3}}

Surface Texture Measurement — Complete Skill

Surface Texture Parameters

Profile Parameters (ISO 21920 — formerly ISO 4287)

R parameters: measured from primary profile after filter; most common specification

Amplitude parameters: Ra = (1/l) × ∫₀^l |z(x)| dx [arithmetic mean deviation; most universally used; monotonic sum of heights] Rq = √((1/l) × ∫₀^l z²(x) dx) [root mean square; Rq ≈ 1.25 × Ra for sinusoidal profile] Rz = average of 5 maximum peak-to-valley heights within sampling lengths [ISO 4287 5-point; not same as old DIN Rz!] Rt = maximum peak-to-valley over evaluation length [single extreme; sensitive to outliers]

Skewness Rsk: Rsk = (1/Rq³) × (1/l) × ∫₀^l z³(x) dx [dimensionless; third moment / Rq³] Rsk > 0: positive skewness (peaks dominate; freshly machined, scratchy surfaces) Rsk < 0: negative skewness (valleys dominate; plateau-honed, run-in bearing surfaces; better load bearing) Rsk ≈ 0: symmetric profile (ground, lapped)

Kurtosis Rku: Rku = (1/Rq⁴) × (1/l) × ∫₀^l z⁴(x) dx [dimensionless; fourth moment / Rq⁴] Rku = 3: Gaussian (normal distribution) Rku > 3: sharper peaks and valleys (leptokurtic; milled surface 4–7) Rku < 3: flat (platykurtic; sinusoidal surface = 1.5)

Spacing parameters: RSm = mean spacing of profile irregularities [mm; = feed in turning; machining wavelength] RPc = peak count per unit length (alternative; depends on threshold H)

Waviness and Primary Profile

P parameters: primary profile (no filter applied); includes roughness + waviness W parameters: waviness profile (filtered with long-wavelength λf cutoff) R parameters: roughness profile (filtered with short-wavelength λs and long-wavelength λc)

Filter hierarchy:

1. Short-wavelength profile filter (λs cutoff): removes high-frequency noise (stylus radius limit)
2. Long-wavelength profile filter (λc cutoff): separates roughness from waviness
3. Very long-wavelength filter (λf): separates waviness from form error

Cutoff Wavelengths and Sampling Length

ISO 4288 / ISO 21920 Cutoff Selection

Standard cutoff λc for Ra:

Ra range [μm]	λc (roughness cutoff) [mm]	Sampling length lr [mm]	Evaluation length ln = 5lr [mm]
0.006–0.02	0.08	0.08	0.4
0.02–0.1	0.25	0.25	1.25
0.1–2.0	0.8	0.8	4.0
2.0–10	2.5	2.5	12.5
10–80	8.0	8.0	40

Short-wavelength cutoff λs: λs/λc ≈ 1/300 (ISO 11562 Gaussian filter); λs = 2.5 μm for λc = 0.8 mm Stylus tip radius must be smaller than λs/2 (typically r_tip = 2 μm for standard measurement)

Note: wrong λc → wrong Ra! Measuring Ra = 0.1 μm surface with λc = 2.5 mm: includes long-wavelength waviness → Ra appears larger than true roughness

3D Areal Parameters (ISO 25178)

Areal vs. Profile

Areal measurement advantage: Profile: single line; misses anisotropic features (lay direction); limited statistical confidence Areal: captures full 3D topography; direction-independent; better correlation with function

S parameters (ISO 25178): Sa = areal equivalent of Ra (arithmetic mean height of areal surface) Sq = areal equivalent of Rq (RMS height) Sz = maximum height of areal surface (10-point mean over entire area) Ssk = areal skewness (Rsk equivalent) Sku = areal kurtosis (Rku equivalent)

Functional areal parameters: Sal = autocorrelation length [mm]; characterizes lateral texture scale Str = texture-aspect ratio: Str ≈ 1 isotropic; Str ≈ 0 strongly anisotropic (directional lay) Std = dominant lay direction [°]

Abbott-Firestone Bearing Ratio Curve

Material Ratio and Functional Volume Parameters

Abbott-Firestone curve: cumulative distribution of surface heights z Horizontal axis: bearing ratio Smr (%) = fraction of surface at height z and above Vertical axis: height z (or depth below peak)

Reading the curve: Smr at z = 0: 0% (top of highest peak) Smr at z = -R_total: 100% (lowest valley) Slope of curve = height distribution (steeper = more uniform plateau; gradual = peaks + valleys)

ISO 25178 functional parameters from Abbott curve:

Material ratio parameters: Smr(c): material ratio at cutting height c [%] Smc: inverse — height at material ratio c [μm] S_mr1, S_mr2: percentage of upper (peaks) and lower (valleys) inflection points

Volume parameters (per unit area): Vmp = peak material volume [μm³/μm²] Vmc = core material volume [μm³/μm²] (main plateau) Vvc = core void volume [μm³/μm²] (lubricant retention volume) Vvv = valley void volume [μm³/μm²] (lubricant retention in valleys)

Functional significance: High Vvc: good lubricant retention → lower friction (engine cylinder bores) High Vmp: sharp peaks → high initial wear rate → reduces quickly (run-in) Low Vvv: little contaminant trapping (pharmaceutical contact surfaces)

Plateau honing design: Target after plateau honing: Rsk = -1.0 to -1.6; Rku = 5–7 (sharp valleys, flat plateaus) Vvc = 0.01–0.05 μm³/μm² (lubricant capacity); Vmp < 0.01 (minimal peaks after run-in) Measure on cylinder bore after honing and break-in to verify

Measurement Methods

Contact Stylus Profilometer

Principle: diamond stylus (2 μm tip radius; 60° or 90° cone) traces surface; vertical displacement measured (LVDT or piezoelectric) Tip radius effect: cannot measure features sharper than r_tip; valleys appear wider; peaks may be truncated Measurement range: vertical: ±0.1–2.0 mm typical; lateral: full traverse (25–100 mm) Advantages: traceable (calibrated with gauge blocks); robust; mature technology Limitations: contact → damage soft surfaces; slow for 3D areal; single line only for 2D

Calibration: Calibrate vertical (height) with certified reference specimens Ra (sinusoidal; grooves; traceable to BIPM) Calibrate lateral with pitch standards; λc from filter verification standard Stylus radius check: profiling steel ball (known r) → verify broadening

Coherence Scanning Interferometry (CSI) / White Light Interferometry (WLI)

Principle: broadband light source → white light fringes; fringe peak corresponds to surface height; full-field 3D capture Resolution: vertical < 1 nm; lateral = optical resolution (0.5–5 μm depending on objective NA) Speed: full 3D areal measurement in seconds (vs. hours for stylus scanning) Advantages: non-contact; high spatial resolution; true areal measurement Limitations: multi-bounce in deep features; noisy on rough/steep slopes; requires clean optics

Software: Zygo, Bruker, Taylor-Hobson; data analysis per ISO 25178

Focus Variation Microscopy (FVM)

Principle: piezo-driven focus scanning; surface = positions of maximum focus variation in each pixel Best for: rough surfaces (Ra > 0.5 μm); large range; field of view up to mm Alicona InfiniteFocus: industry standard for FVM; flexible for roughness + form + edge measurement Lateral resolution: limited by optics NA; 0.5–5 μm typical

Confocal Microscopy

Pinhole confocal: rejects out-of-focus light; depth selectivity < 1 μm Best for: smooth, shiny surfaces; biomedical samples; semiconductor inspection Chromatic confocal: single point; fast; robust to vibration; used in online inspection

Traceability and Calibration

Metrological Chain

National standard → transfer standard → working standard → measurement: NIST (US) / NPL (UK) → calibrated reference specimens → gauge blocks + artifacts → profilometer calibration

Required calibrations (ISO 12179): Vertical magnification: ±1% (calibrated roughness specimen of known Ra) Cutoff filter verification: against step-height or structured artifact Stylus tip radius: steel ball measurement; nominal r_tip ≤ stated Temperature control: ±0.5°C (thermal expansion affects measurement)

Measurement uncertainty budget (ISO 15530): Contributions: calibration artifact uncertainty; repeatability; temperature; probe force; stylus wear Typical combined uncertainty: U(Ra) = ±5–10% of measured value (k=2, 95% confidence)

Drawing Callout and Specification

ISO 1302 — surface texture indication on engineering drawings: Symbol √ with required parameter specification Example: Ra 0.8 (maximum Ra 0.8 μm; λc = 0.8 mm inferred from Ra range; evaluation length = 5× lr) Additional: √Rz 6.3 (maximum Rz); or √ U Ra 1.6/L Ra 0.2 (upper/lower limits)

Lay direction: = (parallel to direction of measurement); ⊥ (perpendicular); × (crossed); M (multidirectional); C (circular) For anisotropic surfaces: specify measurement direction OR use 3D areal parameter Str

Standards and References

Standard	Scope
ISO 21920	Geometrical product specifications — surface texture: profile (replaces ISO 4287/4288 from 2021)
ISO 25178-2	Surface texture: areal — terms, definitions, surface texture parameters
ISO 25178-6	Classification of measurement methods
ISO 12179	Calibration of stylus instruments
ISO 1302	Surface texture indication on drawings
ASME B46.1	Surface texture (US equivalent)

Output

Provide: surface application (sliding/sealing/optical/aesthetic; functional requirement — friction/leakage/reflectivity), specification (Ra or Sa [μm]; Rz [μm]; Rsk target; Vvc [μm³/μm²] if functional areal parameter; lay direction), measurement method (stylus/CSI/FVM/confocal; basis for selection; non-contact requirement? damage concern?), filter selection (λc [mm] from ISO 4288 table; λs [μm]; evaluation length ln = 5×lr [mm]; Gaussian filter), measurement results (measured Ra [μm]; Rq; Rz; Rsk; Rku; RSm [mm] if relevant; pass/fail vs. spec), 3D areal (if measured: Sa; Sz; Ssk; Str; Vvc [μm³/μm²]; Vmp; bearing ratio curve: plateau vs. valley structure), calibration trace (calibration artifact Ra [μm]; last calibration date; measurement uncertainty U(Ra) = ±[%]; temperature [°C] during measurement), drawing callout recommendation (ISO 1302 symbol; all parameters with limits), comparison with process expectations (theoretical Ra from feed/tool; measured vs. theoretical ratio — BUE or vibration indicated?), and applicable standard (ISO 21920 or ISO 4287 legacy; ISO 25178 for 3D areal; ISO 12179 calibration).