metrology

name	metrology
description	Engineering metrology — CMM measurement, GD&T verification, measurement uncertainty (GUM), gauge R&R (MSA), calibration hierarchy, surface texture measurement, coordinate systems.
metadata	{"priority":6,"promptSignals":{"phrases":["metrology","CMM","measurement uncertainty","gauge R&R","MSA","calibration","coordinate measurement","GUM"],"minScore":4}}

Engineering Metrology — Complete Skill

Coordinate Measuring Machine (CMM)

Types

Bridge CMM: most common; granite table, probe on moving bridge; accuracy ±0.5-5 μm Gantry CMM: large workpieces (automotive body, aircraft fuselage) Portable CMM: articulated arm (FARO, Romer); 7-axis; accuracy ±30-100 μm (lower, flexible) CT metrology (XCT): X-ray computed tomography; internal features; non-contact; accuracy 5-20 μm

Probing Systems

Touch-trigger probe (Renishaw TP20/TP200): contact; triggers signal at touch; fast, widely used Scanning probe (Renishaw REVO): continuous contact scanning; 50,000 points/sec; better for complex surfaces Optical probe (laser triangulation): non-contact; good for soft/shiny surfaces; lower accuracy than touch Computed vs. measured: all GD&T features computed from measured point cloud

CMM Programming (DMIS / Calypso / PC-DMIS)

Define: coordinate system (datum reference frame), features (points, circles, planes, cylinders) Measurement: safe travel paths, probe clearance, contact angles Tolerancing: apply GD&T controls to measured features Output: measurement report vs. nominal CAD model

Measurement Uncertainty (GUM — ISO/IEC 98-3)

Sources of Uncertainty

Type A: statistical evaluation (repeatability from repeated measurements) Type B: other sources (calibration, resolution, thermal, elastic deformation)

Combined standard uncertainty: u_c = √(u_A² + u_B² + ...) [combined, assume uncorrelated] For correlated: u_c = √(Σ_i u_i² + 2Σ_i Σ_j c_ij u_i u_j)

Expanded uncertainty: U = k × u_c [k = coverage factor; k=2 for ~95% confidence, normal distribution] Report as: y = ȳ ± U (U at 95% confidence)

Type A Evaluation

s² = Σ(x_i - x̄)² / (n-1) [sample variance] u_A = s/√n [standard uncertainty of mean] Degrees of freedom ν = n-1

Type B Evaluation

Rectangular distribution (digital readout, resolution Δ): u = Δ/(2√3) Normal distribution (calibration certificate, coverage k=2): u = U_cal/2 Triangular distribution (thermal drift, bounds ±a): u = a/√6

Measurement Budget Example

Source	Type	u [μm]
Repeatability	A	0.8
CMM calibration	B	0.5
Temperature (20±1°C, α=12ppm/°C, L=100mm)	B	0.7
Probe qualification	B	0.3
Combined u_c	—	1.2
Expanded U (k=2)	—	2.4 μm

CTE thermal correction: ΔL = α × L × ΔT; u_thermal = α × L × u_ΔT / √3

Gauge R&R (Measurement System Analysis — AIAG MSA 4th Ed.)

Purpose

Quantify repeatability (gauge variation) and reproducibility (operator variation) Assess fitness of measurement system for quality control

ANOVA Method (Gauge R&R)

10 parts × 3 operators × 2-3 replications = 60-90 measurements EV (Equipment Variation = Repeatability): σ²_EV = MS_operator×part_within / n² AV (Appraiser Variation = Reproducibility): σ²_AV = (MS_operator - MS_interaction)/(n_parts × n_reps) GRR = √(σ²_EV + σ²_AV)

%GRR = GRR × 5.15 / (part tolerance or 6 × σ_total_parts) %GRR < 10%: acceptable 10-30%: marginal (may be acceptable based on application) %GRR > 30%: not acceptable → improve gauge or measurement method

Discrimination (Number of Distinct Categories — NDC)

NDC = 1.41 × σ_parts / σ_GRR NDC ≥ 5: adequate discrimination for process control NDC < 2: gauge cannot distinguish parts → useless for SPC

Calibration

Calibration Hierarchy (Traceability)

SI unit → national standard (NIST) → working standard → gauge → measurement Traceability: unbroken chain of comparisons with stated uncertainties

Calibration intervals: risk-based (usage frequency, stability history) Common: 12 months (most gauges), 6 months (critical), 3 months (high-use)

ANSI/ISO 10012: measurement management systems ISO 17025: laboratory calibration accreditation

Common Gauge Calibration

Slip gauges (gauge blocks): ISO 3650, Grade K (reference), Grade 0/1/2 (workshop) CMM: ISO 10360; calibration artifact (ball bar, ball plate) Load cells: ASTM E74 (calibrated by NIST-traceable dead weights) Accelerometers: back-to-back comparison with reference accelerometer

Datum Reference Frame (DRF) and CMM Setup

Establishing DRF (3-2-1 method)

Primary datum A (plane): 3 CMM contact points → constrains 3 DOF (Tz, Rx, Ry) Secondary datum B (line/plane): 2 points → constrains 2 DOF (Tx, Rz) Tertiary datum C (point/line): 1 point → constrains 1 DOF (Ty) Fully constrained: 6 DOF

Best-fit alignment: fit measured points to nominal CAD → minimum zone fitting (not always correct — use constrained/DRF fit for GD&T)

GD&T Verification on CMM

Flatness

Measure N points on surface Flatness = distance between two parallel planes containing all points (minimum zone) Software computes iteratively

Circularity

Measure circle in cross-section Circularity = difference between minimum circumscribed and maximum inscribed radii

Cylindricity

Combine roundness + straightness + taper of cylinder All points within two coaxial cylinders differing by cylindricity tolerance

True Position

Derived feature center vs. nominal position (from DRF) TP = 2√((Δx)² + (Δy)²) [for diameter zone, 2D] Compare to: TP ≤ tolerance + bonus (MMC) or TP ≤ tolerance

Runout (Total) vs. Circular Runout

Circular: max indicator reading in one revolution, one cross-section Total: max indicator reading across full length of surface during full revolution

Surface Texture Measurement

Contact profilometer: stylus traces surface, records z(x) profile Cutoff wavelength λ_c (filter): separates roughness from waviness Typical λ_c = 0.8 mm (Ra 0.1-2 μm), 2.5 mm (Ra 2-10 μm)

Software computes Ra, Rz, Rq from filtered profile — see surface-finish skill

Output

Provide: CMM probe type, measurement points per feature, combined uncertainty U [μm] with k, %GRR, NDC, calibration traceability chain, position tolerance verification vs. drawing call-out.