Overview
ISO 12781-2:2011 is an ISO Geometrical Product Specification (GPS) standard that defines the complete specification operator for flatness of complete integral features (individual features of type plane). It prescribes the ordered, unambiguous set of specification operations needed to define the transmission band for a flatness surface and the associated probing system. The standard is part 2 of ISO 12781 (flatness) and complements ISO 12781-1 (vocabulary and parameters).
Key topics and requirements
- Complete specification operator: Defines a full, ordered set of unambiguous operations (per ISO 17450-2) required to specify flatness uniquely.
- Scope limitation: Applies to complete integral features only - geometrical characteristics of individual planar features.
- Probing system:
- Contacting stylus probe is specified as part of the operator.
- Stylus tip geometry: The theoretically exact geometry is a sphere.
- Probing force: Specified as 0 N to remove elastic deformation effects from the operator.
- Filtering and extraction:
- The standard requires explicit statement of filter cut-off, probe tip radius, and method of association (reference plane). If not stated, the specification is ambiguous and a supplier may choose values when proving conformance.
- Notes explain stylus filtering limits and recommend mean-line filtering (e.g., Gaussian) to avoid spurious high-frequency content; aliasing issues are addressed via the Nyquist criterion.
- Sampling and aliasing:
- Discusses harmonic content of a nominally flat area and how sampling intervals must meet Nyquist considerations to avoid aliasing.
- Recommends at least seven sampling points per Gaussian filter cut-off as a theoretical minimum.
- Extraction strategies (sampling patterns) described and compared:
- Rectangular grid (recommended for general flatness)
- Polar grid (recommended for nominally disk-shaped features)
- Triangular grid (alternative)
- Union Jack (quick, limited coverage)
- Parallel profiles (directional high-resolution)
- Conformance rules: For proving conformance, ISO 14253-1 decision rules apply.
Applications and users
ISO 12781-2 is practical for:
- Quality engineers and metrologists specifying flatness tolerances on drawings and contracts.
- CMM programmers and inspection labs implementing measurement routines.
- Manufacturing engineers selecting sampling and probing strategies for flat parts (plates, mirrors, machined faces).
- Standards writers and product designers requiring unambiguous flatness specifications for procurement or verification.
Practical value includes improved measurement reproducibility, reduced ambiguity in supplier/customer specifications, and guidance on sampling strategies to capture relevant wavelength content.
Related standards
- ISO 12781-1:2011 - Flatness: Vocabulary and parameters
- ISO 17450-2 - GPS: Basic terms, specifications, operators and uncertainties
- ISO 14253-1:1998 - Decision rules for proving conformance
- ISO TR 14638 - ISO/GPS Masterplan
- ISO 8015 - Fundamental rules for GPS
Keywords: ISO 12781-2, flatness specification, geometrical product specifications, GPS, flatness measurement, probing system, stylus tip, extraction strategy, Nyquist, aliasing.
Open preview (PDF)Geometrical product specifications (GPS) — Flatness — Part 2: Specification operators
