Overview
ISO 21771-2:2025, "Cylindrical involute gears and gear pairs - Part 2: Calculation and measurement of tooth thickness and backlash," establishes calculation procedures and measurement relationships for determining specification limits when a desired tooth thickness is known. The standard links backlash to tooth thickness, centre distance and tooth deviations in pinion–gear meshes and applies to a broad range of gear types and configurations. Its formulae are applicable to gears of all sizes, materials and manufacturing methods. Note: the document does not prescribe how to select the nominal tooth thickness or its tolerance.
Key topics
- Scope and terminology: definitions, symbols, units and conventions used for tooth thickness and backlash calculations.
- Gear types covered: external and internal parallel-axis spur and helical gears, involute worms and crossed-axis gears, spur and helical racks, and sector gears.
- Calculation methods: formulae for tooth thickness, space width and relationships with transverse/normal pressure angles, helix/lead angles and reference diameters.
- Measurement methods:
- Measurement by pitch (index)
- Double-flank testing with a master gear (radial composite measurement)
- Single-flank composite measurement
- Span measurement (including angle of rock)
- Three-ball span device and measurements over/between balls or pins
- Datum and specification systems: axis-related vs non-datum-related tooth thickness systems and how measurement methods map to these systems.
- Practical limits and assumptions: selection of measurement diameter, tight-mesh centre distance limits, master gear design considerations, test radii, and applicability constraints.
Applications
ISO 21771-2:2025 is essential for professionals involved in gear design, production and inspection who need rigorous, repeatable procedures to calculate and measure tooth thickness and backlash:
- Gear designers and mechanical engineers ensuring correct tooth engagement and backlash budgets.
- Manufacturing engineers specifying measurement methods after production (single- or double-flank, span or three-ball tests).
- Metrologists and quality assurance personnel establishing acceptance criteria and interpreting test results.
- Suppliers of gear testing equipment and master gears who must design test hardware to the standard’s limits and recommendations.
Practical value & SEO keywords
Using ISO 21771-2:2025 helps ensure consistent measurement of tooth thickness, accurate backlash calculation, and compatibility between design intent and inspection results for cylindrical involute gears, helical gears, pinion and gear mesh, and crossed-axis gears. The standard improves traceability in gear manufacturing and supports reliable gear pair performance.
Related standards
Refer to other ISO and industry standards covering gear design, gear quality, and measurement practice (gear geometry, tolerance systems and metrology) to complement ISO 21771-2:2025 when developing specifications or inspection plans.
Open preview (PDF)Cylindrical involute gears and gear pairs — Part 2: Calculation and measurement of tooth thickness and backlash
