ISO 23509:2016

Overview

ISO 23509:2016 (ISO 23509:2016) defines the standardized geometry for bevel and hypoid gears. It covers straight, spiral, zerol bevel and hypoid gear forms, and is written to be manufacturing-process neutral - applicable to all machining and generating methods (including modern multi-axis CNC). The standard also supplies the geometric basis needed to calculate factors for bevel gear rating (e.g., in ISO 10300). It is intended for experienced gear designers and machine-tool programmers.

Key topics and technical requirements

• Scope of geometry: Definitions and consistent nomenclature for bevel and hypoid gear geometry (straight, spiral, zerol, hypoid).
• Tooth geometry and cutting considerations: Tooth taper, tooth depth configurations (taper vs. uniform depth), cutter radius and mean radius of curvature, dedendum angle modifications.
• Hypoid specifics: Hypoid offset geometry, crossing point and related parameters required to model hypoid pinion/wheel sets.
• Pitch cone and profile parameters: Methods for determining pitch cone parameters (multiple calculation methods are provided), and details for initial data and parameter determination.
• Gear dimensions & checks: Procedures to determine basic data, tooth depth at calculation points, root and face angles, tooth thickness, inner/outer spiral angles and undercut checks for pinion and wheel.
• Supporting annexes: Informative annexes include a formula-structure guide (Annex A), detailed pitch cone and gear-dimension material (Annex B–C), force analysis (Annex D), machine tool data (Annex E), and worked sample calculations (Annex F).

Practical applications

• Designing bevel and hypoid gears for automotive differentials, industrial gearboxes, aerospace drives and other right-angle power-transmission systems.
• Generating consistent CNC programs and machine tool setups that reproduce standardized tooth forms across different production methods.
• Providing geometric inputs for gear capacity and fatigue rating calculations (integration with ISO 10300 rating procedures).
• Performing design validation checks such as undercut avoidance, tooth thickness, and spiral angle limits.

Who should use this standard

• Experienced gear designers and engineers developing bevel and hypoid gearsets.
• Gear manufacturers and machine-tool programmers creating CNC generation routines and toolpaths.
• Technical analysts performing gear capacity/rating calculations and failure analysis.
• Standards bodies and educators seeking a consolidated, machine-neutral geometric basis for bevel/hypoid gearing.

Related standards

• ISO 10300 (gear rating factors)
• ISO 1122-1 (terminology referenced by this document)

SIST ISO 23509 is a practical, formula-driven resource for reliable bevel and hypoid gear geometry that supports consistent design, manufacturing and rating workflows.