Overview
SIST ISO 23509:2020 (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
SIST ISO 23509 is a practical, formula-driven resource for reliable bevel and hypoid gear geometry that supports consistent design, manufacturing and rating workflows.