Gear Geometry
Blank size, cutter setup and inspection span for a spur gear, from its tooth count and pitch.
Full-depth external involute spur gears.
The blank size, cutter setup and inspection span show here once you build the shop plan.
Shop plan
- 1Define— teeth · — (module —) · —
- 2Turn the blankto the blank outside diameter; the tooth tips are the depth reference.
- 3Cut—, — · radial infeed —
- 4Inspectspan over — = —Open Span & Chord Measurement Open Over Pins Measurement
Method & sources
Scope: full-depth external involute spur gears, with optional profile shift x (0 for a standard gear), addendum (1 + x)/P. Tooth depth follows the gear's standard: 2.157/P for 14½° full depth, 2.25/P for 20° and 25°, 2.2/P + 0.002 in at 20 DP and finer, and 2.25 m for metric module.
For the standard full-depth external spur-gear scope, pitch diameter is d = z·m, outside diameter dₐ = (z+2)m, root diameter dᶠ = d − 2·dedendum, circular pitch p = πm, and base diameter dᵦ = d cos α.
Dedendum: 1.157/P for 14½° full depth (ASA B6.1-1932, Brown & Sharpe form cutters); 1.25/P for 20° and 25° full depth (ANSI B6.1); 1.200/P + 0.002 in for 20 DP and finer (ANSI B6.7); 1.25 m for metric module (ISO 53). Profile shift x moves the cutter outward by x·m: outside and root diameters grow by 2x·m, the tooth thickness becomes m(π/2 + 2x tan α), and the whole depth is unchanged. A shift that brings the tooth to a point before the outside diameter is refused; a tip thinner than 0.25 m is warned about; a shift below 1 − z sin²α ÷ 2 is warned about as undercut. Form-cutter numbers follow the standard eight-cutter involute series and its half-number series. Standard pitches are the ISO R54 diametral pitches with the ANSI B6.7 fine pitches, and the ISO 54 modules.
References: FreeCAD Gear Workbench documentation and the BOSL2 gear library.