The Appendix of Spiral Bevel Gears Equations

Symbols with the subscript “G” or “P” are for the gear or the pinion respectively

Number of Teeth: N is a given value

Diametral Pitch: Pd is a given value

Shaft Angle: Σ is a given value

Pressure Angle: φ is a given value (usually 20 degrees)

Ratio: mG=NG/NP

Pitch Diameter: D = N/P

Pitch Angle: Pinion: ϒ = tan-1(NG/NP); Gear: Γ = Σ-ϒ

Outer Cone Distance: Ao=1/2(DP2+DG2)1/2

Face Width: F = Ao/3 or F = 10/Pd (use the smaller value)

Equivalent 90° Ratio: m90=mG

Working Depth: hk = 1.7/Pd

Addendum (at heel of tooth): Gear: aoG=(.46/Pd)+(.390/Pd*m902); Pinion: aoP=hk-aoG

Whole Depth: ht=1.888/Pd

Dedendum (at heel of tooth): Gear: boG=ht-aoG; Pinion: boP=ht-aoP

Dedendum Angle: Gear: δG=tan-1(boG/Ao); Pinion: δP=tan-1(boP/Ao)

Face Angle: Gear: Γo=Γ+δG; Pinion: ϒo=ϒ+δP

Outside Diameter: Gear: DoG=DG+2aoG*cos(Γ); Pinion: DoP=DP+2aoP*cos(ϒ)

Pitch Cone Apex to Crown: Gear: XoG=DP/2-aoG*sin(Γ); Pinion: XoP=DG/2-aoP*sin(ϒ)

Circular Pitch: p=π/Pd

Root Angle: Gear: ΓR=Γ-δG; Pinion: ϒR=ϒ-δP

Back-Angle Distance = Ao