Bevel Gear Calculator

Straight bevel gears on any shaft angle. Enter module and teeth to get cone angles, all diameters and angles for the blank, the gear forces and the bearing loads, following the Gleason system.

Shaft angle Σ
°
mm
For diametral pitch P, module = 25.4 / P.
z₁
z₂
mm
°
rpm
N·m
Pitch cones meet at one apex

Blank and tooth dimensions

Everything you need to turn the blank and set up the cutter. Lengths in mm, angles in degrees.

ItemSymbolPinionGear

How it is calculated

Gleason straight bevel system with constant clearance: working depth 2m, whole depth 2.188m. The face angle of each gear follows the root cone of its mate, so the clearance stays constant along the tooth.

Pitch cone angle δ1 = atan( sin Σ / (z2/z1 + cos Σ) ), δ2 = Σ − δ1 Pitch diameter d = m · z Cone distance R = d2 / (2 sin δ2) Gear addendum ha2 = 0.54m + 0.46m · z1 cos δ2 / (z2 cos δ1), ha1 = 2m − ha2 Dedendum hf = 2.188m − ha Dedendum angle θf = atan(hf / R), addendum angle θa1 = θf2, θa2 = θf1 Outside diameter da = d + 2 ha cos δ Apex to crown X = R cos δ − ha sin δ Virtual teeth zv = z / cos δ Forces (pinion) Ft = 2T1 / dm1, dm1 = d1 − b sin δ1 Fr1 = Ft tan α cos δ1 (= axial force on gear) Fa1 = Ft tan α sin δ1 (= radial force on gear)

Face width should not exceed R/3 or 10m, whichever is smaller. The pinion must have enough teeth to avoid undercut. At 20° the Gleason minimum is 13 teeth (mate ≥ 30), 14 (≥ 20), 15 (≥ 17) or 16 (≥ 16). The axial force always pushes each gear away from the apex, so the bearings must take it.