# 17. Gear Guidelines¶

## 17.2. Gear module¶

The gear module defines the size of a gear tooth. Two gearwheels working together must have the same gear module:

circular_pitch = Pi * gear_module


Per default, the tooth height is defined with the gear module:

addendum_height = gear_module
dedendum_height = gear_module
tooth_height = 2 * gear_module


A small gear module generates less friction and then provides a better energy transmission efficiency. A large gear module supports higher efforts:

Module sizing formula in the literaure:
m>2.34*sqrt(T/(k*Rpe))
with:
T = tangential effort on the tooth = F*cos(a)
torque = C = d*F
d = R*cos(a) (R = primitive radius = Z*m/2)
T = F*cos(a) = C/d*cos(a) = C/R
k = tooth width coefficient (usually k=8 or 10)
tooth width = b = k*m
Rpe = Re/s
Re = Yield = elasticity limit
s = security coefficient