Understanding Spur Gear Design and Tooth Strength
A spur gearbox transmits power between parallel shafts through a pair of gears whose teeth are straight and parallel to the axis. The first design decision is the gear ratio, fixed by the tooth counts: $i = Z_2 / Z_1$. Once the ratio is set, the output speed and torque follow directly from the input conditions and the mesh efficiency.
Module, Pitch Diameter and Center Distance
The module (m) is the fundamental size parameter of a metric gear — the pitch diameter equals $d = m \cdot Z$. Two meshing gears must share the same module, otherwise the teeth cannot engage. The center distance between shafts is simply $a = (d_1 + d_2)/2$, which locks the housing geometry.
Lewis Bending Equation
The classical Lewis equation treats each tooth as a cantilever beam loaded at the tip by the tangential force $F_t$. The resulting root bending stress is $\sigma = F_t / (b \cdot m \cdot Y)$, where $Y$ is the Lewis form factor depending on tooth count and pressure angle. A safety factor of at least 1.2–1.5 is normally required for steady industrial service.
Beyond the Lewis Check
The Lewis equation only covers static bending. A complete design must also verify surface (Hertz) contact stress, dynamic factors from pitch-line velocity, lubrication regime and fatigue life — typically using AGMA 2001 or ISO 6336 standards. This workspace gives you a fast, conservative first pass.