 Gear normal module

Gear normal module $m_n$ is the gear normal pitch divided by $\pi$, measured normal to the tooth direction of a helical gear. It describes a different section from gear transverse module $m_t$, which uses the circumferential spacing in a plane perpendicular to the rotation axis.^[ref]

If $\beta$ is reference gear helix angle, geometric projection givesFor an original inference example, reference diameter $d=60\mathrm{mm}$, tooth count $N=30$ and $\beta =30{}^{\circ }$ imply $m_t=2\mathrm{mm}$ but $m_n=\sqrt{3}\mathrm{mm}\approx 1.73205\mathrm{mm}$. The normal pitch is approximately $5.4414\mathrm{mm}$, compared with transverse pitch $6.2832\mathrm{mm}$. This is a geometric example, not a claim that the inferred normal module belongs to a particular manufacturer's preferred series.

Conversely, specifying $m_n=2\mathrm{mm}$ for the same30 teeth and30degree helix angle gives reference diameter $69.282\mathrm{mm}$. Thus two drawings both labeled “module2” can describe different gears when one means normal module and the other transverse module.

Pressure angles need the same care: for reference tooth geometry, $\tan {\alpha }_t=\tan {\alpha }_n/\cos \beta$. Matching only a module number, without its plane, pressure-angle convention and helix geometry, does not establish a compatible pair. In a conventional parallel-axis external mesh, the two helical gears also require appropriate opposite hands; the normal-module definition alone does not specify that connection.