 Gear normal pitch

Gear normal pitch $p_n$ is the repeat spacing of corresponding helical gear tooth flanks normal to their tooth direction on the developed reference cylinder. It equals $\pi$ times gear normal module $m_n$. It is a different geometric spacing from gear transverse pitch $p_t$, measured circumferentially, and from gear axial pitch $p_x$, measured parallel to the rotation axis.^[ref]

Unwrap the reference cylinder into a plane. The equally spaced tooth traces become parallel straight lines making gear helix angle $\beta$ with the axis. Projecting the transverse spacing onto the normal to those traces givesFor reference diameter $d=60\mathrm{mm}$, $N=30$ teeth and $\beta =30{}^{\circ }$, $p_t=\pi d/N=2\pi \mathrm{mm}$, whereas $p_n=\sqrt{3}\pi \mathrm{mm}\approx 5.4414\mathrm{mm}$. Multiplying $p_n$ by $N$ gives about $163.24\mathrm{mm}$, not the $188.50\mathrm{mm}$ circumference: normal pitch is not the circumferential step.

At $\beta =0$, normal and transverse pitches agree, as expected for a spur gear. For nonzero gear helix angle, using one in place of the other introduces a factor $\cos \beta$. Normal pitch is also distinct from gear base pitch, which refers to the base-circle geometry of an involute. Matching a pitch value without its measurement convention, pressure angle and tooth geometry is insufficient to establish a compatible mesh.