 Helical gear

A helical gear is a cylindrical gear whose teeth follow a helix around the reference cylinder. The gear helix angle $\beta$ measures their inclination to the axis. In a conventional external pair on parallel axes, mating gears have opposite hands with matching helix-angle magnitudes. Inclination makes engagement progress across the face rather than beginning everywhere along a straight tooth at once, but also creates a gear axial force that the supports must carry.^[ref]

A helical gear must specify its reference plane. The gear normal module $m_n$ is based on a section normal to the tooth direction, whereas gear transverse module $m_t$ is based on the plane perpendicular to the gear axis. Their geometric relation isSimilarly, reference pressure angles satisfy $\tan {\alpha }_t=\tan {\alpha }_n/\cos \beta$. Equal numbers labeled “module” in different planes therefore need not specify interchangeable gears.^[ref]

For an original example, take $m_n=2\mathrm{mm}$, $N=20$ and $\beta =30{}^{\circ }$. Reference diameter is $46.188\mathrm{mm}$, rather than $40\mathrm{mm}$. With ${\alpha }_n=20{}^{\circ }$, the transverse angle is about $22.796{}^{\circ }$.

At standard mounting, a transmitted torque $2\mathrm{N}\mathrm{m}$ gives gear tangential force $F_t\approx 86.60\mathrm{N}$. Ideal contact-force resolution gives axial magnitudeIts direction depends on helix hand and transmitted-torque direction. The corresponding radial component uses the transverse gear pressure angle. This illustrates the design trade: distributed engagement can improve smoothness, but the same transmission requires axial-load support. The example concerns parallel-axis cylindrical gearing; it should not be applied unchanged to crossed-axis arrangements.