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Worm and Worm Wheel / Gear
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Worm gears are special gears used in rudders, automobile steering mechanisms, hoists, and rolling mills.

A worm gear drive consists of two elements:

a) Driving element - Screw

b) Driven element - Helical gear

Driving element (screw) is called worm and driven element (helical gear) is called worm gear or worm wheel (fig below). Worm gear drives are typically used for transmission of power between two non-parallel and non-intersecting shafts.

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Worm gears teeth resemble ACME screw thread which mates with a helical gear, except that it is made to envelop the worm as seen along the worm's axis. Operation of worm gears is analogous to a screw. The relative motion between these gears is sliding rather than rolling. The uniform distribution of tooth pressures on these gears enables the use of metals with inherently low coefficients of friction such as bronze wheel gears with hardened steel worm gears. These gears rely on full fluid film lubrication and require heavy oil compounded to enhance lubricity and film strength to prevent metal contact.

Worm Gears - Basic Dimensions and Terminology

The basic dimensions of the worm and worm wheel are shown in the figure below.

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The terminology of worm gear along with notations and formulae is given in the table.

Nomenclature Symbol Formula
Worm 'w' or 1 -
Wheel or gear 'g' or 2 -
Reduction ratio I $\frac{Z_{g}}{Z_{w}}$ Or $\frac{Z_{2}}{Z_{1}}$ or $\frac{N_{w}}{N_{g}}$
Worm velocity $v_{w}$ $\pi D_{w} N_{w} / 60$
Gear velocity $v_{g}$ $\pi D_{g} N_{g} / 60$
Lead angle $\gamma$ or $\lambda$ $\tan ^{-1}\left(Z_{w} / q\right)$, q =10 to 11
PCD of worm $D_{w}$ $ Q_m$
PCD of gear $ D_{g} $ $\mathrm{m} Z_{g}$
Sliding velocity of worm $v_{s} $ $ v_{w} / \cos \lambda$
Drive efficiency H $\tan \lambda / \tan (\lambda+\rho)$
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