= Gear face width
{title2=$b$}
<Gear face width> $b$ describes the width of the toothed portion. For a cylindrical <spur gear> or <helical gear>, it is measured parallel to the rotation axis, rather than along the slanting tooth trace. A projecting hub need not be part of the toothed width. Manufacturer drawings distinguish face width, hub width and total length as separate dimensions.<KHK Gear Nomenclature>[KHK SSG-R catalog dimensional table: face width E, hub width F and total length G]{ref}
The available width of one gear is not necessarily the <gear effective face width> of a pair. For two aligned cylindrical gears with equal width $b$ and relative axial offset $e$, a simple interval-overlap model gives
$$
b_{\rm eff}=\max(0,b-|e|).
$$
An original $b=20\,\mathrm{mm}$ pair offset by $4\,\mathrm{mm}$ has only $16\,\mathrm{mm}$ of common axial extent. If a hypothetical normal load $1000\,\mathrm N$ were uniformly spread across that extent, mean load per axial width would rise from $50$ to $62.5\,\mathrm{N/mm}$. This is bookkeeping for an ideal uniform load, not a tooth-strength prediction. Actual <gear face load distribution> also depends on alignment and deformation.
For <helical gears>, width also enters <gear overlap ratio>:
$$
\epsilon_\beta=\frac{b_{\rm eff}}{p_x}=\frac{b_{\rm eff}\sin|\beta|}{\pi m_n}.
$$
With <gear normal module> $m_n=2\,\mathrm{mm}$ and <gear helix angle> $|\beta|=30\,{}^{\circ}$, reducing engaged width from $20$ to $16\,\mathrm{mm}$ reduces ideal overlap from $1.5915$ to $1.2732$. The overall <gear ratio> is unchanged. Width therefore affects engagement and loading even when tooth counts and shaft speeds remain the same.<Elements of Metric Gear Technology by SDP-SI>[D815 technical section, §11, Table11-3, printed T-111, axial overlap ratio]{ref}
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