 Gear effective face width

Gear effective face width is the usable axial width participating in a stated cylindrical gear mesh. It must be distinguished from each component's nominal gear face width, and from a claim that every part of that width carries equal load. The normal/transverse tooth geometry and gear overlap ratio use this engaged width, while gear face load distribution describes how the load actually occupies it.^[ref]

An elementary geometric model treats the two toothed widths as intervals $I_1=[a_1,b_1]$ and $I_2=[a_2,b_2]$ on their common axial coordinate. Their available overlap isFor one20mm-wide gear occupying $[-10,10]\mathrm{mm}$ and a16mm-wide mate centered at $6\mathrm{mm}$, the second interval is $[-2,14]\mathrm{mm}$. Their overlap is only12mm. The mean line load for a hypothetical uniformly shared normal force of1200N is then100N/mm, rather than the60N/mm obtained by using the first gear's entire nominal width.

With gear normal module $m_n=2\mathrm{mm}$ and gear helix angle $|\beta |=30{}^{\circ }$, gear axial pitch is $p_x=4\pi \mathrm{mm}$. The12mm overlap gives geometric gear overlap ratio $b_{\mathrm{eff}}/p_x=3/\pi \approx 0.9549$, compared with $5/\pi \approx 1.5915$ for20mm. Axial positioning can therefore alter overlap without changing the ideal gear ratio.

The interval calculation assumes the flanks remain usable throughout their common extent. Relief, damaged regions or partial contact can require a more specific working-width convention. Uneven loading is not generally corrected by shrinking width until a uniform-load formula looks plausible; a stated load-distribution model is needed to predict local loading.